Pulsar timing with tempo2
description
Transcript of Pulsar timing with tempo2
CSIRO. Gravitational wave detection
Contents
• Basis of pulsar timing• Getting tempo2• Using tempo2• Developing tempo2
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Must average many thousands of pulses together to obtain stable profile
Must convert to reference frame suitable for the timing model – e.g. solar system barycentre
Must convert to arrival times at infinite frequency
Must convert to conform with terrestrial time standards
Must add extra propagation delays e.g. through the solar system
Pulsar timing: The basics(see Hobbs, Edwards & Manchester 2006, MNRAS)
Obtain pulse arrival times at observatory
Model for pulsar spin down
Form timing residuals – how good is the timing model at predicting the arrival times
Improve timing model
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Tempo2
• Paper 1: Hobbs, Edwards & Manchester (2006), MNRAS, 369, 655
• Paper 2: Edwards, Hobbs & Manchester (2006), MNRAS, 372, 1549
• Paper 3: Hobbs, Jenet, Lee et al. (2009), MNRAS, 394, 1945
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Getting tempo2
• Wiki: http://www.atnf.csiro.au/research/pulsar/tempo2• Main repository: https://sourceforge.net/projects/tempo2/• Get data: • >cvs -z3 -d:pserver:[email protected]:/cvsroot/tempo2 co tempo2
• Email distribution list: http://lists.pulsarastronomy.net/mailman/listinfo/tempo2_lists.pulsarastronomy.net
• Ingrid’s help page for using tempo2: http://www.astro.ubc.ca/people/stairs/tempo2.html
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Paper I: overview
• Tempo2 accurate for known physics to 1ns (factor of ~100 better than tempo1 and ~1000 better than psrtime)
• Tempo2 is compliant with the general relativistic framework of the IAU 1991 and 2000 resolutions - uses the international celestial reference system, barycentric coordinate time and up-to-date precession, nutation and polar motion models
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Paper I: overview
• Two parts to tempo2: 1) Forming the pulse emission time and 2) updating the pulsar timing model
• 1) Forming the pulse emission time
Clock corrections
Atmospheric delays
Solar system Einstein delay
SS Roemer delay
SS Shapiro delay
Dispersive component
Secular motion
Orbital motion
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Forming the pulse emission time: clock corrections
• TOAs are recorded against local observatory clocks• Probably don’t have good long term stability• Can transform to the best terrestrial time-scale by applying
corrections derived from monitoring the offsets between pairs of clocks
• E.g. Parkes clock -> GPS -> UTC(AUS) -> UTC -> TAI• UTC = time-scale formed through the weighting of data from an
ensemble of atomic clocks• TAI = UTC + leap seconds to maintain synchrony with Earth’s
rotation
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Clock corrections
• Clock corrections are in > $TEMPO2/clock
Part of pks2gps.clk
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Atmospheric propagation delays
• Can get effects by the ionised fraction of the atmosphere (ionosphere) and the neutron fraction (mainly the troposphere). It is possible to provide TEMPO2 with lists of surface atmospheric pressure for the most accurate determinations.
• Not normally needed!
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Einstein delay
• Damour & Deruelle 1986• Quantifies the change in TOAs due to variations in clocks at the
observatory and the SSB due to changes in the gravitational potential of the Earth and the Earth’s motion
• Use barycentric corrdinate time (TBC) instead of barycentric dynamical time which was used in tempo1 => tempo1 parameter files can not immediately be used in tempo2
• Note: tempo2 parameters are in SI units …. Tempo1 parameters are not!
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Converting tempo1 files to tempo2
• > tempo2 -gr transform 1939_t1.par 1939_t2.par
• or• > tempo2 …. -tempo1
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Roemer delay
• The vacuum light travel time between the pulse arriving at the observatory and the equivalent arrival time at the SSB
• Calculated by determining the time-delay between a pulse arriving at the observatory and at the Earth’s centre and from the Earth’s centre to the SSB
• Pulsar positions determined in the ICRS (International celestial reference system). Telescope positions are in the ITRF (International terrestrial reference system). Require precession, nutation, polar motion and Earth rotation information to convert between the two. TEMPO1 does not include polar motion
• Use DEXXX or INPOPXX Solar System models for conversion. Recommend DE405.
