Pulsar Analysis Tutorial with LAT Science Tools

1. Hunting for Vela and Crab in the DC2 data A tutorial on pulsar analysis with the LAT Science Tools Massimiliano Razzano (INFN Pisa) DC II Kickoff Meeting (SLAC, March 1-3. 2006) M.Razzano - DC II Kickoff Meeting

2. Summary • In this tutorial we will see how to use the LAT Science Tools to perform a pulsar timing analysis in the DC 2; • The dataset used is the first week of DC 2, available at: • http://glast.gsfc.nasa.gov/ssc/dev/databases/DC2/ • Everyone can gain pratice and reproduce this tutorial ! • The Science Tools version is v6r4p1. Updated tools with respect to previous tutorials (e.g. at the Collaboration Meeting); • We choose Vela and Crab, famous and bright g-ray pulsars (we use just 1 week…) • Step-by-step procedure to test periodicity and recover pulse profile for g-ray pulsars with radio counterpart; • Included command prompt screenshots for your reference; M.Razzano - DC II Kickoff Meeting

3. LAT pulsar Tools The pulsar tools • Select the region and apply the cuts on time, energy etc…; gtselect • Apply the barycentric corrections; gtbary • Retrieve pulsar ephemerides from the pulsar database; gtpulsardb, gtephcomp • Test periodicity; gtpsearch • Assign phase; gtpphase • Display phase curve; What do you prefere: fplot, fv, ROOT, Hippodraw, etc..(here we use fv…) Pulsar tools developed mainly by M.Hirayama and J.Peachey (http://glast.gsfc.nasa.gov/ssc/dev/psr_tools/) M.Razzano - DC II Kickoff Meeting

4. Selecting the region of interest The first week of DC2 • The radius of the sky region selected for the analysis should be chosen in order to maximize S/B ratio; • A radius comparable with PSF is ok (a good choice could be 2 PSF). • PSF depends on energy, so an energy-dependend cut is optimal (as was done in EGRET) • We make here a rough selection: E>100MeV, and PSF(100MeV) ≈3°R=6° For this task we use gtselect M.Razzano - DC II Kickoff Meeting

5. Note that time is in MET ! Vela In a similar way as for Vela, we cut on Crab, but another source seems to be there. To avoid possible confusion on the periodicity test, we use a 3° radius Crab Selecting Vela and Crab M.Razzano - DC II Kickoff Meeting

6. For this task we use gtbary Corrections are: • Conversion TTTDB; • Geometric corrections due to lighttravel time from GLAST location to Solar System Barycenter; • Relativistic delay due to gravitaional field of Sun (e.g. Shapiro delay); Pay attention:gtbary usually overwrites the input file! The barycentric corrections The photon arrival times are affected by the motion of GLAST through Solar System and by relativistic effects. These effects are compensated by the barycentric corrections The barycentric corrections convert the photons arrival times, (expressed in Terrestrial Time TT at the spacecraft), to the arrival times at the Solar System Barycenter (expressed in Barycentric Dynamical Time TDB) M.Razzano - DC II Kickoff Meeting

7. Retrieving pulsar ephemerides Pulsar rotational frequency decreases with time (period increase). Usually the behaviour of frequency with time is approximated by a 2-nd order polynomial: The parameters f0,f1, f2 are called ephemerides and t0 is the epoch, i.e. the time where the ephemerides refers to (usually t0 is in Modified Julian Date MJD) The pulsar ephemerides are stored in our pulsar database (D4). In order to test the periodicity of a pulsar and assign to each photon a rotational phase, it is necessary to know the ephemerides (e.g. from radio) For this task we use gtpulsardb and gtephcomp M.Razzano - DC II Kickoff Meeting

8. A quick look at the pulsar database… Download pulsar database (D4) from GSSC Data Center. Pay attention to names: look at the D4.. (m stands for “-”, p stands for “+”) M.Razzano - DC II Kickoff Meeting

9. There are ephemerides for our pulsar? Because in real life the ephemerides timing solution comes from observations, it is possible that there are no radio ephemerides coverage of our observation time. With gtephcomp it is possible to check that. Strict options force to use ephemerides that cover the input time • In this case the tool checks if there are ephemerides that contains our time (in this case the middle time of the observation. • It also estimates the ephemerides at our input time • In this case we have valid ephemerides covering the observation (MJD 54566-54573) • We will see with Crab the other possibility = no radio ephemerides available… M.Razzano - DC II Kickoff Meeting

