Characterization of Orbiting Wide-angle Light-collectors (OWL)

By:Rasha Usama Abbasi

OUTLINE Motivation Shower Generation and

Reconstruction OWL Simulation Study

Quality cuts Energy and Angular resolution Aperture calculations

OWL optical simulation and design Conclusion

Unsolved problems in Ultra-High Energy Cosmic Rays.

Motivation Origin of these rays. Acceleration mechanism. Determine Energies, chemical composition,

arriving direction . Discovering cosmic rays > Greisen-

Zatsepin-Kuzmin (GZK) cut off 6×1019 eV. Propagation through CMBR ?

Experiment

Fly’s Eye

AGASA

HiRes Auger OWL

Energy range (eV)

1017

6×1019

1018

1.5×1020

1017

4×1020

1019 1021

1019 1022

EnergyResolution

20 % 30 % < 20% 25% 14%

Aperture (km2-str)

40 @ 1020 eV

200 104 7000/array

3×106

Duty cycle 10% 100% 10 % 100% 10%

Events/year 0.4 2 10 70/array

3000

Comparison of UHECR Experiments

OWL Two satellites 1000 km height and 500 km

separation View common volume of the

atmosphere Tilted near the nadir point Obtain a large field of view

FOV with ~106 pixels, ~106 km2

sr

Inclined air shower

Shower Generation

Geometry generation Shower core : randomly simulated location could lie

outside the Field Of View (FOV) of the detector.

Shower direction: randomly simulated isotropic direction

Energy generation Energy is generated with several set of

fixed energies.

Shower generation

Profile generation Profile simulation is based on Gaisser-

Hillas (G-H) parameterization.

)exp()()( max)max(

max

max XX

XX

XXNN OXX

O

O

e

Xo :the point of the first interaction (g/cm2) simulated with an exponential function.

Xmax : the point of the maximum development of the shower (g/cm2) sampled from a Gaussian function.

: constant 70 g/cm2 .

: shower size at maximum.

)exp()()( max)max(

max

max XX

XX

XXNN OXX

O

O

e

maxN

Simulated event

Y-axis angular position vs. X-axis angular position

Pixel size is 0.07o , FOV on ground is 1km2/pixel

OWL Simulation Study

Goals of my study Aperture of the detector Number of events collected each year Energy and Angular resolution

Reconstruction Plane Reconstruction

Determines the Shower Detector (SD) plane that contains the detector and the shower track which depends on the triggered pixel direction.

Plane Reconstruction

N

ii

iiSnn

12

2 )ˆˆ(

n̂

in̂

2

i

iS

: normal to the plane.

:direction of the pixel

:number of photoelectrons triggering the pixel .

:angular error of the pixel ~ 0.07 0 .

Minimizing

Track Reconstruction Track

reconstruction SD’s depends on

triggered tube direction

Intersection between the SD planes of the

orbiting detectors.

Track Reconstruction fit for the 1st and 2nd

eye .

Time (micro seconds) vs. Θ (in degrees)

Profile Reconstruction

Profile reconstruction

Minimizing between the signal that is produced by the shower and detected in the pixels.

2

pfl

N

ii

p

i

m

i

pfl1

2

2

2 )(

Profile Reconstruction

N

ii

p

i

m

i

pfl1

2

2

2 )(

m

i

p

i

2

i

:number of photoelectrons detected per each pixel

:number of photoelectrons predicted by trial simulated event.

:error by adding Poisson fluctuation and ground light noise.

Observed shower profiles

Pe/ 1deg / m2 vs. Xmax (gm/cm2)

Reconstruction of the simulated event

Energy

Direction

Composition (Xmax)

Quality cuts

Optimization between best fractional energy, and angular error while maximizing a usable reconstructible aperture.

Energy and angular resolution

Quality cuts

Zenith angle of the shower > 930

Opening angle between the reconstructed SD’s planes >100

122 ndof

Quality cuts

Track length > 0.70

Geometry of the track

Photoelectron per good tube > 5.2

Low energy events and noise sources

Quality cut

Energy resolution vs. track length for a simulated shower

Energy resolution histogram 3×1019 eV

•Number of events vs. Fractional energy error 14% shift in the mean

Energy resolution histogram 1×1020 eV

•Number of events vs. Fractional energy error -2% shift in the mean

Energy resolution histogram 3×1020 eV

•Number of events vs. Fractional energy error -3% shift in the mean •Energy resolution gets better with higher energies

Angular resolution histogram 3×1019 eV

•Number of events vs. Angular error (deg)

•Half of the events are better than 0.9o

Angular resolution histogram 1×1020 eV

•Number of events vs. Angular error (deg)

•Half of the events are better than 0.6o

Angular resolution histogram 3×1020 eV

•Number of events vs. Angular error (deg)

• Half of the events are better than 0.3o

•Angular resolution also gets better with higher energies

Aperture calculation

To calculate the aperture we need to find.

