A Thesis Submitted to the Department of Physics Banaras Hindu University, Varanasi...

An Observational Study of Gamma Ray Pulsars

A Thesis

Submitted to the

Department of Physics

Banaras Hindu University, Varanasi

in the partial fulfilment of the requirements

for the degree of

Doctor of Philosophyin

Physics

by

Bharat Bhushan Singh( Enrollment No. 231818 )

High Energy Gamma Ray Observatory, Pachmarhi

Tata Institute of Fundamental Research, Mumbai

January, 2008

ii

DECLARATION

This thesis work is a presentation of my research work carried out at High

Energy Gamma Ray Observatory - Pachmarhi (a field station of Tata Insti-

tute of Fundamental Research - Mumbai). As a team member of experi-

ment, my contributions are debugging of Data Acquisition System, various

calibrations of telescope parts, observations and data analysis. All refer-

ences and acknowledgments are mentioned wherever literature, data tables,

figures and contributions of others research work are involved in discus-

sions.

The work was done under the guidence of Professor B. S. Acharya, at the

Tata Institute of Fundamental Research, Mumbai and Professor C. P. Singh,

at Banaras Hindu University, Varanasi.

Bharat Bhushan SinghScientific Officer

HEGR Observatory

Amrak Bhavan-Pachmarhi

Distt.- Hoshangabad, Madhya Pradesh

India

iii

Acknowledgments

I sincerely express my grateful thank to Professor B. S. Acharya (TIFR) and Professor

C. P. Singh (BHU) for their guidance and encouragement during work. I am obliged for

giving me valuable time during my research and supporting the experimental work, data

analysis, discussions and results that came out of that work. I wish to thank Prof. P.R.

Vishawanth and Prof. P.N.Bhat who introduced me this exciting field of research and

helped me for my beginning in gamma-ray astronomy.

My sincere thank to Dr. Varsha Chitnis with whom I had discussions about techniques

of data analysis and simulation results. I would also like to thank Dr. Alok Gupta for

helping me in Latex for thesis writing.

I am very thankful for the contributions from all of the members of HEGRO for their

support and maintenance of PACT system to carry out high quality observations. I have

benefited from discussions with Mr. Suresh Upadhya, Mr. Kiran Gothe and Mr. B.K.Nagesh

on a number of occasions for understanding of DAQ, telescope control and programming

codes. I am thankful to all HEGRO members: Venkatesh, Kamesh, Purohit, Sharma,

Sandeep, Mahesh, Tony, Jenny, Shobha, Sudershanan, Nawang, Lotous, Nandkishore and

Francis.

I am obliged by the endless encouragement and friendly cooperation given to me by

Dr. Debanjan Bose, Dr. Pratik Majumdar and Mr. Atique Rahman.

I thank to J.H.Taylor, R.N.Manchester, D.J.Nice, J.M.Weisberg, A.Irwin, N.Wex and

A.G.Lyne for providing “Tempo” code and clarifications about pulsar data analysis. I also

thank to Prof. Yashwant Gupta (NCRA) for fruitful discussions about pulsar data analysis.

I thank to Princeton/JPL groups members for their monthly maintenance of Crab radio

timing data base. I thank to authors Trevor Weekes, R. Ong, C.M.Hoffman, C.Sinnis,

P.Fleury and M. Punch for providing review articles of gamma-ray astronomy.

I would like to thank research councils of Banaras Hindu University and Tata Institute

of Fundamental Research for their cooperation and permission to do thesis.

Finally, I would like to thank my wife Sangita son Abhimanyu for years of patience,

enthusiasm, companionship and love. I express my deep sense of gratitude to my parents

and dear ones for all their affection, encouragement and moral support during my thesis

work.

With all my efforts, it is Dr. Homi Bhabha and Pt. M. M Malviya that this work is

dedicated.

***

Synopsis

Information about the physical universe reaches us in the form of matter (cosmic-rays) and

radiation (Electromagnetic). Cosmic-rays are mainly charged particles, so in the presence

of interstellar and other magnetic field they get deflected during their journey from source

to Earth. Thus these cosmic charged particles lose information about their direction of

origin. On the other hand neutral particles like neutrons and -mesons (neutral) decay and

get lost before reaching to Earth because of their short lives. Since -ray photons are neu-

tral therefore they preserve directional property and could be used to probe the universe.

Among many celestial sources, Pulsars have been found to be emitting high energy -rays.

Hence the observation of -rays from pulsars may give necessary information about the

particle acceleration and physical processes of high energy emissions taking place in their

environments.

Gamma-ray astronomy started in 1960 and is rapidly developing via satellite and ground

based detectors. Discoveries made by satellite borne experiments on Compton Gamma

Ray Observatory (CGRO) have revolutionized our understanding of the high energy uni-

verse. For energy greater than 10 GeV, the number of -rays detectable by satellite born

detectors are limited by rapidly falling -ray fluxes, exposure time and area of detector.

So astronomy in GeV-TeV energies can only be done by ground based instruments using

Earth’s atmosphere as the detection medium. For most of the wavelengths, the atmosphere

is transparent however ultraviolet, X-ray and -rays are completely absorbed by the atmo-

sphere. At very high energy (VHE), indirect -ray detection is possible through secondary

radiation emission. A VHE -ray initiates electromagnetic cascade or extensive air shower

(EAS) of particles which propagate down through atmosphere. Secondary particle’s field present in the EAS initiate Cherenkov light when they pass through the dielectric

medium of atmosphere. These Cherenkov photons are highly collimated along the direc-

tion of electrons and hence primary -rays, can be detected by ground based atmospheric

Cherenkov detector. Isotropic charged particles constitute formidable background for de-

tection of -rays in this method, but various techniques have been recently developed to

reduce the cosmic ray background.

The study of very high energy radiation (TeV) is very important as the radiation is in-

timately connected with the problems of origin of cosmic rays. A series of Pulsars Crab,

iv

Synopsis v

Vela, Geminga, PSR 1055-52, PSR 1509-58, PSR 1706-14, PSR 1951+32 have been de-

tected to be emitters of low energy -rays (few GeV) by Energetic Gamma Ray Experiment

Telescope (EGRET) instrument on Compton Gamma Ray Observatory. Knowledge of en-

ergy spectrum at higher energies (TeV) is important to estimate the upper limit of particle

acceleration. Measurement of flux, energy-spectrum and arrival direction of TeV -rays

can help to understand the acceleration mechanism and for accurate estimation of mag-

netic field of pulsar and many other processes responsible for the production of cosmic

rays.

The two models which explain the MeV - GeV -rays emissions from pulsars are Polar

cap and Outer gap. Polar cap model assume that particles are accelerated above the pulsar

surface at around the pole region and -rays are originating from either curvature radiation

or inverse Compton induced pair cascade in a strong magnetic field. In Outer gap model,

acceleration take place between the null surface and the light cylinder along the boundary

between the closed and open parts of the magnetosphere and -rays result from photon-

photon pair production-induced cascades.

The search of -rays from pulsars in India was started by TIFR group at Ooty as early

in 1969, and has continued at High Energy Gamma Ray Observatory - Pachmarhi with a

progressively increasing sensitivity and collection area. Advanced data acquisition system

(DAS) has been used to improve the sensitivity of the telescopes.

Array of Cherenkov Telescopes at Pachmarhi (Madhya Pradesh) in central India is de-

signed to detect the celestial TeV -rays by wavefront sampling technique. PACT array

uses 24 telescopes which are arranged in 5 5 matrix with an average telescope separation

of 20 meters. Each telescope consists of 7-parabolic mirrors of 90 cm diameter (f/d 1)

and a Photo multiplier Tube (PMT) fitted at focal point of each mirror. All telescopes are

equatorial mounted and operated through independent control system.

Thesis work is based on the An Observational Study of Gamma ray Pulsars at HEGRO-

Pachmarhi site. Thesis work is summarized in following chapters. Chapter-1, describes

about the general characteristic of a pulsar and status of VHE pulsar observations. The

high energy -ray production, acceleration mechanism and emission cutoff in pulsar mag-

netosphere are discussed with Polar cap and Outer gap models. Chapter-2, deals with the

detection principles of Atmospheric Cherenkov light and few important design parame-

ters of a Atmospheric Cherenkov detector are discussed in brief. A comparison of the

wavefront and imaging technique has also been carried out. In Chapter-3, details of ex-

perimental setup of Pachmarhi Array of Cherenkov Telescopes are described. This will

include calibration of telescope’s transducers, optic axis alignment of reflectors and Data

Acquisition System. In wavefront sampling technique, relative arrival time and density of

Synopsis vi

Cherenkov photons are recorded with fast timing devices. Detectors response and various

aspects of signal digitization require calibration of all latching devices with great accuracy.

Accuracy in the arrival angle estimation depends on the time resolution of latching devices.

Time to digital converters (TDC) with time resolution of 0.25 ns per count are be used for

relative time measurement. Debugging of data acquisition system, checking of hardware

trigger logic, calibration of TDC and charge to digital converters (QDC) will be discussed.

In Observations, zenith (telescopes parked in vertical position) observation is used to esti-

mate the relative time offsets (tzero) of detectors and performance study of detectors. Since

cosmic ray background is isotropic, it necessary to estimate this background by observing

OFF source (same brightness as that of source) regions. Regular observation carried out for

Crab and Geminga pulsar sources (potential high energy -ray pulsar) and OFF-source re-

gions will be presented. Chapter-4, deals the method of data analysis for steady and pulsed

signal in addition to observations and data reduction processes. Arrival direction of primary

-rays will be estimated from the relative arrival times of Cherenkov wavefront latched by

different detectors. Any excess in space angle distribution of ON-source over OFF source

events in a narrow cone along source direction could be attributed to steady -ray signal.

Data will be analyzed with various trigger conditions. Data from individual PMT channel,

Telescope (Royalsum) channel and entire array data will be used for analysis. As the At-

mospheric Cherenkov telescope system can not be calibrated using mono-energetic beam

of -rays of TeV energies, the response of the detectors to Cherenkov light from EAS has

to be determined through detailed Monte Carlo simulations using CORSIKA package for

and proton showers. In this, study of various parameters that could be used to distinguish

the cosmic and initiated Cherenkov light pool of photons, estimation of threshold energy

and collection area of detected -ray photons will be discussed. The periodic analysis of

long stretch of pulsar data is performed in inertial frame system. The equivalent center of

our solar system is most common point for this purpose which is Solar System Barycenter

(SSB). This is achieved through barycentric method and various correction terms will be

discussed. The main idea for search of pulsations in pulsar observation is to classify all

the events according to their phases , which lie between 0 and 1. In the histogram of

phases, any significant excess of events at a particular phase over uniform background is

the measure of pulsations. TEMPO codes for barycentric correction purpose and periodic-

ity tests will be discussed. The Chapter-5 and Chapter-6 will start with brief description of

VHE observations of Crab system and Geminga pulsar. The complete data analysis details

about sources would also be included in these chapters. The summary of thesis work will

be presented in Chapter-7.

List of Publications

Publications in Conference Proceedings:

1 On Pulsed emission of TeV -rays from Crab Pulsar

BSAcharya, BBSingh, DBose, VRChitnis and PRVishwanath, 30

ICRC, Merida,

Mexico, 3-11 July 2007

2 Search for pulsed emission of TeV gamma rays from Geminga Pulsar

BSAcharya, BBSingh, DBose, VRChitnis and PRVishwanath, 30

ICRC, Merida,

Mexico, 3-11 July 2007

3 On Pulsed emission of TeV -rays from Crab Pulsar

BBSingh, BSAcharya, DBose, VRChitnis and PRVishwanath, 29

ICRC, 2005,

Pune, India, vol-4, p-191

4 PACT results of Very High Energy Gamma Ray Emission from Crab Pulsar.

BSAcharya, PNBhat, VRChitnis, PMajumdar, MARahman, BBSingh and PRVish-

vanath, 28th ICRC, Tsukula, OG.2.2(2003), 2392

5 Preliminary Results on the Flux of TeV Gamma Rays from Crab System Ob-

tained with the PACT at Pachmarhi.

BSAcharya, PNBhat, VRChitnis, PMajumdar, MARahman, BBSingh and PRVish-

vanath, 28th ICRC, Tsukula, OG.2.2,(2003), 2392

6 Preliminary Results from the Crab Nebula with PACT Array

PMajumdar, BSAcharya, PNBhat, DBose, VRChitnis, MARahman, BBSingh and

PRVishvanath, The Universe Viwed in Gamma Rays, University of Tokyo(2002)

7 Very High Energy Gamma Ray Emission from Crab and Geminga Pulsars.

PRVishvanath, BSAcharya, PNBhat, VRChitnis,PMajumdar, MARahman and BBS-

ingh, 27th ICRC, Hamburg,OG.2.05(2001), 2392

8 Very High Energy Gamma Ray Emission from the Crab Nebula with the PACT

Array

vii

List of Publications viii

PRVishwanath, BSAcharya, PNBhat, VRChitnis, PMajumdar, MARahman and BB-

Singh, 27th ICRC, Hamburg, OG.2.05(2001), 2415

9 Pachmarhi Array of Cherenkov Telescopes and its Sensitivity

VRChitnis, BSAcharya, PNBhat, KSGothe, AVJhon, PMajumdar, BKNagesh, MARah-

man, BBSingh, SSUpadhya, BLVMurthy and PRVishwanath

27th ICRC, Hamburg,OG.2.05(2001), 2793

Publications in refereed Journals.

1 Observations of AGNs Using PACT

D.Bose, PRVishwanath, PMajumdar, MARahman, BBSingh, ACGupta and BSAcharya,

Astrophysics and Space Science,309, p111,(2007)

2 Angular Resolution of Pachmarhi Array of Cherenkov Telescopes.

PMajumdar, BSAcharya, PNBhat, VRChitnis, MARahman, BBSingh and PRVish-

vanath, Astroparticle Physics, 18(2003), 339-349

3 Performance Studies of PACT Experiment.

PRVishvanath, BSAcharya, PNBhat, VRChitnis, PMajumdar, MARahman and BB-

Singh, Bull. Astro. Soc. India, 30(2002), 367-37

4 TeV Gamma-ray flares from Mkn421 detected by the Pachmarhi Array of Cherenkov

Telescopes.

PNBhat, BSAcharya, VRChitnis, PMajumdar, MARahman, BBSingh and PRVish-

vanath, Bull. Astro. Soc. India, 30(2002), 285-290

Contents

Synopsis iv

List of Publications vii

1 Pulsars 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Pulsar Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Pulsar Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Glitches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Pulsar Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 Pulsar Emission Models . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7 Observed Gamma Ray PULSARS . . . . . . . . . . . . . . . . . . . . . 18

1.8 Observation of Pulsars in 10GeV 100GeV . . . . . . . . . . . . . . . . 24

2 VHE Gamma-ray Observation Technique 27

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Cherenkov Radiation in EAS . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Cherenkov detection technique . . . . . . . . . . . . . . . . . . . . . . . 41

2.5 Atmospheric Cherenkov Telescope . . . . . . . . . . . . . . . . . . . . . 46

2.6 Functions of Atmospheric Cherenkov Telescope . . . . . . . . . . . . . . 47

2.7 Design parameters of ACT . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.8 Cherenkov Signal detection and Energy threshold . . . . . . . . . . . . . 58

3 PACT System 62

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.2 PACT array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3 Distributed Data Acquisition System . . . . . . . . . . . . . . . . . . . . 64

3.4 Chance Rate counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

ix

CONTENTS x

3.5 Auxiliary Control System . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.6 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7 Mechanical Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.8 BSScan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.9 PG Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.10 Trigger Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4 Observations and Data Reduction 84

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.3 Data Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.4 Analysis Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.5 Estimation of Gamma-ray flux . . . . . . . . . . . . . . . . . . . . . . . 98

4.6 PACT Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.7 Pulsar Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.8 Clock correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.9 Geometric Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.10 Einstein correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.11 Dispersion Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.12 Shaprio delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.13 Temporal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.14 Periodicity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5 Crab Nebula and Pulsar 129

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.2 Search for Steady Emission . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.3 Search for Pulse Emission . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.4 Upper Limit on Pulsed Flux of -rays . . . . . . . . . . . . . . . . . . . 151

6 Geminga Pulsar 153

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.2 Search for Steady Emission . . . . . . . . . . . . . . . . . . . . . . . . . 154

6.3 Search for Pulsed Emission . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.4 Upper Limit on Pulsed Flux of -rays . . . . . . . . . . . . . . . . . . . 171

7 Summary 173

List of Figures

1.1 A typical structure of neutron star. . . . . . . . . . . . . . . . . . . . . . 5

1.2 Increase of Crab pulsar period with epoch of observation. . . . . . . . . . 7

1.3 Distribution of pulsars as a function of their period and period derivative.

Large dark dots: seven high-confidence -ray pulsars. Solid lines: Char-

acteristic age. Dotted line: open field line voltage. Dashed line: surface

magnetic field. (figure is taken from Thompson 2001) . . . . . . . . . . . 9

1.4 Glitches observed in Crab Pulsar. (data is from JPL) . . . . . . . . . . . . 11

1.5 Toy model for a rotating neutron star and its magnetosphere. (Figures is

taken from Lorimer

Kramer 2005) . . . . . . . . . . . . . . . . . . . . 13

1.6 Polar Cap model of pulsed emission. (figure is from http://cossoc.gsfc.nasa.gov) 15

1.7 Outer gap model of pulsed emission. (figure is from http://cossoc.gsfc.nasa.gov) 17

1.8 -ray pulse profiles of seven EGRET pulsars. (figure is taken from Fierro,

1995) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.9 Multi wavelength Light curves of seven -ray pulsars. (figure is taken from

Thompson 2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.10 Multiwavelength spectra of seven -ray pulsars. (figure is taken from

Thompson 2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.11 TIFR-IIA HAGAR array of seven telescopes, Hanle (INDIA). . . . . . . 25

1.12 The pulsed photon spectrum of Crab pulsar. The thin solid line is the polar

cap model fit to the EGRET data (Harding 1999). The dotted line is the

outer gap model for the Vela pulsar (scaled to match the EGRET Crab

pulsar flux at peak sensitivity) and is included to indicate the shape of the

cut-off this model predicts (Romani 1999) . The dashed line represents the

power-law fit to the EGRET data (Nolan et al. 1993). The upper limits

for pulsed emission are shown by the open squares. The thick solid curve

depicts the model of unpulsed GeV-TeV emission from the Crab Nebula

(Hillas et al. 1998). (figure is taken from Lessard et al. 1999) . . . . . . . 26

xi

LIST OF FIGURES xii

2.1 A simple model for production of electromagnetic shower. (Figure redrawn

from Longair 1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.2 A simple model for production of hadronic shower. (Figure redrawn from

Longair 1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.3 The polarization set up in the air molecules when a charged particle passes

through (a) Low velocity, (b) High velocity. (figure redrawn from Jelley

1958) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4 Huygens construction to illustrate coherence and to obtain the Cherenkov

angle ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 (a) Production spectrum of Cherenkov radiation, (b) Atmospheric trans-

mission, (c) Cherenkov spectrum at observation level. . . . . . . . . . . . 36

2.6 Important features of atmospheric Cherenkov radiation. . . . . . . . . . . 38

2.7 Geometric model of the emission of the Cherenkov radiation for -rays and

proton showers. The stippled region encloses the main emission region for

production of Cherenkov light from -ray showers. (Hillas 1996) . . . . . 41

2.8 An array of detectors used in wave-front sampling technique. . . . . . . . 42

2.9 A schematic diagram of an Imaging Atmospheric Cherenkov Telescope. . 44

2.10 IACT image parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.11 10 meter IACT telescope of Whipple observatory. . . . . . . . . . . . . . 46

2.12 A heliostat array of STACEE experiment . . . . . . . . . . . . . . . . . . 47

2.13 Arrival of Cherenkov wavefront at ACT. . . . . . . . . . . . . . . . . . . 49

2.14 Geometrical representation of parabolic mirror. . . . . . . . . . . . . . . 50

2.15 Seven paraxial parabolic mirrors in Pachmarhi Array of Cherenkov Tele-

scopes (PACT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.16 Imaging Telescope of VERITAS stereoscopic system. (figure is taken from

http://veritas.sao.arizona.edu/photo/) . . . . . . . . . . . . . . . . . . . . 52

2.17 Reflectance at normal incidence of aluminum, silver and steel. (figure re-

drawn from Jenkins 1981) . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.18 Optical bench used at PACT for fine-tune of focusing of mirrors. . . . . . 54

2.19 Image of an object(light source) formed in focal plane of parabolic mirror. 55

2.20 HEGRO-Pachmarhi ACT are in equatorial and HAGAR-Hanle are Alt-Az

mounting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.21 Variation of Zenith angle, Azimuthal angle, Zenith speed and Azimuthal

speed as function of source hour angle. . . . . . . . . . . . . . . . . . . . 57

3.1 Layout of Pachmarhi Array of Cherenkov Telescopes. . . . . . . . . . . . 63

LIST OF FIGURES xiii

3.2 Logic diagram of Sector Data Acquisition System (SDAS). . . . . . . . . 65

3.3 Logic diagram of Master Data Acquisition System (MDAS). . . . . . . . 66

3.4 Chance counter setup in SDAS. . . . . . . . . . . . . . . . . . . . . . . . 67

3.5 Block diagram of ACTOS. . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.6 TDC calibration setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.7 Variation of TDC counts vs standard start-stop delay. . . . . . . . . . . . 73

3.8 QDC calibration setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.9 Variation of QDC counts vs input charge. . . . . . . . . . . . . . . . . . 75

3.10 (a) Variation of RA clino voltage with hour angle, (b) Variation of DEC

clino voltage with hour angle, (c) Variation of DEC clino voltage with

declination angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.11 Profile of PMT count rates seen by PMT’s of Telescope no 43 for star

-auriga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.12 Rate vs discriminator threshold for single mirror and royalsum rate. . . . 82

3.13 (a) Trigger rate vs Royalsum rate (b) fraction of Chance rate vs Royalsum

rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.1 Event rate (Hz) recorded in the SDAS 4. . . . . . . . . . . . . . . . . . 87

4.2 Absolute arrival times of recorded events. . . . . . . . . . . . . . . . . . 88

4.3 Telescope triggers distribution for sector from TDC and Latch. . . . . . . 89

4.4 TDC distributions for (a) individual PMT, (b) SDAS Royalsum and (c)

MDAS Royalsum channels. . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.5 A QDC distribution of Channel . . . . . . . . . . . . . . . . . . . . 90

4.6 TDC difference distribution (Run 414). . . . . . . . . . . . . . . . . . . 92

4.7 Residue distributions of TDC delay (only six telescopes data). . . . . . . 95

4.8 Zenith(a) and Azimuthal(b) angle distributions of reconstructed shower

from a fictitious source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.9 Zenith and Azimuthal position of PSR 0534+2200. . . . . . . . . . . . . 97

4.10 Space angle distribution of reconstructed shower of vertically falling showers. 98

4.11 Distribution of n-fold triggers. . . . . . . . . . . . . . . . . . . . . . . . 99

4.12 (a) Space angle distribution of unnormalized fictitious source, (b) Excess/deficit

distribution of unnormalized FS1-FS2 events. . . . . . . . . . . . . . . . 101

4.13 Telescope trigger ratio for a fictitious source (Run 884,885). . . . . . . . 101

4.14 (a) Normalized space angle distribution of events from source FS1 and

FS2, (b) Excess/deficit distribution of normalized FS1-FS2 events. . . . . 102

4.15 Excess/deficit count rate of fictitious source of data table-4.5. . . . . . . . 103

LIST OF FIGURES xiv

4.16 Average Cherenkov photon density at Pachmarhi as a function of core dis-

tance for showers initiated by (a) -rays and (b) protons, of various primary

energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.17 Average Cherenkov photon density at various observation level as a func-

tion of core distance for showers initiated by (a) -rays (1 TeV) and (b)

protons (2 TeV). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.18 (a) Average total number of Cherenkov photons at Pachmarhi observation

level as a function of primary energy for -rays and protons, (b) Longitu-

dinal development of Cherenkov photons in atmosphere. . . . . . . . . . 106

4.19 (a) Differential (b) Integral trigger rate for vertically falling -rays. . . . . 107

4.20 Collection area as function of energy threshold for vertically falling showers.107

4.21 Energy threshold and Collection area for PACT array at different incident

angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.22 Annual variation in photon arrival time due to orbital motion of Earth

around the Sun (figure redrawn from Smith 1977). . . . . . . . . . . . . . 110

4.23 The variation of Crab pulsar period as function of time. Dotted curve is a

result of normal slow down of pulsar and the solid line represent the period

variation due to orbital motion of Earth. . . . . . . . . . . . . . . . . . . 112

4.24 Leap seconds added to TAI observed on different Epochs. . . . . . . . . . 115

4.25 The variation of photon arrival time as function of Earth’s geographical

latitude. (figure redrawn from Smart 1977). . . . . . . . . . . . . . . . . 117

4.26 Dependence of Earth radius vector on geographical latitude (figure redrawn

from Smart 1977). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.27 Variation of Earth radius vs geographical latitude. . . . . . . . . . . . . . 119

4.28 Delay in photon arrival time vs zenith angle of source. . . . . . . . . . . 120

4.29 Sun and Earth-Moon system. . . . . . . . . . . . . . . . . . . . . . . . . 121

4.30 Annual variation of Earth position (a) and velocity (b) around the Sun. . . 122

4.31 Celestial sphere to represent the position of source and observer. . . . . . 123

4.32 Annual variation of photon arrival time as a course of orbital motion of

Earth around the Sun. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.1 The MeV-TeV -ray spectrum of Crab nebula by various groups (satellite

detector, atmospheric Cherenkov telescopes and air shower arrays). Filled

points represent confirmed detections; unfilled points with down arrows

represent upper limits. The identification of each experiment is given in

the legend. (figure is from Sinitsyna et al. 2007) . . . . . . . . . . . . . . 131

LIST OF FIGURES xv

5.2 (a) Space angle distributions of events from Crab source and unnormalized

background runs,(b)Excess/deficit events distribution. . . . . . . . . . . . 136

5.3 (a)Space angle distributions of events from Crab source and normalized

background runs,(b) Excess/deficit events distribution. . . . . . . . . . . 138

5.4 Excess/deficit count rate from direction of Crab source. . . . . . . . . . . 139

5.5 Significance as function of observation time(Data set[A]), solid line curve

is for Crab source with 15 background rejection at PACT threshold. . . 139

5.6 5 sigma sensitivity for PACT in terms of Crab flux. . . . . . . . . . . . . 140

5.7 Distribution of phases of Crab pulsar without any cuts on event selection

[data set(A)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.8 Distribution of phases for Crab pulsar at different space angle cuts [data

set(A)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.9 Distribution of phases for Crab pulsar at different space angle cuts[(data

set(B)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.10 Variation of significance with space angle cuts. . . . . . . . . . . . . . . 147

5.11 Significance as function of event rate[data set(A)]. . . . . . . . . . . . . . 148

5.12 Significance as function of event rate[data set(B)]. . . . . . . . . . . . . . 148

5.13 Distributions of significance( )[data set(A)]. . . . . . . . . . . . . . . . . 149

5.14 Distributions of significance( )[data set(B)]. . . . . . . . . . . . . . . . . 150

5.15 distribution of Crab pulsar light curve [data set(A)]. . . . . . . . . . . 150

5.16 distribution of Crab pulsar light curve [data set(B)]. . . . . . . . . . . 151

5.17 Upper limit on integral flux of Crab pulsar detected by ground observa-

tions. Solid line is for the EGRET integral flux (Nolan etal, 1993). The

dashed line represent the extrapolations of EGRET integral fluxes. . . . . 152

6.1 (a) Space angle distributions of events from Geminga source and unnor-

malized background,(b) Excess/deficit events distribution. . . . . . . . . 158

6.2 (a)Space angle distributions of events from Geminga source and normal-

ized background runs,(b) Excess/deficit events distribution. . . . . . . . . 160

6.3 Excess/deficit count rate from direction of Geminga source. . . . . . . . . 161

6.4 Significance as function of observation time (data set[A]), solid line curve

is for Crab like source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

6.5 Distribution of phases of Geminga pulsar without any cuts on event selec-

tion[data set(A)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.6 Distribution of phases of Geminga pulsar at different space angle (data

set[A]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

LIST OF FIGURES xvi

6.7 Distribution of phases for Geminga pulsar at different space angle[data

set(B)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.8 Variation of significance with space angle. . . . . . . . . . . . . . . . . . 167

6.9 Significance as function of trigger rate[data set(A)]. . . . . . . . . . . . . 167

6.10 Significance as function of trigger rate[data set(B)]. . . . . . . . . . . . . 168

6.11 Distributions of significance( )[data set(A)]. . . . . . . . . . . . . . . . . 168

6.12 Distributions of significance( )[data set(B)]. . . . . . . . . . . . . . . . . 169

6.13 A comparison of significances obtained with two post glitch ephemeris. . 170

6.14 distribution of Geminga light curve, (a) On-source, (b) Off-source[data

set(A)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6.15 distribution of Geminga light curve[data set(B)]. . . . . . . . . . . . . 171

6.16 Upper limit on integral flux of Geminga pulsar detected by ground obser-

vations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

List of Tables

1.1 Light cylinder parameters. . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 PACT Telescope parameters. . . . . . . . . . . . . . . . . . . . . . . . . 60

3.1 Telescope Count Rate & Chance rate of PACT. . . . . . . . . . . . . . . 68

3.2 Standard delays of calibrating cables and their TDC counts. . . . . . . . . 71

3.3 TDC calibration constant. . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.4 QDC calibration data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.5 QDC calibration constant. . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.6 Clino calibration data for Telecope 41. . . . . . . . . . . . . . . . . . . 77

3.7 Bright Star Scan data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.8 LATCH triggers status. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.9 TDC data [SDAS]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.10 QDC data [SDAS]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.11 QDC Pedestal data [SDAS]. . . . . . . . . . . . . . . . . . . . . . . . . 81

3.12 Latch and TDC triggers of [MDAS]. . . . . . . . . . . . . . . . . . . . . 81

3.13 MDAS TDC data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.1 Data structure of PACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2 TDC histogram data (Run ). . . . . . . . . . . . . . . . . . . . . . . 87

4.3 Tzero of PACT detectors observed in main control room. . . . . . . . . . 92

4.4 Summary of Fictitious source data observed during year 2005-2006. . . . 100

4.5 Fictitious Excess/deficit analysis. . . . . . . . . . . . . . . . . . . . . . . 103

4.6 Results of fictitious source data. . . . . . . . . . . . . . . . . . . . . . . 103

4.7 Geocentric radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.1 Observation log of Crab source. . . . . . . . . . . . . . . . . . . . . . . 133

5.2 Summary of Crab data observed between Year 2000-2006. . . . . . . . . 134

5.3 CRAB ON OFF Excess/deficit analysis. . . . . . . . . . . . . . . . . . 137

5.4 Overall conclusion of crab ON-OFF analysis of data table-5.3. . . . . . . 140

xvii

LIST OF TABLES xviii

5.5 Ephemeris of Crab Pulsar. . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.6 Crab Pulsar monthly Ephemeris. (JPL, Andrew Lyne et al.) . . . . . . . . 142

5.7 EGRET classification of Crab Pulsar Phase Intervals. . . . . . . . . . . . 144

5.8 Details of Phase analysis[Data set(A)]. . . . . . . . . . . . . . . . . . . . 145

5.9 Details of Phase analysis[Data set(B)]. . . . . . . . . . . . . . . . . . . . 145

6.1 Observation log of Geminga source. . . . . . . . . . . . . . . . . . . . . 155

6.2 Summary of Geminga data observed between Year 2000-2006. . . . . . . 156

6.3 GEMINGA ON OFF Excess/deficit analysis. . . . . . . . . . . . . . . . 159

6.4 Overall conclusion of GEMINGA ON-OFF analysis of data table-6.3. . . 162

6.5 Ephemeris of Geminga Pulsar. . . . . . . . . . . . . . . . . . . . . . . . 162

6.6 Modified Geminga Pulsar Phase Intervals. . . . . . . . . . . . . . . . . . 163

6.7 Details of Phase analysis of Geminga pulsar (Data set[A]). . . . . . . . . 164

6.8 Details of Phase analysis of Geminga (Data set[B]). . . . . . . . . . . . . 165

7.1 Crab Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

7.2 Geminga Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Chapter 1

Pulsars

1.1 Introduction

The discovery of pulsating radio signal from the extra-terrestrial space by Jocelyn Bell and

Anthony Hewish in 1967 triggered interest among astronomers about a new type of celes-

tial source. The short duration of pulsating signal implied that the source had to an object

that did not have orbital motion and had to be very compact. A large extended source is

not expected to send out such signals because any coherent physical changes in it would be

expected to have a much longer repeat time or period. This remarkable source was charac-

terized as ‘PULSAR’ due to pulsating nature of observed signals and given the catalogue

name CP1919 (Cambridge Pulsar) as it was the first pulsar discovered by Cambridge ra-

dio astronomers. The most famous pulsar was discovered shortly after first and lies in the

Crab Nebula (M1), which is about 7000 light year away in the constellation Taurus. Later

the scanning of sky by radio telescopes at Jodrell Bank Observatory (Manchester) and at

Arecibo (Puerto Rico) discovered more than 600 pulsars and these were catalogued with

letter PSR followed by their position in sky. Since their discovery, presently more than

1500 pulsars have been detected.

Progress of space missions allowed astronomers to enhance their knowledge about high

energy (HE) universe which can not be studied from ground observations. In the MeV

energy band, the early discoveries of -ray pulsars by SAS-2 (USA mission, 1972) and

COS-B (European mission, 1975-1982) satellite detectors, the number of -ray pulsars

had grown from two to seven in the past years of observations by Compton Gamma Ray

Observatory (CGRO) and other instruments (European-USA joint mission, 1991-2000).

