Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 1

Fourier Transform with differences on Fourier Transform with differences on Simulated and Real Pulsar DataSimulated and Real Pulsar Data

UPDATE UPDATE

Gamma-ray Large Gamma-ray Large Area Space Area Space TelescopeTelescope

Marcus Ziegler

Bill Atwood

Brian Baughman

Robert Johnson

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 2

Basic IdeaBasic Idea

take only differences with t < max_diff

typical max_diff = 10 000stypical EGRET viewingperiod ~ 1 000 000s

Calculate the Fourier-Transform of the

time differences of the photon arrival times tn.

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 3

Dependence on max_diffDependence on max_diffThe dependence of the signal width on max_diff

-0 .001 -0.0005 0 0.0005 0.0010

0.2

0.4

0.6

0.8

1

FT+differnces

F + f in Hz0

Po

we

r

max_diff = 2000 s

-0. 001 -0.0005 0 0.0005 0.0010

0.2

0.4

0.6

0.8

1

FT+differnces

F + f in Hz0

Pow

er

max_diff = 10000 s

-0. 001 -0.0005 0 0.0005 0.0010

0.2

0.4

0.6

0.8

1

FT+differnces

F + f in Hz0

Pow

er

max_diff = 100000 s

Pulse width ~ 1/max_diff

Simmulated Pulsar at 10Hz

Power RMS off peak is called Noise

Small max_diff+ Small number of differences (fast)+ Coarse stepping in Frequency space (fast)-Large noise (Small S/N ratio)

Large max_diff+ Good S/N ratio- Large number of differences (very slow)

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 4

Blind Search for VELABlind Search for VELAVELA Viewing Period VP 7max_diff 10 000sScan region 1 Hz – 100 Hz

S/N

F in Hz

VELA

S/N

F in Hz

VELA

Number of Photons 1 197Number of differences 22 700Number F trials 2 000 000Calculations 52 800 000 000took 4h 30 min

F0 catalog 11.19888756F0 from search 11.19882249

F1 catalog -0.1557 E-10F1 from search 0.0850 E-10

F0 trials with S/N > 10

Refined search around good F0 candidates

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 5

Blind Search for GEMINGABlind Search for GEMINGAGEMINGA Viewing Period VP 10max_diff 10 000sScan region 1 Hz – 100 Hz

Number of Photons 1 200Number of differences 12 300Number F trials 2 000 000Calculations 2 400 000 000took 3h 30 min

F0 catalog 4.2177501F0 from search 4.2176815

F1 catalog -0.00195 E-10F1 from search -0.00935 E-10

0 20 40 60 80 100

10

20

30

40

50

60

70S/N

F in Hz

0 2 4 6 8 10 12 14 16 18 200

100

200

300

400

500

600

700S/N

F in Hz

F0 trials with S/N > 10

Refined search around good F0 candidates

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 6

The large F1 of CRABThe large F1 of CRAB

Simmulate Pulsar F0 = 10HzF1 = -3.0 E-10

F1 GEMINGA -0.00195 E-10F1 VELA -0.15666 E-10F1 CRAB -3.86228 E-10

Scan in F1 @ 10 Hz, max_diff 10 000s

-F1

Po

wer

-F1

Po

wer

Scan in F1 CRAB max_diff 10 000s

Marcus Ziegler SCIPP/UCSC Pulsar Meeting DC2 7

F0 and F1 Scan for CRABF0 and F1 Scan for CRAB

Scan in F CRAB max_diff 10 000sF1 steps @ 10Hz 0.05 E-10F1 steps @ 30Hz 0.15 E-10

F0 catalog 30.2254F0 from search 29.9493

F1 catalog -3.8623 E-10F1 from search -3.7719 E-10

Epoch CRAB 40000Epoch Search 48393

Calculations took 4d 16h