pulsar timing with tempo2 george hobbs australia telescope national facility [email protected]

Pulsar timing with tempo2

George Hobbs

Australia Telescope National Facility

[email protected]

CSIRO. Gravitational wave detection

Contents

• Basis of pulsar timing• Getting tempo2• Using tempo2• Developing tempo2


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


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


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

https://sourceforge.net/projects/tempo2/

http://lists.pulsarastronomy.net/mailman/listinfo/tempo2_lists.pulsarastronomy.net


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


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


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


Clock corrections

• Clock corrections are in > $TEMPO2/clock

Part of pks2gps.clk


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!


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!


Converting tempo1 files to tempo2

• > tempo2 -gr transform 1939_t1.par 1939_t2.par

• or• > tempo2 …. -tempo1


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.


More tempo2 files

• $TEMPO2/ephemeris contains the planetary ephemerides• $TEMPO2/observatory contains observatory coordinates

Observatory.dat


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.


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)


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


Fitting routines

Tempo2 can carry out normal single pulsar fits and also global fits to multiple pulsars


The timing model

• Use:

• The frequency derivative terms are fitable parameters • Can also include glitch events in the model


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)


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


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


Standard usage of tempo2

• No plugins: tempo2 -f mypar.par mytim.tim


Standard usage of tempo2

• Using plk: tempo2 -gr plk -f mypar.par mytim.tim


More plugins

• Tempo2 -gr spectrum -f mypar.par mytim.tim


The splk plugin


Output plugins: general


Output plugins: general2

• Tempo2 -output general2 -s “Hello: {sat} {post}\n” -f mypar.par mytim.tim


Many plugins exist ….

• Plotting• Spectral analysis• Simulating data• Adding noise to data• Adding gravitational wave signals to data• ….


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


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


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• …


Tempo2 demonstration

• No plugins• General2• Plk - plot options, filter, pass, zoom, delete, measure, highlight,

turning jumps on and off• Splk• Spectrum

pulsar timing with tempo2 george hobbs australia telescope national facility [email protected]

Documents

tempo2 slide

timing model slide

pulsar timing model

tempo2 wiki

psrtime tempo2

solar system pulsar

pulsar http

overview tempo2 accurate