The detailed observations of -ray pulsars, eg. Crab (Nolan et al. 1993), Vela (Kanbach

et al. 1994), Geminga (Halpern

Holt 1992, Bertsch et al. 1992, Mayer-Hasselwander

et al. 1994), PSR 1509-58 (Wilson et al. 1992), PSR 1706-44 (Thompson et al. 1992),

PSR 1055-52 (Fierro et al. 1993) and PSR 1951+32 (Ramanamurthy et al. 1995) by space

1

Chapter 1. Pulsars 2

detectors have identified as MeV-GeV pulsating sources. The sensitivity of space detec-

tors are very poor at few hundreds of GeV due to limited size of photons collector. The

search of pulsed emission above few hundreds of GeV to TeV remains to be successful for

ground-based Atmospheric Cherenkov telescopes. The new detections and exploration of

observed pulsars are beginning to provide clues to the origin of high energy radiation in

the form of emerging patterns and correlations among observed quantities such as -ray

efficiency and spectral index vs age etc but there are still many questions about the location

of emission region and its association to the radio, optical and X-ray pulses. The details of

pulsar structure and high energy emission models of pulsars will be discussed in the next

sections.

1.2 Pulsar Period

When normal stars end their lives ie when most of their nuclear fuel has been consumed,

compact objects like white dwarfs, neutron stars and black holes are born. White dwarfs

are stars of about one solar mass ( ) with characteristic radii about 5000 km and mean

density of around 10 kg/m . These stars no longer burn nuclear fuel and they are slowly

cooling object and radiating away their residual energy. When mass of white dwarf is

1.4 (Chandrashekhar limit, 1935), star achieves highest density and smallest radius.

Neutron stars are stars of about 1-3M solar mass, smaller radius (10-15 km), mean density

equal to 10 kg/m and much gravitationally bound than an ordinary star.

The possible candidates of observed pulsations are white dwarf, binary system and neutron

stars. The rotation period of these objects can be calculated as follows.

If is the angular speed of rotation and R is its radius then

or

where is the density. So period of rotation is given by

For white dwarfs, the maximum density is the order of kg/m so rotation period is

equal to,

!#" %$ !#"&! (' *) ,+.-*/10 "


In binary white dwarfs system, R 2R =14

km and for 1M , mean density

10 kg/m , the binary period is

! "&! '' *) ,+.-*/10 "Since, observed periods from most of the pulsars are less than 1 second so these results

rule out the pulsating signals from rotating white dwarfs or binary system.

For neutron stars, the mean density is order of 10 kg/m , so its rotation period is

) ,+.-*/10) "

This period agree with observed periods of pulsating sources so, a neutron star is a possible

candidate of periodic signal.

1.2.1 Characteristics of Pulsar

For a given pulsar, period between the successive pulses repeats with very high accuracy

(1 part in 10 million). The amount of energy in pulses however varies considerably and

some time complete pulses are missing (pulse nulling) from a sequence. Average of many

pulses from the same pulsar defines a unique shape. The period of pulsars observed, range

from milliseconds to few seconds. An increase in the periods have been seen during radio

observations of pulsars. The typical rate of slow down is about 10 sec in a year. Pul-

sar properties provide clues to the physical properties of these precise clocks. The pulsar

duration indicates the largest size of the bodies emitting pulsed radiation and pulse width

is proportional to emission region of neutron star. A neutron star of typical densities 10 kg/m can rotate once in every millisecond in equilibrium, provides the clock mechanism

for pulsar.

A rotating magnetic neutron star is known as the light house model of pulsed emission.

Like magnetic poles of Earth, a region close to the neutron star where magnetic field di-

rectly and strongly affects the motion of charged particles is called the pulsar’s magneto-

sphere and in this region energy conversion takes place. When pulsar spins, its strong mag-

netic field also spins with it and induces enormous electric field on its surface. This electric

field pulls charged particles (electrons) away and electrons flow into magnetic sphere and

rotating magnetic field lines accelerate these charged particles. The accelerated electrons

emit synchrotron radiation. If magnetic axis falls within our line of sight, each time a pole

swings around to our view and these synchrotron emissions are observed at rotation period,

which is equal to the time difference between two successive pulses.


1.3 Pulsar Fundamentals

A neutron star is the strong candidate for the observed periodic signals of 1 second or less

from astronomical objects. This was the situation before 1980. Now days, periodic signals

are also observed from other compact systems like binary objects etc but their periods are

few seconds order or higher. The physical properties of neutron stars are explained as

follows.

1.3.1 Mass and radius

Neutron stars consist of highly compressed matter than nuclear matter. The maximum

mass of neutron star is order of 2M (Lattimer and Prakash 2001, 2004) is derived based

on various models. The neutron star gravity causes redshift in the observed thermal flux

and temperature. So a distant observer measures temperature that is smaller than the real

temperature at surface. The corresponding radius R inferred is larger than the intrinsic

value R (Lewin et al. 1993)

(1.1)

where R "

km is the Schwarzschild radius and M, R are the gravita-

tional mass and radius of neutron star. The upper and lower limit of neutron star radius is

given by (Lattimer et al. 1990, Glendenning 1992)

" +

!#" " (1.2)

"!$# &% !#" $'

" &% ( )) *% (1.3)

For a rotating neutron star of period P=1 ms and mass M=1.4M , minimum and maximum

radius of neutron star is 6.2 km and 16.8 km respectively. Most neutron star models predict

the radius in the range of 10-12 km and this is almost three times of Schwarzschild radius

R for 1.4M mass star. So the pulsars or neutron stars are very compact objects and result

to large gravitational effects near the surface.

1.3.2 Structure

Actually, a neutron star is not a sphere of uniform density. The average mass density + '

of neutron star is about 6.7 10 kg/m , which is larger than the nuclear mass density


Fig. 1.1: A typical structure of neutron star.

2.7 10 kg/m . Figure-1.1 shows typical structure of a neutron star. The mass of shown

neutron star is 40 massive than the Sun but its overall radius is about 16 km whereas

Sun’s radius is 700,000 km. The inner 11 km is a fluid core of mostly neutrons and average

density in this region is order of 7.35 10 kg/m . The next 4 km out makes an inner crust

of a neutron-rich fluid or solid lattice and the density in this region varies from 2.0 10 kg/m to 4.3 10 kg/m . The outer crust of about 1 km thick is a crystalline solid similar

to the interior structure of white dwarf. In the outer few meters, where density falls quickly

to kg/m , the neutron star has an atmosphere of atoms (Iron nuclei), electrons and

protons.

Since neutron star is very dense, it has enormous surface gravity. In the region where

density is of 10 kg/m , the inward pull due to gravity forces causes inverse beta decay to

occur.

/At density of 10 kg/m , the neutrons are no longer bound to the nuclei and begin to

form a separate gas. At 10 kg/m , the nuclei suddenly fall apart into a gas with almost

80 neutrons. At this density the neutron become degenerate and provide a degenerate

pressure and balance the inward pull of gravity. This pressure allows the formation of a


stable neutron star, which is mainly composed of neutrons.

1.3.3 Period and Luminosity

The period of all known pulsars range from milliseconds to few seconds and measured

period is constant almost up to six and more digits. The fluctuations in pulsar period

is random, but its characteristic deviation does not usually amount to more than several

milliseconds (Lyne

Smith 1998). The rotation period of pulsars are observed to increase

with time as shown in figure-1.2 and for Crab pulsar it is 36.35 ns per day. The rate of

increase in the period () is stable and ranges between and sec/sec. For most

of the pulsars, increase in period can be seen through observed spin down luminosity. The

rate of loss of rotational kinetic energy is given by

0 0

The rotational energy is given by , where I is the Moment of Inertia

or (1.4)

where is the period of rotation.

is called spin-down luminosity and represents

the total power output of the neutron star. For a typical value of Mass and radius (M=M and R=10 km), I=10

gm.cm and spin down luminosity is

#" #) ) ,+ (

) ,+ ) (1.5)

Equation-1.5 (Becker

Truemper 1997) suggests that the bulk of the observed pulsed

X-ray and -ray emissions take place at the expense of the rotational energy of neutron

star. For Crab pulsar, P=0.03358 second and

" ! ) ,+ ) ,+ , the spin down

luminosity is 4.4 ergs/sec and this has been observed from radio to high energy

radiation (MeV), however only a small fraction of

is converted into radio emission. The

bulk of rotational energy goes to high energy radiation and pulsar wind.

1.3.4 Braking Index and Age

One of the most important parameter of a pulsar is the rate at which the pulsar period

changes with time. For most of the pulsars, this rate can be measured and can be used to


Fig. 1.2: Increase of Crab pulsar period with epoch of observation.

derive an age estimate. This slow-down property of a pulsar is described by a parameter

called braking index (n). Since pulsars have very strong dipole magnetic field, according

to classical electrodynamics, a rotatory magnetic dipole of moment radiates an elec-

tromagnetic wave at its rotation frequency and the radiated power (Longair, 1981) is

! + (1.6)

where is the magnetic dipole moment of neutron star. In the case of rotating magnetic

dipole moment,

where is the angle between magnetic moment and spin axis. From equation-1.4,

! + ! +

or (1.7)


where is the rotational frequency, n is the braking index and K is a constant. For Crab

Pulsar, n=2.515 0.005 (Lyne

Smith 1990).

If pulsar deceleration can be described by a constant braking index through out its life time

then pulsar age is estimated by integrating equation-1.7 as 0

0

The integration of this with limits t=0, , gives following

/

(1.8)

where is the characteristic age of pulsar and is its initial angular velocity. For n ' 1

and '' the age is

/

/ (

/

/

(1.9)

For n=3, , a plot of P vs

is shown in figure-1.3, where large dark circles are

EGRET -ray pulsars. The typical life time for majority of pulsars is about years. The

Crab pulsar has the largest spin down rate among all pulsars which corresponds to =1400

years and is of the same order of magnitude of age of Crab nebula observed in 1054 AD.

From figure-1.3, it is seen that -ray pulsars tend to concentrate in a region with high

magnetic fields and relatively young ages.

1.3.5 Magnetic Field Strength

An estimate of magnetic field strength at the surface of neutron star can be done by assum-

ing that spin down process is dominated by its dipole braking process. Magnetic field at

the surface of neutron star (Longair 1981) by a dipole field of magnetic moment is

(1.10)

From equation-1.7,

! +

Therefore,

! +

! + $ +


Fig. 1.3: Distribution of pulsars as a function of their period and period derivative. Large dark dots:

seven high-confidence -ray pulsars. Solid lines: Characteristic age. Dotted line: open

field line voltage. Dashed line: surface magnetic field. (figure is taken from Thompson

2001)


For a uniform sphere rotating about its axis, . So the surface magnetic field is

given by,

+ &% +

&% &% (1.11)

or #" &% (1.12)

The magnetic field strength typically lies in the range of 2 to 2 for most

of the pulsars and it is shown in figure-1.3. The surface magnetic filed of Crab pulsar

estimated from its rotation period is " G.

1.4 Glitches

Pulsar period and its deceleration rate are remarkably stable for a course of time. The rota-

tional instabilities in pulsars is known as glitches and their observations allow us to probe

the interior structure of neutron stars. Observations of these glitches and their recovery

provide strong evidence of existence of a fluid component inside the solid outer crust of

the neutron star. During a glitch, small but sudden increase in rotation rate is observed in

the arrival time of pulses. After glitch, pulsar eventually settles down to a steady slow-

down.

As pulsar slows down, the centrifugal forces becomes weak and the crust attempts to es-

tablish a new equilibrium with lower moment of inertia. Since the moment of inertia de-

creases, this results in speed up of the neutron star rotation. So a change in the moment of

inertia of neutron star as this slows down is the reason for abrupt change (glitch) in pulsar

period (I =const). The glitches observed for Crab pulsar are shown in figure-1.4. In each

of the three large glitches observed so far, the maximum increase in period was 36.30 ns

while the regular rate of increase is about 36.35 ns per day.

1.5 Pulsar Magnetosphere

As discussed in earlier sections, Pulsars are usually known as highly magnetized neutron

stars with rotation periods from few milliseconds (PSR 1937+214 P=1.558 ms ) to seconds

(PSR 1845-19, P=4.308 sec). A pulsar may be considered as a non-aligned rotating magnet,

but the magnetic field strength on the surface is very strong . So the Lorentz forces on the

charges in the neutron star interior are huge compared to the gravitational forces as, !* ! ! %+

, +


Fig. 1.4: Glitches observed in Crab Pulsar. (data is from JPL)

In the case of Crab pulsar, this ratio is about

for electrons confined in 1 km distance.

Thus the surface structure of a neutron star is completely dominated by electromagnetic

forces. The induced electric field due to spinning magnetic lines of forces on surface of

neutron star are so strong and therefore exceeds the work-function of the surface material

and consequently there must be plasma surrounding the neutron star. As result of this, there

is fully conducting plasma surrounding the neutron star and electric current can flow in the

magnetosphere. The plasma filled surrounding of neutron star dominated by the magnetic

field is known as pulsar magnetosphere.

At any point within the rotating magnetized sphere, there will be an induced electric field

, (where is Lorentz velocity) due to presence of magnetic field B. For

a perfectly conducting sphere this will be balanced by the distribution of charges giving

an electric field E. At any point inside the sphere a force free state is obtained and can be

expressed as follows. ( +

) (1.13)


Table 1.1: Light cylinder parameters.

Pulsar R

B

(km) (Gauss)

Crab 1.588 4.415 Geminga 11.30 1.792

In equilibrium condition, the charge density in the magnetosphere is given by the

Maxwell’s equation, "

"

+ "

(1.14)

This is known as Goldreich-Julian density. The plasma in magnetosphere experience same

force as neutron star interior and forces it to corotate rigidly with the star and form a

corotating magnetosphere. This co-rotation can only be maintained up to a maximum dis-

tance where the plasma speed reaches to the speed of light. This limit defines an imaginary

surface around pulsar magnetosphere known as light cylinder and radius is given by

+

+ " ( ) ) (1.15)

The magnetic field strength at the light cylinder radius is given by

( + ) #" ( ) ) %

&% (1.16)

The radius and magnetic field at surface of light cylinder for Crab and Geminga pulsars are

given in table-1.1. Figure-1.5 shows schematic diagram of a rotating neutron star with its

magnetosphere and the light cylinder. The magnetic field lines which passes through light

cylinder are open field lines and these are swept at the speed of light to form a toroidal field

component. The regions on the neutron star surface from which these field lines originate

define two polar caps. Charged particles stream out along these open field lines. Within

corotation radius (light cylinder), the charged particles are tied to the magnetic field lines.

The rotating strong magnetic field causes a strong electric field at the poles of the neutron

star and this can be equivalent to !

Volts/meter (Goldreich 1999). Particle acceleration

can take place because of the strong electric field present within the magnetosphere. As

a result of this, electrons are dragged off from the surface of neutron star and are rapidly

accelerated to very high energy, more than 10

times their rest mass energy.


Fig. 1.5: Toy model for a rotating neutron star and its magnetosphere. (Figures is taken from

Lorimer Kramer 2005)

1.6 Pulsar Emission Models

Soon after the discovery of pulsating sources, efforts towards understanding of pulsed

emission, neutron stars attracted attention of astronomers as strong sources for these pe-

riodic signals. The detailed observation of -ray pulsars like Crab (Nolan et al. 1993),

Geminga (Halpern

Holt 1992), PSR 1951+32 (Ramanamurthy et al., 1995) from CGRO

and other instruments needed explanation about the emission mechanism. Pacini (1968)

and Gold (1968) suggested that pulsating signals are generated by rotating magnetized

neutron star and the radiation luminosity derive ultimately from rotational energy. The es-

sential prediction of this hypothesis was based on that rotation must slow down due to the

energy loss after several months of observations and this small change of frequency was

found in radio detection and the hypothesis was proven.

In pulsar magnetosphere, particles ( ) arrange themselves such that E.B=0. At a radius

where field lines are traveling at the speed of light, pulsar wind region starts and this region

terminates with shocks and beyond this a nebulae region starts. The condition E.B=0 pro-

hibits the particle acceleration and this can occur in regions full of plasma where E.B .The charge density moves everywhere at the speed of light along divergent field lines. As

result of this, electrons will be stripped from the neutron star surface while ions will be


retained due to their larger surface binding energies. Since no positive charges will be

supplied from the neutron star surface to replace the positive charges in the magnetosphere

which are accelerated outwards, a vacuum gap will form above the polar caps and this gap

will continue to expand near the light cylinder until this reaches a maximum height equal

to radius of polar cap region. These vacuum gaps are thought to form near the magnetic

pole and near the light cylinder and pulsed emission from the radio wavelength to GeV -

rays is thought to originate from these regions. At present two general type of -ray pulsar

models explain the emission pattern and energy cutoff under certain approximations.

1.6.1 Polar Cap Model

Polar cap model was first proposed by Sturrock (1971) and later studied by numerous

authors (Ruderman

Sutherland 1975, Harding 1981, Daugherty and Harding 1982) as-

sumes that emission is produced by electrons accelerated to high energy just above the

surface of magnetized rotatory neutron star, in the vicinity of magnetic poles. The salient

features of polar cap model (Daugherty and Harding 1994) are as follows, The -ray emission is initiated by acceleration of electrons from neutron star surface

just above the magnetic polar cap regions which encloses the open magnetic field lines

extending to the velocity-of-light cylinder. The emission originates as curvature radiation (CR) produced by electrons as they

follow the curvature of the open magnetic field lines. The process of direct pair conversion (magnetic pair production, Erber

1966) by the neutron star magnetic field and synchrotron radiation by the emitted pairs

produce photon-pair cascades from which the observed -radiation emerges. The rotational and magnetic axis of the radiating neutron star are nearly aligned

so that the inclination (angle between spin and magnetic axis) is small enough to be

comparable with the polar cap half angle " The acceleration of electrons occur over an extended distance above polar cap surface,

where they reach their peak energies at heights of a few neutron star radii. Above these

heights, the acceleration is cut off by an overlying force-free plasma.

The magnetic field lines which touches the light cylinder defines the edge of the polar cap

regions. This dipolar field lines obey the equation

+.-*/ ) "The is the polar cap half-angle equal to

, where is radius of emission

region and is the neutron star radius. The angular radius of the polar cap region is the


ΩB

αLight

Cylinder

polar cap beam

outer gapbeam

Ω . B = 0

Fig. 1.6: Polar Cap model of pulsed emission. (figure is from http://cossoc.gsfc.nasa.gov)

last closed field line touching the light cylinder at 90 , ie when then R

( ) &% (

+ ) &%

Therefore the radius of polar cap region is

+ &%

(1.17)

The potential difference between the center and edge of the polar cap region due to spinning

magnetic field is

" 0)

+ (1.18)

The potential drop falls as pulsar slow down. For Crab pulsar, " , taking

typical radius R=10 km and surface magnetic field equal to G, the polar cap angle and

potential drop between center and edge are 4.56 degree and 2.01 volts respectively.


The charged particles streaming out of the polar cap will travel along the curved magnetic

field lines at relativistic velocities and emit curvature radiation in the form of high energy

-rays. These high energy -rays further produces electron positron cascades when travel

through strong magnetic B field,

The resulting charged particles will in turn be accelerated along the curved magnetic field

lines and produces more high energy -rays through curvature radiation. At some point

in the process of high energy emission through curvature radiation, the secondary photons

will no longer have sufficient energy to produce pair and will escape from the pulsar mag-

netosphere, resulting in a beam of high energy photons swept along the open field lines

from the polar cap. The attenuation in the pair cascade due to magnetic pair production

slow down the further acceleration of charged particles and a cutoff in the high energy

emission is possible at several GeV-TeV energy ranges.

The observed double peak profile in light curves of Crab, Geminga, Vela pulsar is either

results from enhanced emission along certain region of the polar cap surface or sufficiently

large inclination angle between the rotation and magnetic axis. Also, double peak profiles

would be expected if the radiation beams were in the form of a hollow cone. This occurs

when the line of sight of the observer intersects the polar cap beam where the highest en-

ergy emission originates. When the line of sight exit, the beam forms the trailing peak.

The inner part of the beam produces emission between the peaks or bridge emission. If the

line of sight passes near the edge of the radiation beam as star rotates, a single profile will

be observed. For an almost aligned rotator, the inclination angle ( ) of the magnetic axis

to the rotation axis is small by definition. Irrespective of polar cap model, this angle should

be small, once we say they are almost aligned. Polar cap model assume that opening angle

(4.56 degree) for -ray emission should be small.

1.6.2 Outer Gap Model

The Outer gap model (Cheng, Ho

Ruderman 1986a, 1986b) or known as CHR model

assumes that the acceleration of charged particles occurs much higher in the neutron star

magnetosphere, in vacuum gaps formed within a charge separated plasma. A null surface

exist in the magnetosphere between the region " and the light cylinder along the

last closed line. This region defines a null surface which act as accelerator for energetic

electrons. The four outer gaps, which can co-exist in a pulsar magnetosphere extend from

the null surface to the light cylinder along the last closed magnetic lines. The emission


ρc= 0 Ω µ

α

Light Cylinder

gamma-ray emission beam from outer accelerator gap

radio emission beam

Fig. 1.7: Outer gap model of pulsed emission. (figure is from http://cossoc.gsfc.nasa.gov)

produced by the two longer gaps is expected to be much greater than the emission from the

two shorter gaps.

Inside the gap " and electrons and positrons are accelerated along the curved

magnetic field lines and large potential difference across the gaps, radiates the rays

via curvature radiation or through the Inverse Compton (IC) scattering. Since the magnetic

field in the outergap region is weak, the magnetic pair production is not an efficient process

as in the case of polar cap region. In an extended gap, these secondary -ray beams will

interact with each other in the magnetosphere and produces pair as

Thus if E.B is large, then it will boost the -ray production rate and then pair production

will replenish the charge deficiencies in the outer magnetosphere and prevent the further

growth of gap. Therefore in outer gap model of CHR, the charged particles are accelerated

between the null surface and the light cylinder along the boundary between the closed and

open parts of the magnetosphere and the acceleration is a self-sustaining (Tuneyashi

Yutaro, 1994) process and can be expressed as follows.

/ %) + - - /)*+ /


+ - ) - /

)/1+ - %-*/

+.- ) -*/

)/1+ %- %-*/ The Inverse Compton Scattering between accelerated and the soft photons produces

highest energy -rays. The collision between the primary -rays and the soft photons

produces secondary pairs. The synchrotron photons from these secondary pairs pro-

duces tertiary pairs. The synchrotron photons from these tertiary pairs supply the soft

photons. All these inter-related processes make up a self sustaining outer gap accelerator

and the tertiary pairs refuel the gap.

The observed X-rays and -rays are the sum of primary -ray and synchrotron photons

emitted by the secondary pairs. Since the magnetic field is weak in the outer gap re-

gion, high energy photons can escape freely once emitted and hence emission spectra can

extend to few hundreds of GeV. Since magnetic attenuation is weak in outer gaps, cutoff

in VHE emission is more gradual than the polar cap emission. Since the outergaps are

mirror image of each other, the beams from one outer gap is parallel to the beam from the

opposite side of gap. Hence the observed double peaked -ray pulse profile of Crab and

Vela pulsars is consequence of the symmetry inherent to the outer gap geometry.

1.7 Observed Gamma Ray PULSARS

The study of -ray emission from pulsars had started with the Small Astronomy Satellite

(SAS-II) launched in 1972 (Fichtel et al. 1975) and COS-B missions launched by the

European Space Agency (Swanenburg et al. 1981), in which Crab (PSR 0531+21) and

Vela (PSR 0833-45) were identified as pulsating sources of high energy -rays. These

satellite detectors scanned -ray sky in the energy range of 20 MeV-1 GeV and 2 keV-

5 GeV respectively. However the detailed observations of -ray pulsars had come from

OSSE, COMPTEL (1 MeV-10 MeV) and EGRET (100 MeV-1 GeV) instruments on board

the Compton Gamma Ray Observatory (CGRO). Before the launch of CGRO, Crab and

Vela pulsars were the only known -ray sources of pulsed nature at energy ' 100 MeV.

From ROSAT X-ray data, (Halpern and Holt, 1992) discovered Geminga as 237 ms pulsar

and confirmed the early observations of (Fichtel et al. 1976, Thompson et al. 1977) and

(Grenier et al. 1991). In the EGRET data (Bertsch et al. 1992, Mayer-Hasselwander et al.

1993) detected Geminga as a -ray pulsar of energies ' 100 MeV. The PSR 1706-44, was

first detected as -ray source in the COS-B satellite data (Swanenburg et al. 1981) and later


confirmed by the EGRET data (Thompson et al., 1992) as a source of emitting pulsed radiation of energy ' 100 MeV at radio period of 102 ms. Two more pulsars PSR 1055-52

and PSR 1951+32 have been discovered above 30 MeV by EGRET mission. One more

pulsar PSR 1509-58, was detected by the low energy instruments on CGRO (COMPTEL)

up to 30 MeV (Kuiper et al. 1999) and not above 100 MeV by EGRET detector. Therefore

only seven pulsars have been detected at highest energies of ' 10 GeV so far. In this

section, the light curves at MeV-GeV, multiwavelength light curves and emission spectrum

of satellite observed -ray pulsars will be discussed.

1.7.1 Light curves

The study of high energy -rays from compact objects not only explain the total power

emitted from pulsars but also the acceleration of high energy particles by rotating neutron

stars. A rotating beam pattern of a emitting source is characterized by its light curve or

phasogram of observed events. The pattern of light curves give us a direct view of the

origin of high energy photons and beaming nature of radiation. The light curves of seven

major - ray pulsars observed from EGRET instruments at energy ' 100 MeV are shown

in figure-1.8. The pattern of light curves looks quite different in each pulsar. At higher

energy, four pulsars Crab, Vela, Geminga and PSR 1951+32 shows -ray light curves with

two peaks separated by about 0.4 to 0.5 in phase ( $ ) of rotation. The light

curves of PSR 1706-44 and PSR 1055-52 are very broad and not very well defined. The

PSR 1706-44 has possibly three peaks extending over about 120 of phase and PSR 1055-

52 shows two overlapping peaks with phase separation of 70 , and possibly a third peak

separated by a phase of 180 which partly overlaps. PSR 1509-58 has been detected in

low -ray energies by BATSE and COMPTEL and shows single peak at about 0.45 phases

in lightcurve.

1.7.2 Multi-Wavelength Light Curves and Spectra

The investigation of pulsar light curves at different energies probe directly into the radia-

tion mechanism as well as region from where these radiations are produced through direct

interaction between particles, photons and field of pulsar magnetosphere. Therefore these

multiwavelength comparisons are useful to distinguish different emission processes. The

multiwavelength light curves and spectrum of seven EGRET -ray pulsars are shown in

figure-1.9 and figure-1.10 respectively.

The spectral intensities are displayed in terms of , which is equivalent to power emitted

per unit of . In all these seven spectra, it is clear that emission in the X-ray and -ray


Fig. 1.8: -ray pulse profiles of seven EGRET pulsars. (figure is taken from Fierro, 1995)


Fig. 1.9: Multi wavelength Light curves of seven -ray pulsars. (figure is taken from Thompson

2003)


Fig. 1.10: Multiwavelength spectra of seven -ray pulsars. (figure is taken from Thompson 2003)


energy band dominates the total emission of radiation from these sources. Light curves

of pulsar shows two peaks separated by 0.4 0.5 phase from radio to ' 100 MeV

(EGRET energy) and these peak position appears at same phase interval as well as posi-

tion. This identity in light curves of Crab pulsar indicates that emission from radio to GeV

is from same region of pulsar magnetosphere. At radio frequencies below about 700 MHz,

a third pulse component known as the precursor can be detected preceding the main pulse.

It has steeper spectrum than the rest of the radio emission. The scattered radiation of radio

beam into background concentrates along the ambient magnetic field. The scattering from

the different harmonics of the particle gyro frequency takes place at different characteris-

tics altitudes in the magnetosphere. Because of rotational effect, this give rise to different

components in the pulse profile. Induced scattering from the first harmonic into the state

under the resonance can account for the so called low frequency components (precursor)

in the radio profile of Crab pulsar. The Crab pulsar emits, maximum power in X-ray band

at 100 keV. Above 100 MeV, Crab pulsar spectrum continues with harder power law

distribution up to few GeV and above this only upper limits of pulsed emission are given

by all instruments. Similarly double peak light curves are observed for pulsar

which is weakly observed at radio and optical frequencies. Apart from this, two peaks do

not retain their position on light curves at different energy bands and indicate that emis-

sion in different energy bands is not from the same region of pulsar magnetosphere. The

spectrum of Geminga pulsar is generally very hard and shows marked variation over the

rotation period. The maximum power emitted in spectrum of Geminga is at about 1 GeV.

Since this is weakly detected at radio frequency, it is known as “radio-quiet pulsar” but

first specimen of a true high energy pulsar. is well observed by low en-

ergy instruments up to 30MeV by BATSE, OSSE and COMPTEL (Carraminana

Bennett

1995). EGRET data shows only upper limits above 100 MeV, therefore the spectrum must

turn over at these energies. Since !#"$ pulsar is a strong and steady -ray emitter, the

detailed spectra for the individual phase components eg: the peak and interpulse regions

are well studied. The spectra of the emission peaks are generally softer than the spectrum

of inter-peak region. The softest components are observed in the leading and trailing wings

of the peak, which is the result of a low energy spill-out from the main -ray producing

cascades in the outer-magnetosphere of the pulsar. %'&'( )) has been detected as

a steady emitter at TeV energies (Kifune et al. 1995) and the maximum power of this

source is at 1 GeV. * ,+- was identified as weak -ray source at energies above

300 MeV and EGRET confirmed pulsation in -ray at E ' 100 MeV. The spectrum of this

pulsar does not show a characteristic fall in energies above several GeV, unlike the other

pulsars. ./ - shows maximum power emission around 1 GeV and no break in


the spectrum up to 4 GeV so it has a very hard energy spectrum that extends from X-ray to

-ray energy.

All -ray pulsars discussed above exhibits a high energy spectral break and no pulsed

emission is seen above 30 GeV which is the upper limit of CGRO/EGRET observations.

In TeV energy region, figure-1.10 shows only upper limits. These limits for Crab and

Geminga pulsars are less than 1 of maximum emission. Since the typical size of satellite

detector is of the order of 1 meter therefore detection efficiency is poor at higher energies

due to falling fluxes as compared to ground based detectors. The -ray Large Area Space

Telescope (GLAST) and Atmosphereic Cherenkov telescopes (ACT) can explore these -

ray pulsars in GeV to TeV energy range.

1.8 Observation of Pulsars in 10GeV 100GeV

Many Gamma ray sources including pulsars have been detected by space based EGRET

detector on CGRO in the energy range of MeV to GeV. This energy range range is well

explained by the Polar Cap and Outer Gap emission models. The polar cap model predict

that -ray spectra would show cutoff very sharply due to magnetic photon-pair production

attenuation in the magnetic field of neutron star whereas the outer gap extends the pulsar

emission to few hundreds of GeV. So the pulsars in the unexplored energy region ie 10

GeV-100 GeV and more may able to discriminate the two emission models. Figure-1.12

shows the pulsed -ray fluxes and upper limits detected from Crab system. A key predic-

tion of Outer Gap model is that pulsed -ray emission should continue to energies up to 20

GeV.

It is a great challenged to the -ray astronomers to explore this energy range and this

can be achieved by joint mission of both ground-based and satellite based detectors. The

collection area of satellite detectors is too small to detect -rays above 10 GeV and num-

ber of Cherenkov photons produced by -rays is not sufficient to trigger the small area

Cherenkov detectors. A new generation space detector, Gamma Ray Large Area Space

Telescope (GLAST) scheduled to be launched in early 2008 has a wide field detector cov-

ering the energy range of about 10 KeV to 300 GeV for exploring the -ray pulsars. Glast

has better sensitivity than EGRET and hence expected to see many more pulsars.

A new generation Cherenkov telescope such as HESS (Hofmann et al. 2003), MAGIC

(Martinez et al. 2003), VERITAS (Wakely et al. 2003), CANGAROO-III (Asahara et

al. 2004, Kubo et al. 2004) are quite efficient at low energies. These new generations

Cherenkov telescopes would be able to detect -rays up to 50 GeV or less. STACEE (Oser

et al. 2001) and CELESTE (Naurois de et al. 2002) used the wavefront sampling technique


Fig. 1.11: TIFR-IIA HAGAR array of seven telescopes, Hanle (INDIA).

with many mirrors to collect the Cherenkov photons and have succeeded to detect - rays

below 100 GeV from Crab nebula and upper limit of pulsed emission. Cherenkov light

density caused by the cosmic ray is about four-five times larger at high altitude of 5 km

(Tanimori et al. 1995, Cowsik et al. 2001). The HAGAR array at Hanle (India) at altitude

of 4200 meter above mean sea level with seven telescopes (figure-1.11) could be able to

detect -rays in the low energy range (50 GeV - 60 GeV).


Fig. 1.12: The pulsed photon spectrum of Crab pulsar. The thin solid line is the polar cap model fit

to the EGRET data (Harding 1999). The dotted line is the outer gap model for the Vela

pulsar (scaled to match the EGRET Crab pulsar flux at peak sensitivity) and is included

to indicate the shape of the cut-off this model predicts (Romani 1999) . The dashed line

represents the power-law fit to the EGRET data (Nolan et al. 1993). The upper limits

for pulsed emission are shown by the open squares. The thick solid curve depicts the

model of unpulsed GeV-TeV emission from the Crab Nebula (Hillas et al. 1998). (figure

is taken from Lessard et al. 1999)

Chapter 2

VHE Gamma-ray Observation

Technique

2.1 Introduction

Satellite-based detector can explore the high energy sky map up to 100 MeV of electro-

magnetic spectrum. At energies 10 GeV and higher, the flux of -ray photons is so low

( 1 photon meter year ) that no significant data can be acquired with typical size detec-

tors on board satellites. Therefore at these energies observations are only conducted with

ground-based detectors, though indirectly.

The Earth’s atmosphere blocks all electromagnetic radiation of energies greater than 10 eV.

