Pulsar timing with tempo2 George Hobbs Australia Telescope National Facility

CSIRO. Gravitational wave detection Contents Basis of pulsar timing Getting tempo2 Using tempo2 Developing tempo2

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection Getting tempo2 Wiki: Main repository: Get data: > cvs -z3 co tempo2 distribution list: Ingrid’s help page for using tempo2:

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection Clock corrections Clock corrections are in > $TEMPO2/clock Part of pks2gps.clk

CSIRO. Gravitational wave detection 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!

CSIRO. Gravitational wave detection 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!

CSIRO. Gravitational wave detection Converting tempo1 files to tempo2 > tempo2 -gr transform 1939_t1.par 1939_t2.par or > tempo2 …. -tempo1

CSIRO. Gravitational wave detection 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.

CSIRO. Gravitational wave detection More tempo2 files $TEMPO2/ephemeris contains the planetary ephemerides $TEMPO2/observatory contains observatory coordinates Observatory.dat

CSIRO. Gravitational wave detection 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.

CSIRO. Gravitational wave detection 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 ) and You, Hobbs, Coles et al. (2007ApJ )

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection Fitting routines Tempo2 can carry out normal single pulsar fits and also global fits to multiple pulsars

CSIRO. Gravitational wave detection The timing model Use: The frequency derivative terms are fitable parameters Can also include glitch events in the model

CSIRO. Gravitational wave detection 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)

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection Standard usage of tempo2: Input pulsar model Require a parameter file (traditionally *.par) Require: PSRJ RAJ DECJ F0 PEPOCH DM Each parameter Label value MODE 1 = fit with weights MODE 0 = fit without weights SINI KIN => Link the parameters SINI and KIN JUMP -f flag 0 1 FJUMP -f

CSIRO. Gravitational wave detection Standard usage of tempo2 No plugins: tempo2 -f mypar.par mytim.tim

CSIRO. Gravitational wave detection Standard usage of tempo2 Using plk: tempo2 -gr plk -f mypar.par mytim.tim

CSIRO. Gravitational wave detection More plugins Tempo2 -gr spectrum -f mypar.par mytim.tim

CSIRO. Gravitational wave detection The splk plugin

CSIRO. Gravitational wave detection Output plugins: general

CSIRO. Gravitational wave detection Output plugins: general2 Tempo2 -output general2 -s “Hello: {sat} {post}\n” -f mypar.par mytim.tim

CSIRO. Gravitational wave detection Many plugins exist …. Plotting Spectral analysis Simulating data Adding noise to data Adding gravitational wave signals to data ….

CSIRO. Gravitational wave detection 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

CSIRO. Gravitational wave detection A very simple ‘output’ plugin #include #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

CSIRO. Gravitational wave detection 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