Dec 16, 2005GWDAW-10, Brownsville Population Study of Gamma Ray Bursts S. D. Mohanty The University of Texas at Brownsville

Dec 16, 2005GWDAW-10, Brownsville GRB Death of a massive star

Dec 16, 2005GWDAW-10, Brownsville GRB (and three others) Evidence for binary NS mergers Bottom-line: The GW sources we are seeking are visible ~ once a day! HETE error circle Chandra (Fox et al, Nature, 2005)

Dec 16, 2005GWDAW-10, Brownsville SWIFT in operation during S5 We should get about 100 GRB triggers Large set of triggers and LIGO at best sensitivity = unique opportunity to conduct a deep search in the noise Direct coincidence: detection unlikely, only UL UL can be improved by combining GW detector data from multiple GRB triggers Properties of the GRB population instead of any one individual member

Dec 16, 2005GWDAW-10, Brownsville Maximum Likelihood approach Data: fixed length segments from multiple IFOs for each GRB –x i for the i th GRB Signal: Unknown signals s i for the i th GRB. –Assume a maximum duration for the signals –Unknown offset from the GRB Noise: Assume stationarity Maximize the Likelihood over the set of offsets {  i } and waveforms {s i } over all the observed triggers –Mohanty, Proc. GWDAW-9, 2005

Dec 16, 2005GWDAW-10, Brownsville Detection Statistic Segment length Max. over offsets x 1 [k] x 2 [k] Cross-correlation (cc)   x 1 [k] x 2 [k] offset Integration length  i (“max-cc”) Final detection statistic  =  i, i=1,..,N grb Form of detection algorithm obtained depends on the prior knowledge used

Dec 16, 2005GWDAW-10, Brownsville Analysis pipeline for S2/S3/S4 H1 H2 Band pass filtering Phase calibration Whitening Correlation coefficient with fixed integration length of 100ms Maximum over offsets from GRB arrival time 1 for on- source segment Several (N segs ) from off-source data On-source pool of max-cc values Off-source pool Data Quality Cut Wilcoxon rank-sum test Empirical significance against N segs /N grbs off- source values LR statistic: sum of max-cc values

Dec 16, 2005GWDAW-10, Brownsville Data Quality: test of homogeneity Off-source cc values computed with time shifts Split the off-source max-cc values into groups according to the time shifts –Terrestrial cross-correlation may change the distribution of cc values for different time shifts. Distributions corresponding to shifts  t i and  t j Two-sample Kolmogorov-Smirnov distance between the distributions Collect the sample of KS distances for all pairs of time shifts and test against known null hypothesis distribution Results under embargo pending LSC review

Dec 16, 2005GWDAW-10, Brownsville Constraining population models The distribution of max cc depends on 9 scalar parameters   jk =  h , h  jk, – , = +,  –j,k = detector 1, 2  x, y  jk =  df x(f) y * (f) / S j (f) S k (f) Let the conditional distribution of max-cc be p(  i | [   jk ] i ) for the i th GRB

Dec 16, 2005GWDAW-10, Brownsville Constraining population models Conditional distribution of the final statistic  is P(  | {[   jk ] 1, [   jk ] 2,…, [   jk ] N }) Astrophysical model: specifies the joint probability distribution of   jk Draw N times from   jk, then draw once from P(  | {[   jk ] 1, [   jk ] 2,…, [   jk ] N }) Repeat and build an estimate of the marginal density p(  ) Acceptance/rejection of astrophysical models

Dec 16, 2005GWDAW-10, Brownsville Example Euclidean universe GRBs as standard candles in GW Identical, stationary detectors Only one parameter governs the distribution of max-cc : the observed matched filtering SNR  Astrophysical model: p(  ) = 3  min 3 /  4

Dec 16, 2005GWDAW-10, Brownsville Example 100 GRBs; Delay between a GRB and GW = 1.0 sec; Maximum duration of GW signal = 100 msec PRELIMINARY: 90% confidence belt: We should be able to exclude populations with  min  1.0; Chances of ~ 5  coincident detection: 1 in 1000 GRBs.

Dec 16, 2005GWDAW-10, Brownsville Future Modify Likelihood analysis to account for extra information (Bayesian approach) –Prior information about redshift, GRB class (implies waveforms) Use recent results from network analysis –significantly better performance than standard likelihood Diversify the analysis to other astronomical transients Use more than one statistic

Dec 16, 2005GWDAW-10, Brownsville Probability densities The astrophysical distribution is specified by nine scalar quantities   jk =  h , h  jk, – , = +,  –j,k = detector 1, 2 Max-cc density depends on three scalar variables derived from   jk –Linear combinations with direction dependent weights –Detector sensitivity variations taken into account at this stage Density of final statistic (sum over max-cc) is approximately Gaussian from the central limit theorem Confidence belt construction is computationally expensive. Faster algorithm is being implemented.