The total vertical thickness of atmosphere above sea level is 1030 gm/cm or 28 radia-

tion lengths since the radiation length for VHE -rays is 37.1 gm/cm . This is equivalent

to blocking particles with about 1 meter thickness of lead. Therefore stopping power of

earth’s atmosphere can be used for detection of celestial -rays or particles.

Earth atmosphere plays a significant role for the detection of these VHE radiations. Al-

though these VHE -ray photons get absorbed in the Earth’s atmosphere, they can be ob-

served, though indirectly, using detectors placed on ground. Gamma rays coming to Earth

from outer space interact with air molecules high in the atmosphere, giving rise to a shower

of secondary particles . These electrons radiate energy through bremsstrahlung and

results to an electromagnetic cascade. A dipole field setup by electrons along the axis of

shower cascade radiate a brief electromagnetic pulse (Cherenkov) in the visible and ul-

traviolet region of electromagnetic spectrum as they propagate down through atmosphere.

The Cherenkov photons arrive at ground level in the form of thin ( 1 meter) disk and

these photons spread out over a large area

meter . These Cherenkov photons

are detected by optical parabolic reflectors and photomultiplier tube placed in-axis of -ray

source direction. This technique of observing VHE -ray sources is called as Atmospheric

27

Chapter 2. VHE Gamma-ray Observation Technique 28

Cherenkov Technique (Galbraith 1953, Boley 1964, Jelly 1964).

The temporal characteristics of Cherenkov emission (5-10 ns flash) makes it possible to

detect over vast and random background of night sky light with coincidence technique.

Background light of night sky (LONS) is brighter by factor of 10 (Blackett 1948) than

Cherenkov light. Since Cherenkov light is very faint, VHE observations are confined

to only clear and moonless dark nights which limits the duration of observations. The

isotropic cosmic rays also produces Cherenkov radiation and adds further background

for detection of ray signal, limiting the sensitivity of ACT. The important features

of Cherenkov light phenomenon associated with and cosmic (proton) rays will be briefly

discussed in the next sections.

2.1.1 Extensive Air Showers

A high energy particle incident on the top of the atmosphere loses its energy in successive

collisions as it propagates down. The high energy nuclear particles are produced in each

collisions with the air nuclei which start their own nuclear cascades. The products of these

cascades travel along the direction of the primary with a small lateral spread and arrive on

the Earth. In journey from top of the atmosphere to the Earth surface, millions of charged

secondary are produced which spread over a wide area and reaches on the gorund almost

simultaneously and causing a shower of particles called extensive air showers (EAS) (Rao

Sinha 1988).

Air showers are usually studied with large number of detectors placed several meters apart

and connected in the coincidence. In an air shower, about 90% of the charged particles

are electrons, 6-9% muons and rest 1% are strongly interacting particles. Near the core of

shower, the electron densities are high (90%). The relative number of muons increases as

one move away from core and beyond a several hundred meters, muons are the dominant

charged particles in EAS.

When a high energy charged particle pass through the atmosphere, it undergoes several

interaction processes such as ionization (as result of inelastic collision with atmospheric

atomic electrons), the deflection of the particle from its incident direction (due to coulomb

scattering with the atmospheric atomic nuclei) and other processes like the emission of

radiation through bremsstrhalung, nuclear interactions with atmospheric nuclei and decay

process.

The bremsstrahlung radiation is the electromagnetic radiation emitted by a charged particle,

mainly by electrons and positrons, when they are accelerated by electric field of nucleus.

At energies of few MeV or less, this process is relatively small but as the energy increases,


the probability of bremsstrahlung quickly shoots up and at few 10’s of MeV, loss of en-

ergy by bremsstrahlung radiation is comparable to or greater than the collision-ionization

energy loss.

The behavior of photons in the atmosphere is different from that of charged particles due to

lack of electrical charge. The main process through which a VHE ray interacts in the

Earth atmosphere is pair production, which involves the transformation of a photon into

an electron-positron pair. The pair production begins to be important at energies higher

than 1.02 MeV and it is a dominant effect at energies higher than 25 MeV. Other kinds of

interactions that can take place at lower energies are Compton scattering and photoelectric

effect. The Compton process is dominant at energies around few hundreds of MeV and

photoelectric effect is only relevant at energies below 100 keV.

The different physical processes that take place when atmospheric shower is initiated by

rays and protons (cosmic-rays), leads to an observational difference between both kinds

of showers. A brief description of -ray photon and proton interactions through the Earth’s

atmosphere are given in next sections.

2.1.2 Electromagnetic shower

Photon showers

A high energy -ray photon when enters in the Earth’s atmosphere, it soon interacts with an

air nucleus and creates an electron-positron pair. These electrons and positrons, which still

have high energies, undergo bremsstrahlung process and emit high energy photons. These

photons, in turn materialize and create more pairs of electrons and positrons. Thus, as the

particles propagate down in the atmosphere, more and more electrons-positron pairs and

photons are created. The resulting avalanche of electrons and photons is called the electro-

magnetic cascade or electromagnetic showers. This electromagnetic cascade continue

to increase in size until the average energy of the particles falls below the critical energy .When energy of -ray photons reaches to its critical value, they no longer produce pairs

and are absorbed by the atmospheric molecules. The electrons and positrons also can not

produce bremsstrahlung radiation and lose energy by ionization process. Figure-2.1 shows

the schematic representation of -ray induced electromagnetic cascade.

Proton showers

When a high energetic nucleus(proton) interacts with atmospheric nuclei, it produces electron-

photon and nucleonic cascades. The nucleonic cascade consists of secondary nucleons,


Fig. 2.1: A simple model for production of electromagnetic shower. (Figure redrawn from Longair

1981)

charged pions ( ), neutral pions ( ) and other mesons. The charged pions, which have

sufficient energy continue to multiply in successive generation of nuclear collisions until

the energy per particle drops below the threshold (1 GeV). The secondary protons also

interacts (nuclear collisions) and also loses energy by ionization and excitation of atmo-

spheric nuclei. The neutral pions ( ) which have very short life time (1.78 sec),

decay to two photons, initiates an electromagnetic cascade.

Many of the charged pions decay in flight into muons with mean life time 2.55 seconds as

The low energy muons decay to positrons, electrons and neutrino with mean life time

2.2

seconds as

The development of proton initiated cascade is shown schematically in the figure-2.2.


Fig. 2.2: A simple model for production of hadronic shower. (Figure redrawn from Longair 1981)

Development and propagation of EM shower

The relativistic electrons and positrons in EM cascade subsequently lose their energy

through the process of bremsstrahlung. The rate of energy loss by bremsstrahlung is given

by (Heitler 1944) 0 0 (2.1)

Where E is the energy of relativistic electron and X is the radiation length. The radiation

length (X) is defined as the mean distance over which a -ray or a high energy electron

loses 1/e of its energy. A -ray loses its energy by pair production and high energy electron

via bremsstrahlung process. The development of an electromagnetic cascade consist of a

succession of acts of pair production and bremsstrahlung. Each photon on average, travel a

distance (X ) and then undergoes pair production, whilst each electron travels the same

distance and then radiates half its energy as photon. If initially the primary photon has

an energy E then after traveling a distance X into atmosphere, it materializes into an

electron-positron pair with each particle having an energy E /2. After a further distance

X each particle radiates a photon with energy E /4 and continue with same energy.

The two secondary photons then materializes into electron-positron pair and in this way


the number of photons and charged particles increases, whilst the energy of individual

particles decreases. The number of particles, N at depth (t ) is given by (Greisen 1956,

Hiller 1984),

/ 0 ) -%) +0 (2.2)

Therefore (2.3)

and the energy of each particle is given by

(2.4)

The development of the cascade ceases when the energies of the individual electrons and

positrons are approximately equal to the critical energy , because at this energy, ionization

becomes dominant over bremsstrahlung energy loss. The maximum number of particles is

reached at depth (t !*# ) when

"!$# (2.5)

or

"!*# (

) (2.6)

At the shower maximum, total number of particles are given by

"!*# ( ) (2.7)

From equation-2.6, it is clear that total track length of is equal to

radiation length,

which is proportional to primary energy of -rays and a suitable parameter for measure-

ment of primary energies of incoming celestial -rays.

2.2 Cherenkov Radiation

Cherenkov radiation was first observed in the early 1900’s by the experiments developed

by Mary and Pierre Curie while studying radio-activity emission. The first attempt to un-

derstand the Cherenkov phenomenon was made by Mallet in 1926. He found that the light

emitted from a wide variety of transparent bodies placed close to a radioactive source al-

ways had the same bluish-white quality and the spectrum was continuous, not possessing

the line or band structure characteristic of fluorescence. Mallet found such an emission but

he could not find its nature. A series of experiments commenced by Cherenkov, gave more


Fig. 2.3: The polarization set up in the air molecules when a charged particle passes through (a)

Low velocity, (b) High velocity. (figure redrawn from Jelley 1958)

confirmation about this radiation. Frank and Tamm in 1937 gave the theoretical explana-

tion and Ginsburg in 1940 produced a quantum theory of the phenomenon. This radiation

was later known as Cherenkov radiation.

The Cherenkov radiation is an electromagnetic radiation emitted when a charged particle

moves in dielectric transparent medium at a speed (v) higher than the phase velocity (c/n)

of the light in that medium. When the charge particle passes through, atoms in the dielectric

medium momentarily polarizes as shown in figure-2.3. If velocity of the particle is small,

the induced dipoles arrange themselves symmetrically around the instantaneous position

of the particle. Since v c/n, the electric field of the particle reach the molecules around

the instantaneous position of the charged particle in almost same time. Therefore, no re-

sultant polarization of the medium at large distance takes place and no radiation is emitted.

If velocity of the particle is higher than the phase velocity of the light in the medium, no


Fig. 2.4: Huygens construction to illustrate coherence and to obtain the Cherenkov angle ( ).

instantaneous dipoles are set in the region ahead of the moving particles, because the par-

ticle travels faster than its own electromagnetic field (Fig-2.3b). Thus a net polarization is

produced along the particle’s path direction, which consequently radiate brief electromag-

netic flash. In this condition, the wavelets from all portions of the tracks are to be in phase

with one another and interfere constructively as shown in figure-2.4 and at a distant point

of observation, there will be a resultant field. From figure-2.4, it is understood that this

radiation is only observed at a particular angle called Cherenkov angle, with respect to

the track of the particle. This angle represents the position in which waves from arbitrary

point such as A, B over the track AB are coherent and combine to form a plane wave front

BC. This coherence takes place when the particle travels from A to B in the same time that

the light travels from A to C. If n( ) is the refractive index of medium and is the phase

velocity of light in the medium then from geometrical consideration, the Cherenkov angle

( ) is obtained as

or

/ + (2.8)


This is known as Cherenkov relation or coherence condition (Jelly 1958). From this rela-

tion it is clear that for a medium of refractive index (n), there is in fact a threshold velocity , below which no radiation is emitted. For this critical velocity, the direction of

radiation coincides with that of the particle. The maximum emission angle corresponds to a

ultra-relativistic particles (

=1). The radiation occurs mainly in the visible and uv-visible

regions of the electromagnetic spectrum for which n ' 1. Emission in other wavelengths

like X-ray and -ray region is not possible because n( ) is + 1 for these energies, which

will not satisfy the equation-2.8, therefore Cherenkov emission in the X-ray and -ray en-

ergies are forbidden.

There are two further conditions to be fulfilled to achieve coherence, in addition to that

stated in equation-2.8. First, the length l of the track of the particle in the medium should

be large compared to the wavelength of the radiation, otherwise diffraction effects will

become dominant and the light will be distributed over an angle

instead of ap-

pearing at one angle . Secondly, the velocity of the particle must be constant during its

passage through the medium, or, to be more specific, the differences in the times for particle

to traverse successive distances l should be small compared to the period of the emitted

light. If we take into consideration of the Maxwell theory of electro-magnetic waves, a

charged particle moving uniformly does not radiate and this proves that the Cherenkov

radiation is not related to Bremsstrahlung radiation.

Spectrum of Cherenkov light

The energy radiated (dE) by a charged particle of charge e in the form of Cherenkov radia-

tion passing through a track of length (dl) of medium with refractive index (n) and velocity

(

c) is (Jelly 1958)0 0

+

/ 0 (2.9)

If there are N Cherenkov photons produced then and

, thus most of the

Cherenkov light is emitted in the ultraviolet region of visible spectrum. For a particular

case of an electron moving along a track of length l, number of photons within a spectral

region defined by wavelengths and is given by

(

) / (2.10)

where is fine structure constant. In figure-2.5, curve (a) shows the Cherenkov photon

spectrum at production level and curve (b) shows the atmospheric transmission (Konard

2000) in visible band. Curve(c) is the resulting Cherenkov photon spectrum at observation


Fig. 2.5: (a) Production spectrum of Cherenkov radiation, (b) Atmospheric transmission, (c)

Cherenkov spectrum at observation level.

level. For an electron of energy 100 MeV moving through a depth of 1 meter of water

(n=1.33), the Cherenkov yield (photons) is 10000 photons and while same electron trav-

eling through air (n=1.00029) and same depth at sea level produces 12 photons between

wavelength range of 400 nm and 500 nm.

2.3 Cherenkov Radiation in EAS

The emission of Cherenkov light by the Extensive Air Showers (EAS) is a of great impor-

tance for the ground based -ray astronomy. In the case of primary particles of energies

less than 20 TeV the cascades die out in the upper atmosphere but the Cherenkov radiation

produced by the charged component of the shower penetrates up to ground level where

these photons can be collected with large reflectors. Although subject to fluctuations in the

point of origin of the cascade and its subsequent development, the Cherenkov light carries

with it information pertaining to the direction of origin of the primary -ray and also the

energy of the primary particle. Cherenkov light produced by EAS cascades is very weak

than light of night sky (LONS) but temporal property of Cherenkov light allows the ground

based detectors to detect such faint signal in presence of bright background of LONS.

Most of the Cherenkov radiation is produced by the electrons and positrons. As it is


seen from equation-2.8 that Cherenkov radiation is emitted when velocity or energy of the

charged particle exceeds a minimum threshold energy E . Since electrons and positrons

have to move at relativistic speed in the atmosphere to radiate Cherenkov photons so their

threshold energy (E " ) will be that which corresponds to a relativistic particle moving at

velocity , where c is the speed of light in vacuum and n(h) is the refractive index

at a given atmospheric height h in km. At sea level, the refractive index of air is 1.00029

and this varies with atmospheric height as,

/ (2.11)

where is 0.00029 and h is the scale height of atmosphere which is equal to 7.1 kilome-

ters. The variation of refractive index of air with atmospheric height is shown in figure-

2.6(a). The relativistic kinetic energy of particle whose rest mass is m , is given by

+

+ (2.12)

For threshold energy,

= , so

" + (2.13)

From equation-2.13, threshold energy for an electron to produce Cherenkov radiation is 21

MeV at sea level and this increases with atmospheric height. The reason for this change

in the " is the variation of index of refraction of the atmosphere with height from sea

level. The variation of threshold energy with atmospheric height for an electron is shown

in figure-2.6(c). Similarly, threshold energy for the muons ( ), pions ( , ) and protons

are 4.38 GeV, 5.60 GeV and 38.95 GeV respectively. From equation-2.8, the maximum

angle of Cherenkov light emission obtained is 1.38 degree at sea level for ultra-relativistic

particles (electron) and decreases with increase of atmospheric height. The variation of

Cherenkov emission angle as function of particle (electron) energy at sea level is shown

in figure-2.6(d). Cherenkov emission angle is zero for threshold energy (21 MeV) and

maximum (1.38 degree) for ultra-relativistic energy (

=1). From equation-2.13, it is seen

that at a given altitude, the threshold velocity depends on particle rest mass energy ( + ).Therefore threshold energies for particles heavier than electrons will increase by their rest

mass factor and this is shown in figure-2.6(e). The Cherenkov light front arrives at ground

level in the form of circular disk and radius of this light cone at sea level is given by

" $

% (2.14)


Fig. 2.6: Important features of atmospheric Cherenkov radiation.


which is found to have a maximum value when , ie when

" km and r "!$# is

125.8 meter. This light cone spreads over a circle of 250 meter diameter. The dependence

of the radius of light pool is shown in figure-2.6(f). The flash of Cherenkov pulse arrive on

ground level in few microseconds and photons are distributed laterally.

%

(2.15)

where r is the distance in meter from the shower core (axis). Eqution-2.15 shows that

the intensity falls off slightly more rapidly than 1/r. The other features like longitudinal

and lateral distribution of atmospheric Cherenkov radiation will be discussed along with

Monte-Carlo simulation studies using CORSIKA in chapter-4.

An approximate number of Cherenkov photons produced by a 1 TeV -ray in the atmo-

sphere and detected at ground level is explained in following example.

Let a primary -ray of energy E interact at top of atmosphere and produce an EM cascade.

The total track length in units of radiation length of in cascade is given by (Rossi 1958,

Gandhi 1992) (2.16)

where is the critical energy of in the air and is equal to 84.2 MeV. From equation-

2.10, the number of Cherenkov photons produced per unit length in air between wavelength

range 300-550 nm, at sea level is

0 0

" - -*/ +

Number of Cherenkov photons at depth of X gm/cm are given by

0 0 " (

) - - /1) + (2.17)

where is the depth of atmosphere at sea level and equal to 1030 gm/cm . Now one

radiation length (X ) in air is equal to 36.2 gm/cm , the track length at depth of X gm/cm corresponding to one radiation length is

where is density of air at depth X, given by

(

)where

is the density of air at sea level, so

(

) (2.18)


Therefore, the numbers of Cherenkov photons produced in one radiation length are given

by 0 0

or " ! (2.19)

When energy of e in EM cascade fall below the threshold kinetic energy (E =21.0 MeV

at sea level) then there will be no more emission of Cherenkov radiation, so actual track

length used for Cherenkov emission will be the fraction of given by equation-2.16. Now

the depth at which number of e in EM cascade is maximum is given by equation-2.6

!*# !#" (

) (2.20)

so for a 1 TeV -rays, "!$# " %+

and threshold kinetic energy of e at this depth is

"!$# !#"

Hence the fraction of the track length for which the energy of e is more than the threshold

energy E is given by

(

) $ " !#" $ "

"

so, total numbers of Cherenkov photons emitted in the shower are

( )

where T is average transmittance (Konard 2000) of atmosphere for Cherenkov photons,

therefore total number of Cherenkov photons at sea level is

( " ! " ) " $ " " ! ! " - -*/ )

These Cherenkov photons spread over an area of 300 meter radius circular pool, therefore

the number of Cherenkov photons/meter are

" - -*/ )

The size of the Cherenkov pool is determined by the interaction height of primary -


Fig. 2.7: Geometric model of the emission of the Cherenkov radiation for -rays and proton show-

ers. The stippled region encloses the main emission region for production of Cherenkov

light from -ray showers. (Hillas 1996)

rays in the atmosphere and Cherenkov emission angle. Figure-2.7 illustrates the geometry

of Cherenkov rays in air showers and also the focusing effect caused by varying density

profile of the atmosphere. Since the number of Cherenkov photons produced is determined

by total track length covered by EM cascade or primary energy of -rays, therefore measure

of Cherenkov photons at ground level is a good measure of energy of primary -rays.

2.4 Cherenkov detection technique

In previous section, it is shown that Atmospheric Cherenkov radiation arrives on ground

in few microseconds and spread over a circle of 300 meter radius at sea level. The obser-

vations are usually carried at mountain where ambient light is less and atmospheric atten-

uation of Cherenkov light is very low. The two methods used for detection of Cherenkov

photon showers are

Wavefront sampling of Atmospheric Cherenkov Radiation

Imaging Atmospheric Cherenkov Technique


Fig. 2.8: An array of detectors used in wave-front sampling technique.

2.4.1 Wavefront sampling of Atmospheric Cherenkov Radiation

According to Huygen’s theory of wave-front, a point source of light sends out waves in all

direction and these rays of light diverging from a point give rise to a spherical wave front.

At large distances, curvature of wavefront is small and can be approximated to a plane

wavefront. Similarly, a -ray photon acts as point source at top of atmosphere, Cherenkov

light produced by electromagnetic cascades propagate along the direction of primary -

rays and Cherenkov photons wavefront arrive on the ground. Since Cherenkov light is a

coherent (maximum emission angle 2 is 2.7 degree at sea level), a conical envelope of

Cherenkov photons propagates towards ground. In this technique (Chitnis

Bhat 2002,

Bhat et al. 2002), wave-front timing, the arrival time of the Cherenkov pulse are measured

at a number of detectors distributed on the ground within the light pool. The relative

arrival time of wavefront can be recorded with fast timing system. A surface fit (plane or

spherical) to the arrival times at each detector, gives the direction of shower-axis and thus


the direction of the incident -ray. Near the shower axis, a plane wave fit can be applied to

shower front, the arrival direction of shower-front is obtained by fitting the relative arrival

times recorded by detectors to a plane wavefront as follows.

/ (2.21)

where l,m,n are direction cosines of normal to shower front (shower axis), are

coordinates of i

detector, t is the arrival time of shower-front and t is the time-offset

(tzero) of the detector. The intensity (photon density) of Cherenkov photons recorded by

detectors gives an estimate of about the energy of primary -rays. The estimation of axis of

wavefront (shower axis) is very crucial in this technique, so we need an array of detectors

distributed in the circular field of 300 meter radius at sea level. Since duration of this light

wave front is very short (5-10 ns), a very fast data recording system is required with proper

logic to record complete information about primary -rays. The difference in the lateral,

density fluctuations (Chitnis

Bhat 2002), distributions of Cherenkov photons generated

by /hadron allow us to use this technique for detection of TeV -rays in presence of

isotropic cosmic ray background at ground level.

2.4.2 Imaging Atmospheric Cherenkov Technique

The Imaging Atmospheric Cherenkov Technique (IACT), is based on obtaining an image

of the atmospheric shower (Week

Turver 1997) by collecting the Cherenkov photons

spread on the ground. The basis of the technique is the use of an array of photomultiplier

tubes (PMTs) in the focal plane of a large optical reflector to record the Cherenkov image

of an air shower. Figure-2.9 shows a model of Atmospheric Imaging Cherenkov telescope.

An imaging telescope consist of large number of parabolic reflectors mounted confocally

on a single parabolic dish. A PMT camera (cluster of PMT’s) is fixed at common focal

point of dish to record the images formed by parabolic reflectors. In an Imaging telescope,

the light coming from different heights are focused by the reflectors in different points

on focal plane. The orientation and the shape of an image obtained by the camera of

telescope gives differences in the showers produced by and hadron. Gamma ray initiated

showers start higher up in the atmosphere and spread out less than the hadronic showers due

to smaller transverse momentum in electromagnetic interaction compared with hadronic

interactions, allow distinguishing the two types of showers. The images formed by -

rays are characterized by narrow and compact size. Cosmic ray induced showers produce

Cherenkov light images which are much broader, diffuse and less well aligned with the

arrival direction. The difference in the two type of images are characterized by means


Fig. 2.9: A schematic diagram of an Imaging Atmospheric Cherenkov Telescope.

of suitable parameterization of shower images, known as Hillas parameters (Hillas 1985).

By selecting only those images which have like appearance and by means of suitable

discrimination algorithms based on Monte Carlo Simulation, almost 99.99 cosmic ray

events can be removed from the mixture of and hadron events.

The different parameters used in imaging analysis can be classified as shape parameters,

which characterize the size of the image and orientation parameters. In figure-2.10, an

ellipse is drawn to represent a shower image and different shape parameters are shown

below.

Size: This is the total integrated light content of the shower. Another parameter is

Cone that represents the degree of light concentration, determined from the ratio of

the five largest pixel signals to the sum of all signals.

Length: The + ) ' spread of light along the major axis of an image. This

parameter carries information about the longitudinal development of shower.

Width: This is + ) ' spread of light along the minor axis of an image and

carries information about the lateral development of shower.

The other orientation parameters are:


Fig. 2.10: IACT image parameters.

Distance: This is the distance from the centroid of an image to the center of the

field of view of the camera and gives information about impact parameter of shower

with respect to the center of field of view.

Miss: This is the perpendicular distance between the major axis of an image and

the center of field of view of the camera and is a measure of shower orientation.

Aziwidth: This is the + ) ' spread of light perpendicular to the line connecting

the centroid of an image to the center of the field of view. In other words it is the

projection of width along a line which is perpendicular to line joining the center of

the camera and center of image this contains the centroid and measure of both the

shape and orientation of image.

Alfa: This is the angle between the major axis of an image and radius drawn from

the center of the camera to the center of image and related with the angle between

the shower axis and axis of the telescope.

All the above parameters are used to distinguish a or hadron generated image.


Fig. 2.11: 10 meter IACT telescope of Whipple observatory.

2.5 Atmospheric Cherenkov Telescope

When a -ray of energy 1 TeV interacts at the top of Earth’s atmosphere, it produces ap-

proximately 150 Cherenkov photons/m in the wavelength range of 300 nm - 550 nm at

sea level and these photons carry information about the primary energy of -rays. Detec-

tion of TeV -rays is based on the detection of these Cherenkov photons and this is carried

through Atmospheric Cherenkov Telescope (ACT). Since these photons are distributed in

the field of large area (300 meter radius), so just single or small detector is not sufficient

to get complete information about the primary -rays. For collection of these distributed

Cherenkov photons, either a large diameter (IACT type) or small detectors but distributed

in the fields (wave front sampling type) are required. An example of 10 meter Imaging

Atmospheric Cherenkov Telescope of Whipple observatory on Mt. Hopkins in southern

Arizona at elevation of 2.3 km from msl (Cawley 1990) is shown in figure-2.11. The tele-

scope collection area is =78.5m and field of view is 3.0 degree in diameter. The High

Energy Stereo Scopic System (HESS), an array of four imaging telescopes and MAGIC are

the new generation IACT telescopes which will scan GeV-TeV -ray sky. These telescopes

will look for objects which were not detected by the earlier atmospheric Cherenkov tele-


Fig. 2.12: A heliostat array of STACEE experiment

scopes due to their low sensitivity. Solar Atmospheric Cherenkov Experiment (STACEE)

is an example of a wavefront sampling type setup as shown in figure-2.12, which is lo-

cated at the National Solar Thermal Test Facility (NSTTF) at Sandia National Laboratories

in Albuquerque (34.9N, 106.5W, 1705 meter from msl). The small size parabolic reflec-

tors are distributed in the field of xy matrix and has detected -rays up to 200 GeV (Oser

et al. 2001) from celestial sources. In the next section, various aspects of Atmospheric

Cherenkov Telescope and its design parameters will be discussed.

2.6 Functions of Atmospheric Cherenkov Telescope

2.6.1 Light collection

The primary function of a telescope is to gather light which incident on the reflecting

surface and concentrate them at its focus, so that any light sensitive transducer fixed at

focal point of reflecting surface of telescope can detect incident light. The amount of light,

a telescope can gather depends on the area of its reflecting surface, this is proportional to

the square of its diameter. Diameter of a primary reflector in any telescope determines the

light gathering power (LGP) (Zelik 2002) and this is proportional to its area of reflecting

surface. For circular mirror,

(2.22)


The ratio of focal length (f) and diameter (D) called as ! or

also gives an idea

about the LGP of reflector and given by

! (2.23)

The smaller the ! , brighter will be the image at focal point. Therefore a mirror of focal

length 1 meter and diameter 1 meter will give less bright image than 1 meter focal length

and 2 meter diameter mirror. In Atmospheric Cherenkov Telescopes, the ! of reflector

is kept 1.

2.6.2 Resolution

The second most important feature of a telescope is to separate or resolve images of objects

that are close together in the sky and this ability is called telescope’s angular resolution and

expressed in terms of minimum angle between two points that can be clearly separated.

The main optical property of telescope depends on the primary concentrator or reflector

which is a parabolic mirror in case of Atmospheric Cherenkov Telescope. The theoretical

resolution (TR) (Zelik 2002) of a telescope depends on the wavelength of incident light

and diameter of mirror and given by

+ ) ,+ "

(2.24)

In case of Atmospheric Cherenkov emission, the spectrum peaks at 400 nm so for a 1

meter diameter mirror,

"

" " %+.) ,+

Therefore optics of an Atmospheric Cherenkov telescope gives good angular resolution.

In case of wave-front sampling system, overall angular resolution (Majumdar et al. 2003)

depends on two factors which are the average distance D between the telescope and t, the

uncertainty in the measurement of arrival time of photons at the telescopes. If two ACT

telescopes are separated by distance D and is zenith angle of Cherenkov wavefront then

from figure-2.13,

+

where t is the relative arrival time of Cherenkov wave front at detector and c is speed of

light. The error in the arrival direction is given by

+


Fig. 2.13: Arrival of Cherenkov wavefront at ACT.

If there are n detectors separated by same distance D then angular resolution of array of

detector (Gupta et al. 1985) is given by

+

/ (2.25)

Therefore, large number of telescopes and separated by large distances estimate the arrival

direction more accurately. On the other hand, in case of imaging technique the angular

resolution is limited by PMT (pixel) size which is a typically of the order of 0.25 degree.

The detailed study of angular resolution of PACT array have been done (Majumdar et al.

2003) and this is equal to 0.04 degree for array of 24 telescopes distributed in rectangular

matrix of $ and average separation between the telescope of 25 meter.

2.7 Design parameters of ACT

2.7.1 Parabolic mirror

When a parallel beam of light incident on a small size concave reflector (5-10 cm diame-

ter), it makes a sharp and point image of a point source. Since the light gathering power


Fig. 2.14: Geometrical representation of parabolic mirror.

depends on diameter of reflector, therefore large size (typical 1 meter diameter in wavefront

sampling and 10 - 15 meter dish in IACT) reflectors are used for collection of Cherenkov

light photons. In case of large diameter mirrors, paraxial and marginal rays do not meet

at single point and therefore gives a blurred image of point source. So a simple concave

mirror is not suitable for large size reflectors but a parabolic mirror makes sharp image of

a point source. This is explained as follows.

If the shape of the parabolic mirror is defined by equation

(2.26)

and slope of tangent line can be expressed as

0 0

from the figure-2.14, the focal length f is given by

!* or

(2.27)


Fig. 2.15: Seven paraxial parabolic mirrors in Pachmarhi Array of Cherenkov Telescopes (PACT).

From equation-2.27, the focal length of parabolic mirror is independent of x (point of

incident) but in case of spherical surface represented by simple equation of circle

(2.28)

the focal length is given by

!

(2.29)

and therefore, marginal and paraxial rays do not meet at single focal point and gives blurred

image of a point source. Since it is difficult to make single large size parabolic mirror free

of all geometrical and optical defects, so multiple paraxial or confocal mirrors are used

to increase the collection area of Cherenkov detectors. A set of seven coplanar, paraxial,

parabolic mirrors used in Cherenkov telescopes of Pachmarhi array is shown in figure-2.15

and large number of small parabolic mirrors but placed on large parabolic shape surface,

which gives common focal point used in VERITAS IACT system is shown in figure-2.16.

2.7.2 Reflectivity

In general, highly polished metallic surfaces have higher reflectance than any other sub-

stances. Experiments show that the reflectance depends not only on the particular metal

but on the preparation of surface, on the wavelength and the direction of incident light.

The reflectance of metal usually varies considerably with wavelength of incident light.


Fig. 2.16: Imaging Telescope of VERITAS stereoscopic system. (figure is taken from

http://veritas.sao.arizona.edu/photo/)

Figure-2.17 shows the variation of reflectance as function of wavelength (Jenkins 1981)

for three different metals. In spite of irregularities at the shorter wavelengths, all metals

shown in figure-2.17 reflects very well in the red and infrared region. Since Cherenkov

spectrum peaks in blue region of optical band, steel is not a very good polishing mate-

rial for Cherenkov detector. Silver and aluminum are of particular importance for general

use because they maintain their high reflectance through the visible spectrum. Since alu-

minum retains its high reflectance in the near ultraviolet as well as in the visible range and

also polished surface does not easily tarnish even after years of exposure to air, therefore

depositing metal films by evaporation in vacuum has rendered aluminum as most satis-

factory substance for mirrors in optical instruments. It is now standard substance to coat

the mirrors of large reflecting surfaces with evaporated aluminum. A freshly made silver

mirror actually has a slightly greater reflectance in the visible but it soon tarnishes and

become poorer than aluminum. For the detection of ultraviolet light, aluminum or mixture

of aluminum and magnesium is better for polishing of optical reflectors.

Further, depending upon the thickness of glass used, either front or back coating is done

on the parabolic surfaces. A front coated surface gives almost 85-90 reflectivity than the

back coated 70-80 . For atmospheric UV detection, a front coated reflector is preferred to

minimize the absorption due to refraction at lower wavelengths (UV range) by SiO glass.

Therefore back coated reflectors are not good for the detection of UV photons produced in

Cherenkov spectrum.


Fig. 2.17: Reflectance at normal incidence of aluminum, silver and steel. (figure redrawn from

Jenkins 1981)

2.7.3 Focusing of reflectors

The flash of Atmospheric Cherenkov light pulse exist for very short duration (5-10 ns) and

propagate in the forward direction of incident particle. Therefore the alignment of optical

axis of parabolic mirrors used in IACT or wavefront sampling detectors is very crucial. In

IACT, it is done with artificial source (LASER) of light fixed at center of each parabolic

mirror. Images of all point sources are obtained on the screen fixed in front of PMT camera

and these images are further processed by the CCD (charge coupled device) camera fixed

at center of parabolic dish. A point spread function obtained from the common images of

all reflectors gives an idea about accuracy of alignment of their optical axis.

Since in wavefront sampling method, large numbers of reflectors are used in distributed

array, method used in IACT is not practical and therefore mirror axis are aligned with

natural source of star light. An artificial source of light placed at distance of 1000 meter can

also be used for alignment of mirror axis and focusing if telescope orientation allows for

large zenith angle observation. An optical bench designed for the improvement of focusing

of parabolic mirrors used in A Pachmarhi Atmospheric Cherenkov telescope is shown in

figure-2.18. For focusing, a point light source is fixed at focal point of source mirror and

parallel rays are reflected, which act as a distant source for the test mirror. Figure-2.19

shows the spot size of an image formed at focal point of parabolic mirror while doing


Fig. 2.18: Optical bench used at PACT for fine-tune of focusing of mirrors.

focusing on optical bench.

