Dec 16, 2005 GWDAW-10, Brownsville

Population Study of Gamma Ray Bursts

S. D. Mohanty

The University of Texas at Brownsville

Dec 16, 2005 GWDAW-10, Brownsville

GRB030329Death of a massive star

Dec 16, 2005 GWDAW-10, Brownsville

GRB050709 (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, 2005 GWDAW-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, 2005 GWDAW-10, Brownsville

Maximum Likelihood approach

• Data: fixed length segments from multiple IFOs for each GRB– xi for the ith GRB

• Signal: Unknown signals si for the ith 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 {si} over all the observed triggers

– Mohanty, Proc. GWDAW-9, 2005

Dec 16, 2005 GWDAW-10, Brownsville

Detection Statistic

Segment length

Max. over offsets

x1[k]

x2[k]

Cross-correlation (cc) x1[k] x2[k]

offsetIntegration length

i (“max-cc”)

Final detection statistic= i , i=1,..,Ngrb

Form of detection algorithm obtained depends on the prior knowledge used

Dec 16, 2005 GWDAW-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 (Nsegs) from off-source data

On-source pool of max-cc values

Off-source pool

Data Quality Cut

Wilcoxon rank-sum test Empirical

significance against Nsegs/Ngrbs off-source values

LR statistic: sum of max-cc values

Dec 16, 2005 GWDAW-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 ti and tj

• 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, 2005 GWDAW-10, Brownsville

Constraining population models

• The distribution of max cc depends on 9 scalar parameters

jk = h, hjk ,

, = +, – j,k = detector 1, 2

x, yjk = df x(f) y*(f) / Sj(f) Sk(f)

• Let the conditional distribution of max-cc be p(i| [

jk ]i) for the ith GRB

Dec 16, 2005 GWDAW-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, 2005 GWDAW-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 min3 / 4

Dec 16, 2005 GWDAW-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, 2005 GWDAW-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, 2005 GWDAW-10, Brownsville

Probability densities

• The astrophysical distribution is specified by nine scalar quantities

jk = h, hjk , , = +, – 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.