1. Improving the sensitivity of searches for an association between Gamma Ray Bursts and Gravitational Waves Soumya D. Mohanty The University of Texas at Brownsville Acknowledgement: Exttrigg group for helpful discussions

2. 18 Dec 2004GWDAW9 Intrinsic delay depends on where shocks form Gamma Ray Bursts Gamma Ray Burst Central Engine Possible progenitors Core collapse of massive, high angular momentum stars Merger of NS stars Relativistic ejecta Internal and/or external shocks Beamed Gamma Ray emission Followed by afterglow Gravitational wave emission formation, activity and decay of central engine Neutrino etc. Black Hole accreting rapidly Estimates Kobayashi, Meszaros, ApJ, 2002: 1 collapsar/year, marginal, Adv LIGO Van Putten et al, PRD, 2004: 0.2 M  in GWs

3. 18 Dec 2004GWDAW9 Detectability Cosmological distances: direct detection unlikely XRFs, weaker GRBs could be off-axis and close by Detect association : Accumulate SNR over several GRBs Finn, Mohanty, Romano, PRD, 1999 (FMR) Deep searches possible Matched filtering SNR = h rms  signal duration /  PSD (white) FMR 95% UL: h rms  2  10 -23, 1000 GRBs,  PSD=3  10 -24, 100 Hz band  10msec signal, Integration length=0.5 sec Matched filtering SNR ~ 2.0 Accumulation algorithms: observational constraints Astone et al, 2002, 2004

4. 18 Dec 2004GWDAW9 Objective Explore ways to improve the sensitivity of FMR FMR works by Cross-correlating pairs of segments for every GRB trigger (on-source sample) … and also away from any GRB (off-source samples) Testing for a statistically significant difference in the sample means of on- and off source distributions Virtue: eliminate any weak common terrestrial signal

5. 18 Dec 2004GWDAW9 Main limitation of FMR Unknown delay between GRB and GW  cross correlation integration length set equal to max expected delay ~ 1 to 100 sec >> typical expected burst signal duration of ~ 100 msec

6. 18 Dec 2004GWDAW9 Likelihood Ratio Approach What is the maximum likelihood ratio statistic for Gaussian, white noise & Independent (co-aligned) detectors Signal with unknown waveform, time of arrival t a and duration  Key point: consider signal time samples as parameters to be maximized over Frequentist version of similar calculations (Anderson et al, Vicere) carried out in a Bayesian framework Note: no formal proof of optimality exists for max LR. However, often performs the best.

7. 18 Dec 2004GWDAW9 Results Known t a,  Maximum LR statistic  : /2+ /2+ Only the cc term is retained : non-Gaussianity of real data Can be generalized to a network of misaligned detectors W. Johnston, Master’s thesis, UTB, 2003 Unknown t a and  Cross-correlate  sec (M < N samples) subsegments CORRGRAM (Mohanty et al, Proc GWDAW8; R-statistic / CORRPOWER, Cadonati, Marka, Poster, this conference)

8. 18 Dec 2004GWDAW9 CORRGRAM x1x1 x2x2

9. 18 Dec 2004GWDAW9 Unknown t a and  cont… However : we are also searching over unknown waveforms The scan over max  should cover smaller  automatically  Only one scan needed in integration length No formal proof yet (also note on optimality of LR) FMR fits in : max waveform duration same as integration length

10. 18 Dec 2004GWDAW9 Extend to Multiple triggers Unknown time of arrival and duration for each trigger Max LR statistic : Final statistic : Sum of individual maxima

11. 18 Dec 2004GWDAW9 LR inspired alternatives to FMR 1. Max of CORRGRAM for each trigger, rank-sum test for shift in median between on- and off-source samples (common signal subtraction preserved) 2. Same but scan with a single value of duration ( M) – Appears to follow from the full application of LR 3. MULTICFT: uses CORRGRAMs for each trigger

12. 18 Dec 2004GWDAW9 MULTICFT Multi-trigger Corrgram FFTs 2 D FFT The “signal” in the corrgram is shifted to low frequencies apart from a phase factor. Magnitude : gets rid of the phase factor Average the FFTs across multiple triggers Integrate out the power along a narrow vertical strip near the origin Max of integrated power is the test statistic

13. 18 Dec 2004GWDAW9 Metric for comparison What is the expected 90% UL for a given matched filtering SNR (  Euclidean norm of the signal) ? lower Uls are better Subtlety: UL is an estimator. Integrating the bulk of the test statistic pdf, not its tail. Monte Carlo simulation: Each trial is a full analysis with N GRB GRBs Fixed signal waveform and Euclidean norm (Matched filtering SNR in white noise) Randomly distributed times of arrival for each trigger One test statistic value for each trial 10 th percentile of test statistic sample : 90% confidence level upper limit confidence belt Mean of test statistic sample: read off UL from confidence belt

14. 18 Dec 2004GWDAW9 90% mean Confidence belt Mean Mean UL

15. 18 Dec 2004GWDAW9 Comparison MULTICFT FMR Total segment length = 5 sec@1024Hz Sine-Gaussian: 256Hz,  =0.05 sec Number of GRBs = 50 Integration lengths: 20 to 100 msec in steps of 10msec

16. 18 Dec 2004GWDAW9 Total segment length = 2 sec@1024Hz Sine-Gaussian: 256Hz,  =0.05 sec Number of GRBs = 100 Integration lengths: 100 msec Comparison cont … FMR MAX CORRGRAM Single integration length

17. 18 Dec 2004GWDAW9 Comparison cont … Total segment length = 10 sec@1024Hz Sine-Gaussian: 256Hz,  =0.05 sec Number of GRBs = 100 Integration lengths: 100 msec FMR MAX CORRGRAM Single integration length

18. 18 Dec 2004GWDAW9 Comparison cont… Total segment length = 30 sec@1024Hz Sine-Gaussian: 256Hz,  =0.05 sec Number of GRBs = 100 Integration lengths: 100 msec FMR MAX CORRGRAM Single integration length

19. 18 Dec 2004GWDAW9 Comparison cont … Total segment length = 10 sec@1024Hz Sine-Gaussian: 256Hz,  =0.05 sec Number of GRBs = 100 Integration lengths: 100 msec FMR SINGLE MAX CORRGRAM Single integration length

20. 18 Dec 2004GWDAW9 Summary and Conclusions Objective: Improve the sensitivity of FMR for the (expected) case of signal duration << delay range. Max. Likelihood Ratio as a guide – further refinements in its application are possible Improvement possible: Rank Sum, two sample test with a single integration length performs better than FMR in all cases This strategy also follows from the max LR statistic Limited study so far – ratio of signal to data length, max integration length, number of GRBs Obtain analytic approximations