1. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 1 A Time Differencing Technique for doing Blind Pulsar Searches Bill Atwood, Brian Baughman, Marcus Ziegler, and Robert Johnson

2. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 2 Pulsar Basics at High Energies 1)The data is sparse. Crab: 1 photon every ~ 1000 turns 2)Faint sources could require months-to-years of exposure to find 3)Presents of Period Derivative compromises direct use of Fourier Transforms 4)However the Period Derivatives are very small and to lowest order cause a phase slip rather then shift the frequency significantly Differencing Concept If a time series has a periodicity – the time differences will exhibit the same. Time differences cancel out long term phase slips and glitches Differencing starts the "clock" over (and over, and over...)

3. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 3 Phase Slippage Caused by the Period Derivative Period Period elongation caused by Period Derivative: Time After N Periods Phase Slip  (in sec) after N Periods is just the sum of the  P's Or more conveniently the relative Phase Slip is Geminga Light Curve A reasonable value for  can be estimated from a "typical" light curve...

4. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 4 T(sec)  Crab Geminga Tmax(Crab) = 23k sec Tmax(Geminga) = 10 6 sec Estimation of the maximum length of the time differencing window For Geminga – an entire EGRET Viewing period can be used, while for the Crab, due to its short period and large period-derivative, only about ¼ of a day is usable. Additional Phase shift due to Frequency Drift As time progresses the period (frequency) slowly change (as well as shifting in phase). Time differences from a differencing time window started at a time t after the start of data collection will be further limited: Solving for T Diff :

5. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 5 T Diff (max) (sec) t (sec) Crab Geminga Crab – Approx. Soln. Max. Allowed Time Differencing window allowing a Phase Slip  <.1 Again – Crab is hard to find due to its short period and large period derivative An estimation of the min. flux required can be arrived at by note that for time differencing we need at least 2 photons within the diff. window. Assuming the window is opened by a source photon, then in TDiff(max) we need on average 1 photon.

6. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 6 Flux Limit for Time Differencing Blind Searches This must be compared with the overall flux limit for the mission where F 0 is mission specific Flux(cm -2 sec -1 ) t (sec) Where the 2 Flux estimates cross is the limit. Solving for t and re-inserting it for F Lim one finds:

7. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 7 The Plane from Dave Thompson's Talk LAT - 10 -8 LAT - 10 -7 EGRET - 10 -6 The "one number" result is that Time Differencing requires ~ 10X higher flux then the mission's limit Finally we can sweep out contours in the plane for various values of F Lim

8. Bill Atwood, SCIPP/UCSC, Jan., 2006 GLAST 8 Closing Remarks 1)Real Data with noise will corrupt things – see Marcus' Talk 2)Improvements possible a)Selection of Start Photon b)More efficient freq. search alg. c)... 3)Applications to GRBs and AGN Flares if there is a common underlying frequency – differencing allows compiling statistics directly.