1. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 1 Fourier Transform with differences on Simulated and Real Pulsar Data Gamma-ray Large Area Space Telescope Marcus Ziegler Bill Atwood Brian Baughman Robert Johnson

2. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 2 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 500 000s (5.7 days) Period of pulsar P 0 = 0.1 s (10 Hz) Number of events ~ 500 (= bright Geminga like pulsar)

3. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 3 Dependence on max_diff The dependence of the signal width on max_diff Pulse width ~ 1/max_diff

4. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 4 Dependence on max_diff The influence of max_diff on the Signal to noise ratio

5. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 5 Adding a Gaussian distribution Phase diagram Normal FT FT on differences Sigma = P/5 Sigma = P/20 Sigma = P/100

6. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 6 Adding a Second Peak Two peaks with 180 deg phase difference cancel the contribution to the power spectrum.

7. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 7 Adding a period derivative max_diff = 100 000 s Phase diagram Normal FT FT on differences Pd = 1E-14 1E-13 3E-13 1E-12 3E-12

8. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 8 Changing Max_diff with a Pd Phase diagram Normal FT FT on differences Pd = 3E-12 max_diff = 100 000s 20 000s 5 000s 1 000s 500s

9. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 9 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 = 57 000s

10. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 10 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

11. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 11 Looking at real pulsar data Select photons within a 2 deg radius around the source. (no cut on the photon energy was made yet) - 1200 photons were collected for this viewing period (about 14 days) Ephemeris for GEMINGA Epoch 43946 F0 4.21775012277 F1 -0.1952379E-12 F2 0.28E-24

12. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 12 Ft on differences Max_diff 10 000s Max_diff 100 000s Frequency scan around GEMINGAs F0 with correction for F1

13. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 13 Search for GEMINGA no correction for F1, max_diff = 10 000s

14. Marcus Ziegler SCIPP/UCSCPulsar Meeting 1/17/2006 14 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