First the Generation aperture 22RAgen

)(500 boundarylocationcoreofradiuskmR

srkmAgen

26105.2

Aperture calculation

eventsgenerated

eventstriggeredAA

gentrig #

#

Find the triggered aperture (Monte Carlo integration)

Find the reconstructed aperture

eventstriggered

eventstedreconstrucAA

trigrec #

#

Trigger Aperture

Aperture (×106 km2 sr) vs. Log(E(EeV)) Note: that it saturate at 2.4×106 km2 sr

Reconstruction Aperture

Aperture (106 km2 sr) vs. Log(E(EeV))

Large drop between the trigger and the reconstruction aperture at 3×1019eV because there is not enough photoelectrons to fit it to the G-H function (can not find minimum because of insufficient SNR).

Knowing that

The assumed flux j(E) is taken from Fly’s Eye spectrum, extrapolated to beyond 1020 eV.

)()( EjEATEN

Number of events per energy bin.

Fly’s Eye stereo spectrum

The number of events collected by the detector in a year duration (10% duty cycle) of time that holds energies between

Ei = 5 × 1019eV and Ef = 3 × 1020 eV

is equal to 2376 events.

fE

iE

dEEjEATN )()(

Number of events per energy bin.

Log(E(Eev))

#events Log(E(Eev))

#events

1.7 805 2.6 24

1.8 544 2.7 16

1.9 368 2.8 11

2.0 249 2.9 7

2.1 168 3.0 5

2.2 114 3.1 3

2.3 77 3.2 2

2.4 52 3.3 2

2.5 35 3.4 1

Number of events per energy bin.

From the simulation results

Angular resolution ( 0.3o 0.9o ) .

The directional accuracy of OWL is comparable to HiRes.

OWL does not provide us with an astronomical quality accuracy.

i.e. important for ID and sources.

From the simulation results

Although the threshold of the trigger aperture is ~ 1×1019 eV, the threshold of the reconstructed aperture is much higher ~ 4×1019 eV

High threshold is problematic: not knowing how the detector acts in low energies will compromise the accuracy of our experiment.

OWL optical simulation Construct a photon-by-photon ray

tracing simulation. Use the ray tracing simulation to

characterize the proposed system. Without a Schmidt corrector plate. With a Schmidt corrector plate.

Comparison.

OWL optics Wide angle viewing

camera (400 FOV)

Pixel size is 0.070, 4.4mm on the focal

plane with FOV of (1km2/pixel) on the ground.

OWL optics

Spherical mirror (7.1 m diameter , 6.0 m radius of curvature). Spherical focal plane surface ( 3.0

m radius of curvature, 3.15 m focal length and 2.3 m diameter)

3.0 m corrector plate with an aspherical front and a planer back surface .

Schmidt camera geometry

Lego plot (m) without the corrector, angle of incidence =00

~18 pixels across each side

Note: coma

Lego plot (m) without the corrector, angle of incidence =100

~18 pixels across each side Note: coma

Corrector plate The profile of the corrector plate is

T(r) : thickness of the corrector plate at a radial

distance r from the center f: focal length of the mirror n : the refractive index of the plate

Rd: the radius of the entrance from center

32

24

)1(32

)()0()(

fn

ArrTrT

22

3dRA

Lego plot (m) with the corrector plate, angle of incidence =00

The size of the center is comparable to a pixel

Lego plot (m) with the corrector plate, angle of incidence =100

The size of the center is comparable to a pixel

Number of particles/radial position vs. Radial position (without the corrector plate)

Entrance aperture

Number of particles/radial position vs. Radial position (with the corrector plate)

Angle Mean without corrector plate (mm)

Means with corrector plate (mm)

0o 7.3 5.5

5o 6.5 5.5

10o 8.0 5.5

15o 8.3 5.2

20o 8.3 5.3

Comparison of the Means for the image with and without the corrector plate

Optics Conclusions Corrector plate improves spot size and

quality:

Focal plane location is optimized by minimizing the spot size.

Improves spot size, suppression of coma.

The size of the spot is of the order of the pixel (when corrector is added)

Summary

OWL does not provide us with an astronomical quality.

The threshold of the reconstructed aperture is high ~ 4×1019 eV

Corrector plate improves the spot size and quality

Things to be done. Composition study Calculating the light loss (need to know

actual material used) Interface the optical simulation with the OWL simulation (Any volunteers??)