A short tutorial on LAT pulsar analysis tools Gamma-ray Large Area Space Telescope Massimiliano Razzano (Istituto Nazionale di Fisica Nucleare, sec. Pisa) Masaharu Hirayama James Peachey (NASA Goddard Space Flight Center) GLAST LAT Collaboration Meeting (SLAC, August 29 th -31 th 2005)
Outline or: What we want to do? The starting point: simulate pulsars in the sky The barycentric decorrections Assigning phases The Pulsar Database Periodicity tests If we don t know exactly radio ephemerides? Conclusions and possible other analysis
Simulating pulsars in the sky We describe how to create and simulate pulsar sources with PulsarSpectrum, a package included in /celestialsources/pulsar Main features: The user can insert new models in the simulations; The default model simulates lightcurves and spectra according to the observed γ ray pulsars; Simulations of barycentric effects due to motion of GLAST and Earth, and gravitational time delays. Takes into account period variations with time; Interfacing with LAT software; The simulated pulsars can be easily put in the D4 Database. The lightcurve and spectrum are combined in a ROOT 2-d histogram like this, and from here the photons are extracted according to the flux
Simulating with gtobsim To create a pulsar source suitable with gtobsim you have to follow 2 steps: 1 - Edit the PulsarDataList.txt file (located in /Pulsar/vXrYpZ/data), where are stored the general parameters of the pulsars know by the simulator Flux E>100MeV Period (or frequency) and derivatives Ephem. validity range T(>t0) where phi(t) = 0.0 2 Create an XML source entry in a xml file, where are stored the position, energy range and modeldependent parameters of the pulsar Model parameters Name as in Datalist RA,dec Emax,Emin Model (=1) & random seed For more informations, please see at: www.pi.infn.it/~razzanopulsar/pulsarsptutor/pulsarsptutor.htm
One week of EGRET Pulsars Now we could run gtobsim: here we include all Egret Pulsars B1951+32 Geminga Crab We will use The Vela pulsar B1055-52 Vela B1706-44
The barycentric corrections First of all, we select with gtselect (/DataSubSelector package) the region of the pulsar, with a radius compatible with the PSF, in order to reduce the number of background photons. Alternatively One could vary the radius with energy, because PSF vary with radius. We choose a fixed radius of 2 degrees Then we have to apply the barycentric corrections, in order to convert the photons arrival times, (expressed in Terrestrial Time TT at the spacecraft), to the arrival times at the Solar system Barycenter (adn expressed in Barycentric Dynamical Time TDB) For this task we use gtbary (/timecorrect package) Parameters Input filename:vela_1week_sub.fits Orbit filename: OrbitFor1Week_scData.fits Position of the source (RA,Dec.):128.83,-45.18 Output filename:vela_1week_bari.fits 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); Note: It s preferable that time range of this file is be greater than time range of events file
The pulsars Database Because of the low number of gamma rays from pulsars, in order to fold correctly the times we need pulsars ephemerides from radio astronomy. All the ephemerides and other relevant infos are stored in the pulsar Database (D4) Let s suppose for the moment that are available radio ephemerides that covers the time range of data. We want to extract the ephemerides We use gtpulsardb (/pulsardb package) Parameters Input filename:egretpulsardb.fits Filtering parameters: e.g. NAME Pulsar Name: F_B0833m45 Start time of observations : 54101 It creates an output Fits file (eg. Vela_ephem.fits) that we can use for phase assignment End Time of observation : 54108
Phase assignment The next step is to assign to each photon a phase, in order to construct the lightcurve.the phase is defined as: 1 2 1 φ( t) = φ( t ) + f 0( t t0) + f 1( t t0) + f 2( t t 2 6 1 f ( t) = f 0 = f ( t 0) f 1 = f& ( t0) f & 2 = f ( t0) P( t) 3 0 0 + )... dt=t-t 0, t0 is the epoch For this task we use gtpphase (/pulsephase package) Parameters Input filename:vela_1week_bari.fits Ephemerides style (DB,PER,FREQ) : FREQ Epoch:-3.88454e+08 Phase at the given epoch: 0.0 Freqs. and derivatives: FREQ: frequency and derivatives PER: period and derivatives DB: Database Fits file(e.g D4 or Vela_ephem.fits) T0 relative to the reference time MJD 54101,expressed in seconds. In our case t0 =49592 (49592-54101) x 86400 = -3.88454 x 10^8 Phase shift (optional)
And now the lightcurve! Plotting the PULSE_PHASE entries in the Vela_1week_bari.fits The real Vela observed by Egret (Kanbach et al.,1994)
Periodicity tests Now we want to test is there s periodicity in the signal. For Vela thes pulse shape is evident, but for fainter pulsars this could be not the case. For testing periodicity we use gtpsearch (/periodsearch package) We restrict to the case of known pulsars, i.e. we exclude for now blind periodicity searches (not yet included). We ll examine 2 cases: 1. The period of observation is covered by radio ephemerides; 2. There s no radio ephemerides available for this particularly observation time Tests against the null hypotesis: H0 = no periodicity Tests implemented: Chi-squared test (Leahy et al. 1983,ApJ 266; Z 2 n test (Buccheri et al. 1983 A&A128),Rayleigh test; H test (De Jager et al., 1989 A&A 221)
An example with Chi2 As in gtpphase # of trial periods Freq steps (Fres=1/T max ) # of phase bins for Chi2 Case 1 Radio ephemerides available: Let s suppose that the best estimate of frequency is 11.1973 Hz. We ll try it with our data and Chi2 test. The test returns the Chi2 statistics and the chance probability that there s no periodic signal. Now we can go on
A deeper investigation with Chi2 Encouraged by our results, we run gtpsearch taking into account the frequency derivatives
Finding the peak with Chi2 We could run again gtpsearch and zoom in order to find better the centroid of the peak The simulated f0 was: 11.197226013404 Hz 1/P est -1/P sim 2 ns
Z 2 n test and H test The other 2 tests give similar results. The number of bins is Z2n is equivalent to the number of harmonics we want to consider. Z 2 n has p.d.f of χ2 2n (See for details: Buccheri et al. 1983, A&A128)
Z 2 n test and H test The other 2 tests give similar results The H test is more efficient for unknown a priori lightcurves (see for details: De Jager et al., 1989 A&A 221)
We don t know radio ephemerides.. Case 2 :Suppose that there are no available radio ephemerides covering our observations. We could try to estimate them and then use gtpsearch for refining search We use gtephcomp (/pulsardb package) f ( t) = 2 f 0 f 0= f ( t0) f 1= f& ( t0) f = && f ( t ) 0 + f dt 1 + 1 2 f ( t) = f dt = t t 0 2 dt 1 P( t) 2 In this example we want a set of ephemerides relative to start of observation (MET = 0)
Then we repeat the procedure with gtpsearch with a first iteration without derivatives and a second one with the frequency derivatives Using gtpsearch again
Conclusions We ve presented the basic steps to obtain a lightcurve from a known pulsar and test its periodicity; The Pulsar analysis tools allow user to perform the basic data reductions and more complex periodicity analysis; With simulation tool is possible to create specific pulsar sources; The database contains radio ephemerides available to users; Currently there s not yet a blind search tool (blind search is not a goal for DC2) Other more detailed analysis could be performed (e.g. phase resolved analysis) Link to Pulsar Tools dev page: http://glast.gsfc.nasa.gov/ssc/dev/psr_tools/ We re almost at the 3 Checkout Have Fun!