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More tempo2 files
• $TEMPO2/ephemeris contains the planetary ephemerides• $TEMPO2/observatory contains observatory coordinates
Observatory.dat
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Solar system Shapiro delay
• Accounts for the time-delay caused by the passage of the pulse through curved space-time
• Mainly due to the Sun, but significant Shapiro delay caused by Jupiter.
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Dispersive effects
• Caused by the ISM - assume delays propto f^-2. • Also dispersive delay caused by the Solar wind. Approximated
in tempo2 with the electron density decreasing as an inverse square law from the centre of the sun.
• You Xiaopeng developed this model - see You, Hobbs, Coles et al. (2007MNRAS.378..493) and You, Hobbs, Coles et al. (2007ApJ...671..907)
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Shklovskii effect and radial motion
• Pulsar-timing measurements are affected by the motion of the pulsar relative to the SSB. This includes radial velocity, the Shklovskii effect and radial acceleration.
• Can be absorbed by other parameters or included individually
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Fitting routines
Tempo2 can carry out normal single pulsar fits and also global fits to multiple pulsars
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The timing model
• Use:
• The frequency derivative terms are fitable parameters • Can also include glitch events in the model
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Binary models
• Have various models implemented from tempo1 (BT, ELL1, DD, MSS …)
• Recommend use of T2 binary model• Can assume GR (DDGR model) or small eccentricities (ELL1)
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Standard usage of tempo2: Input arrival times
• Require a file containing arrival times.
Required
File identifier Observing frequency (MHz)
Arrival time (MJD)
TOA uncertainty (us)
Telescope code
User defined flags
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Standard usage of tempo2: Input pulsar model
• Require a parameter file (traditionally *.par)
Require:
PSRJ
RAJ
DECJ
F0
PEPOCH
DM
Each parameter
Label value <fit> <error>
MODE 1 = fit with weights
MODE 0 = fit without weights
SINI KIN
=> Link the parameters SINI and KINJUMP -f flag 0 1
FJUMP -f
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Standard usage of tempo2
• No plugins: tempo2 -f mypar.par mytim.tim
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Standard usage of tempo2
• Using plk: tempo2 -gr plk -f mypar.par mytim.tim
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More plugins
• Tempo2 -gr spectrum -f mypar.par mytim.tim
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The splk plugin
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Output plugins: general
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Output plugins: general2
• Tempo2 -output general2 -s “Hello: {sat} {post}\n” -f mypar.par mytim.tim
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Many plugins exist ….
• Plotting• Spectral analysis• Simulating data• Adding noise to data• Adding gravitational wave signals to data• ….
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Developing tempo2
• Anyone can create more plugins.• Talk to me if you want to modify the main tempo2 code.• Easiest to use C/C++ and pgplot, but can use other
languages/libraries
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A very simple ‘output’ plugin
• #include <stdio.h>#include “tempo2.h”
extern "C" int tempoOutput(int argc,char *argv[],pulsar *psr,int npsr){ int i; printf(“Number of observations = %d\n”,psr[0].nobs); printf(“Name of pulsar = %s\n”,psr[0].name); printf(“A list of site-arrival-times, observing frequencies and residuals\n”); for (i=0;i<psr[0].nobs;i++){ printf(“sat = %g, freq = %g, res = %g\n”,(double)psr[0].obsn[i].sat, (double)psr[0].obsn[i].freq,(double)psr[0].obsn[i].residual); }}
See documentation on the tempo2 wiki
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Ideas for new plugins
• Want to analyse the residuals in a new way (wavelet analysis?)• Want to model the effect of precession in pulsar timing• Want to look for correlated signals in multiple pulsar timing
residuals• Want to simulate thousands of realisations of realistic timing
residuals• …
CSIRO. Gravitational wave detection
Tempo2 demonstration
• No plugins• General2• Plk - plot options, filter, pass, zoom, delete, measure, highlight,
turning jumps on and off• Splk• Spectrum