Soumya D. Mohanty The University of Texas at Brownsville

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

3. 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 = hrmssignal duration / PSD (white) • FMR 95% UL: hrms 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 GWDAW9

4. 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 GWDAW9

5. 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 GWDAW9

6. 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 ta 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. GWDAW9

7. Results • Known ta,  • Maximum LR statistic : <x1,x1>/2+<x2,x2>/2+<x1,x2> • 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 ta and  • Cross-correlate  sec (M < N samples) subsegments • CORRGRAM (Mohanty et al, Proc GWDAW8; R-statistic / CORRPOWER, Cadonati, Marka, Poster, this conference) GWDAW9

8. CORRGRAM x1 x2 GWDAW9

9. Unknown ta 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 GWDAW9

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

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

12. 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 GWDAW9

13. 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 NGRB 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 • 10th percentile of test statistic sample : 90% confidence level upper limit confidence belt • Mean of test statistic sample: read off UL from confidence belt GWDAW9

14. Confidence belt Mean UL 90% mean Mean GWDAW9

15. 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 GWDAW9

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

17. 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 GWDAW9

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

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

20. 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 GWDAW9