Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Fourier Transform with differences on Simulated and Real Pulsar Data Gamma-ray Large Area Space Telescope Marcus Ziegler Bill Atwood Brian Baughman Robert Johnson

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Fourier Transform on Differences Calculate the time between two photons t diff = t j – t i where (t j – t i ) < max_diff phase n = F0 * t diff power = sqrt ((  sin (2  phase n )) 2 + (  cos (2  phase n )) 2 ) /n max_diff = 5000s Create series of evens distributed over s (5.7 days) Period of pulsar P 0 = 0.1 s (10 Hz) Number of events ~ 500 (= bright Geminga like pulsar)

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Dependence on max_diff The dependence of the signal width on max_diff Pulse width ~ 1/max_diff

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Dependence on max_diff The influence of max_diff on the Signal to noise ratio

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Adding a Gaussian distribution Phase diagram Normal FT FT on differences Sigma = P/5 Sigma = P/20 Sigma = P/100

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Adding a Second Peak Two peaks with 180 deg phase difference cancel the contribution to the power spectrum.

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Adding a period derivative max_diff = s Phase diagram Normal FT FT on differences Pd = 1E-14 1E-13 3E-13 1E-12 3E-12

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Changing Max_diff with a Pd Phase diagram Normal FT FT on differences Pd = 3E-12 max_diff = s s 5 000s 1 000s 500s

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ S/N vs. max_diff The dependence of Signal/Noise on max_diff P1 = 3e-12 F1 = 3E-10 1/s 2 max_diff = 1/ sqr(F1) max_diff = s

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Looking at real pulsar data Brian Baughman wrote a Program to - read in the EGRET low level data - calculate the solar system baric center corrected photon arrival times - create new output file with corrected times

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Looking at real pulsar data Select photons within a 2 deg radius around the source. (no cut on the photon energy was made yet) photons were collected for this viewing period (about 14 days) Ephemeris for GEMINGA Epoch F F E-12 F2 0.28E-24

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Ft on differences Max_diff s Max_diff s Frequency scan around GEMINGAs F0 with correction for F1

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Search for GEMINGA no correction for F1, max_diff = s

Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/ Conclusion and Outlook  The Fourier Transform on the differences is very simple and powerful  This method tolerates uncertainties in the ephemeris data  A very good “noise” separation can be achieved by tuning max_diff  Further optimize the algorithm  Look for pulsars in the EGRET data