Active Mirror Control

A large diameter telescope has strong requirement on the stiffness of the reflector frame.

When directing the telescope to different elevation angles, the reflector’s surface deviates

from its ideal shape under gravitational load. Two solutions are possible to counteract the

deformations and these are either to construct a very heavy and stiff frame or allow for

small deformations by constructing a light-weight structure and correct its mirror profile.

For this purpose, the mount point (baking) are equipped with actuators to adjust its position

on the frame. This method of on-line control of mirror optics by using sensors and com-

puter controlled motors (actuators) to produce sharp image is referred to as Active Mirror

Optics (AMO) and this technique has been used in MAGIC telescopes.

2.7.4 Mounting

In search of celestial high energy -rays from point sources, the pointing accuracy of tele-

scope is very crucial. The two types of mounting which is used for telescope orientation


Fig. 2.19: Image of an object(light source) formed in focal plane of parabolic mirror.

is:

Equatorial mounting

Altazimuth mounting (Alt-Az)

The choice of either type mounting depends on the diameter of reflector, weight of tele-

scope assembly and geographical latitude. Since average diameter of most of the Imaging

Atmospheric Cherenkov telescope is in range of 10-20 meter and weight is several hun-

dreds of tons, altazimuth mounting is preferred for this purpose. The main advantage of an

Alt-Az mounting is that telescope weight is supported uniformly on a horizontally placed

central thrust-bearing. For an Alt-Az mount, the immobile axis is set towards the zenith

and the telescope guidance is provided by the azimuth and the zenith angles. If source

coordinates Right Ascension and Declination are known in equatorial coordinate

system, the instantaneous position and speed of the celestial source along either axis of

telescope is given by (Smart 1971)

(2.30)

(2.31)


Fig. 2.20: HEGRO-Pachmarhi ACT are in equatorial and HAGAR-Hanle are Alt-Az mounting.

(2.32)

(2.33)

where

is the observatory latitude, Z is zenith angle measured from local vertical, A is

Azimuthal angle measured from geographical South with clockwise direction and t is hour

angle of the source given by

where LST is local sidereal time.

The equatorial mounting is comparatively more straight forward to use for the detection

of Atmospheric Cherenkov light and more useful for light weight telescopes and locations

closer to equator. This type of mounting requires a long drive shaft which must be inclined

with respect to the horizontal plane at angle equal to the local geographical latitude. The

control drive in equatorial mounting is simpler and the Right Ascension axis of telescope

is required to be rotated at a uniform angular speed to lock on to a given source direction

and no correction is required in the direction of declination. Figure-2.20 shows the pictures

of equatorial mounting in HEGRO-Pachmarhi and alt-Az in HAGAR-Hanle (TIFR-IAA).


Fig. 2.21: Variation of Zenith angle, Azimuthal angle, Zenith speed and Azimuthal speed as func-

tion of source hour angle.

2.7.5 Control Drive System

Drive

The telescope drive system consists of two powerful Stepper/Servo motors for azimuth

and elevation changes, which produces sufficiently large torque to change the orientation

of telescope. The instantaneous position of telescope axis is measured by angle sensors

like shaft encoders/clinometers. The maximum re-positioning time of telescope depends

upon mechanical structure, power output of stepper motors and read-out system for control

drive.

Tracking

The main function of this mode is to provide an independent movement control for zenith

and azimuth axis of telescope pointing direction and source position with in expected ac-

curacy of few arc minutes/seconds. In case of equatorial mounting, tracking of source

is controlled through constant frequency (equal to Earth’s rotation frequency) controller

which drive Right Ascension stepper motor shaft at constant rotation speed. In case of alt-

azimuth mounting, the drive encoders are read after every fixed interval of time while the

source coordinates are updated after every second. At start of the ‘tracking’ module, the


two stepper motor controllers are programmed to provide tracking speeds in accordance

with equation-2.32 & 2.33. The variation of zenith angle, azimuthal angle, time-rate of

change of zenith and that of azimuthal angle as function of source hour angle is shown in

figure-2.21(a),(b),(c),(d) respectively. The individual drive continue to move at this speed

even though the actual values of azimuthal and zenith angular speeds (

and) changes

continuously with time. As result of this mismatch, offset between the actual encoder

reading and the desired angle starts growing and this is allowed to happen as long as the

accumulated offset remains less than the pointing accuracy. A correction is applied when-

ever this offset becomes more than set parameters. This correction is applied by either

momentary halt of the stepper motor or its faster movement. This correction cycle contin-

ues till the corresponding offset minimizes to few arc minutes/seconds. This ON-OFF type

of tracking works for source (latitude). For

, at the time of source transit, very

high correction rate is required and practically not possible to correct with control motors.

Therefore, in this region ( degree) near transit point, the tracking is usually kept off.

2.8 Cherenkov Signal detection and Energy threshold

The energy threshold of an atmospheric Cherenkov telescope is determined by the number

of Cherenkov photons needed to generate a trigger above the light of night sky background

(LONS). If is the Cherenkov photon density which is proportional to the energy E

of primary -ray, received at detector, then detected Cherenkov signals (S) is proportional

to mirror surface area A, ie /

where n is Cherenkov yield ( ) at primary energy E. When photons fall on the mir-

rors, only a fraction of the photons are reflected and these photons are converted to photo-

electrons at quantum efficiency of PMT. If is overall conversion efficiency then

/ (2.34)

The typical value of is 10 . Noise due to night sky background fluctuation is given

by

(2.35)

where B is density of LONS (photons/cm /sec/sr), is opening angle of field of view

(FOV) and t is the integration time of PMT for photon conversion. On clear moonless

(dark) night, at a dark site for 1075 meter from asl, the night sky background light between


300-650 nm is 3.3 photons/cm /sec/sr. The signal to noise ratio can be express as

/

(2.36)

From above equation, it is clear that signal to noise ratio can be improve by increasing

collection area (A), conversion efficiency ( , higher reflectivity and photon conversion ef-

ficiency) and decreasing the opening angle (limited by Cherenkov emission angle of 1.38

degree at sea level) and integration time t (limited by 5-10 ns flash of Cherenkov light) of

PMT.

2.8.1 Energy threshold

The energy threshold of Cherenkov telescope is the minimum -ray energy for which the

signal to noise ratio is adequately sufficient to trigger the instrument. For a given tele-

scope, the energy threshold of detection for primary -rays depends on telescope parame-

ters (FOV, integration time, collection area, conversion efficiencies), level of night sky and

observation point from sea level. The energy threshold (E ) is obtained from equation-

2.36 under condition

/

so energy threshold of single atmospheric Cherenkov telescope is

/

(2.37)

Thus energy threshold of Cherenkov detector can be lowered by working at darker site,

by increasing the collection area of Cherenkov reflectors and using many telescopes in

coincidence. Alternatively, by operating the telescope at high altitude, the energy threshold

can also be lowered. At higher altitudes, the density of Cherenkov photons for a given

energy are more than lower altitudes.

The signal to noise and energy threshold using typical values for a 1 TeV - ray shower,

LONS, conversion efficiencies etc for a telescope of the order of the size of PACT are as

follows.

PACT telescope and site parameters are summarized in table-2.1. The average number of

photo-electrons produced by light of night sky (LONS) photons are

"&! " !The average number of photo-electrons produced by Cherenkov light photons are

#" "


Table 2.1: PACT Telescope parameters.

LONS (B) 3.3x10 photons/m /sec/str

FOV ( ) 0.00215 str

Area (A) 4.45 m Integration time of PMT (t) 20 nanoseconds

Conversion efficiency ( ) 10 Mirror Reflectivity (R) 50 Cherenkov photon (C) 150 photons/m for a 1 TeV -photon

Putting for photo-electrons produced by Cherenkov photons and LONS in equation-2.36,

signal to noise is

" !#" Photons due to light of night sky are numerous compared to Cherenkov photons. In inte-

gration time (20 ns) of PMT, there will be 50 MHz triggers due to NSB if the detection

threshold is set at the average NSB photo-electrons. So to have trigger rate of about 10 Hz,

the NSB have to be rejected at the level of 1/10

or it has to be rejected at the level of high

sigma (S/N). Using S/N=10, number of Cherenkov photons at observation level will be

"&! " " "

#" Since, Cherenkov photons 119.2 corresponds to a observation level so number of Cherenkov

photons at production level will be

#" " !

! "&! - -*/ ) Since 150 Cherekov photons are produced from a 1 TeV -ray photon so photon number

196.6 per meter corresponds to threshold energy of 1.3 TeV for a single PACT telescope.

2.8.2 Sensitivity

The second important parameter after energy threshold that defines the performance of

Cherenkov telescope is its -ray flux sensitivity. If there is no background signal then

sensitivity is simply given by the collection area of telescope as function of energy and

observation time. The sensitivity of Atmospheric Cherenkov telescope is determined by

its ability to detect a minimum -ray signal over the cosmic ray background. At threshold

energy E, the -ray signal (S) is (Ong, 1998)

(2.38)


where

is the integral -ray flux, A is collection area and T is observation time. The

background signal B due to cosmic ray showers, which are isotropic, for same observation

time T is

(2.39)

where is opening angle of field of view. The cosmic ray flux obeys a power law spectrum

so

Assuming that the -ray flux is also represented by similar power law spectrum then inte-

gral -ray flux can be given as

where C and C

are constant and and

are spectral indices for cosmic and -rays

flux respectively. The -ray signal over cosmic ray background is

or

&% (2.40)

where the number gives an idea about the signal strength. If this number is greater than

some specified value then it is said that detected signal is acceptable. The sensitivity of

signal detection can be optimized or maximized ( ) by increasing the observation time.

( .

The sensitivity of a telescope could be improved significantly by identifying and rejecting

cosmic-ray initiated showers. An elaborate Monte Carlo simulation of showers propagating

in the atmosphere and detector response are needed for calculating various quantities like

collection area, energy threshold and sensitivity.

Chapter 3

PACT System

3.1 Introduction

The ground based -ray research in India was first started by the TIFR-group in 1969 at

Ooty with two mirrors, each of diameter 1.5 meter. Later the number of mirrors were

increased to 20 in 1977, eight of them of diameter 1.5 meter and the other twelve mirrors

of 0.9 meter diameter. Since astronomy work is limited by the sky conditions so in the

favour of better weather condition and spectroscopic nights, the entire setup with 20 mirrors

was shifted to Pachmarhi (Longitude: 78 East, Latitude: 22

North and

Altitude:1075 meter from asl) in 1986. In the first phase of observations, these telescopes

were deployed in the form of a compact array and in the second phase, telescopes were

distributed in the field area of 100m 80m. During first two phases, several new -ray

sources eg. Pulsars, Vela, Geminga, PSR 0355+54 in addition to standard Crab Pulsar

were observed in TeV energy band. Later to improve the signal detection efficiency, an

array of Atmospheric Cherenkov Telescopes with seven paraxial mirrors in each have been

designed for the search of celestial -ray sources.

3.2 PACT array

Pachmarhi Array of Cherenkov Telescopes (PACT) is a ground based atmospheric Cherenkov

experiment at High Energy Gamma Ray Observatory, Pachmarhi in central India (Bhat et

al. 1998). It has been setup to study VHE -rays from celestial sources. This experiment is

based on the wavefront sampling technique and consists of an array of 24 Cherenkov tele-

scopes deployed over an area of 100 80 meter in the form of rectangular matrix. Figure-

3.1 shows the layout of PACT array. These telescopes are separated by 20 meter in E-W

direction and 25 meter in N-S direction from their neighbouring telescopes. PACT array is

divided into four sectors of six telescopes. Each sector can be operated as an independent

62

Chapter 3. PACT System 63

Fig. 3.1: Layout of Pachmarhi Array of Cherenkov Telescopes.

unit. At the centre of each sector, there is station housing field signal processing center

(FSPC) that collects, process and records information from nearby six telescopes of cor-

responding sector. At the centre of the array, there is a control room which houses master

signal processing centre (MSPC). Information relevant to entire array such as arrival time

of shower front at individual telescopes, absolute arrival time of the event and triggering

telescopes are recorded in the MSPC. The data acquisition system and control as well as

monitoring PC’s of FSPC and MSPC are networked through local area network (LAN).

Each telescope consists of seven (marked as A to G) para-axially mounted parabolic re-

flectors of diameter 0.9 meter and f/d 1. These reflectors are fabricated indigenously

and their optical quality gives image size of a point source less than 0.2 degree. These

mirrors are back-coated and their reflectivity in visible range was about 80 , got degraded

to 50 over the years. They are mounted in hexagonal pattern and total reflector area per

telescope is 4.45 m . A fast photomultiplier tube (PMT) of type EMI9807B is mounted at


the focus of each reflector, behind a mask of diameter of 3.0 degree field of view (FOV).

An elbow-telescope, which is mounted in-paraxial with other seven mirrors at northern

point of each telescope. Pulses/signal from phototubes are brought to the respective FSPC

centre through low attenuation RG213 cables of length 40 meter. It is necessary to pre-

serve the shape and size of the Cherenkov pulses to have good angular as well as energy

resolution. Therefore PACT array is divided into four sectors to reduce the length of pulse

cables thereby minimizing the distortion and attenuation of low energy/weak pulses from

phototubes during their transmission through cables to FSPC. Pulses from individual mir-

ror PMT’s are processed and the information regarding pulse height and arrival time of

shower front at each mirrors are recorded in FSPC.

3.3 Distributed Data Acquisition System

The Distributed Data Acquisition System (DDAS) consists of a Sector data Acquisition

System (SDAS) in each sector and a Master Data Acquisition System (MDAS) in the main

control room. The details of Data Acqusition system (Bhat et al. 1998, Upadhya et al.

2002) are discussed in following sections.

3.3.1 SDAS

Sector data acquisition system is designed to process the pulses from each phototubes, to

generate a trigger and record the relevant information locally. Two types of data recorded

by SDAS are the event data and monitoring data. In an event data, absolute arrival time

of event, relative arrival time of Cherenkov shower-front and Cherenkov photon density

at individual mirrors are recorded. In monitoring data, counts rates from all PMT’s are

recorded periodically. Figure-3.2 shows the block-diagram of SDAS setup. Pulses from

phototubes are fed to linear Fan-out unit, which produces four replica of each input pulse.

One set of outputs from this module are given to linear Fan-in-Fan-out module, which

adds all seven analog pulses from phototubes of a telescope. These analog sums are called

Royalsums signal. Second set of outputs are given to the discriminator module and their

digital outputs are given to digital delay module through NIM-to-ECL translator, output of

which form the TDC Stops signal. The other set of ECL outputs are fed to CAMAC scalars,

which measure the count rates. The third set of fan-out are given to an integrating type

QDC, which records the pulse height details of Cherenkov photons. The Royalsum pulses

are discriminated at pre-determined threshold and event trigger is generated whenever there

is four-fold coincidence among six royalsums signals. Once an event trigger is generated,


Fig. 3.2: Logic diagram of Sector Data Acquisition System (SDAS).

CAMAC controller initiates the data recording process. TDC start signal is generated from

trigger and suitable delayed (200 ns) signals from individual PMT’s are used as TDC stop

signals. Discriminated Royalsum pulses, which are logically AND with trigger are used

as QDC gate for each individual channel of same Telescope. Pulses from various PMT’s

are digitized by QDC whenever start trigger is generated. Finally, CAMAC controller

interrupts Linux based PC, which initiates the data recording process. Recorded data are

the Latch information that tells us whether a telescope has valid signal in an event or not,

absolute arrival time of events with a resolution of 1 sec in addition to TDC and ADC

information. In addition to event data, monitoring data are also recorded periodically.

Monitoring interrupts are generated at MSPC and fed to each of FSPC’s, which initiates

recording of monitoring data comprising of PMT’s rates and Royalsum pulse rate along

with absolute time. The discriminated Royalsum pulses and station trigger information are

also sent to the main control room using Router circuit. The data size of an event consists

of 119 words (238 bytes) and monitoring consists of 57 words (114 bytes).


Fig. 3.3: Logic diagram of Master Data Acquisition System (MDAS).

3.3.2 MDAS

Logic diagram of Master data acquisition system (MDAS) is shown in figure-3.3, records

data relevant to the entire array. Event and monitoring data of all 24 telescopes are recorded

by MDAS with CAMAC based data acquisition system similar to SDAS. Royalsum and

start trigger from all FSPC’s are brought to the control room through router module and

70 meter long twisted-pair cables. The start trigger in MDAS is enabled through the logic

OR of all four FSPC’s triggers. When a trigger in MDAS is generated, CAMAC controller

is interrupted to record TDC data, absolute event arrival time from RTC, Latch indicating

the sector participation in event, number of events recorded in each FSPC etc and store

in the event file. Similarly for each periodic monitoring interrupts, Royalsum rates are

recorded in monitoring file. The data format of an event consists of 52 words (104 bytes)

and monitoring consists of 41 words (82 bytes).


Fig. 3.4: Chance counter setup in SDAS.

3.4 Chance Rate counter

In PACT data acquisition system, four-fold coincidence trigger initiates data recording.

Each sector of PACT consists of six telescopes, therefore if at least four out of six tele-

scopes receive the signal from same Cherenkov shower-front only then an event will be

recorded. The monitoring of spurious triggers due to PMT noise signal or fluctuation in

night sky background is done through chance rate counter. A chance counter setup has

been introduced in each FSPC. Since Royalsum signals are used to generate trigger, these

are taken for chance counter setup. In chance setup as shown in figure-3.4, all six discrim-

inated Royalsum pulses are delayed wrt each other by 100 ns and their linear sum is given

to four-fold logic level. The logic output is connected to one of the channels of CAMAC

event scalar.

The chance count rate (CR) for n-fold logic is given by

/ (3.1)

where R is telescope count rate (Hz), T is resolving time for coincidence and n is number of

detectors used in coincidence logic. The expected chance rate for four-fold logic in SDAS

with 90 ns coincidence time are tabulated in the table-3.1 for various input rates.


Table 3.1: Telescope Count Rate & Chance rate of PACT.

Royalsum rate 4-fold chance

KHz Hz

25.0 0.02

35.0 0.07

45.0 0.18

55.0 0.40

65.0 1.78

75.0 1.38

3.5 Auxiliary Control System

Auxiliary control system include orientation of telescopes, remotely controlled phototube

shutter mechanism and high voltage control to phototubes. The details of this system have

been discussed in GAME-2001 meeting (Mt Abu, India).

3.5.1 ACTOS

The Automated Computerized Telescopes Orientation System (ACTOS) (Gothe et al. 2002)

controls slow, fast movement and tracking of all telescopes. All the telescopes of PACT are

equatorially mounted and each telescope is independently steerable in both E-W and N-S

directions up to 45 degree. The hardware of ACTOS is designed in-house for remotely

controlling the telescopes. The control-movement consists of semi-intelligent closed loop

feed back system with built-in safety features. The angular position sensors which are ba-

sically a gravity based transducer (LUCAS sensing system, USA) called clinometers are

used as absolute angle encoders. The DC output of these clinometers are linearly pro-

portional to their offset angles from vertical (60 mV/degree). In each telescope, two cli-

nometers are used, one to get telescope angle in N-S direction and other for E-W direction.

These clinometers are calibrated by aligning telescopes to bright stars at various angles and

measuring their output voltages. Clinometers outputs are given to a low pass filter and an

integration type ADC which is readout by the host PC. The motor-controller, an interface

between the host PC and the stepper motor, carry-out the task of the movement of stepper

motors as instructed by the host- PC. Variable slew speeds are used to control the stepper

moter speed in steps. At present four different speeds (70 Hz, 50 Hz, 30 Hz and tracking

7.569 Hz) are used. The tracking frequency is calculated as follows.

The step angle (degree/count) of Right Ascension stepper motor is 1.8 degree (manufac-


Fig. 3.5: Block diagram of ACTOS.

tures specification) and gear ratio is 3270:1 (PACT RA gear-box). To rotate Right As-

cension shaft by one degree, the corresponding motor shaft would move by 3270 degree

ie 3270/360 or 9.083 rotations. The Earth rotation rate is 1 degree in 4 minutes or 1/240

degree/second. If n is the number of counts per second applied to Right Ascension motor

which rotate the telescope RA axis at rate of 1/240 degree/second, tracking frequency is

given by " $ /

Therefore required frequency n is equal to 7.569 Hz, so to keep telescope axis in source

direction, Right Ascension stepper motor needs constant frequency driving at 7.569 Hz.

The dispersion clinometer reading from calibration data shows 6 mV. Since sensitivity of

clinometer is 60 mV per degree so possible erorr due to fluctuations in clinometer reading

will be 0.1 degree. The ACTOS system can orient telescopes to known source in sky from

an arbitrary initial position with an accuracy of 0.1 degree. The telescope pointing is

monitored at an accuracy of 0.05 degree and corrected in real time.


3.5.2 CARAMS

It is necessary to ensure that the gains of all PMT and mirror system are more or less

equal. Partially this is achieved by setting the high voltage to each phototube to get count

rates approximately equal (5 kHz). Due to differences in the characteristics of individual

phototubes as well as difference in the reflectivity of mirrors, high voltage requirement

differ from one phototube to another. In addition to these differences, count rates are

sensitive to sky brightness, sky transparency, ambient temperature and local light level and

hence the applied high voltages to PMT’s need to be adjusted every night. Computerized

Automated Rate Adjustment and Monitoring System (CARAMS) is developed for this

purpose (Bhat et al. 1990). It consists of microprocessor based 64 channel high voltage

divider units (CAEN model SY170), which is controlled by CAMAC based controller

module (CAEN model Y117B). CARAMS is developed for setting the phototube voltage

as well as for reading back using suitable CAMAC commands to the controller module.

High voltages of all 168 PMT’s are controlled through CARAMS as well as manual voltage

dividers.

3.5.3 APES

Long time exposure of PMT cathode to light limits the life of phototube, therefore Auto-

mated Photo-multiplier Exposure System (APES), was designed to control the PMT ex-

posure to incident light and protect it from any other bright light. This is achieved by

motor controlled shutter fixed to each PMT and remotely controlled from each FSPC. The

open and closed status of each shutter is displayed by red and green LED’s on the panel

fixed in FSPC’s. The PMT shutters are kept open only during observations. The system

open/closes all the shutters within 2 minutes.

3.6 Calibration

3.6.1 TDC calibration

The relative arrival times of Cherenkov shower front at each detector are recorded by CA-

MAC based 16 and 8 channel TDC (Phillips 7186, Lecroy 2228) modules. These modules

accepts NIM inputs with lemo connection and convert/process with in 7.8 microsecond

with 12 bit dynamic range and resolution of 0.25 nanosecond. This module converts any

relative time between start and stop within the dynamic range 500 ns. To read back actual

relative times, these modules have to be calibrated. For calibration of TDC module, the


Table 3.2: Standard delays of calibrating cables and their TDC counts.

Delay cable Start-Stop delay Mean TDC

(nano-second) (nano-second) counts

54.0 80.5 100.7

98.0 126.5 321.3

170.0 202.0 681.2

230.0 265.0 985.6

284.0 324.0 1268.8

386.0 432.5 1790.2

440.0 486.0 2082.6

Table 3.3: TDC calibration constant.

Channel Slope Intercept no m (ns/count) c (ns) /dof

1 0.2058 61.15 4.23

2 0.2083 56.73 4.40

3 0.2081 57.22 4.23

4 0.2081 59.58 4.22

standard delay cables are used.

Figure-3.6 shows the logic-diagram of TDC calibration setup. Different delay cables

are introduced between start and stop inputs of TDC module and corresponding counts

are recorded for each individual channels. This exercise is repeated for 6-7 known delay

cables within the dynamic range of TDC module. The delays of different calibrating cables

and the corresponding TDC counts for a channel are summarized in table-3.2. These TDC

counts and standard delays are plotted and shown in figure-3.7, are fitted to a polynomial

function of first order.

+ (3.2)

where m and c are coefficients of polynomial. The calibration coefficients of a typical

TDC channel is shown in table-3.3. Using these coefficients, TDC counts of actual data

are converted back to time scale unit.

0 /1) (+ - / + (3.3)

where c is the TDC channel offset for zero delay.


Fig. 3.6: TDC calibration setup.

3.6.2 QDC calibration

The lateral distribution of Cherenkov photons in PACT array are recorded by 16 channel

CAMAC QDC (Phillips 7166, Lecroy 2249). This module digitizes charge at the input

within 7.8 microseconds. This module has 12 bit dynamic range and resolution down

to 125 femto-coulomb per count. Similar to TDC module, QDC does also need to be

calibrated. For QDC calibration, a NIM pulse of fixed width (100 ns) is used to generate a

standard gate signal, one such signal is given to start of QDC module while another is used

to generate a 6 ns wide NIM pulse. This NIM pulse is connected to a 16 channel FAN-OUT

through an attenuator. The output of FAN-OUT are connected to QDC modules as shown

in figure-3.8. The total charge of any time varying voltage signal/pulse V(t) is given by

(3.4)

where R is 50 and C is pedestal count of QDC channel. Input charge to QDC are

controlled through a pulse attenuator. For a NIM input pulse of 1.24 volt and 6 nano-

second width, corresponding charges and QDC counts are tabulated in table-3.4 at different

attenuation factor. These QDC counts as function of input charge are plotted and shown in


Fig. 3.7: Variation of TDC counts vs standard start-stop delay.

Table 3.4: QDC calibration data.

Attenuation Charge QDC counts

factor (pico-coulomb)

1.0 150.3 1229

0.9 132.8 1087

0.8 118.1 970

0.7 99.5 818

0.6 86.5 711

0.5 71.8 595

0.4 59.3 490

0.3 40.9 345

0.2 27.9 240

0.1 14.6 132


Fig. 3.8: QDC calibration setup.

Table 3.5: QDC calibration constant.

Channel Slope Intercept no M (pc/count) C (pc) /dof

1 0.124 -1.67 0.03

figure-3.9 and fitted to a polynomial function of first order.

(3.5)

where C is pedestal count of QDC channel. The calibration constants of a typical QDC

channel is shown in table-3.5

These coefficients are further used for converting back to the units of charge of Cherenkov

and night sky photon density recorded by QDC.

+ - / ) (3.6)


Fig. 3.9: Variation of QDC counts vs input charge.

3.6.3 Clino calibration

Orientation of all telescopes is controlled through ACTOS, which uses clinometers to read

the instantaneous angular position of telescopes. ACTOS first read the East-West move-

ment angle called Right Ascension (RA) clinometers and second read the North-South

angle called declination (DEC) clinometers. The offsets, if any, between clinometers axis

and telescope shaft axis should be known for the accurate orientation of telescope through

ACTOS.

For in-site calibration of clinometers, all telescopes are aligned to a chosen bright star

in extreme position (40 degree East) direction and then star is acquired at center of cross-

wire in guiding-elbow telescope and then kept in manual tracking mode. Both clinometers

voltages of each telescope and hour angle are recorded periodically after a step of 5 degree

movement while the bright star is being tracked. This exercise is repeated at least for five

bright stars of different declinations. The variation of RA clinometers voltage with hour

angle ( ) gives RA clinometers constant. Similarly DEC clinometers voltage with decli-

nation angle at time of transit gives North-South clinometers constant. Both clinometers

voltages and corresponding angles are fitted to a polynomial. The corresponding calibra-

tion constants are calculated as

(3.7)


Fig. 3.10: (a) Variation of RA clino voltage with hour angle, (b) Variation of DEC clino voltage

with hour angle, (c) Variation of DEC clino voltage with declination angle.

Where M and C

are coefficients of polynomial fitted and are used as RA clino cal-

ibration constant. The variation of DEC clinometer voltage with hour angle ( ) is propor-

tional to , so

(3.8)

where A, B, C’ are DEC clino calibration constants. DEC clino constant (C’) at transit

time ( =0) is calculated as

" (3.9)

Where = Declination-22.47 degree (Latitude of Pachmarhi). The variation of RA and

DEC clinometers voltages with hour angle and declination angle are shown in figure-3.10.

The clino calibration constants for Telescope no. 41 are given in table-3.6, which are used

for acquiring source position in the sky by ACTOS.


Table 3.6: Clino calibration data for Telecope

41.

Constant Magnitude unit

M 58.917 mV/deg

C 163.0 mV

A -0.193 mV/deg

B 4.019 mV/deg

C’ 571.117 mV

M 58.070 mV/deg

C 183.0 mV

3.7 Mechanical Alignment

As explained in earlier sections, seven parabolic mirrors are mounted in the same plane on

a telescope and a guiding elbow telescope at the Northern end is fitted in each telescope. To

align the axis of all seven parabolic mirrors as well as guiding elbow-telescope paraxially,

a bright star is acquired at the centre of guiding elbow-telescope’s cross-wire and then by

physically looking into the mirrors one by one along the axis, the star image is brought at

center of 3 degree opening mask with the help of three screws holding the mirror plate. All

parabolic mirror axis are aligned wrt guiding elbow-telescope axis with in the accuracy of 0.25 degree.

3.8 BSScan

The accuracy of mechanical alignment of PACT telescope is checked through Bright Star

Scan (BSScan), which gives an idea about the pointing of mirror axis wrt guiding elbow-

telescope. In BSScan, an isolated star of magnitude (1.5 2) is chosen and acquired in all

telescopes through ACTOS. All telescopes are moved by 5 degree to West of bright star

after correcting any offsets seen in elbow-telescope and kept in tracking mode. All PMT’s

are powered and their count rates are adjusted to 500 Hz. Bright star scan starts after

switching off the tracking frequency of ACTOS. At this stage, telescopes are stationary

and star walks in the field of view as it moves from East to West. When star moves from

East to West, star-image approaches towards the axis of each mirror and corresponding

PMT shows rise in count rates. Star walks at center of field of view after 20 minutes and

at this time all PMT shows maximum count rates. After transit, star image recesses away

from mirror axis and PMT count rates start decreasing to their original count rate set before


Fig. 3.11: Profile of PMT count rates seen by PMT’s of Telescope no

43 for star -auriga

starting the BSScan.

Profiles of PMT counting rate obtained from scan data are shown in figure-3.11. This scan

profile is fitted to a polynomial and the difference in transit time from profile (broken line)

and expected transit time (solid line) gives an offset of mirror axis wrt elbow-telescope

axis in East-West direction. The Full Width at Half Maxima (FWHM) of same profile

gives qualitative idea about offset in North-South direction. The offset of each mirror and

other details of scan profiles from Bright Star Scan are tabulated in table-3.7. The results

shown in table-3.7 are for Tel 41. For each mirror of telescope, peak count rates, FWHM

of profile (expected is 2.8 degree), offset and goodness of polynomial fit etc are estimated.


Table 3.7: Bright Star Scan data.

Mir Pk CR FWHM:d FWHM:F Off:F Off:CG Lim1 Lim2 Rem

A 2.55e+03 2.58 2.83 0.32 0.39 70 170 GOOD

B 3.13e+03 2.88 2.75 0.07 0.09 70 170 GOOD

C 1.13e+04 2.33 2.79 0.36 0.43 70 170 GOOD

D 2.53e+03 1.88 2.54 0.15 0.18 70 170 GOOD

E 2.34e+04 1.46 2.79 -0.26 -0.40 70 170 FAIR

F 9.26e+03 2.25 2.58 0.03 0.01 70 170 GOOD

G 2.90e+03 2.50 2.75 -0.05 -0.06 70 170 GOOD

3.9 PG Run

The proper functioning and stability of SDAS and MDAS is checked through Pulse Gener-

ator (PG) run. In this test, a synchronous NIM signal of 10 Hz is generated at main control

room and four replica of same signals are sent to each station DAQ through RG50 cables.

In each station again seven outputs are generated using resistive fan-out circuit and six of

them are given to A’s of each telescope PMT channel. The seventh output is used as an

independent trigger to CAMAC system. Signal path is checked through monitoring count

rate of each channel. In PG run, event and monitoring data are recorded as in actual ob-

servations. The recording of data is simultaneously done in all stations as well as in main

control room. This PG run data is also used to obtain the relative delays between triggers

of individual sectors. Later this data is analyzed event by event and different channel data

of TDC, ADC, LATCH, count rates are compared to pre-assigned value of input signal.

The analysis results of SDAS and MDAS PG run data are shown in table-3.8 to table-3.13.

Table-3.8 shows the triggers recorded by Latch module. TDC data of each channel for tele-

scope 41 is shown in table-3.9. In this mean counts, standard deviation ( ), FWHM(D)

(polynomial fit to data points), FWHM(M) (equal to 2.35 ) and total numbers of triggers

are calculated and given in column-2,3,4,5 and 6 respectively. ADC data and pedestal of

same telescope’s channels are shown in table-3.10 and 3.11 respectively. Details of con-

trol room PG data is shown in table-3.12 and 3.13. Triggers obtained from Latch module

and TDC are compared for each telescope channel and shown in column-2,3 and 5,6 of

table-3.10. Details of TDC data are given in column-2,3,4,5 and 6 of table-3.13.


Table 3.8: LATCH triggers status.

Telescope No. of Triggers

41 6800

42 6800

43 6800

44 6800

45 6800

46 6800

Table 3.9: TDC data [SDAS].

Channel Mean Sigma FWHM(D) FWHM(M) Total Events

MIR:41A 711.73 0.65 1.52 1.00 859

MIR:41B 722.15 0.59 1.39 1.00 720

MIR:41C 731.61 0.52 1.24 2.00 993

MIR:41D 716.37 0.51 1.19 2.00 944

MIR:41E 703.08 0.43 1.01 1.00 927

MIR:41F 706.37 0.50 1.18 2.00 997

RYS:41A 993.66 0.51 1.20 2.00 859

RYS:41B 994.79 0.41 0.97 1.00 720

RYS:41C 993.98 0.14 0.34 1.00 993

RYS:41D 994.20 0.40 0.95 1.00 944

RYS:41E 992.32 0.47 1.10 1.00 927

RYS:41F 991.06 0.24 0.57 1.00 997

RYS:41G 991.02 0.15 0.36 1.00 1360

GRS 992.57 1.61 3.79 4.00

Table 3.10: QDC data [SDAS].