10. Periodicity tests For this task we use gtpsearch Once we know that D4 contains valid ephemerides of Vela, we can test if our gamma source has the same periodicity of the radio counterpart. In this case we have identified the source as a gamma-ray pulsar! Tests against the null hypotesis: H0 = no periodicity Tests implemented: • Chi-squared test (Leahy et al. 1983,ApJ 266; • Z2n test (Buccheri et al. 1983 A&A128),Rayleigh test; • H test (De Jager et al., 1989 A&A 221) When we will find the periodicity, we can assign phases to each photon and build the lightcurve M.Razzano - DC II Kickoff Meeting

11. For each photon a phase is assigned for a trial frequency, then an histogram of phase bin mj is created; • In absence of pulsation every phase bin will have the same mean count mexpected; • The quantity: • is computed; • For large counts is every bin, S is distributed as a c2 • Then it is possible to test the non-periodicity hypothesis and give a chance probability p(c2>S) Example ofc2periodicity test Frequency space is scanned in fractions of Fourier resolution fF=1/T, where T is the duration of the observation. It represents the spacing between 2 independent frequencies in FT. For our data fF 1/(86400*7)≈1.6E-06 Hz Periodicity test on the profile Here we use gtpsearch (/periodsearch package) and use as example the c2 test M.Razzano - DC II Kickoff Meeting

12. Testing Vela periodicity (I) • As first approximation we use the DB option that tell gtpsearch to extract ephemerides from D4. • Pay attention to specify the psrdbfile parameter! • The cancelpdot parameter tells to take into account the period derivatives M.Razzano - DC II Kickoff Meeting

13. Testing Vela periodicity (II) As a first iteration we adopt as central frequency the frequency of the maximum at the previous run. The frequency has the same value as before, we can proceed to a refined scan in frequency M.Razzano - DC II Kickoff Meeting

14. Testing Vela periodicity (III) • After this last run we’ve found that our source has the periodicity of the radio counterpart. • fmax=11.197226035062 Hz with a freq. sampling of≈8E-8 Hz • We can compare with the value f0=11.197226013404 Hz |f0 – fmax| < freq. sampling M.Razzano - DC II Kickoff Meeting

15. dt=t-t0, t0 is the epoch Gtppphase add a PULSE_PHASE column. We make an histogram with fv 1 1 = + - + - + - + 2 3 φ( t ) φ( t ) f ( t t ) f ( t t ) f ( t t ) ... 0 0 0 1 0 2 0 2 6 Folding at the radio ephemerides Once the periodicity is known, to each photon can be assigned a rotational phase as: For this task we use gtpphase Here we choose to use the D4 ephemerides, but they can be also entered manually M.Razzano - DC II Kickoff Meeting

16. The H test is more efficient for unknown-a-priori lightcurves (see for details: De Jager et al., 1989 A&A 221) The other 2 tests give similar results. The number of bins is Z2n is equivalent to the number of harmonics we want to consider. Z2n has p.d.f of χ22n (See for details: Buccheri et al. 1983, A&A128) Z2n test Htest Z2n test and H test Other 2 tests are implemented in gtpsearch: Z2n test and H-test. For more details, please see references. M.Razzano - DC II Kickoff Meeting

17. What happens if Crab is not in D4? With strict=yes we see that no radio ephem are available It can be possible that no radio ephemerides cover our observation. To perform timing analysis in this case we’ve shifted ephem of Crab outside the DC2 It is possible to use the D4 entries in the D4 to estimate ephemerides in our dataset (by using the 2 nd order approx.) T is in MET ! Then we will use strict=no to extrapolate our ephemerides at the center of the observation time For this task we use gtpephcomp We will use these extrapolated data to test periodicity M.Razzano - DC II Kickoff Meeting

18. Testing periodicity (I) We use gtpsearch by entering manually ephemerides In this case the ephemerides validity ends just before DC2 starts, so extrapolation works fine. In addition Crab is bright, but this will be not the case for other pulsars in DC2… For instance, this is ad hoc example: at least Crab has a complete ephemerides coverage in the official DC2 pulsar database… M.Razzano - DC II Kickoff Meeting

19. We then assign phases according to the found frequency and we find lightcurve Testing periodicity (II) We make another iteration with refined freq-scan M.Razzano - DC II Kickoff Meeting

20. Concluding remarks • This tutorial shows basic analysis steps using the Science Tools. More refined analysis can be done. • No spectral analysis shown. You can make spectral analysis as for other sources (e.g. with likelihood or with other specific packages, e.g XSpec); • When retrieving ephemerides, please refer to our D4 (most of DC2 pulsars are not in the real sky…); • For major info on Pulsar Tools, please see the User Workbook or the Pulsar Tools page at: http://glast.gsfc.nasa.gov/ssc/dev/psr_tools/; • Take this tutorial as a template to have pratice with basic analysis for DC2; • You can also have exercises by simulating pulsars with gtobssim and PulsarSpectrum; There are many pulsars out there: good luck and enjoy! M.Razzano - DC II Kickoff Meeting