Mir:41A 204.63 3.32 7.81 5.00 859

Mir:41B 199.88 2.84 6.70 7.00 720

Mir:41C 193.83 2.42 5.70 5.00 993

Mir:41D 195.03 2.62 6.16 5.00 944

Mir:41E 205.49 2.39 5.63 4.00 927

Mir:41F 201.89 3.16 7.44 7.00 997


Table 3.11: QDC Pedestal data [SDAS].


41A 45.56 1.93 4.54 4.00 1360

41B 44.58 1.91 4.51 4.00 1360

41C 39.10 1.85 4.36 4.00 1360

41D 42.42 2.02 4.75 4.00 1360

41E 46.35 1.70 4.01 2.00 1360

41F 44.04 1.98 4.66 3.00 1360

Table 3.12: Latch and TDC triggers of [MDAS].

Telescope Latch TDC Telescope Latch TDC

ID Trigger trigger ID Trigger Trigger

31 6789 6774 41 6781 6774

32 6782 6775 42 6792 6792

33 6781 6784 43 6789 6798

34 6783 6734 44 6785 6743

35 6787 6794 45 6796 6799

36 6785 6754 46 6793 6798

Table 3.13: MDAS TDC data.

Telescope ID TDC count Sigma FWHM(D) FWHM(M) Total Events

31 1130.73 1.66 3.90 3.00 6774

32 1102.96 1.73 4.08 4.00 6775

33 1106.85 1.76 4.13 4.00 6784

34 1127.74 1.58 3.73 2.00 6734

35 1099.57 1.76 4.14 4.00 6794

36 1126.14 1.53 3.61 2.00 6754

41 1273.97 1.53 3.59 3.00 6774

42 1238.20 1.38 3.25 2.00 6792

43 1212.49 1.25 2.95 2.00 6798

44 1330.96 1.53 3.61 2.00 6743

45 1298.69 1.30 3.05 2.00 6799

46 1307.68 1.37 3.22 2.00 6798


Fig. 3.12: Rate vs discriminator threshold for single mirror and royalsum rate.

3.10 Trigger Rate

In order to achieve the best trigger rate in sector’s of PACT array and to keep chance rate

as low as possible, various studies of individual PMT rates and Royalsum rates as function

of discriminator threshold (pulse height study) have been done. In Figure-3.12, pulse-

height distribution of single PMT and Royalsum (sum of seven PMT signal) as function

of discriminator thresholds are plotted. Royalsum signal trigger the DAQ at higher rate

than single PMT signal. It is seen that at lower discriminator threshold, the Royalsum

rate is dominated by light of night sky (LONS) and PMT noise. At higher discriminator

threshold ( 100mV), the Royalsum rate is due to Cherenkov photons generated by the

air showers. Night sky contribution in Cherenkov triggers can be reduced using n-fold

coincidence between detectors. The LONS and other local light is of random nature but

Cherenkov flashes are produced for very short duration (5-10 ns) and highly coherent. The

n-fold coincidence reduces the LONS contribution in trigger generation and improve signal

to noise ratio. The 4-fold trigger and chance rates as function of Royalsum rates are shown

in figure-3.13(a) and fraction of chance rate at different Royalsum rates is shown in figure-

3.13(b). The best trigger rate from sector’s data is obtained when Royalsum rate is kept


Fig. 3.13: (a) Trigger rate vs Royalsum rate (b) fraction of Chance rate vs Royalsum rate.

at 30-40 KHz, which trigger the sector’s DAQ approximately at rate of 4.0 Hz and keep

chance rate as minimum (less than ). Data recording of any known or unknown -ray

source is done at this trigger rate.

Chapter 4

Observations and Data Reduction

4.1 Introduction

The three basic properties associated with Very High Energy (VHE) -ray pulsar studies

are the spatial, temporal and spectral distribution of photons. The method of analysis

varies from one band to other band of observation of source’s electromagnetic spectrum.

The primary difference between -ray astronomy and lower energy bands is the relative

sparseness of the data. Unlike radio wavelength, where a deep survey consists of a few

minutes of integration time but -ray observations must be of the order of hours/days to

detect even the brightest source. The goal of this chapter is to describe the method, used for

the search of steady as well as periodic signals from the pulsars PSR 0534+2200 and PSR

0633+1733 in the voluminous bits of information accumulated using the PACT system. In

this way, first data are calibrated to appropriate units using calibration constants of TDC

and QDC modules. After applying preliminary cuts and boundary limits on the data, the

reduced data are used for the search of steady and pulse emission from VHE pulsar source.

The PACT data are sub-divided into two categories, timing and density information of

Cherenkov photons. Data structure of subarray and complete array is summarized in table-

4.1. The data acquired from the Crab and Geminga sources have been divided into 4

different sets, on the basis of trigger criteria and the information which are to be extracted

from data. Data set-A consists of Royalsum TDC from main control station which includes

data from all four sectors and monitoring data. We had 40 channels of TDC’s, which were

not sufficient to record all 42 PMT pulses and 6 Royalsum (summed) pulses. We did not

use the central PMT pulse of all telescopes for TDC and QDC. For TDC, only 6 PMT

pulse (a to f) of telescope 1 to 5 and 4 PMT pulse (a to d) of the 6

telescope were

used. The remaining 6 channels were used to record Royalsum pulses of six telescopes

of a sector. For QDC, 6 PMT pulses (a to f) of all 6 telescopes were used. The Data

set-B is extracted from event data recorded in individual stations and contains 34 mirrors

84

Chapter 4. Observations and Data Reduction 85

TDC of each sector. Data set-C is the royalsum TDC of telescopes from sector’s event

data. Data set-D is from 36 mirror QDC channel of each sector event data. The collection

area and triggering threshold for these data sets corresponds to different energy threshold

of primary -ray detection. Both Crab and Geminga pulsars have been observed during

nights of November-January every year between 2000-2006. In this chapter, the method

used for the search of steady and pulsed emission of -rays from these pulsars will be

discussed.

4.2 Observations

PACT started functioning fully in 2001. Since then it is being used for observations of

celestial -ray sources to confirm their presence and learn the various physical processes

that take place in the source emissions. The Crab (0534+2200) nebula is observed every

year since it is stable and does not show any large variability in flux. Crab nebular emis-

sion is being used as standard candle in VHE astronomy. The Geminga pulsar, Mrk421

and Mrk501 are observed every year to check their flux variability. Other observed sources

are Blazar 1es1426+42, ON231, OJ287 and NGC2419 etc. The estimation of true flux of

the observed -ray sources depends upon the ability to reject cosmic-ray (back-ground).

Therefore equal importance is given to background observation along with the source ob-

servations in the same night to avoid the daily variation in the night sky brightness and

transparency. For observation of OFF-source (background) region, a region having same

brightness and declination as that of source but offset in Right Ascension (RA) from the

source position is chosen. Both source and background regions are observed over the same

zenith angle range.

Every month at least two vertical observations are carried out by parking all telescopes at

zenith (local vertical direction, declination=latitude). The vertical observation data is used

for estimation of detector’s time offset (for details see section-4.4.1) and performance study

of PACT. In addition to these observations, QDC pedestal observations are also carried out

after vertical observation with independent but synchronized triggers. The QDC pedestal

data are used for estimation of night sky pedestal contributions in the source data.

4.3 Data Diagnosis

A clear sky is an important requirement for the detection of atmospheric Cherenkov ra-

diation during moon less dark nights. The low flux of Cherenkov photons over night sky


Table 4.1: Data structure of PACT.

Array Degree of freedom Data set

(Total no of Channels)

Full array 24 Royalsum TDC (6 Tel 4 Sectors) A

Individual Sectors 34 Mirror TDC (Tel 1-5 (a to f)+Tel 6 (a to d)) B

6 Royalsum TDC (Tel 1 to 6) C

36 Mirror QDC (Tel 1-6 (a to f)) D

background light limits the efficiency of atmospheric Cherenkov technique. A small varia-

tion in sky transparency may add to many systematic in the data of steady source emission.

Therefore on line monitoring of data improve the quality of data recording. Besides,

noise or spurious triggers produced by ambient light and electrical fluctuations also affect

the quality of data. A detailed check on data quality is essential to ensure the 99.9 confi-

dence level on the obtained results.

In data reduction process, first the bit pattern of each word in event data is compared with

the expected distribution. Event rate plot (binned over 10 seconds) of a regular observation

data is shown in figure-4.1 and it is seen that the trigger rate is stable during observation.

For a steady source, this event rate is expected to follow variation as function

of zenith angle( ). Data segments corresponding to any sharp rise or decline in the event

rate plot is rejected from data-file before further analysis. Figure-4.2 shows the number

of recorded and also the number of triggers generated (from event counter) as function of

RTC time. The agreement between two suggests that we do not lose events due to dead

time (240 sec) of data acquisition system which is small. Royalsum signals are used to

generate the start-trigger in each sector’s FSPC and Latch module records the individual

ID’s of the telescopes which participate in the event. Also, from TDC data we can find out

the ID’s of telescopes which have participated in the event. ie. Those TDC channels which

have unsaturated

valid TDC data. Information from Latch and TDC are compared and

plotted as shown in figure-4.3 to see any discrepancy in data recording. If there is any mis-

match, the corresponding telescopes are discarded from further analysis. A histogram of

typical TDC counts in an observation is shown for 3 cases:(a) individual PMT, (b) SDAS

Royalsum and (c) MDAS Royalsum in figure-4.4. The mean and FWHM of TDC dis-

tributions of TDC channel for Telescope are given in table-4.2. TDC histogram of

individual PMT channel is narrower than Royalsum channels and accounts for better an-

gular resolution. The density of Cherenkov photons are recorded by QDC in each sector’s

of FSPC. The histogram of QDC counts of a typical channel is shown in figure-4.5. The


Fig. 4.1: Event rate (Hz) recorded in the SDAS 4.

Table 4.2: TDC histogram data (Run

).

Channel Mean TDC counts FWHM Total Events

41A 409.6 17 739

41SRS 851.1 20 2576

41MRS 906.5 28 3776


Fig. 4.2: Absolute arrival times of recorded events.

Pedestal subtracted (night sky pedestal) sum of all QDC counts recorded by different de-

tectors are proportional to the primary energy of -rays. The QDC data of all events are

used for estimation of energy spectrum of -ray source recorded by PACT.

4.4 Analysis Procedure

After preliminary data diagnosis, only those observations are accepted which were ob-

served during spectroscopic (clear) nights. Data collected during cloudy and bad weather

conditions were rejected.

The analysis procedure for searching steady emission (either pulsed or unpulsed) , transient

and pulsed emissions are all different. In PACT data, it was not possible to separate out

-ray initiated events from those of cosmic-ray initiated ones event by event. The -rays

from point source are expected to arrive from the direction of source (telescope pointing di-

rection), as they are neutral, while cosmic ray background is isotropic. A fraction of more

abundant cosmic ray events could be rejected by selecting ON-axis events. The steady flux

of -rays from celestial sources are estimated on statistical way by comparing the num-

ber of events from the source direction (which contain -rays from source and cosmic-ray


Fig. 4.3: Telescope triggers distribution for sector from TDC and Latch.

Fig. 4.4: TDC distributions for (a) individual PMT, (b) SDAS Royalsum and (c) MDAS Royalsum

channels.


Fig. 4.5: A QDC distribution of Channel

.

background) with that from the OFF-source direction (pure cosmic ray background events)

within a specified space angle. The comparison of ON-source data with OFF-source data

were done as follows.

The Cherenkov shower front is reconstructed from the information on the relative arrival

time of pulses at telescopes. A plane front approximation is used for the reconstruction and

the direction normal to this front gives the direction of arrival of showers. The space an-

gle ( ) between the direction of source and shower direction are computed for each event.

Thus the distribution of space angle is constructed for all ON-source and OFF-source data

taking care that same zenith angle region is covered by a pair of ON/OFF source data sets

which corresponds to observation carried out during the same night. The two ON/OFF-

source distributions are normalized as the number of events in the two data sets needs

more or less same for reasons explained below. A cut on the space angle distribution is

imposed to select on-axis events. By subtracting normalized background from the source

space angle distributions, the resultant excess/deficit of events within a space angle of 2.5

degree is used as an estimate of -ray signal. Tighter cut on the space angle is imposed by

choosing a cut-off value in the range 2.0 degree to 2.5 degree. A tighter cut on space angle,

no doubt, rejects more cosmic ray background events but also rejects the -ray events.


4.4.1 Time offsets

For reconstructing the Cherenkov wave-front, we need to know the relative arrival time of

photons at the telescope. But relative arrival time of pulses at the PMT’s get altered as they

arrive in the control room due to difference in path lengths of cables carrying signals from

PMT’s to recording point, differences in electronic propagation delays, difference in transit

time of PMTs (2 3 ns). This additional delay time is treated as time offset or tzero ( )and is constant for a given channel. This time offset is same for all events. To decipher the

TDC data and get the relative arrival time of photons at telescopes, we need to know the

time offsets for all channels or at least, the relative time offsets (ie time offsets wrt to any

one channel).

The relative time offsets are derived from data using “Vertical run data”, data obtained with

all telescopes stationary and pointing to zenith. In this case, after correcting for difference

in the Z-coordinates of telescopes, the arrival time of pulses at all PMT’s (T ) should be

identical as the shower front arrives simultaneously. So the time difference between a pair

of channel is equal to

)

This time difference is equal to , the measured delay between the two channel i

and j using TDC. Thus

(4.1)

For n channels, we can write

(4.2)

where W are statistical weight factor and given by

(4.3)

where is the uncertainty in determination of C . To estimate the tzero of each detector,

is minimized wrt T and T which gives set of n equations given by (4.4)

All these set of equations can be written in the form of matrix.


Fig. 4.6: TDC difference distribution (Run

414).

Table 4.3: Tzero of PACT detectors observed in main control room.

Tele. Tzero Tele. Tzero Tele. Tzero Tele. Tzero

ID (ns) ID (ns) ID (ns) ID (ns)

11 -35.71 21 -47.96 31 -57.14 41 -18.02

12 -41.14 22 -56.83 32 -61.89 42 -25.63

13 -48.37 23 -65.26 33 -74.10 43 -34.54

14 -35.76 24 -67.06 34 -74.27 44 -12.38

15 -27.14 25 -46.11 35 -69.70 45 10.80

16 -54.17 26 -49.75 36 -51.14 46 00.00


After solving these simultaneous equations by matrix method, we get tzero’s of each

channel wrt the last one. The histogram of time difference between 2-TDC channel corre-

sponding to a pair of neigbhouring PMT’s is shown in figure-4.6. Tzero of all 24 telescopes

of PACT array wrt last one are computed from vertically falling showers (Run 414) and

are given in table-4.3.

4.4.2 Arrival angle determination

The Cherenkov wavefront produced by electromagnetic cascade in the atmosphere prop-

agate towards sea level and spread over in a circle of 300 meter diameter. Atmospheric

Cherenkov detectors deployed in this light pool detect these Cherenkov flashes resulting

from VHE cosmic/ -ray events. The Cherenkov shower front has larger radius of curva-

ture. Therefore at distances up to 100-120 meter from the axis (shower core) the shower

front is almost plane.

If there are only two telescopes separated by a distance D as shown in figure-2.13, an

inclined ( ) Cherenkov shower arrives first at T2. The arrival angle ( ) is given by

+

where

is the delay of Cherenkov wave-front between T1 and T2. If there are many

telescopes distributed on ground then a generalized approach (Sinha 1987, Acharya 1993)

is implemented to estimate the arrival direction. The arrival angle of primary /cosmic

rays are determined accurately using the method of least square fit. Let are the

positions of i

Cherenkov detector of PACT and t is the relative arrival time of Cherenkov

shower then arrival angle of primary /cosmic rays or axis of Cherenkov shower front is

calculated by minimizing the term

/ + * (4.5)

where

(4.6)

is the statistical weight factor and is the error in the estimation of relative arrival time of

i

detector, (l,m,n) are the direction cosines of axis of Cherenkov shower-front and is

the arrival time at reference point of PACT array. The values of l,m,n and t are calculated

as follows:

*

(4.7)


and

/ (4.8)

In this method, the arrival time at reference detector (t ) is a free parameter and takes any

of the detector of PACT. This ensures that fitted shower front is not constrained to pass

through any specific detector. The plane approximation method is valid near the shower

axis. At large core distances, arrival times lags behind that expected for the plane front

since the shower front has a finite curvature. The error in the arrival angle estimation due

to plane front approximation increases rapidly with core distance.

Estimation of (

) of source position from data

Only those TDC values which is within 1.5 of mean counts are used for the plane

front fit. A residue distribution of each channel is obtained from expected and observed

TDC delays. A typical residue distribution for six telescopes of sector from data-set(A)

are shown in figure-4.7. These distributions are expected to follow a Gaussian type with

mean count equal to zero and sigma one. If the residue of a channel is more than 3 then that channel is dropped from the plane front fit. This reconstruction of shower front

and estimation of arrival angle continue to many iterations till of plane-front fitting

and residue distributions approaches to a minimum value. The zenith ( ) and Azimuth

(

) angle distributions of reconstructed shower-front for Run 534 of a fictitious source

(arbitrary RA and DEC) are shown in figure-4.8. In this figure, the continuous line is the

expected position of source calculated from known RA, DEC and time of day (section-

4.4.3) and dots are the zenith and azimuth angle obtained from TDC data-set(A).

4.4.3 Estimation of true position of source

The altitude (angle along a vertical circle from the horizon to a point on the celestial sphere)

and azimuthal (angular position along the horizon measured clockwise from north) of an

astronomical source keeps on changing wrt to observation point on Earth due to its spin

motion. The instantaneous position of source at observation point is calculated as follows.

Let is the interval of time, measured in Julian centuries of 36525 days of universal time

(mean solar day) elapsed since epoch 2000 January UT [Astronomical Almanac] is

" %! (4.9)


Fig. 4.7: Residue distributions of TDC delay (only six telescopes data).

Fig. 4.8: Zenith(a) and Azimuthal(b) angle distributions of reconstructed shower from a fictitious

source.


where JD is Julian day number. Universal time in terms of Greenwich mean sidereal time

(GMST) ie the hour angle of mean equinox of date is given by

" $ $ ! $ " $ %$ ! ! " ! "

! (4.10)

If is the UT time at which source position is to be calculated then

" (4.11)

where 1 mean solar day is equal to 1.00273790935 of mean sidereal days ie %!#"

of mean sidereal time. If geographical longitude of observation point is expressed in time

(hours, 15 degree = 1hour) then Local Sidereal Time (LST) is given by

-*/ 0 ) (4.12)

or

-*/ 0 *) (4.13)

The longitude is subtracted or added to GMST depends on whether observation point is

East or West of Greenwich respectively. If Right Ascension ( ) and Declination ( ) of the

celestial source are expressed in hours and degree respectively then Hour angle (HA) of

source at observation point is

(4.14)

The zenith( ) and azimuthal(

) angle of source position in celestial sphere is given by

(4.15)

) /

(4.16)

and altitude angle (4.17)

The variation of zenith angle and azimuthal angle as function of hour angle for PSR

0534+2200 ( ) on January,1,2006 between 15:00 and 20:00

hours of UTC time at PACT site are shown in figure-4.9.

4.4.4 Space Angle

The angle between the direction of arrival of reconstructed shower axis and the source

direction (telescope axis direction) is called space angle ( ). If ( ) and (

) are the

zenith and azimuth angles of reconstructed and telescope axis then


Fig. 4.9: Zenith and Azimuthal position of PSR 0534+2200.

/

and

/

where ( / ) and ( / ) are the direction cosines of axis of reconstructed and

telescope axis respectively. The space angle( ) is given by

/ / (4.18)

Figure-4.10 shows the distribution of space angle of Cherenkov showers falling vertically

on PACT array using the royalsum TDC data of entire array [Data Set (A)]. The distribution

shows maxima at 1.2 degree and beyond that it starts decreasing. A better estimate of

arrival direction of Cherenkov shower is possible with use of individual PMT TDC data

(Data set[B]). The angular resolution (Majumdar et al. 2003) obtained using individual

PMT channel data of one sector is 0.24 degree. In the entire array, the average telescope

separation doubles while the number of degree of freedom is 24, consequently there will

be improvement in the accuracy of arrival angle estimation of Cherenkov shower.


Fig. 4.10: Space angle distribution of reconstructed shower of vertically falling showers.

4.5 Estimation of Gamma-ray flux

The sensitivity of atmospheric Cherenkov detection of celestial -ray source is limited by

the isotropic cosmic rays background radiation, which is present along with -ray events

in source data. Therefore equal importance is given to background observations along with

source observations and further to minimize the effect of sky transparency and brightness

variation, both ON-source and OFF-source observation are carried on the same night be-

tween same zenith angle range. Data collection uses four-fold logic to start data recording

and in analysis, a further software trigger is applied on an event selection. The distribution

of n-fold triggers observed from vertically falling Cherenkov showers are shown in figure-

4.11 and it is seen that maximum number of triggers corresponds to 7 or 8 fold coincidence

of entire array telescopes.

Two types of software triggers are applied on data, first is the minimum number of de-

grees of freedom (dof or NDF) which is equal to 8 to ensure same trigger rate during

ON/OFF observation and second is the value of plane wave fitting. All events with

+ ' " (standard deviation) are rejected. In the next section the detail

analysis of a fictitious source (cosmic ray) background data will be discussed.


Fig. 4.11: Distribution of n-fold triggers.

4.5.1 Fictitious Source

To check any systematic present in analysis technique, the complete procedure is verified

with fictitious source (FS) observations. The space angle distributions of a pair of fictitious

sources (FS1 and FS2) for same zenith angle range are shown in figure-4.12(a) and dis-

tribution of excess/deficit events are shown in figure-4.12(b). Since both sources (FS1

FS2) are chosen from star map with region of same brightness therefore, the excess/deficit

counts for such type of fictitious sources are expected to be equal to zero count. Both

distributions need to be normalized before calculating the excess/deficit signal. As the ob-

servations on FS1 and FS2 are carried out at different times, though on same night, the

atmospheric conditions differ and hence, the total number of events in these two samples

need not be same. Therefore these data sets have to be normalized before comparing. The

normalization and excess/deficit rate are estimated as follows.

(4.19)

where N and N

are the total number of ON-source and OFF-source counts observed

for same zenith angle range,

is the duration of observation and R is normalization

constant. An estimate of + ) ' error in the excess or deficit rate is given by

%- !

(4.20)


Table 4.4: Summary of Fictitious source data observed during year 2005-2006.

SN Run ON Obs. Date Tel trig Peak FWHM 85 DOF Dur. Accepted/

OFF std. dev deg. deg. deg. hour. Rejected

1 819 OFF 26/12/05 0.93548 1.2 2.0 2.6 10 1.87 Accepted

820 OFF 0.00 1.2 2.0 2.6

2 884 OFF 22/03/06 0.91419 1.2 2.0 2.6 11 1.29 Accepted

885 OFF 0.03 1.4 2.0 2.6

3 886 OFF 23/03/06 1.46770 1.4 2.0 2.7 11 1.78 Rejected

887 OFF 1.10 1.2 1.8 2.4

4 888 OFF 24/03/06 0.99431 1.2 1.8 2.5 10 1.63 Accepted

889 OFF 0.02 1.2 1.8 2.5

5 890 OFF 25/03/06 1.17348 1.4 2.2 2.7 10 2.26 Accepted

891 OFF 0.01 1.2 2.0 2.8

6 895 OFF 28/03/06 0.96664 1.0 1.6 2.3 10 1.31 Accepted

896 OFF 0.02 1.0 1.8 2.4

The normalization factor (R) is taken to be equal to the average of ratios of triggered tele-

scope of ON-source to OFF-source events. Figure-4.13 shows a typical telescope trigger

ratio’s of two sector (12 telescopes) data ( plot is only for 11 telescopes because one got

rejected during data reduction process), which gives mean ratio equal to 0.91419 0.04 and

this mean ratio is used as normalization constant (R) of respective data sets.

The fictitious source observations were taken during clear nights between the 30 degree

zenith angle range. The Right Ascension of fictitious source are chosen arbitrary from star

sky-map (dark region) and Declination is of Crab pulsar source. The summary of fictitious

source data, observed during year 2005-2006 is given in table-4.4

The space angle distribution of each run is checked and three parameters, peak position

of the space angle distribution, FWHM and the space angle below which 85 events lie

are calculated. These parameters for data set(A) are given in column-6, 7 and 8 of table-

4.4. The normalization constant and its standard deviations are given in column-5. The

maximum number of valid triggered telescopes and duration of observation are given in

column-9 and column-10 respectively. These parameters give idea about the quality of

data. A wider space angle distribution indicate about the offset in pointing of telescope,

spurious triggers due to fluctuating PMT counts and add errors in the source excess/deficit

counts. Figure-4.12(b) shows the distribution of excess/deficit space angle (unnormalized)

of a pair of run data taken on same night. All events of data taken on 23/03/06 are rejected

as it showed large standard deviation (1.10) in the telescope trigger ratio. If two distribution


Fig. 4.12: (a) Space angle distribution of unnormalized fictitious source, (b) Excess/deficit distri-

bution of unnormalized FS1-FS2 events.

Fig. 4.13: Telescope trigger ratio for a fictitious source (Run

884,885).


Fig. 4.14: (a) Normalized space angle distribution of events from source FS1 and FS2, (b) Ex-

cess/deficit distribution of normalized FS1-FS2 events.

peaks do not superimpose, this may give large positive or negative excess counts. Figure-

4.14(a) shows the space angle distribution (normalized) of a pair of run from table-4.5 and

figure-4.14(b) is the excess/deficit events as function of space angle. The excess/deficit rate

per minute of fictitious source events are shown in figure-4.15 and others details are given

in table-4.5.

The mean excess/deficit rate obtained from fictitious source data is 0.86 0.62 per

minute (table-4.6). This result will be considered as systematic error in the signal de-

tection. A similar approach was made for other fictitious source (Bose et al. 2007) using

PACT data and mean excess/deficit rate found to be -1.64 0.44 per minute. In the next

chapter, all procedures described above will be used for search of steady emission from

Crab and Geminga sources and further search of pulsations at TeV energy using PACT

data.


Fig. 4.15: Excess/deficit count rate of fictitious source of data table-4.5.

Table 4.5: Fictitious Excess/deficit analysis.

SN N N

Norm. Dur.

Excess Rate/min Sigma

min. + ) ' + ) ' 1 12666 13367 0.93549 112.4 12504.6 161.4 1.43 1.02 156.1 1.39

2 8119 8865 0.91419 77.4 8104.3 14.7 0.19 0.12 124.6 1.61

4 9730 9751 0.99431 98.1 9695.6 34.4 0.35 0.25 139.2 1.42

5 10933 9244 1.17348 135.9 10847.6 85.4 0.63 0.58 153.8 1.13

6 7352 7463 0.96664 78.6 7214.0 138.0 1.75 1.14 119.7 1.52

Table 4.6: Results of fictitious source data.

Total ON events 48800.0

Total OFF events 48366.1

Total excess 433.9 311.8

Total duration 502.4 minutes

Mean rate/min 0.86 0.62


4.6 PACT Simulation Results

As the Atmospheric Cherenkov telescope system cannot be calibrated using mono-energetic

beam of -rays of TeV energies, the response of detectors to Cherenkov light from Exten-

sive Air Shower (EAS) has to be determined through detailed Monte Carlo simulations.

CORSIKA package is used for the simulation of and proton initiated showers in the at-

mosphere.

CORSIKA (COsmic Ray SImulation for KAscade) is a detailed Monte Carlo program de-

veloped by Heck et al. (1998) to study the evolution of EAS in the atmosphere due to

primary photons, protons, nuclei or any other particles. The VENUS model is used for

high energy hadronic interaction.

4.6.1 Lateral distribution of Cherenkov photons

Extensive air showers were generated for -rays and proton primaries of five different

energies using CORSIKA package. The energy of primaries considered were 100 GeV,

250 GeV, 500 GeV, 1000 GeV and 2000 GeV. 100 showers were generated for each case.

The Cherenkov photons produced by secondary charged particles in the shower within uv-

visible band with 300-650 nm is propagated to observational level, Pachmarhi (at mean sea

level of 1075 meter). A fictitious array of 357 telescopes (arranged in a matrix of 17 21)

spread over an area of 600 m 600 m with inter-telescope separation same as that of PACT

is used. Like, PACT, these telescopes are also have seven mirrors with total area of 4.45 m per telescope. All showers were assumed to be incident vertically and shower core (axis)

is fixed to be at the center of the array.

Figure-4.16, shows the average Cherenkov photon density (without any atmospheric ab-

sorption) at the observation level (1075 meter from asl) as function of core distance for

showers initiated by -rays and protons of various energies. The lateral distribution shows

a characteristic hump as shown in figure-4.16(a) at about 130-140 meter from the core due

to effective focusing of Cherenkov photons in the case of Gamma ray initiated showers.

The corresponding lateral distribution for proton initiated shower is steeper and smoother

with practically no hump, which is shown in figure-4.16(b). As the altitude of observation

increases, the distance to shower maxima from the observation level decreases for a given

primary energy resulting an increase in photon density. The average Cherenkov photon

density at various observation levels (1.0, 2.0, 3.0, 4.2 km) above mean sea level as a func-

tion of core distance are shown in figure-4.17 for showers initiated by -ray of 1 TeV and

proton of 2 TeV energies. Lateral distribution of Cherenkov photons at higher observation

level becomes steeper and hump disappears (Rao

Sinha 1988) at higher altitude because


Fig. 4.16: Average Cherenkov photon density at Pachmarhi as a function of core distance for show-

ers initiated by (a) -rays and (b) protons, of various primary energies.

Fig. 4.17: Average Cherenkov photon density at various observation level as a function of core

distance for showers initiated by (a) -rays (1 TeV) and (b) protons (2 TeV).


Fig. 4.18: (a) Average total number of Cherenkov photons at Pachmarhi observation level as a

function of primary energy for -rays and protons, (b) Longitudinal development of

Cherenkov photons in atmosphere.

the contribution from higher energy electrons becomes appreciable at near-core distances

as these electrons come closer to the observation level.

Figure-4.18(a) shows the average total number of Cherenkov photons as function of pri-

mary energy for and protons at Pachmarhi observation level. An increase in primary

energy of particle gives higher Cherenkov yield and difference between the number of

Cherenkov photons produced by and proton primaries further increase with increase of

energy. Figure-4.18(b) shows the longitudinal development of Cherenkov photon showers

for -rays of 1 TeV, and protons of energy 1 TeV and 2 TeV respectively.

4.6.2 Energy threshold of PACT

The energy threshold of detection for primary -rays depends on telescope parameters

(FOV, integration time, collection area, conversion efficiencies), observation site from sea

level and night sky light brightness. The showers generated using CORSIKA package

were passed through the detector simulation package developed in house (Bose et al.).

The detector simulation package takes into accounts all parameters of PACT system and

generates the event triggers as in the real observations.

The differential and integral rates were calculated for and protons primaries. The spectral

index of differential energy spectrum is taken to be equal to -2.49 and -2.70 for -ray and


Fig. 4.19: (a) Differential (b) Integral trigger rate for vertically falling -rays.

Fig. 4.20: Collection area as function of energy threshold for vertically falling showers.


Fig. 4.21: Energy threshold and Collection area for PACT array at different incident angles.

proton primaries respectively. Figure-4.19 shows the differential and integral trigger rates

due to -rays, obtained by generating 2000 -ray showers. The energy corresponding to the

peak of the differential rate distribution is defined as the threshold energy. Thus, estimated

energy threshold for vertically incident -rays for PACT (an array of 24 telescopes) is equal

to 750 GeV. The efficiency of detection of shower is primary energy dependent. Also, this

efficiency decreases with increasing core distance. The effective collection area (efficiency

times the collection area) for the geometry of PACT is calculated. The collection area

for vertically incident -rays is 1.40 . Figure-4.20 shows the collection area as a

function of energy threshold of PACT array for vertically falling showers. Further energy

threshold and collection area depends on the incidence angle and increases as function of

incidence angle which is shown in figure-4.21.

Most of the observations used in analysis have been carried out within 15 degree of zenith

angle range. Therefore average value of energy threshold and collection area between 0

and 15 degree are 825 GeV and 1.45 meter . These values would be used in the

estimation of upper limit on the time averaged integral flux of -rays from Crab and

Geminga pulsars.

Sensitivity of PACT at 5 sigma detection level above threshold energy has been esimated

for Crab like source. The required observation duration as function of Crab flux is shown

in figure-5.6 at 5 detection level. The present cuts used in search of steady signal analysis

reject only 15 of cosmic ray background events from source data. Under this limit,


required duration will be 41 hours at 5 detection level for Crab source. If cosmic ray

rejection is achieved to 99.99 then same source will be detected in 1 hour duration at

same significance. If say pulsed signal is less than 10 of steady Crab flux then required

duration will be more than 400 hours for 5 detection of pulsed signal, assuming pulsed

signal is confined to 10 of rotational cycle.

The present PACT sensitivity is not good for search of steady sources in comparison to

modern IACT detectors, where they claim 99.99 of cosmic ray rejection. However PACT

sensitivity is slightly better for pulsed emission searches than steady emission search for

the same signal strength. In search of pulsed emission, background rejection is better by 4

- 5 times of steady signal search. In periodic search events are classified according to their

phases , which lie between 0 and 1. Gamma ray events populate in particular phase

bins whereas cosmic ray background events populate uniformly over all phase bins. Any

significant excess of events at a particular phase (10-20 of rotation cycle) over uniform

background is the measure of pulsations. PACT system could be used for detecting signals

from flaring objects like mkn421 and for search of periodic signal in VHE band.

Most of the recent observations and periodic search indicate that cutoff in high energy

emission is below 100 GeV from pulsars but they can not rule out another component of

emission at higher energies. If there is emission in VHE range, like as envisaged by the

outer gap model, which could explain emission at high energy, further motivate to look for

periodic signals.

4.7 Pulsar Data Analysis

The method of searching extended, non-uniformly sampled data for the presence of a pe-

riodic signal when period is very short, requires careful attention to the details of the tim-

ing. The frame of reference play an important role in the observation of any pulsating

astronomical source. These pulsating sources (pulsars, binary) are studied in a stationary

reference-frame wrt to source position otherwise motional properties of observing point

will dominate over any significant change in rotational period of emitting source. The ne-

cessity of reducing observed arrival times to some stationary inertial point can be derived

from the result of Doppler effect caused by the relative motion of source and observer.

Light takes about 500 seconds to travel from Sun to reach at surface of Earth. If orbit of

the Earth around the Sun is taken as circular, then light will take same time to reach Earth

surface throughout the year. Photons from the distant celestial periodic sources (pulsars)

lying in the plane of ecliptic as shown in figure-4.22, will therefore arrive early on the Earth

than at Sun when the Earth is closest to the pulsar. Six month later, the photons will arrive


Fig. 4.22: Annual variation in photon arrival time due to orbital motion of Earth around the Sun

(figure redrawn from Smith 1977).

late by the same amount of time. Assuming Earth orbit is circular and Sun at center, the

delay (t ) of path AC or BC is given

(4.21)

where is the angular velocity of Earth in its orbit and

, are the ecliptic longitude and

latitude of a pulsar.

Let $ is the phase of an event at time t then phase of an event at time t is given by

*

0 (4.22)

where P(t) is the pulsar period and any change in the pulsar period is only due to Doppler

effect (the change in the pulsar period due to glitches, spin-up or spin-down are ignored).

If

is the rate of change of pulsar period due to Doppler shift then

(4.23)

where is the true pulsar period, therefore phase from equation-5.2 is

*

0


Let * = 0 at t = 0 , therefore

0

" " " " " (4.24)

If

ie there is no change in pulsar period then

, therefore the difference

in excess phase introduced by is given

( )

If the error in the phase estimations is to be maintained as

" then

( ) "

or

"

&% (4.25)

The variation of pulsar period of of Crab pulsar due to orbital motion of Earth around Sun

is shown in figure-4.23 (solid line)

The value of is calculated as: Average velocity of Earth in its circular orbit around

Sun is given by

!#" %$ " #"

#" %) ,+ -*/10so Doppler shift in pulsar period(P) due to orbital motion of Earth around Sun is given as

+

for Crab pulsar P=33.33ms, #"

Doppler shift will vary sinusoidally

as amplitude of motion, so it can be written as #"

where is the angular position of Earth at time t in its orbit around Sun, so

0 0

#"

0 0


Fig. 4.23: The variation of Crab pulsar period as function of time. Dotted curve is a result of normal

slow down of pulsar and the solid line represent the period variation due to orbital motion

of Earth.

and 0 0

0 / ) ,+so,

"!$# !#" !

therefore from equation-4.25, the duration t is given as

"

!#"&! &% " - ) (4.26)

Hence pulsar data (timings) cannot be linked together when intervals are greater than 5.0

hours for given phase error

" , therefore the barycenteric corrections are necessary

if phases are to be linked between different data intervals.

4.7.1 Solar System Barycenter

The effect of the Earth’s motion (orbital + spin) on the observed arrival times of photons

from pulsar are corrected by shifting observation point to some inertial stationary point

to keep relative distance between source and virtual observation point constant of motion.


The equivalent center of our solar system is the most common point for this purpose and

called as Solar System Barycenter (SSB). An ephemeris of the Earth’s motion derived from

planetary radar observation (Ash et al. 1967) have been used to compute the propagation

times from the telescope to the barycenter (SSB). In the correction process of arrival times,

compensation for two other effects is necessary to obtain arrival times in an inertial frame

of reference (SSB). First is the delays due to interstellar dispersion (which is negligible in

the case of keV to TeV observations) must be removed and second, the terrestrial clock

times must be corrected for an annual variation in rate resulting from the changing time

dilation as the Earth moves in its elliptical orbit around the Sun. The correction term in the

observed arrival times of a solitary pulsar can be expressed as

* *

$ ! (4.27)

where t : barycentric arrival time,

t : observed arrival time,

t : to convert local clock time to geocentric TT or TDT,

t : time delay in Solar system,

t : Einstein relativistic correction,

t : delay due to propagation through interstellar medium (ISM),

t ! : correction due to gravitational lensing effect

All these corrections for barycentric position will be discussed in next sections.

4.8 Clock correction

The time of arrivals (TOA) of pulsar photons are determined from the local clock, which

is compared to Coordinated Universal Time (UTC) by using the Global Positioning Sys-

tem (GPS), which provides UTC measured by the US National Institute of Standards and

Technology (NIST) and is often referred to as UTC(NIST).

Atomic clocks provide most accurate and consistent means of time measurement. Inter-

national Atomic Time (TAI) was introduced in 1972 and fundamental unit of TAI is the

SI second, which is defined as the duration of 9,192,631,770 cycles of radiations cor-

responding to the transition between two hyperfine levels of the ground state of cesium

(cs ) atoms. TAI is the international atomic time scale based on large number of atomic

clocks and the basis of civil time. The TAI is maintained as an average of a large number

of selected atomic clocks by the

(BIPM),

a uniform atomic time standard known as Terrestrial Time (TT). Universal time (UT) is

counted from 0 hours at midnight with unit of duration of mean solar day. Coordinated


Universal Time (UTC) differs from TAI by integral number of seconds called as leap sec-

onds.

Astronomers everywhere in the world use a single time system to coordinate their obser-

vations. This system of time is called Universal Time (UT or UTC) is same as Greenwich

Mean Time (GMT), a time scale in which the mean position of the Sun at noon, averaged

over the year above the Greenwich meridian (longitude zero).

Leap second: Earth rotation period (diurnal motion) was the basis for time scale before

atomic clocks. The Earth is constantly undergoing deceleration caused by the braking ac-

tions of tides and this deceleration causes the Earth’s rotational frequency to slow down wrt

to atomic clock’s time. From the records of ancient observations of eclipses, it is possible

to determine the average deceleration of Earth rotation. The Earth is rotating slower over

time, while the atomic clocks are not slowing down. In an average day, the difference is

around 2.0 milliseconds, which mean after 500 days, the difference between the Earth ro-

tation time and atomic time would be 1 second. In order to synchronized the atomic clocks

with the Earth’s observed rotation, the atomic clocks are occasionally instructed to add an

extra second (leap). The Leap seconds are inserted so that the difference between the UTC

and UT1 (mean solar time - observed Earth rotation) is kept below 0.9 seconds. Leap sec-

ond is added at end of June or December month whenever this difference is greater than

0.9 second. It is also possible to have a negative leap second when one second is removed,

in a case where the Earth is rotating faster, but such a negative second has never been used

and is rather unlikely to be used in future. The International Earth Rotation and Reference

System Service (IERS), an international body located at the Paris Observatory observes the

Earth’s rotation and declare through their “Bulletin C” message, which reports whether or

not to add a leap second at end of June and December. First leap second was introduced

on June,30,1972. Figure-4.24 shows the leap seconds added to TAI at different epoch of

observations.

For the study of astrophysical objects, the time scale which include correction for any

leap second, rotational period of Earth, statistical drift in atomic clocks etc are the dynam-

ical time. Terrestrial Time (TT) or Terrestrial Dynamic Time (TDT) is the theoretical time

scale of apparent geocentric ephemerid of solar system bodies. It applies in principle to

the Earth bound clocks at sea level and for practical purposes, it is tied to the atomic time

scale (TAI) as

" $ ) ,+ -*/10)

(4.28)

where

) ,+ - / 0 ) (4.29)


Fig. 4.24: Leap seconds added to TAI observed on different Epochs.

The unit of TT or TDT is SI seconds and an offset of 32.184 second wrt TAI is fixed. Total

number leap seconds till December 2007 are 33 seconds, so

" " $ ) ,+ - / 0 ) (4.30)

4.8.1 Barycentric Dynamical Time:

Barycentric Dynamical Time (TDB) differ from TDT only by periodic variation and it

is a consequence of the TDT clock being on the Earth rather than in empty space. The

orbit of Earth around Sun is slightly elliptical (e=0.01671) therefore TDT clock speed and

gravitational potential vary slightly during the course of the year and as result of this, its

rate as seen from outside observer varies due to transverse Doppler effect and gravitational

redshift. The TDB (Robin 1985) can be expressed in terms Earth eccentricity and other

parameters of orbital motion as

/ (4.31)


where a : semi-major axis of Earth orbit=1.496 10 km,

n : mean motion of earth= = ! =1.990011914 10 radian/sec,

E : eccentric anomaly and given by

E - eE E=M, where M is mean anomaly

and e E=e (M+eE E) e M+ e 2M

2m : Schwarzschild radius = =2.956 km for Earth-Sun system

from equation-4.31 and all above constants, the barycentric time is given

/

(

)or

" ! $ " $ (4.32)

where M is given as

" " $ %! $ " (4.33)

where JD is Julian Day number.

In case of Moon motion around the Earth, e=0.0547, a=3.844

km, T=27

#" and

!* =0.000000479442 is very small compared to Earth-Sun parameter, therefore this effect

can be ignored in time correction for clock situated at moon.

Julian Day Number: Julian Day Number(JD) is a count of days elapsed since Green-

wich mean noon on January 4713BC, Julian proleptic calendar. The Julian date is the

Julian day number followed by the fraction of the day elapsed since the preceding noon.

Modified Julian Date (MJD) is defined as the

" (4.34)

A MJD day begin at midnight of civil date and for the record of astrophysical events MJD

or JD is taken as reference date.

4.9 Geometric Corrections

(a) Correction due to Observer’s displacement from Earth geo-center:

Since shape of the Earth surface is not completely spherical, therefore the time taken by a

photon from Earth surface to reach at center (geo-center) will vary with latitude of obser-

vation point. The different location on Earth surface for same photon arrival will record


Fig. 4.25: The variation of photon arrival time as function of Earth’s geographical latitude. (figure

redrawn from Smart 1977).

different times. To keep arrival time of pulse photons independent of geographical latitude,

surface arrival times are shifted to Earth-geocenter. From figure-4.25, if is the angle that

position vector of pulsar position makes with zenith at observer’s site then time taken by

photon from Earth surface to geo-center is

* +

(4.35)

where c=3 10 m/s and R is the displacement of observer from Earth geocenter to sur-

face.

Calculation of R The approximate figure of Earth is called geoid and shown in figure-4.26. If major and

minor axis of Earth are a (CB) and b (CP) then eccentricity of meridian section is

(4.36)

and equation of ellipse POBQ is

(4.37)

In figure-4.26, DOZ is the normal to surface/plane of observer and this is equal to ob-

server’s zenith or astronomical zenith,

is astronomical latitude of observer. Similarly


Fig. 4.26: Dependence of Earth radius vector on geographical latitude (figure redrawn from Smart

1977).

is observer’s geocentric zenith,

is geocentric latitude and angle ZO

is the angle of

vertical. If (x,y) are the coordinates of O wrt axis CX and CY then

/10

so

(4.38)

from equation-4.38 and equation-4.38, x and y are calculated and given by

) / /10

) / (4.39)

If R is radius vector(CO) then

/10 ),-

Hence the radius vector is

) /

) / (4.40)

For Pachmarhi latitude (

=22.47 degree) and a=6378.160 km, b=6356.7747 km, e=0.00669454,


Fig. 4.27: Variation of Earth radius vs geographical latitude.

Table 4.7: Geocentric radius.

Site Latitude(degree) R (km)

Equator 0.00 6378.160

Pachmarhi 22.47N 6375.059

Hanle 32.76N 6371.936

Pole 90.00 6356.774


Fig. 4.28: Delay in photon arrival time vs zenith angle of source.

the radius R is equal to 6375.059 km and radius for the Equator, Hanle (latitude=32.76

degree) and Pole are give in table-4.7. The variation of R with latitude is shown in figure-

4.27. Figure-4.28, shows the variation in the photon arrival time at Earth geocenter as

function of zenith angle of source. The maximum delay (21.25 ms) is observed at the

transit time of source therefore this correction in the arrival times of pulsar photons is

necessary.

(b) Correction due to Observer’s displacement from SSB:

Earth revolve around the Sun in elliptical orbit and distance between Earth and Sun does not

remain constant throughout the year. Earth approaches closest (Aphelion) on 4

January

and farthest (Perihelion) on 4

July of every year. Therefore the correction due to this

variation in distance is necessary in the arrival times of pulsar photons. This correction is

the time (t & ) or Romer delay (R ) taken by photon to travel from Earth-geocenter to Solar

Bary Center (SSB) and given as follows.

$&& /+ (4.41)


Fig. 4.29: Sun and Earth-Moon system.

where is the vector from SSB to the Earth-geocenter, c is speed of light and/ is the unit

vector pointing to the astrophysical source. The magnitude of/ depends on the position of

source in the sky ie Right Ascension (RA) and Declination (DEC). The is calculated

at arrival times of photons from JPL Ephemeris data. JPL ephemeris for planetary system

is a table of Chebyshev coefficients and these are used in Chebyshev polynomial equation

with time as variable. For calculation of , let M and m are the masses of Earth and

Moon respectively then from figure-4.29,

(4.42)

where R is the distance between the Earth-geocenter and Moon, R is the distance be-

tween SSB and Moon at time of arrival of pulsar photons. In figure-4.29., O is the common

center of mass of Earth-Moon system and R is the distance between the Sun and O,

is written as

(4.43)

from equation-4.42 and 4.43,

(4.44)


Fig. 4.30: Annual variation of Earth position (a) and velocity (b) around the Sun.

where EMART is ratio of Earth to Moon mass. Similarly velocity vector of an observer

at Earth geo-center is given by

(4.45)

where is the orbital velocity of Moon around the Earth and is the orbital

motion of center of mass of Earth-Moon system around the SSB. The annual variation of

and is shown in figure-4.30(a) and figure-4.30(b) respectively.

Unit vector in the direction of source:

Let us consider a celestial sphere of unit radius shown in figure-4.31 and a source is situated

at the surface of sphere and observer (Earth) at center (O). Let (x,y,z) are the cartesian

coordinates of source and (r, ,

) are corresponding spherical coordinates. Since radius of

celestial sphere is taken as unit so,

and

/10


Fig. 4.31: Celestial sphere to represent the position of source and observer.

If ( ) are the unit vector along the positive direction of X,Y,Z axis then

/

and

/10

are direction cosines of unit vector and after resolving the component of radius vector along

X,Y,Z axis,

For a given source position ( ), the source and

is calculated from equation-2.30

and 2.31 explained in chapter-2 and unit vector/ is calculated at arrival time of pulsar

photons. The annual variation in the photon arrival time measured from Earth based clock

due to orbital motion of Earth around the Sun is shown in figure-4.32. The maximum delay

observed is 418.0 seconds and agree with the time taken by light from Sun to reach on the

Earth surface.


Fig. 4.32: Annual variation of photon arrival time as a course of orbital motion of Earth around the

Sun.

4.10 Einstein correction

It is a consequence of the clock situated in a moving frame of reference. According to

Einstein relativistic theory, if t & is the proper time of pulsar photon measured at SSB

(stationary) and is the time measured in Earth or space-craft based clock moving with

speed v then $

%+ (4.46)

Thus the time appears to the moving observer to be lengthened or dilated ie moving clock

always appears to go slow.

The Einstein delay is the combined effect of time dilation (equation-4.46) due to the motion

of the Earth and gravitational redshift caused by the other bodies in Solar System. This

delay is time varying because the atomic clock situated on the Earth is under the changing

gravitational potential as the Earth follows elliptical orbit around the Sun. The Einstein

delay (

) is given by expression (Backer

Hellings 1986)

0 0

+ + (4.47)

where sum is over all the bodies in solar-system excluding Earth and v is velocity of the

Earth relative to Sun given by equation-4.45 and r is the relative distances between the


Earth and i

body of solar system.

4.11 Dispersion Delay

When pulsar signal propagates through the interstellar medium (ISM), it is delayed due

to dispersion in medium. The presence of free electrons in the interstellar medium delay

the group velocity ( ) of radio waves slightly than velocity of light and is a function of

frequency (f). When a radio wave propagate in the homogenous isotropic medium, the

group velocity (Gingburg 1970) is

+ &%

(4.48)

where is the plasma frequency and f is the wave frequency of observation. The plasma

frequency (in Gaussian units) is given by

/ &%

(4.49)

where / is the electron density, e and m are charge and mass of electron respectively. The

propagation of a radio signal along the path of length d from pulsar to Earth will be delayed

in time wrt a signal of infinite frequency by

0 0

+for

. the delay is

+ / 0

(4.50)

where / 0 is the column density of electrons in the path to the source and known as

dispersion measure (DM) are expressed in +%+ . The dispersion constant

"

+ + ) , the delay between two frequency( ) is given by

"

)

" (4.51)

Thus the dispersion delay is proportional to and this delay must be removed from

photon arrival times at SSB. In case of Optical, X-ray and ray pulsar observations, the

observed frequencies of photons are very high ( Hz), therefore the dispersion delay

for TeV pulsar observation will be taken zero.


4.12 Shaprio delay

This is a relativistic correction that correct for extra delay due to the curvature of space-

time caused by the presence of masses in the solar system and it is given (Shaprio

1964) as

+ / / (4.52)

where G is Newton’s gravitational constant, M is the mass of i

body, is the pulsar

position relative to it, is the telescope position relative to that body at the time of closest

approach of the photon and/ is a unit vector pointing from SSB to the position of the

pulsar. In practice, only Sun (120 ) ) and Jupiter (200 ns) contributes maximum delay in

solar system. The Sun’s contribution in Shaprio time delay is

( + )

(4.53)

where is the Pulsar-Sun-Earth angle at time of arrival of pulsar photon.

All above corrections in arrival time of pulsar photon are for single-pulsar (non-binary

system) and observation of pulsars in binary orbit shows a periodic variation in pulse arrival

time due to orbital motion. Therefore to incorporate this additional motion of the pulsar as

this orbits around the common center of mass of the binary system needs another correction

terms (Blandford

Teukolsky 1976).

4.13 Temporal Analysis

A definite association of VHE pulsar with a radio pulsar can be established by finding a

modulation of the -ray signal at known periods of radio pulsations. Since photon flux

at TeV energies is very low, long duration exposure of source is required to explore the

VHE sources. Therefore data from several independent observations are to be linked. For

pulsar analysis, each detected event from the direction of the pulsar must be tagged with

corresponding rotational phase ie the fraction of a revolution at which a -ray is emitted

from pulsar corresponding to the arrival times.

The pulsation frequency of pulsar may be expanded as a Taylor series

" " " " " " " " (4.54)

where is the pulsar frequency at time ,

and

are first and second order deriva-

tives of its fundamental frequency. In the inertial frame of pulsar, the number of revolution


(dN) completed in time dT is

0 0 (4.55)

The rotational phase at any time is obtained by integrating equation-4.55 and taking the

fractional part of the phase, therefore

0 or

! (4.56)

where is the phase at epoch is taken as reference phase. Since the Earth is revolv-

ing around the Sun in elliptical orbit, as a result of this it is under significant acceleration

relative to the pulsar, therefore the arrival times of events from pulsar direction measured

by PACT array need to be corrected for any relative motion between pulsar and observa-

tion point. The transformation of arrival times of events from observation point to Solar

System Barycenter (SSB) is performed through the barycentring method. All these time

corrections have been included in standard pulsar analysis code “Tempo” developed by

Princeton.

4.14 Periodicity tests

The absolute phases of events are grouped into phase bins and a phasogram is constructed

for each observed data. Any indication for pulsations will show up as peaks in the pha-

sogram. Three statistical tests are generally applied on the absolute phase data to check

whether they indicate any pulsed signal or not.

4.14.1 test

It is computed from the binned data of a phasogram. There are n-1 degrees of freedom for

n-bin phasogram and defined as

(4.57)

where n is the number of bins and is the number of counts in the

bin and is standard

deviation of phase distributions. The probability of observing a large value of (Pugh

Winslow 1966) is given as

%

# % 0 (4.58)


where / degree of freedom. A strong periodic signal in the data will result a

large deviation from uniform distribution of phases and large . This test depends on the

number of bins in histogram. Since only magnitude of total deviation is considered, a pulse

that happens to be split evenly between two bins will contribute half as much power to than it is entirely contained in a single bin.

4.14.2 Z

test

This statistics (Beran 1969, Buccheri et al. 1983, Buccheri

Sacco 1985) estimates the

difference between measured and uniform phase distribution. The Z (m=1,2,3,......) test

is independent of any event binning and uses Fourier power in the first m harmonics. If

f(

) is the measured phase density function, then Fourier series of this function is

(4.59)

where

0

0

where, N is the number of events and

is the phase of the i

events. The Z statistics is defined as

(4.60)

In case of no signal, Z statistics is distributed according to with 2m degree of free-

dom. For m=1, Z test becomes Rayleigh statistics (Mardia 1972), which is sensitive to

sinusoidal pulse profile while higher order Z (n=2,3,4,...) test are sensitive to sharp peaks.

4.14.3 H-test

The H-test proposed by De Jager, Swanepoel

Raubenheimer (1989) is derived from Z statistics to optimize the choice of m within the first 20 harmonics and is defined as

(4.61)

In case of no signal, H-test is distributed approximately exponentially.

Applying these different tests thus allows an assessment about the significance of a pulse

signal of different pulse profile.

Chapter 5

Crab Nebula and Pulsar

5.1 Introduction

The Crab system (Pulsar+nebula) is one of the most studied object in all bands of astron-

omy. It is a brightest supernova remnant in the sky. Due to its steady emission nature, the

Crab nebula has been in the focus of observers for centuries. It belongs to type-II supernova

and was first seen by the Chinese, Japanese, Korean amateur astronomers which appeared

on July 4, 1054AD. When this supernova explosion occurred, it was so bright and therefore

was visible in day light during first few weeks. Due to the high flux from the source relative

to other known VHE sources, it is conventionally used as a standard reference source for

VHE astronomy. The 33.34 ms Crab pulsar (PSR 0534+2200) was detected at the center

of nebula (Staelin

Reifenstein 1968). It was one of the strongest radio and X-ray source

detected. It was the first pulsar confirmed to be decelerating (Richards

Comella 1969).

Pacini (1967) explained that a rapidly rotating highly magnetized neutron star could be

powering the entire Crab nebula.

The early observations of Crab nebula, from the first satellite borne spark chamber tele-

scope SAS-2 has explored the energy spectrum from 30 MeV to 500 MeV. The COS-B

data revealed the steady emission in addition to pulsed component. The nebular emission

spectrum is well fitted from X-ray to MeV energies by a single power law with spectral

index -2.08 (Toor

Seward 1974) and is consistent with primary emission mechanism

of synchrotron radiation. The position of the two peaks in the pulsar light curve (figure-

1.8(a), Chapter-1) are consistent with that measured at radio, optical and X-ray observa-

tions. The radiation from nebula is polarized in optical and radio wave region. The high

degree of polarization is due to synchrotron process which require the presence of very

high energetic ( ' eV) electrons gyrating around the magnetic fields ( 10 G) in the

nebular region. The first attempt to use atmospheric Cherenkov technique was done by

Lebedev group (Chudakov et al. 1963) at Pamir. From these observations an upper limit

129

Chapter 5. Crab Nebula and Pulsar 130

of 10 photons/cm /sec was obtained for -rays of energies ' 5 TeV from nebu-

lar emission. The first positive detection of TeV -rays from the nebula was reported by

Fazio et al. in 1972. From 150 hours of observations, they detected signal at 3 level

and estimated flux was (5.7 1.8) 10 photons/cm /sec for energies 0.14 TeV. The

Whipple group (Cawely et al. 1985) in early eighties obtained 5 signal and reported flux

of ! 10 photons/cm /sec for -rays of energies ' 0.4 TeV from 10 meter imaging tele-

scope. This group during 1986-88, detected (Week et al. 1988) the source at 9 level,

which was the most significant signal from Crab at that time. These observations yielded

a flux of " $ 10 photons/cm /sec at E ' 0.7 TeV. Since then the Crab nebula was ex-

tensively studied by ground based telescopes at energies above few hundreds of GeV. In

the past few years, the Crab nebula has been detected by many ground based experiments

using variety (Imaging, Wavefront, Particle shower) of techniques. The Crab nebula was

detected by STACEE group at 5 significance level in each of the 1998-1999, 2002-2003

and 2003-2004 observing seasons, at an energy threshold of around 170 GeV (Oser et al.

2001). The integral flux of (2.2 " ! " ) photons/cm /sec from the Crab nebula

for energies ' E (190 60 GeV) was reported by this group. The Observation of Crab

nebula by HESS telescopes detected integral flux of ( " " ! " ) photons/cm /sec (Masterson et al. 2005) above 1 TeV. The observations of Crab nebula

by MAGIC telescope taken between October 2005 to December 2005 showed average in-

tegral flux of (1.96 " ! ) photons/cm /sec (Otte et al. 2007) above 200 GeV.

Figure-5.1 shows the integral photon spectrum of Crab nebula observed by various ground

observations (Atmospheric Cherenkov, Air-shower) and satellite detectors. The recon-

structed energy spectrum of ground observations is well fitted by a straigh power law from

GeV to TeV.

In long term observation of steady emission, no pulsed component of VHE emission have

been noticed by Atmospheric Cherenkov telescopes and cutoff in the pulsed emission at

energies 10 GeV was predicted. The first positive pulsed detection was reported by

Grindlay et al. in 1972. They detected 3.5 and 5.4 signals in the main and interpulse

regions respectively. The flux estimated from these observations was (1.25 " ! ) photons/cm /sec at energy ' 0.68 TeV. Tata group (Gupta et al. 1978) observed two peaks

in phasogram of Crab pulsar from data collected at Ootacamund during 1977. The esti-

mated flux was (8 ) photons/cm /sec at energy ' 6.4 TeV. Observations between

1980-1990 periods have shown transient emission of several minutes duration. A burst

of 15 minute duration observed by Durham group (Gibson et al. 1982) in October 1981

and detected flux was (2.0 " ) photons/cm /sec at energy ' 3.0 TeV. Tata group

(Bhat et al. 1988) also observed burst of same duration and a flux of (2.5 " ! )


Fig. 5.1: The MeV-TeV -ray spectrum of Crab nebula by various groups (satellite detector, atmo-

spheric Cherenkov telescopes and air shower arrays). Filled points represent confirmed

detections; unfilled points with down arrows represent upper limits. The identification of

each experiment is given in the legend. (figure is from Sinitsyna et al. 2007)

photons/cm /sec for energies ' 1.2 TeV was estimated during the burst. Durham group

(Dowthwaite 1984) observed Crab pulsar from September 1982 to November 1983 (103

hours) and evidence of positive pulsed emission was reported. The resulting flux obtained

is (7.9 1.8) photons/cm /sec for energies ' 1.0 TeV. The upper limits of steady

pulsed flux over the 102.7 hours of observations (1996) by CAT experiment (Musquere

et al. 1999) showed 1.5 photons/cm /sec, 3.0 photons/cm /sec, 5.0 photons/cm /sec above 250 GeV, 1 TeV and 5 TeV respectively. The most recent observa-

tions of Crab pulsar by HESS, MAGIC and STACEE groups did not show any convincing

evidence of pulsed emission. Therefore ground observations have given only upper limit

of their detection level at few hundreds of GeV. Crab pulsar was very well explored by

Whipple (November 1994 and March 1997) and HEGRA (1997-2002) groups up to 250

GeV and 548 GeV respectively. STACEE group observed (Oser et al. 2001) Crab pulsar

between November 1998 and February 1999 and found no evidence of pulsed emission

from 43 hours of data for energies ' 190 GeV. Whipple group with their high resolution

GRANITE III camera observed Crab pulsar between January 2000 and February 2002 and

from 97 hours of data, no evidence of pulsed -ray emission for energies ' 106 GeV was

found from data. MAGIC group (Lopez et al. 2005) during 2004 used their 17 meter tele-

scope to search for pulsed -ray from Crab pulsar and no evidence of pulsed emission was


found in their data, therefore only upper limits at different energies (90 GeV, 150 GeV) for

3 confidence level were obtained. The PACT observations between 2000-2005 (45 hours)

also did not show any evidence of pulsed emission (Singh et al., 2005).

In this chapter, detailed analysis of steady and pulsed emission from Crab system is re-

ported.

5.2 Search for Steady Emission

The arrival direction of primary -ray is estimated from the relative arrival times (TDC)

of Cherenkov wavefront at different detectors. The space angle ( ), an angle between the

direction of arrival of reconstructed shower axis and the source direction is calculated for

each event. Any excess in space angle distribution of ON-source over OFF source events in

a narrow cone along source direction could be attributed to -ray signal from point sources.

Data collected have been divided into different groups and analyzed with various trigger

conditions. Data from individual PMT channels (Data set(B)) and entire array channels

(data set (A)) were used for analysis as explained in chapter-4.

Observations taken during nights of 2000 to 2006 years have been used in this analysis. The

summary of Crab data sorted for nebular and pulsar analysis are given in table-5.1, where

duration is in minutes and numbers of observations are given in column-3 and column-5

for nebular and pulsed emission analysis.

5.2.1 Space Angle Distribution

After preliminary data diagnosis, the relative times of arrival of Cherenkov photons are

fitted to a plane shower front and the direction of arrival of shower axis is obtained for each

event. The space angle ( ), between the direction of arrival of shower axis and the source

direction is obtained for each event. The space angle distributions were obtained for each

data set as explained in Chapter-4. The space angle distributions were obtained for both

ON and OFF source events. The OFF-source data covering the same zenith angle range

as that of ON-source taken on the same night are selected for analysis. The space angle

distribution of Crab source data (Run=821) and unnormalized background (Run=822) data

are shown in figure-5.2. The space angle distribution for each ON-OFF pair are compared

and then normalization constant and other parameters are calculated. These are peak posi-

tion of the space angle distribution, FWHM and the space angle below which 85 events

lie. These parameters for data set(A) are given in column-6, 7 and 8 of table-5.2. The

normalization constant and its standard deviation are given in column-5. The maximum


Table 5.1: Observation log of Crab source.

Nebula Pulsar

Year Duration(min.) #Runs Duration(min.) #Runs

2000 454.2 5 1308.9 13

2001 93.0 1 725.4 8

2003 738.0 7 963.3 8

2004 918.0 12 763.7 7

2005 1302.6 13 1366.9 12

2006 210.6 3 234.0 2

Total 3716.4 41 5362.2 50

number of valid triggered telescopes and duration of observation are given in column-

9 and column-10 respectively. The two cuts applied on event selection are the minimum

number of triggered telescopes which is 8 with valid ‘timing’ data and goodness of plane

wave fit parameter (chi-square). Those events for which + ' " (standard

deviation of distribution) are discarded.

The condition for a pair of Run to be accepted is imposed based on profile parameters of

space angle distribution. All runs for which 85 limit (column-8) is more than 3.5 degree

(wider space angle distributions) and those runs data with ON OFF peak difference 0.4

degree are rejected. If the two peaks (ON and OFF) do not coincide properly then it may

lead to either large positive or negative excess. A remark on the quality of analyzed data is

indicated by A (Accepted) or R (rejected), which is shown in the last column of table-5.2.

The OFF-source space angle distribution is normalized as stated in chapter-4. The back-

ground space angle distribution (Run 822) is normalized with factor (R=0.71319) and

normalized background events are subtracted from the ON-source events to estimate the

excess -ray counts. The excess -ray counts are calculated between 0 - 2.5 degree of space

angle range. The space angle distribution of Crab-ON source and normalized background

source data is shown in figure-5.3(a). The excess counts obtained are 633.6 146.9 which

correspond to 4.0 level at 5.57 1.29 counts per minute. The distribution of excess/deficit

counts as function of space angle is shown in figure-5.3(b). Similarly excess/deficit counts

are calculated for each accepted run data and details of each individual ON/OFF combi-

nation is shown in table-5.3. The RMS value of the estimated -ray signal is taken as a

measure of systematic error on the obtained signal.

The excess count rate or -ray signal from Crab source obtained on different observa-

tion days are shown in figure-5.4. The results of all accepted summed events are shown


Table 5.2: Summary of Crab data observed between Year 2000-2006.

SN Run ON Date Tel trig Peak FWHM 85 DOF Dur. Rem.

OFF MJD

sigma deg. deg. deg. hr. A/R

1 120 ON 29/10/00 0.80303 1.9 1.8 3.5 08 0.54 A

119 OFF 51846 0.00 2.3 2.4 2.2

2 132 ON 21/11/00 1.03266 1.2 1.8 2.4 12 0.93 R

131 OFF 51869 0.03 1.6 2.2 2.9

3 136 ON 23/11/00 0.88114 1.4 2.2 2.8 09 2.04 R

135 OFF 51871 0.17 2.0 2.6 3.5

4 138 ON 24/11/00 1.36245 1.4 2.2 2.8 12 2.01 R

137 OFF 51872 0.04 1.8 2.4 3.1

5 140 ON 25/11/00 0.35717 2.2 2.8 3.8 12 2.05 A

139 OFF 51873 0.11 2.4 2.8 3.8

6 171 ON 21/01/01 0.69597 2.0 2.0 2.9 11 1.55 R

172 OFF 51930 0.62 2.4 2.2 3.2

7 493 ON 21/11/03 0.93269 1.6 3.0 4.5 09 1.35 R

494 OFF 52964 0.11 1.8 3.2 3.2

8 496 ON 22/11/03 0.60386 1.2 2.6 3.3 08 1.92 A

495 OFF 52965 0.00 1.2 2.0 2.7

9 498 ON 23/11/03 1.94470 1.2 1.8 2.5 12 0.88 R

497 OFF 52966 0.19 1.4 2.2 3.1

10 503 ON 25/11/03 1.23987 1.6 2.8 4.1 10 2.47 A

502 OFF 52968 0.04 1.6 2.6 4.0

11 505 ON 26/11/03 1.00450 1.8 2.6 3.9 10 2.36 A

504 OFF 52969 0.03 2.2 3.4 4.6

12 507 ON 27/11/03 0.97819 1.8 3.0 4.3 08 2.47 A

506 OFF 52970 0.03 1.8 4.0 4.9

13 508 ON 29/11/03 0.74193 1.2 2.8 3.7 10 0.85 A

509 OFF 52972 0.01 1.6 2.4 3.6

14 534 ON 16/01/04 0.70901 1.0 2.0 2.7 10 1.59 R

535 OFF 53020 0.22 1.2 2.0 2.4

15 536 ON 17/01/04 0.64038 2.4 2.6 3.7 16 1.31 R

537 OFF 53021 0.07 1.0 1.8 2.4

16 538 ON 18/01/04 1.31649 1.2 2.0 2.5 16 1.45 R

539 OFF 53022 0.34 1.2 2.0 3.1

17 541 ON 20/01/04 0.87201 1.8 2.4 3.3 16 1.46 A

542 OFF 53024 0.06 1.6 2.4 3.0



OFF MJD


18 543 ON 13/02/04 0.90715 2.2 2.6 3.6 16 1.16 R

544 OFF 53048 0.05 1.4 2.4 3.0

19 682 ON 06/12/04 0.84376 1.2 2.0 2.6 16 1.24 R

681 OFF 53345 0.05 2.2 2.4 3.4

20 684 ON 07/12/04 0.76286 1.2 2.0 2.6 16 1.50 A

683 OFF 53346 0.04 1.2 1.8 2.4

21 686 ON 08/12/04 0.47941 1.4 2.2 2.8 17 1.49 R

685 OFF 53347 0.11 1.2 2.0 2.4

22 686 ON 08/12/04 0.38866 1.6 2.4 3.4 14 0.74 R

687 OFF 53347 0.04 2.8 2.6 4.0

23 689 ON 09/12/04 0.69439 2.2 3.2 4.6 15 1.23 R

690 OFF 53348 0.69 1.8 2.4 3.6

24 692 ON 10/12/04 0.40411 1.6 2.2 3.5 17 0.83 R

691 OFF 53349 0.05 1.2 1.8 2.4

25 692 ON 10/12/04 0.89123 1.8 2.6 4.6 15 1.30 A

693 OFF 53349 0.09 2.0 4.0 5.5

26 713 ON 06/01/05 0.44705 1.0 1.0 2.3 17 1.54 R

714 OFF 53376 0.17 1.0 2.0 2.5

27 715 ON 07/01/05 1.11566 1.0 1.6 2.4 18 2.28 R

716 OFF 53377 0.29 1.6 3.8 5.1

28 731 ON 02/02/05 0.91056 1.2 2.0 2.7 10 0.93 A

732 OFF 53403 0.09 1.4 2.2 2.8

29 733 ON 03/02/05 0.80329 1.6 2.2 3.0 11 1.09 A

734 OFF 53404 0.02 1.6 2.2 3.0

30 736 ON 05/02/05 0.77121 1.0 1.8 2.3 17 2.08 A

737 OFF 53405 0.05 1.0 1.8 2.3

31 801 ON 29/11/05 0.39903 1.4 3.0 5.3 12 2.48 R

800 OFF 53703 0.02 1.0 1.8 2.5

32 806 ON 04/12/05 0.55627 2.4 4.2 5.6 11 1.97 R

805 OFF 53708 0.03 1.2 2.0 2.7

33 808 ON 05/12/05 0.85289 1.4 2.4 3.2 09 1.34 A

807 OFF 53709 0.00 1.2 2.0 2.9

34 811 ON 06/12/05 0.97907 1.0 1.8 2.6 10 0.74 A

812 OFF 53710 0.02 1.2 2.0 2.7



OFF MJD


35 813 ON 07/12/05 0.85338 1.0 1.8 2.4 10 1.37 A

814 OFF 53711 0.05 1.0 1.8 2.4

36 821 ON 27/12/05 0.71319 1.2 2.0 2.5 11 2.48 A

822 OFF 53731 0.02 1.2 2.0 2.7

37 823 ON 28/12/05 0.86457 1.4 2.2 2.8 12 1.89 A

824 OFF 53732 0.03 1.2 2.0 2.7

38 827 ON 30/12/05 0.75144 1.2 2.0 2.6 11 1.52 A

828 OFF 53734 0.01 1.2 2.0 2.6

39 841 ON 22/01/06 0.98644 1.2 2.0 2.6 12 0.64 A

842 OFF 53757 0.17 1.4 2.0 2.7

40 843 ON 23/01/06 1.79432 1.2 1.8 2.5 12 0.92 A

844 OFF 53758 0.47 1.4 2.2 3.0

41 847 ON 25/01/06 1.15083 1.4 2.2 3.1 12 1.95 R

848 OFF 53760 0.04 1.6 2.6 3.4

Fig. 5.2: (a) Space angle distributions of events from Crab source and unnormalized background

runs,(b)Excess/deficit events distribution.


Table 5.3: CRAB ON OFF Excess/deficit analysis.

SN RUN N N

Norm. Dur.

Excess Rate/min. Sigma

factor min. normal. + ) ' + ) ' 1 120 157 182 0.80303 32.4 146.2 10.8 0.33 0.62

119 16.6 0.50

5 140 2510 6376 0.35718 123.0 2277.4 232.6 1.89 3.36

139 57.6 0.47

8 496 971 1851 0.60384 115.2 1117.7 -146.7 -1.27 -3.21

495 40.6 0.35

10 503 2129 1803 1.23987 148.2 2235.5 -106.5 -0.72 -1.61

502 70.0 0.47

11 505 3076 2334 1.00450 141.6 2344.5 731.5 5.16 9.94

504 73.7 0.52

12 507 935 791 0.97819 148.2 773.7 161.3 1.09 3.90

506 41.1 0.28

13 508 627 832 0.74930 51.0 623.4 3.6 0.07 0.10

509 33.1 0.64

17 541 8083 10264 0.87202 87.6 8950.4 -867.4 -9.86 -6.65

542 126.0 1.43

20 684 12072 16326 0.76287 90.0 12454.6 -382.6 -4.23 -2.44

683 146.9 1.62

25 692 2777 2282 0.89123 78.0 2033.8 743.2 9.51 10.72

693 67.7 0.87

28 731 853 948 0.91056 55.8 863.2 -10.2 -0.18 -0.25

732 40.5 0.72

29 733 3725 4632 0.80329 65.4 3720.9 4.1 0.06 0.05

734 81.9 1.25

30 736 14834 19374 0.80329 124.8 15563.0 -729.0 -5.99 -4.18

737 165.3 1.36

33 808 3338 4406 0.85289 80.4 3757.8 -419.8 -5.19 -4.98

807 80.9 1.00

34 811 3261 3636 0.97907 44.4 3559.9 -298.9 -6.70 -3.62

812 82.1 1.84

35 813 7138 8379 0.85338 82.2 7150.5 -12.5 -0.15 -0.10

814 115.1 1.39

36 821 12852 17132 0.71319 148.8 12218.4 633.6 5.57 4.00

822 146.9 1.29


SN RUN N N

Norm. Dur.


factor min. normal. + ) ' + ) ' 37 823 11434 13546 0.86457 113.4 11711.5 -277.5 -3.03 -1.82

824 146.8 1.60

38 827 11320 14976 0.75144 91.2 11253.6 66.4 0.54 0.44

828 140.6 1.14

39 841 4105 4024 0.98645 38.4 3969.5 135.5 3.49 1.51

842 89.6 2.31

40 843 5717 3087 1.79432 55.2 5539.1 177.9 3.23 1.68

844 125.1 2.27

Fig. 5.3: (a)Space angle distributions of events from Crab source and normalized background

runs,(b) Excess/deficit events distribution.


Fig. 5.4: Excess/deficit count rate from direction of Crab source.

Fig. 5.5: Significance as function of observation time(Data set[A]), solid line curve is for Crab

source with 15 background rejection at PACT threshold.


Fig. 5.6: 5 sigma sensitivity for PACT in terms of Crab flux.

Table 5.4: Overall conclusion of crab ON-OFF analysis of data table-5.3.



Total excess -350.6 457.4

Total duration 1915.2 min.

Rate/min -0.18 0.24

Significance -0.76


in table-5.4. The mean count rate of all data shows -0.71 level excess in 31.92 hours at

-0.18 0.24 -ray per minute. The excess signal or -ray rate obtained on different MJD

shows variation and this is due to difference in triggering energy threshold of PACT, cosmic

ray rejection efficiency and systematic errors. The variation of significance ( ) as function

of observation time (T) is shown in figure-5.5, which is expected to follow dependence

but does not indicate any steady increase in the obtained signal. For 5 signal from PACT,

required observation duration as function of Crab flux is shown in figure-5.6. Therefore, at

least 41 hours of data is required to detect 5 signal from Crab source.

The present approach towards detection of steady -ray signal in presence of isotropic cos-

mic rays do not reject all cosmic rays (background) events from source data which was

demonstrated using fictitious source observations. (see figure-4.15 and table-4.6). Cuts on

the distribution of plane wavefront fit are intended to reject some fraction of cosmic

ray showers while retaining the -ray signal. In addition to this, the excess count rates are

highly dependent on the normalization factor and shape of two profiles of space angle dis-

tributions. Therefore, -ray signal obtained will be either overestimated or underestimated

from actual signal and have large systematic errors.

5.3 Search for Pulse Emission

The radio position (J2000) of the Crab pulsar (RA " and DEC=22

" )was assumed for the timing analysis. The Crab pulsar parameters are given in table-5.5.

The monthly ephemeris used in the analysis of Crab pulsar data were extracted from Jo-

drell Bank CRABTIME data base (Andrew Lyne et al., Jodrell Bank Obsevatory), which

are listed in table-5.6. Each set of timing parameter is known to be valid over the ranges

of dates shown in column-1. The quantities T , F , and

refer to the epoch, pulsar

frequency and frequency derivatives respectively. The epoch of ephemeris is given in unit

of Modified Julian Day (MJD). The radio peak for Crab pulsar is defined as the ‘centre of

mass’ of the first peak in the radio pulse profile, this is the highest point of the first(main)

pulse of Crab pulsar light curve.

For search of pulsed signal, first the absolute phase of each event is obtained using

“Tempo” codes (maintained by Princeton group) in prediction mode corresponding to

PACT site (Longitude=78 , Latitude=22

and Altitude=1075m), using con-

temporaneous pulsar elements (table-5.5). This code converts the event arrival times to So-

lar System Barycenter (SSB) position and then computes the absolute phase. For barycen-

tric correction, TEMPO use the JPL DE200 Solar System Ephemeris (Standish 1982). In

prediction or ‘tz’ mode, “Tempo” calculates pulsar ephemeris over short period of time


Table 5.5: Ephemeris of Crab Pulsar.

PSR 0534+2200

RA " DEC % " EPOCH 2000.0

PMRA ( ) -17.0 3 mas/yr

PMDEC ( ) 7.0 3 mas/yr

PX 0.5 mas/yr

Distance 2000pc

Table 5.6: Crab Pulsar monthly Ephemeris. (JPL, Andrew Lyne et al.)

Valid Dates Epoch( ) F

MJD Oct 1 2000-Nov 1 2000 51834.000000091 29.8367712566662 -3.74377 5.74

Nov 1 2000-Dec 1 2000 51864.000000038 29.8358009219099 -3.74340 1.38

Dec 1 2000-Jan 2 2001 51895.000000187 29.8347983440997 -3.74307 9.45

Jan 1 2001-Feb 1 2001 51925.000000127 29.8338281792907 -3.74287 4.17

Nov 1 2001-Dec 1 2001 52229.000000176 29.8240004330897 -3.74079 2.89

Dec 1 2001-Jan 1 2002 52260.000000151 29.8229985468276 -3.74047 3.59

Jan 2 2002-Feb 1 2002 52291.000000200 29.8219967357223 -3.74016 2.24

Nov 1 2003-Dec 2 2003 52960.000000296 29.8003951530036 -3.73414 1.18

Dec 1 2003-Jan 1 2004 52989.000000350 29.7994595586114 -3.73380 2.49

Jan 1 2004-Feb 1 2004 53020.000000046 29.7984595223382 -3.73364 2.36

Feb 1 2004-Mar 2 2004 53051.000000050 29.7974595531458 -3.73334 1.62

Dec 2 2004-Jan 2 2005 53356.000000302 29.7876216193308 -3.73235 1.55

Jan 2 2005-Feb 2 2005 53387.000000089 29.7866219974152 -3.73198 1.87

Nov 1 2005-Dec 2 2005 53691.000000207 29.7768234426680 -3.72922 1.75

Dec 1 2005-Jan 1 2006 53721.000000115 29.7758568787755 -3.72885 1.35

Jan 1 2006-Feb 1 2006 53752.000000054 29.7748582020453 -3.72853 1.29


Fig. 5.7: Distribution of phases of Crab pulsar without any cuts on event selection [data set(A)].

(typically hours) in the form of a simple polynomial expansion. Reference phases are cal-

culated over period of 3 hours centered with the transit time of Crab pulsar at Pachmarhi

observatory in the steps of 20 minute interval for each run data. By using these polynomi-

als and reference phase ( ), absolute phase of an events at arrival time T is obtained by

interpolations.

(5.1)

! +.- + - + - " " " " " " " (5.2)

where T and are in units of MJD, is the pulsar frequency and coef(1), coef(2) etc are

the coefficients of polynomial obtained from “Tempo” barycentric correction.

The rotational phase ( ) at observed arrival time is the fractional part of an absolute phase

and integral part is the number of rotations since a reference time (epoch). Distribution

(phasogram) of pulsar phases is formed for each observation data. We searched for mod-

ulation at Crab pulsar frequency by folding all arrival times (phases) in a 20 phase bin

histogram. A typical phasogram obtained without any cuts on event selection is shown in

figure-5.7.

The phasograms are also obtained with constrains on space angle. Only those events

were used for signal detection for which space angle ( ) is

2.5 degree. For data set(A),


Table 5.7: EGRET classification of Crab Pulsar Phase Intervals.

Region Phase interval

First Pulse P1 0.94 - 0.04

Inter-region 0.04 - 0.32

Second Pulse P2 0.32 - 0.43

background 0.43 - 0.94

Fig. 5.8: Distribution of phases for Crab pulsar at different space angle cuts [data set(A)].


Table 5.8: Details of Phase analysis[Data set(A)].

Parameter " " " " Total Events 289922 232868 158772 81931

Duration(min.) 5362.1 5362.1 5362.1 5362.1

Main Pulse(P1) 28953 23372 15904 8366

Inter-region 86649 69763 47561 24504

Inter Pulse(P2) 28987 23180 15935 8311

Background 145333 116553 79372 40750

N 57940 46552 31839 16677

N

58133.2 46621.2 31748.8 16300.0

P2/P1 1.00 0.99 1.00 0.99

Rate (rms) -0.036 0.053 -0.013 0.048 0.017 0.039 0.070 0.028

Significance( ) -0.68 -0.27 0.43 2.48

Table 5.9: Details of Phase analysis[Data set(B)].


Duration(min) 4471.4 4469.6 4465.3 4447.9

Main Pulse(P1) 13652 10052 6402 3180

Inter-region 40771 29959 12275 9501

Inter Pulse(P2) 13435 9963 6387 3138

Background 68159 50343 31928 15530

N 27087 20015 12789 6318

N

27263.6 20137.2 12771.2 6212.0

P2/P1 0.98 0.99 1.0 0.99

Rate ) -0.038 0.044 -0.027 0.038 0.004 0.030 0.024 0.021

Significance( ) -0.89 -0.71 0.13 1.13


Fig. 5.9: Distribution of phases for Crab pulsar at different space angle cuts[(data set(B)].

cuts are applied on the number of telescope (NDF) 8 and on the goodness of fit parameter

( ). For data set(B), cuts are applied on the number of valid mirror TDC (NDF) 8 (at

least one mirror TDC channel from each telescope) and on the goodness of fit parameter

( ). The summary of phasograms for these events are shown in table-5.8 (data set-A) and

table-5.9 (data set-B) respectively. The subsequent columns in these tables corresponds to

events with space angle " , " , " , " respectively.

Pulsed emission of radiation in VHE band is expected to be at phases corresponding to

radio main pulse (P1) and interpulse (P2). The phasogram is divided into 4-regions, as de-

fined by the EGRET observations shown in table-5.7. The first pulse (P1) corresponds

to phase interval of 0.94-0.04, Inter-region:0.04-0.32, second pulse (P2):0.32-0.43 and

background:0.43-0.94. The number of events with phases within the P1 and P2 intervals

constitutes the number of ON pulsed events (N ). The background events (

) are

obtained by adding number of events in the background region. The background events

are normalized by multiplying the ratio of ranges spanned by the pulse and non-pulse re-

gions (Lessard et al. 1999) to get

events. The expression (Li

Ma, 1983) used in


Fig. 5.10: Variation of significance with space angle cuts.

clculation of statistical significance of excess count is as follows.

+ + (5.3)

where c is the normalization constant. The number of counts for main pulse (P1), inter-

region, Inter-pulse (P2) and background regions are calculated in the respective phase in-

tervals. The pulse emission rate per minute is estimated from the excess counts of P1 and

P2 interval regions. The Phasograms of all episodically added data for NDF 8 at " are shown in figure-5.8 and figure-5.9 respectively for set(A) and set(B). A further cut on

space angle is applied to narrower the acceptance angle, to reject OFF-axis events in pulsar

phasogram. In continuation of this, phasograms at space angle " " and " are

added episodically which are shown in figure-5.8 and figure-5.9 for data set(A) and data

set(B) respectively. An increase in the significance is seen when tight cuts are applied on

the selection of events for space angle less than 2.5 degree. This increase in significance

( ) as function of space angle is shown in figure-5.10 for two data sets.

The variation in the statistical significance of Crab pulsar events as function of event rate

for all observations of six years data set(A) and set(B) are shown in figure-5.11 and figure-

5.12 respectively. No correlation between significance and event rate is seen in both sets


Fig. 5.11: Significance as function of event rate[data set(A)].

Fig. 5.12: Significance as function of event rate[data set(B)].


Fig. 5.13: Distributions of significance( )[data set(A)].

of the Crab pulsar data. The distribution of significances of individual run data compared

with the mean and having zero and sigma equal to one. These distributions for space

angle " " " and " are shown in figure-5.13 and figure-5.14 for data set(A)

and set(B) respectively. Mean and (standard deviation) for these distributions are shown

in each figure.

5.3.1 Statistical test

A test for the possibility of pulsar photon modulation is conducted on the binned data.

The of phasogram as explained in chapter-4, for each individual run data at different

phase (20 bins) are calculated. These are checked for main pulse (P1) and inter-pulse

(P2) and compared with the background counts. The per dof at P1, P2, and background-

region are calculated from light curves of Crab on-source and off-source (background) data,

which are shown in figure-5.15 for data set(A). Similar, test was applied for the data

set(B) and results are shown in figure-5.16. The average per dof for data set(A) of on-

source at P1, P2 and background regions are 1.13, 0.90 and 0.91 for " . Similarly,

average per dof for data set(A) of off-source at P1, P2 and background regions are 1.22,


Fig. 5.14: Distributions of significance( )[data set(B)].

Fig. 5.15: distribution of Crab pulsar light curve [data set(A)].


Fig. 5.16: distribution of Crab pulsar light curve [data set(B)].

1.01 and 0.83 . The results of test on these phase bins (P1

P2) do not indicate any

large at rotational period of 33 ms for Crab pulsar events in TeV energy band. Similar

results were obtained for data-set(B) also.

5.4 Upper Limit on Pulsed Flux of -rays

The Crab pulsar data collected during 2000-2006 have been analyzed for the search of

steady and pulsed emission at TeV energy. If obtained signal is within the fluctuation limit

of background counts then one can determine the upper flux limit. This is obtained by

converting + ) ' error of excess count rate to flux units as,

+ ' (5.4)

where is the effective collection area over which the detected Cherenkov photons

are distributed in ground, + ' is + ) ' error per second on count rate

and ul is upper limit number. At TeV energy, pulsed -ray detected from Crab pulsar

events are 2.48 and 1.13 for data set(A) and set(B) respectively at " . The upper

limits on flux have been derived for the phase regions defined according to EGRET peak

regions. The collection area 1.45 for the showers near zenith at 825 GeV threshold

energy has been used for the estimation of integral flux at PACT threshold energy. The


Fig. 5.17: Upper limit on integral flux of Crab pulsar detected by ground observations. Solid line

is for the EGRET integral flux (Nolan etal, 1993). The dashed line represent the extrap-

olations of EGRET integral fluxes.

time averaged -ray flux obtained for Crab pulsar data set(A) at 3 upper limit is #" $

- -*/ )%+ ) ,+ . This flux corresponds to events for which space angle is

1.0

degree. Similarly, time averaged -ray flux obtained for Crab pulsar data set(B) at 3 upper limit is " - -*/ )%+ ) ,+ . Figure-5.17 show the upper limits on integral

pulsed flux of Crab pulsar as a function of energy by various ground based observations and

PACT result for data set(A). The straight line represents the extrapolated points of EGRET

detected flux. The present 3 upper limit is within the upper limits quoted by Whipple and

HEGRA groups at 1 TeV energy.

Chapter 6

Geminga Pulsar

6.1 Introduction

Soon after the detection of Crab Pulsar, exploration of -ray sky by SAS-2 and COS-

B satellite detector in 1972 discovered second brightest isolated Geminga pulsar in the

galactic plane (Thompson et al. 1977, Bennett et al. 1977, Bertsch et al. 1992). The

X-ray observation (Bignami et al. 1983) identified Geminga as a weak X-ray source

from data of Einstein X-ray satellite observatory. The optical observations (Bignami et

al. 1987, Halpern

Tytler 1988) resulted Geminga as a weak pulsating source in the op-

tical band. Low frequency detection of Geminga (Kuzmin

Osovsky 1977, Maalofeev

Malov 1997, Shitov

Pugachev 1997) showed positive results but weakly detected at

100 MHz in radio band. A 59 second periodicity was found (Thompson et al. 1977) from

data of SAS-2 during 1972-1973 at energy 35 MeV. Since it was not strongly detected at

radio frequency, it remained as mysterious object for almost a decade till the discovery

of 237 ms periodicity by ROSAT (Halpern

Holt 1992) and later by EGRET data. In

EGRET catalog, Geminga is a brightest -ray source in the sky of northern hemisphere.

The Geminga pulsar profile from SAS-2 (Mattox et al. 1992) and COS-B (Bignami

Caraveo 1992) showed similar double peaked profile as shown by Crab and Vela pulsars.

In the past, a few groups have observed Geminga pulsar using the atmospheric Cherenkov

technique. Early observations of Geminga pulsar indicated as a source of very high energy

(VHE) -rays and was confirmed by ground observations (Bowden et al. 1993, Vishwanath

1992, Neshpor et al. 2001) using atmospheric Cherenkov telescopes. Crimean Astrophys-

ical Observatory group observed Geminga Pulsar between 1996-1997 and a VHE -ray

flux was detected at 4.4 confidence level for energies ' 1 TeV. The evidence for mod-

ulation of VHE emission with a periodicity of about 59 seconds (Neshpor

Stepanyan

2001) was also reported by same group. Durham group observed Geminga pulsar with

their very high energy (VHE) -ray telescopes at Dugway, Utah, in 1983. The analysis

153

Chapter 6. Geminga Pulsar 154

of these data revealed pulsations at X-ray/ -ray pulse period, with the VHE -ray pulses

being in phase with the lower-energy -ray pulses. The detected VHE -ray signal cor-

responds to a flux of about 3 - - / %+ ) ,+ for energies ' 1.0 TeV (Bowden

et al. 1993). However observation of Geminga pulsar from more sensitive imaging tele-

scopes by Whipple group during 1989-1991 and HEGRA group during 1996 did not show

any evidence of pulsed emission (Akerlof at al., 1993, Aharonian at al., 1999) contrary

to positive detection by other groups. A glitch phenomenon was noticed by Jackson

Mattox during 1996-1997, from long term observations of hard X-ray pulse profile with

ASCA satellite detector between 1994 and 1999. A phase-connected, post-glitch refined

ephemeris (Jackosn

Halpern, 2005) were presented spanning the period from 22 April

1991 to 13 March 2004 using data from X/ -ray satellite detectors. This ephemeris is valid

between MJD50320 to MJD53078. Since Geminga pulsar is not strongly confirmed in the

radio and X-ray bands therefore detection in VHE has become challenge to VHE pulsar

astronomers. The possible evidence (Acharya et al. 2003) of pulsed emission at energy '1.6 TeV were presented from PACT data which were analyzed with pre-glitch ephemeris.

The results of data collected in 2000 at PACT shows no excess events at any phase in the

phasogram (Vishwanath et al. 2005). EGRET detected only pulsed emission but a pulsar

wind nebula (PWN) has been observed in the X-ray/lower energies (Carveo et al. 2004).

Recently, evidence for steady emission of -rays have been reported by few groups. The

integral -ray flux detected by SHALON group is " $ " - - / %+ ) ,+at energies ' 0.8 TeV (Sinitsyna et al. 2007) and energy spectra of Geminga supernova

remnants is found to be harder than Crab nebula spectrum. The MILAGRO group has also

detected 4.9 steady signal (Abdo et al. 2007) from Geminga location during their all

sky survey. The complete data have been re-analyzed and we searched for the evidence

of pulsed emission of -rays. In this chapter the detailed analysis of steady (dc signal)

emission and possibility of pulsed emission will be presented from data collected between

2000-2006 year using PACT array.

6.2 Search for Steady Emission

Data collected for Geminga source have been divided into different groups and analyzed

with various trigger conditions. Data from individual PMT channels (data set(B)) and

entire array channels (data set(A)) data were used for analysis. Observations taken during

nights of 2000 to 2006 year have been used in this analysis. The summary of Geminga data

sorted for steady and pulsar analysis are given in table-6.1, where duration is in minutes

and numbers of observations are given in column-3 and column-5 for steady and pulsed


Table 6.1: Observation log of Geminga source.

Steady (DC) Pulsar

Year Duration(min.) #Runs Duration(min.) #Runs

2000 136.2 3 838.3 8

2001 109.8 1 99.3 3

2003 511.2 6 542.1 5

2004 983.4 10 701.6 6

2005 549.0 6 687.3 5

2006 477.0 6 517.9 5

Total 2766.6 32 3384.9 32

emission analysis.

6.2.1 Space Angle Distribution

After preliminary data diagnosis, the relative times of arrival of Cherenkov photons are

fitted to a plane shower front and the direction of arrival of shower axis is obtained for

each event. The space angle ( ), between the direction of arrival of shower axis and the

source direction is obtained for each event. The space angle distributions were obtained

for each data set as explained in chapter-4. These distributions were obtained for both ON

and OFF source data. The OFF-source data covering the same zenith angle range as that of

ON-source taken on the same night are selected for analysis. The space angle distribution

of Geminga source data (Run=831) and unnormalized background (Run=832) data are

shown in figure-6.1. The space angle distribution for each ON-OFF pair are compared

and normalization constant and other parameters are calculated. These are normalization

constant, peak position of the space angle distribution, FWHM and the space angle below

which 85 events lie. These parameters for data set(A) are given in column-5, 6, 7 and 8

of table-6.2.

Cuts applied on event selection were kept same as that Crab data analysis. The wider

space angle distributions and large shift in ON OFF pair of data were discarded from

further analysis. The background space angle distribution of (Run 832) is normalized

with factor (R 0.81452) and normalized background events are subtracted from the ON-

source events to estimate the excess -ray counts. The excess -ray counts are calculated

between 0 - 2.5 degree of space angle range. The space angle distribution of Geminga-

ON source and normalized background source data are shown in figure-6.2(a). The excess


Table 6.2: Summary of Geminga data observed between Year 2000-2006.


OFF MJD

sigma deg. deg. deg. hrs. A/R

1 162 ON 24/12/00 1.10270 1.6 2.4 3.2 11 1.22 A

161 OFF 51902 0.05 1.8 2.4 3.2

2 164 ON 25/12/00 1.02498 1.4 2.0 2.6 09 0.39 A

163 OFF 51903 0.02 1.2 2.0 2.6

3 167 ON 27/12/00 1.036582 1.4 2.4 3.0 09 0.66 A

166 OFF 51905 0.01 1.6 2.4 3.1

4 177 ON 24/01/01 0.758439 1.4 2.0 2.6 09 1.83 A

178 OFF 51933 0.04 1.4 2.0 2.7

5 521 ON 22/12/03 0.885528 1.0 1.6 2.2 12 1.11 A

520 OFF 52995 0.05 1.0 1.8 2.4

6 521 ON 22/12/03 1.457910 0.8 1.8 2.3 12 2.01 A

522 OFF 52995 0.03 0.8 1.6 2.3

7 524 ON 23/12/03 0.883590 1.0 1.6 2.6 11 1.40 A

525 OFF 52996 0.03 1.0 1.8 2.7

8 527 ON 24/12/03 0.810224 0.8 1.6 2.1 11 1.18 A

526 OFF 52997 0.12 0.8 1.4 2.1

9 527 ON 24/12/03 0.881493 1.0 1.8 2.7 11 1.28 A

528 OFF 52997 0.03 1.0 1.6 2.6

10 529 ON 29/12/03 0.641424 2.0 2.6 4.3 11 1.54 A

530 OFF 53002 0.03 1.6 2.8 4.5

11 545 ON 14/02/04 1.078720 1.6 2.4 4.8 17 1.29 A

546 OFF 53049 0.05 1.4 2.2 3.7

12 547 ON 15/02/04 0.857716 2.9 2.4 4.0 12 0.94 R

548 OFF 53050 0.04 1.0 1.6 2.2

13 549 ON 16/02/04 0.842008 1.0 1.8 2.4 13 1.82 R

550 OFF 53051 0.04 1.2 2.0 2.8

14 551 ON 17/02/04 0.832683 1.0 1.6 2.3 18 1.97 A

552 OFF 53052 0.06 1.0 1.6 2.1

15 699 ON 13/12/04 0.644156 1.4 2.4 3.0 10 2.57 A

698 OFF 53352 0.04 1.2 2.0 2.7

16 701a ON 14/12/04 1.062420 1.2 2.0 2.8 17 0.92 A

700 OFF 53353 0.92 1.0 1.8 2.4

17 701a ON 14/12/04 0.632143 1.2 2.2 3.0 17 1.35 A

702 OFF 53353 0.03 1.2 2.0 2.6



OFF MJD

sigma deg. deg. deg. hrs. A/R

18 704 ON 16/12/04 1.051300 1.2 2.0 2.5 11 2.38 R

705 OFF 53355 0.06 1.2 2.2 2.8

19 706 ON 17/12/04 0.906069 1.2 1.8 2.4 11 1.80 A

707 OFF 53356 0.04 1.0 1.8 2.4

20 708 ON 18/12/04 0.911824 1.2 1.8 2.4 13 1.35 A

709 OFF 53357 0.05 1.0 1.8 2.4

21 719 ON 09/01/05 0.838306 0.8 1.6 2.0 15 0.76 A

718 OFF 53379 0.06 0.8 1.8 2.1

22 719 ON 09/01/05 0.829705 0.8 1.6 2.0 15 1.52 R

720 OFF 53379 0.10 1.0 1.8 2.5

23 722 ON 10/01/05 0.479412 0.8 1.6 2.1 18 0.30 R

721 OFF 53380 0.11 1.0 1.8 2.3

24 722 ON 10/01/05 0.894942 1.0 1.6 2.2 18 2.39 A

723 OFF 53380 0.06 1.0 1.8 2.4

25 724 ON 11/01/05 0.890838 0.8 1.6 2.0 12 2.13 A

725 OFF 53381 0.03 0.8 1.6 2.0

26 726 ON 12/01/05 1.225550 1.0 1.8 2.6 10 2.08 A

727 OFF 53382 0.03 1.0 2.0 2.9

27 829 ON 01/01/06 0.817315 1.2 2.0 2.6 12 1.52 A

830 OFF 53736 0.04 1.2 2.2 2.8

28 831 ON 02/01/06 0.814520 1.2 2.2 2.9 12 2.24 A

832 OFF 53737 0.01 1.4 2.2 2.9

29 833 ON 03/01/06 0.921368 1.6 2.8 4.3 12 1.60 R

834 OFF 53778 0.04 2.2 3.4 4.5

30 835 ON 04/01/06 0.482985 2.4 3.4 4.6 12 1.71 R

836 OFF 53779 0.02 2.0 2.6 3.5

31 872 ON 21/02/06 0.941015 1.4 2.4 3.0 11 0.81 A

873 OFF 53787 0.03 1.4 2.4 3.0

32 874 ON 22/02/06 0.970728 0.8 3.2 3.3 09 0.07 R

875 OFF 53788 0.01 1.7 2.4 2.9


Fig. 6.1: (a) Space angle distributions of events from Geminga source and unnormalized back-

ground,(b) Excess/deficit events distribution.

counts obtained are 121.4 154.4 which correspond to 0.75 level at 0.90 1.15 counts per

minute. The distribution of excess/deficit counts as function of space angle is shown in

fig-6.2(b). Similarly excess/deficit counts are calculated for each accepted run data and

details of each individual ON/OFF combination is shown in table-6.3. The RMS value of

the estimated -ray signal is taken as a measure of systematic error on the obtained signal.

The excess/deficit count rate or -ray signal from Geminga source obtained on different

observation days are shown in figure-6.3. The results of all accepted summed events are

shown in table-6.4. In this figure solid line is for Crab like source. The mean count rate

of all data show 1.15 level excess in 35.8 hours at 0.33 0.22 -ray per minute. The

excess signal or -ray rate obtained on different MJD shows variation and reason for this is

same as explained in the previous chapter. The variation of significance ( ) as function of

observation time (T) is shown in figure-6.4, which is expected to follow dependence

but does not indicate any steady increase in the obtained signal.

6.3 Search for Pulsed Emission

The monthly timing ephemeris of Geminga Pulsar have been derived using refined, phase-

connected, post-glitch ephemeris (Jackson

Halpern, 2005). The position (J2000) of


Table 6.3: GEMINGA ON OFF Excess/deficit analysis.

SN RUN N N

Norm. Dur.



161 107.3 1.47

2 164 1289 1259 1.02498 23.4 1290.4 -1.4 -0.06 -0.03

163 51.1 2.14

3 167 1579 1398 1.06582 39.6 1490.0 89.0 2.24 1.61

166 56.3 1.42

4 177 15070 19131 0.75844 109.8 4509.7 560.3 5.08 3.26

178 61.5 1.47

5 521 6223 7443 0.80553 66.4 5995.5 227.5 3.41 2.06

520 05.1 1.57

6 521 11137 7502 1.45791 120.6 10937.2 199.8 1.65 1.34

522 64.6 1.36

7 524 5762 6352 0.88359 84.0 5612.6 149.4 1.77 1.40

525 03.5 1.23

8 527 4794 5881 0.81022 70.8 4764.9 29.1 0.41 0.30

526 93.0 1.31

9 527 3541 4181 0.88149 76.8 3685.5 -144.5 -1.87 -1.70

528 82.4 1.07

10 529 2346 3829 0.64142 92.4 2456.0 -110.0 -1.19 -1.59

530 2.6 0.68

11 545 1811 2075 1.07872 77.4 2238.3 -427.3 -5.51 -6.72

546 65.0 0.84

14 551 19617 23934 0.83268 118.2 19929.4 -312.4 -2.64 -1.57

552 90.3 1.61

15 699 7694 13066 0.64416 154.2 8416.5 -722.5 -4.69 -5.69

698 14.5 0.74

16 701a 5838 5809 1.06242 55.2 6171.6 -333.6 -6.01 -3.04

700 111.3 2.01

17 701a 8407 13784 0.63214 81.0 8713.5 -306.5 -3.78 -2.34

702 118.0 1.46

19 706 12570 14981 0.90607 108.0 13573.8 -1003.8 -9.99 -6.21

707 157.7 1.57

20 708 11245 12348 0.91182 81.0 11259.2 -14.2 -0.17 -0.09

709 146.7 1.80


SN RUN N N

Norm. Dur.



718 116.4 2.53

24 722 22661 23942 0.89494 143.4 21426.7 1234.3 8.60 5.88

723 204.5 1.43

25 724 12955 14431 0.89084 127.8 12855.7 99.3 0.78 0.62

725 156.2 1.22

26 726 6707 5069 1.22555 124.8 6212.3 494.7 3.95 4.35

727 119.7 0.96

27 829 9738 11491 0.81731 91.2 9391.8 346.2 3.78 2.50

830 132.0 1.44

28 831 13201 16058 0.81452 134.4 13079.6 121.4 0.90 0.75

832 154.4 1.15

31 872 4310 4486 0.94102 48.6 4221.4 88.6 1.81 0.96

873 91.0 1.86

Fig. 6.2: (a)Space angle distributions of events from Geminga source and normalized background

runs,(b) Excess/deficit events distribution.


Fig. 6.3: Excess/deficit count rate from direction of Geminga source.

Fig. 6.4: Significance as function of observation time (data set[A]), solid line curve is for Crab like

source.


Table 6.4: Overall conclusion of GEMINGA ON-OFF analysis of data table-6.3.



Total excess 730.0 617.6

Total duration 2148.0 minutes

Rate/min 0.33 0.28

Significance 1.15

Table 6.5: Ephemeris of Geminga Pulsar.

PSR 0633+1746

RA ! " DEC ! " EPOCH 2000.0

PMRA ( ) 138.0 4 mas/yr

PMDEC ( ) 97.0 4 mas/yr

PX 6.3694 mas/yr

Distance 157pc

Geminga pulsar (RA ! " and DEC

! " ) was assumed for the

timing analysis. The reference data refer to MJD 50497.718748124877 and has been ex-

trapolated for periods of PACT observations (2000-2006). The period " !

sec and its first derivative =1.0970874194e-14 sec/sec were used to compute the Geminga

pulsar period and its derivative for observation span of PACT. Using these results, derived

ephemeris for the MJD51544.0 (January 1, 2000) are T0=0.23710043345 sec, =1.0970965974e-

14 sec/sec and for MJD 53736.0 (January 1, 2006), T0=0.23710251125 sec, =1.0971158260e-

14 sec/sec. Similarly monthly ephemeris for Geminga pulsar were calculated for each ob-

servation month and used in phase analysis.

After barycentric corrections by “Tempo” codes, absolute phase of each event obtained

using contemporaneous pulsar elements given in table-6.5. Reference phases are calcu-

lated over period of 3 hours centered with the transit time of Geminga pulsar at Pachmarhi

observatory in the steps of 20 minute interval for each run data. The rotational phase ( )

at observed arrival time was obtained for each event. Distribution (phasogram) of pulsar

phases is formed for each observation data. We searched for modulation at Geminga pul-

sar frequency by folding all arrival times (phases) in a 20 phase bin histogram. A typical

phasogram obtained without any cuts on event selection is shown in figure-6.5


Table 6.6: Modified Geminga Pulsar Phase Intervals.

Region Phase interval

First Pulse P1 0.565 - 0.765

Inter-region(Bridge) 0.765 - 0.065

Second Pulse P2 0.065 - 0.260

background(Off pulse) 0.260 - 0.565

Like Crab pulsar analysis, phasograms are also obtained with constrains on space angle.

Only those events were used for signal detection for which space angle ( ) is

2.5 degree.

Cuts are applied on the number of telescopes (NDF) 8 and on the goodness of fit param-

eter ( ). These cuts for data set(A) and data set(B) were kept same that of Crab source

data analysis. The summary of phasograms for these events are shown in table-6.7 (data

set-A) and table-6.8 (data set-B) respectively. The subsequent columns in these tables cor-

responds to events with space angle " " " and " respectively.

The reference data for Geminga pulsar phase profile are taken from results of EGRET ob-

servation by (Fierro 1995) which are given in table-6.6. The phasogram is divided into 4-

regions, as defined by the EGRET results. These are, first pulse (P1) corresponds to phase

interval of 0.565-0.765, Inter-region or Bridge:0.765-0.065, second pulse (P2):0.065-0.260

and 0.260-0.565 for background. Pulsed emission of radiation is expected at phases corre-

sponding to First (P1) and Second (P2) pulse intervals. The number of events with phases

within the P1 and P2 intervals constitutes the number of ON pulsed events (N ). The

background events (

) are obtained by adding all events in the background region and

normalized by multiplying the ratio of ranges spanned by the pulse and non-pulse regions.

The statistical significance of the excess counts is calculated using equation-5.3 ( Li

Ma, 1983).

The number of counts for first pulse (P1), bridge-region, second-pulse (P2) and back-

ground regions are calculated in the respective phase intervals which are given in table-6.7

(data set(A)) and table-6.8 (data set(B)) respectively. The pulse emission rate per minute is

estimated from the excess counts of P1 and P2 interval regions. Phasograms of all episodi-

cally added data for set(A) and set(B) for NDF 8 at " are shown in figure-6.6 and

figure-6.7 respectively. A further cut on space angle is applied to narrower the acceptance

angle, to reject OFF-axis events in pulsar phasogram. In continuation of this, phasograms

at space angle " " and " are added episodically which are shown in figure-6.6

and figure-6.7 for data set(A) and data set(B) respectively. An increase in the significance

is seen when tight cuts are applied on the selection of events for space angle less than 2.5


Fig. 6.5: Distribution of phases of Geminga pulsar without any cuts on event selection[data set(A)].

Table 6.7: Details of Phase analysis of Geminga pulsar (Data set[A]).


Duration(min.) 3384.9 3384.9 3384.9 3384.9

Main Pulse(P1) 52775 43945 31406 16820

Inter-region 79013 65710 46661 25049

Inter Pulse(P2) 53085 43861 31097 16440

Background 79184 65706 46472 24429

N 105860 87806 62503 33260

N

105578.7 87608.0 61962.7 32572.0

P2/P1 1.01 1.00 0.99 0.98

Rate (rms) 0.083 0.147 0.059 0.134 0.160 0.113 0.203 0.082

Significance( ) 0.57 0.44 1.42 2.49


Fig. 6.6: Distribution of phases of Geminga pulsar at different space angle (data set[A]).

Table 6.8: Details of Phase analysis of Geminga (Data set[B]).


Duration(min.) 2629.5 2629.5 2629.5 2629.5

Main Pulse(P1) 16786 13276 9075 4705

Inter-region 25328 20020 13619 7036

Inter Pulse(P2) 17031 13458 9104 4764

Background 25559 20092 13657 7161

N 33817 26734 18179 9469

N

34078.7 26789.3 18209.3 9548.0

P2/P1 1.01 1.01 1.00 1.01

Rate (rms) -0.100 0.107 -0.021 0.095 -0.012 0.078 -0.030 0.057

Significance( ) -0.93 -0.22 -0.15 -0.53


Fig. 6.7: Distribution of phases for Geminga pulsar at different space angle[data set(B)].

degree. This increase in significance ( ) as function of space angle is shown in figure-6.8

for two data sets.

The variation in the statistical significance of Geminga pulsar events as function of

event rate for all observations of six year data set(A) and set(B) are shown in figure-6.9

and figure-6.10 respectively. No correlation between significance ( ) and trigger rate is

seen in both sets of the Geminga pulsar data. The distribution of significances of indi-

vidual run data compared to the mean and having zero and sigma equal to one. These

distributions for space angle " " " and " are shown in figure-6.11 and

figure-6.12 for data set(A) and set(B) respectively. Mean and (standard deviation) for

these distribution are shown in each figure.

Prior to discovery of 237 ms rotation period of Geminga pulsar, claimed had been made

for various periods in the range of 59-60 sec in the TeV -rays. To check the modulation

of pulsar events at this rotation period, T0=61.940673828 sec and =4.3322008251e-09

sec/sec at MJD 50753 (Neshopr

Stepanyan 2001) were used as reference ephemeris

data. The pulsar period and its derivative for our observations span were derived. The ob-

tained period and its derivatives are: T0=62.237478007 sec, =4.3637217098e-09 sec/sec

for MJD 51544 and T0=63.075039854 sec, =4.4819617087e-09 sec/sec for MJD 53736.


Fig. 6.8: Variation of significance with space angle.

Fig. 6.9: Significance as function of trigger rate[data set(A)].


Fig. 6.10: Significance as function of trigger rate[data set(B)].

Fig. 6.11: Distributions of significance( )[data set(A)].


Fig. 6.12: Distributions of significance( )[data set(B)].

The phasograms for each observation data were obtained using these pulsar periods with

20 phase bins and results of analysis compared with 237ms period. No significant differ-

ence in have been found between these two periods. The significance level is within the+ ) ' level of background counts therefore no periodicity is seen in Geminga pulsar

data at 61-63 sec periods.

With refined ephemeris, there is slight improvement in the excess counts at P1 and P2 of

phasogram than earlier post-glitch ephemeris. A comparison between significances ob-

tained with these two post glitch ephemeris is shown in figure-6.13. From this figure, it

is seen that though excess signal is within the fluctuation limit of background counts but

there is good agreement between two results up to data of year 2003. After this, difference

increases because a possibility of another glitch (Jackson

Halpern 2005) during year

2003 and 2004 make ephemeris data provisional after 2003.

6.3.1 Statistical test

The test for the possibility of pulsar photon modulations is conducted on the binned data.

The of phasogram as explained in chapter-4, for each individual run data at different

phase (20 bin) are calculated. These are checked for first pulse (P1) and second-pulse

(P2) and compared with the background counts. The per dof at P1, P2 and background-


Fig. 6.13: A comparison of significances obtained with two post glitch ephemeris.

Fig. 6.14: distribution of Geminga light curve, (a) On-source, (b) Off-source[data set(A)].


Fig. 6.15: distribution of Geminga light curve[data set(B)].

region are calculated from light curves of Geminga on-source and off-source (background)

data, which are shown in figure-6.14 for data set(A). Similar, test was applied for data

set(B) also and results are shown in figure-6.15. The average per dof for data set(A) of

on-source at P1, P2 and background regions are 1.09, 0.88 and 0.83 for " . Similarly,

average per dof for data set(A) of off-source at P1, P2 and background regions are 0.92,

0.88 and 0.93 . The results of test on these phase bins (P1

P2) do not indicate any large

at rotational period of 237 ms for Geminga pulsar events in TeV energy band. Similar

results were obtained for data-set(B) also.

6.4 Upper Limit on Pulsed Flux of -rays

The Geminga pulsar data collected during 2000-2006 have been analyzed for the search

of steady and pulsed emission at TeV energy. Since in this case also the detected pulsed

signal is within the fluctuation limit of background counts therefore only upper flux limits

have been determined. The + ) ' error of excess rates are converted to flux units as

explained in previous chapter (equation-5.4). At TeV energy, the pulsed -ray signal ob-

served from Geminga pulsar is 2.49 . The upper limits on flux have been derived for the

phase regions defined according to EGRET peak regions. The collection area 1.45

m for the showers near zenith at 825 GeV threshold energy has been used for the estima-


Fig. 6.16: Upper limit on integral flux of Geminga pulsar detected by ground observations.

tion of integral flux at PACT threshold energy. The time averaged -ray flux obtained

for Geminga pulsar [data set(A)] at 3 upper limit is $ " - -*/ )%+ ) ,+ .This flux corresponds to events for which space angle is

1.0 degree. Similarly time

averaged -ray flux are obtained for Geminga pulsar data set(B) at 3 upper limit is

$ " - -*/ )%+ ) ,+ . Figure-6.16 shows the upper limit on integral -ray pulsed

flux as a function of energy by various ground based observations and PACT result for data

set(A). The present 3 upper limit of PACT data is within the upper limits quoted by Whip-

ple and HEGRA group at 1 TeV energy.

Chapter 7

Summary

This thesis is based on an observational study of very high energy -ray emissions from

Crab and Geminga pulsars. Source data were collected between 2000-2006 using Pach-

marhi array of Cherenkov Telescopes, which is designed for the search of celestial -rays

in the TeV energy band. An introduction about pulsar has been briefly outlined, which in-

clude general characteristics and pulsed emission mechanism. Of the two pulsar emission

models, polar cap and outer gap, the motivation for pulsar observation at high energies is

from outer gap model. According to this model the spectral cut-off in high energy emission

is more gradual than magnetic attenuation mechanism of polar cap model. The light curves

of 7 -ray pulsars observed by EGRET have been described and their double peak profiles

discussed. The pattern of light curve gives us a direct view of the origin of high energy

photons and beaming nature of radiation. To distinguish emission processes in different

energy bands, multi wavelength light curves and energy spectrum of these pulsars were

also discussed. The investigation of pulsar light curves at different energies probe directly

into the radiation mechanism as well as the region from where these radiations originate

through direct interaction between particles, photons and Electromagnetic field of pulsar

magnetosphere.

The Atmospheric Cherenkov technique for detecting primary -rays and cosmic rays (pro-

tons) have been studied and various features of Cherenkov radiation were explained. A

brief description of two complimentary methods of detection of -rays using wave-front

and Imaging system is also included. The wave front sampling technique is presently used

in Pachmarhi experiment for -ray detection against cosmic ray background. A detailed

description of the experimental setup of PACT array has been given to elaborate the system.

The method of data analysis, various calibrations of detector and data acquisition system

were also discussed. The results of Monte Carlo simulations carried out for PACT array

using CORSIKA package have been discussed to obtain the detector response to primary

-ray and cosmic-ray (proton) particles. The energy threshold for vertically falling -rays

173

Chapter 7. Summary 174

Table 7.1: Crab Pulsar

Data Set (A) Data Set (B)

Significance ( ) 2.48 1.13

3 upper limit 9.8 7.2

- -*/ %+ ) ,+

Table 7.2: Geminga Pulsar

Significance ( ) Data Set (A) Data Set (B)

2.49 -0.57

3 upper limit 28.2 18.9

- -*/ %+ ) ,+

at PACT array is found to be 750 GeV. The collection area for vertically falling -rays

at PACT threshold energy was estimated to be 1.40

m . Most of observations used in

search of steady as well as pulsed signal were carried out within 15 degree range of zenith

angle. Since energy threshold and collection area vary with zenith direction of shower axis,

therefore average values of energy threshold and collection area were calculated in zenith

range of observations. The average value of energy threshold and collection area are 825

GeV and 1.45

m . These values were used in the estimation of upper limit on the time

averaged integral flux of -rays from Crab and Geminga pulsars, using the excess events

over the background.

For periodicity analysis, various barycentric correction terms have been studied and used

for converting arrival times of pulsar photons to solar barycentric position. “Tempo” code,

which was originally developed for radio pulsar analysis, various key parameters set for -

ray band and prediction mode (‘tz’) have been used for correction in arrival times. Monthly

Crab ephemeris (P,

, Epoch) were extracted from Princeton Crab time database. Since

Geminga pulsar is not yet detected strongly in radio wavelength, its monthly ephemeris

is not available. The reference data for Geminga monthly ephemeris were taken from the

post-glitch parameterization of pulsar elements by Jackson

Halpern (2005).

The data bank of Crab and Geminga sources have been divided for steady and pulsed

signal analysis. A total of 105 hours of data on Crab pulsar and 70 hours on Geminga

pulsar were collected. After applying preliminary cuts, approximately 89.4 hours and 56.1

hours of data were analyzed from these sources for search of pulsed emission. To have bet-

ter signal to noise ratio, all the data were added. Since the detected signals in both sources

were within the fluctuation limit of background region, only upper limits on flux levels


could be set. The time averaged integral flux of pulsed -rays from Crab and Geminga

pulsars at threshold energy of PACT (825 GeV) are summarized in table-7.1 and 7.2 re-

spectively. No evidence of pulsed emission of -rays from these pulsars were seen in our

data at the pulsar period as observed at lower energies. It was assumed that, the light curve

to be same as that at lower energies and signal is confined to the phase region as defined

by the EGRET detector. A weak signal of 2.48 excess of events over the background was

obtained in the case of Crab Pulsar. Jackson et al. (2002) had reported that Geminga pulsar

underwent a minor glitch during late 1996 and derived a phase-connected ephemeris span-

ning the years 1973-2000. The Geminga data have been analyzed both by using pre-glitch

and post-glitch pulsar elements extrapolated to our epoch of observation. Our observation

of Geminga pertains to post-glitch period. For Geminga also, a weak signal of 2.49 ex-

cess of events over the background was obtained. The obtained pulsed signal have been

compared with the other ground based observations, which are shown in figure-5.17 and

figure-6.16 respectively. Present PACT results are consistent with other recent results ex-

cept for Geminga. Recently, Neshpor et al. have reported pulsed emission of ultra high

energy -rays from this object based on their observations during 1996-97. The conflicting

results on the pulsed emission of -rays from Geminga may be attributed to the variability

of the source.

The obtained signals of steady emission from Crab nebula, do not show any acceptable

results. The excess signal obtained on different MJD showed large variations. The major

reasons for the anomalies on results of steady emission are difference in triggering effi-

ciency, cosmic ray rejection factor and large systematics present in acquired data. Data

collection was done in stretch, lasting for 1 to 3 hours, first either ON-source and followed

by OFF-source region with equal exposure or vice versa during same night. The ON-OFF

observations were conducted during same night to minimize the effect of sky condition on

data. During observations, the gains of all PACT telescopes are equalized by adjusting high

volatges to PMT’s. Due to variation in sky condition as well region of sky, high voltages

to PMT’s and discriminator threshold for 4-fold trigger logic are varied during runs. The

change of PMT high voltage, discrminator thresholds and sky brightness alter the trigger-

ing efficiency for a pair of run and results in large difference in number of data events. In

some cases, presumbly due to sky conditions during runs, this difference in the number of

events do not vanish even after normalization of background data for trigger efficiences.

These manifestations result in large excess or deficit events, when one subtract the normal-

ized background data from On-source data. The second reason is the cosmic ray rejection

factor used in search of excess counts. Though, in present method of detection of -rays in

presence of isotropic cosmic rays, rejection is 15 but it varies from run to run and could


be seen in space angle profiles. Figure-5.4 and 6.3 show large variation on obtained excess

rates and cumulative significances do not follow expected Crab signal shown in figure-5.5.

To verify the technique used for search of steady signal, few fictitious source observations

were also carried out. The result of fictitious source data given in table-4.6 is an excess

rate 0.86 0.62 per minute and this gives an idea of systematic error. The uncertainty about

a key parameter of the shower, which is a location of axis of detected Cherenkov shower

front, add further systematic to results. In the pulsed analysis, cosmic-ray rejection is better

by a factor of 4 5 as pulsed signal is confined in P1 and P2 (total 5 bins out of 20 bin pha-

sogram) phase-region only. The lateral distribution of Cherenkov photons is linear up to

120 meter from shower core and then starts decreasing as shown in figure-4.16(a) for -ray

photons. QDC’s (charge to digital converters) have been used for measuring Cherenkov

photons density at each detector. The density of incident Cherenkov photons and hence

primary energies of -rays have been recorded by QDC. A higher energy shower whose

axis is far from telescope array would give almost same QDC values as of a lower energy

shower with axis near the array (see figure-4.16(a) and 4.16(b)). Therefore, for any given

energy there is large spread in QDC values. Hence, it was not possible to estimate the

energies of primary -rays without locating the shower axis.

Future Prospects: The major Atmospheric Cherenkov detectors have scanned

the -ray sky up to 100 GeV energy. These detectors are still under development and

intended to bring down their energy threshold of detection via either increasing collec-

tion area or setting up their detectors at high altitude. In continuation of this, High Al-

titude Gamma Ray Observatory (HAGAR), a joint program of TIFR and IIA at Hanle

(Longitude=78.9 , Latitude=32.8 , Altitude=4300 m) is in development stage and designed

to achieve energy threshold of few tens of GeV. Observation of -ray pulsars at this energy

band is sufficient to fill up the gap between satellite ( ) and ground based obser-

vations ( ) to confirm the emission cutoff and discriminate between Polar cap

and Outer gap models of pulsed emission.

Bibliography

http://cossc.gsfc.nasa.gov/docs/cgro/images/epo/gallery/pulsars/

http://veritas.sao.arizona.edu/photo/

Abdo, A.A. et al., 2007, ApJ, 664, L91-L94

Acharya, B.S. et al., 1993, Journal of Physics G, 19, 1053

Acharya, B.S. et al., 2003, In 28

ICRC ,OG 2.2

Asahara, A. et al., 2004, Nuclear Instruments and Methods in Physics and Research

Bertsch, D.L. et al., 1992, Nature, 357, 306

Becker, W., Helfand, D.J. and Szymkowiak, A.E., 1982, ApJ, 255, 557

Boley, F.I., 1964, Review of Modern Physics, 36, 792

Bhat, P.N. et al., 2002, Bulletin of Astronomical Society of India, 30, 135-145

Bhat P.N., 1998, In Proceedings of the International Colloquium to commemorate the

Golden Jubliee year of Tata Institute of Fundamental Research, Ed. P.C.Agrawal and

P.R.Vishwantah, University Press, 370

Bhat, P.N. et al., 1990, Nuclear Instruments and Methods in Physics and Research,

A292, 494-504

Bose, D., 2007, PhD thesis, TIFR (Deemed University)

Bose, D. et al., 2007, Astrophysics and Space Science, 309, 111

Bennett, K. et al., 1977, A

A, 56, 469-471

Bignami, G.F., Caraveo, P.A. and Lamb, R.C., 1983, ApJ Letter, 272, L9

Bignami, G.F. et al., 1987, ApJ, 319, 358

Bignami, G.F. and Caraveo, P.A., 1992, Nature, 357, 287

Bowden, C.C.G. et al., 1993, Journal of Physics G, 19, L29-L31

Bhat, P. N. et al., 1986, Nature, 319, 127

Caraveo, P. A. et al., 2004, Science, 305, 376

Cheng, K.S., Ho, C. and Ruderman, M.A., 1986a, ApJ, 300, 500

Cheng, K.S., Ho, C. and Ruderman, M.A., 1986b, ApJ, 300, 522

Carraminana, A. et al., 1995, Advances in Space Research 15, 65

Chitnis, V. R. et al., 2005, In Proceedings of 29

ICRC, Pune (India), 5, 235

Chitnis, V.R. and Bhat, P.N., 2002, Bulletin of Astronomical Society of India, 30,

177

BIBLIOGRAPHY 178

345-349

Chitnis, V.R. and Bhat, P.N., 2002, Experimental Astronomy, 13, 77-100

Cawley, M.F. et al., 1990, Experimental Astronomy, 1, 173

Cawley, M.F. et al., 1985, In Proceedings of 19 ICRC, La Jolla, 1, 173

Cowsik, R. et al., 2001, In Procedings of the 27

ICRC, Hamburg, OG2.05, 2796

Chudakov. A.E. et al., 1963, In Proceedings of the 8

ICRC, Jaipur, 4, 199

Daugherty, J.K. and Harding, A.K., 1982, ApJ, 252, 337

Daugherty, J.K. and Harding, A.K., 1984, ApJ 429, 325

Duncan Lorimer and Michael Kramer, 2005, Handbook of Pulsar Astronomy, Cam-

bridge

Daugherty and Harding, 1995, arXiv:astro-ph/950855 v2 1Sep 1995

Dowthwaite, J.C. et al., 1984, ApJ Letters, 286, L35

Erber, T., 1966, Review of Modern Physics, 38, 626

Fierro, J.M. et al., 1993, ApJ, 413, L27

Fichtel, C.E. et al., 1975, ApJ, 198, 163

Fierro, J.M., 1995, PhD thesis

Francis, A. Jenkins and Harvey E. White, 1981, Fundamentals of Optics, IV

ed.

Fazio, G.G. et al., 1972, ApJ. 175, L117

Glendenning, N.K., 1992, Phys. Rev. D46, 4161

Gold, T., 1968, Nature, 218, 731

Grenier, I.A. et al., 1990, In Proceedings of the Conference on the High Energy Gamma

Ray Astronomy, Ed. J. Mathews, New York, 220, 3

Galbraith, W. and Jelly, J.V., 1953, Nature, 171, 349

Greisen, K., 1956, Progress in Cosmic Ray Physics, 3,1

Gandhi, V.N., 1992, PhD thesis, University of Bombay, Unpublished

Gupta, S.K. et al., 1985, Astrophysics and Space Science, 115, 163

Gothe, K.S. et al., 2000, Indian Journal of Pure

Applied Physics, 38,269

Gothe, K.S. et al., 2002, Bulletin of Astronomical Society of India, 30,397-402

Goldreich, P. and Julian, W.H., 1969, ApJ, 245, 267

Grindlay, J.E., 1972, ApJ Letters, 174, L9

Gupta, S.K. et al., 1978, ApJ, 221, 268

Gibson, I.A. et al., 1982, Nature, 296, 833

Halperin, J. and Holt, S., 1992, Nature, 357,222

Harding, A.K., 1981, ApJ, 245, 267

Hofmann, W. et al., 2003, In Proceedings of 28

ICRC, Tsukuba, 2811

Hillas, A. M., 1996, In Proceeding of TeV Gamma-ray Astrophysics, (Heidelberg), 17

BIBLIOGRAPHY 179

Hillas, A.M., 1985, In Proceedings of 19

ICRC, La Jolla, 1, 1455

Heck, D. et al., 1998, Report FZKA 6019, Forshungszentrum, Karlshruhe

Hoyle, F., Narlikar, J.V. and Wheeler, J.A., 1964, Nature, 203, 914

Halpern, J.P. and Tytler, D., 1988, ApJ, 330, 201

Jelly, J.V., 1967, In Proceeding of Elementary Particles and Cosmic Ray Physics, IX,

North Holland, Ed. Wilson and Wouthuysen, 41-159

Jelly, J.V., 1958, Cherenkov Radiation and its applications, Pergamon Press

Jackson, J.D., 1975, Classical Electrodynamics, John Wiley

Sons, New York

Juan Cortina, astro-ph/0407475

Jackson, M.S. et al., 2002, ApJ, 578, 935-942

Jackson, M.S. and Halpern, J.P., 2005, ApJ, 633, 1114-1125

Kanbach, G. et al., 1994, A

A, 289, 855

Kuiper, L. et al., 1999, A

A, 351, 119-132

Kubo, H. et al., 2004, In New Astronomy Reviews

Konrad Bernlohr, 2000, ApJ, 12, 255-268

Kildea, J. et al., 2003, In Proceedings of 28

ICRC, Universal Academy Press,

2377-2380

Kuzmin, A.D. and Losovskii, B.Y., 1997, Astronomy Letters, 23,283

Kildea, J. et al., 2005, In Proceedings of 29

ICRC, 4, 89-92

Lattimer, J.M. and Prakash, M., 2004, Science, 304, 536-542

Lewin, W. et al., 1993, Space Science, 62, 223

Lattimer, J.M, 1990, ApJ, 340, 426

Longair, M.S., 1981, High Energy Astrophysics, Cambridge Univ. Press

Lessard, R.W. et al., arXiv:astro-ph/9912520 v1 27Dec 1999

Leo, R. William, Technique for Nuclear and Particle Physics Experiment

Lopez, M. et al., 2005, In Proceedings of 29

ICRC, Pune(India)

Li and Ma, 1983, ApJ, 272, 317-324

Mayer-Hasselwander, H.A. et al., 1994, ApJ, 421, 276

Martinez, M. et al., 2003, In Proceedings of 28

ICRC, Tsukuba, 2815

Michael Zeilik, 2002, Astronomy-The Evoluing Universe, 9

ed., Cambridge Univer-

sity

Majumdar, P. et al., 2003, Astroparticle Physics, 18, 339-349

Majumdar, P., 2003, PhD thesis, University of Bombay, Unpublished

Malofeev, V.M. and Malov, O.I., 1997, Nature, 389,697

Mattox, J.R., Halpern, J.P. and Caraveo, P.A. 1998, ApJ, 493, 891-897

Mattox, J.R. et al., 1992, ApJ Letter, 401, L23

BIBLIOGRAPHY 180

Masterson, C. et al., 2005, In Proceedings of 29

ICRC, 4, 143-146

Musquere, A. et al., 1999, In Proceedings of 26

ICRC, Salt Lake city, OG 2.05

Nolan, P., Arzoumanian, Z., Bertsch, D.L., 1993, ApJ, 409, 697

Naurois, de. et al., 2002, ApJ, 566, 343-357

Neshpor, Yu.I. et al., 2001, Astronomy Letter, 27, 228, p-613 (Erratum)

Neshpor, Yu. I. and Stepanyan, A.A., 2001, Astronomy Letters 27(12), 794-798

Oser, S. et al., 2001, ApJ, 547, 949-958

Otte, A.N. et al., 2007, In Proceedings of 30

ICRC, Merida (Mexico)

Pacini, F., 1968, Nature, 219, 145

Ramanamurthy, P.V., Bertsch, D.L., and Dingus, B.L., 1995, ApJ, 447, L109

Ruderman, M.A. and Sutherland, P.G., 1975, ApJ, 196, 51

Rao, M.V.S. and Sinha, S., 1988, Journal of Physics G, 14, 811-827

Rodney Hiller, 1984, Gamma Ray Astronomy, Oxford University Press, New York

Rene A. Ong, 1998, Physics Reports, 305, 93-202

Robin M. Green, 1985, Spherical Astronomy

Richards, D.W. and Comella, J.M., 1969, Nature, 222,551

Sturrock, P.A., 1971, ApJ, 164, 529

Swanenburg, B.N. et al., 1981, ApJ Letters, 243, L69-L73

Smart, W.M., 1977, Spherical Astronomy

Smith, F.G., 1977, Pulsars, Cambridge University Press

Sinha, S., 1987, PhD thesis, University of Bombay

Staelin, H. and Reifenstein, 1968, Science, 162, 1481

Shitov, Yu. P. and Pugachev, P.D., 1997, New Astronomy 3, 101

Singh, B.B. et al., 2005, In Proceedings of 29

ICRC, 4, 191

Sinitsyna, V.G. et al., 2007, In Proceedings of 30

ICRC, Merida (Mexico)

Thompson, D.J., Azoumanian, Z. and Bertsch, D.L., 1992, Nature, 359, 61

Tuneyashi, K. and Yutaro, S., 1994, In Proceedings of “ Towards a Major Atmospheric

Cherenkov detector-III”, Ed. T. Kifune, Universal Academy Press, Tokyo, 25-27

Thompson, D.J. et al., 1977, ApJ, 213, 252

Thompson, D.J, 2004, In Proceedings of Young Neutron Stars and Their Enviroments,

IAU Symposium, 218

Thompson, D.J., arXiv:astro-ph/01011039 v1-3, Jan. 2001

Tanimori, T. et al., 1995, In Proceedings of Towards a Major Cherenkov Detector-IV,

316

Tickoo, A.K. et al., 1999, Experimental Astronomy, 9, 81-101

Taylor, J.H., Manchester, R.N. and Lyne, A.G., 1993, ApJ, 88, 529

BIBLIOGRAPHY 181

Toor, A. and Seward, F.D., 1974, Journal of Astronomy, 79, 995

Upadhya. S.S. et al., 2002, Bulletin of Astronomical Society of India, 30, 411-416

Vishwanath, P.R., 2002, Journal of Astronomy and Astrphysics, 23, 45-51

Vishwanath, P.R et al., 2005, In Proceedings of 29

ICRC , 4, 197-200

Wakely, S.P. et al., 2003, In Proceedings of 28

ICRC, Tsukuba, 2803

Weekes, T.C. et al., 1989, ApJ, 342, 379

Weekes, T.C. and Turver, K.E., 1997, In Proceedings of 12

ESLAB Symposium, 279

Wilson, R.B. et al., 1993, In Isolated Pulsars, Ed. K Van Riper, R. Epstein

C. Ho,

Cambridge Univ. Press, p257

A Thesis Submitted to the Department of Physics Banaras Hindu University, Varanasi...

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