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

18 Dec 2004 GWDAW9

Intrinsic delay depends on where shocks form

Gamma Ray Bursts

Gamma Ray BurstCentral 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

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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 = hrmssignal duration / PSD (white)

• FMR 95% UL: hrms 210-23, 1000 GRBs, PSD=310-24, 100 Hz band 10msec signal, Integration length=0.5 sec

• Matched filtering SNR ~ 2.0

• Accumulation algorithms: observational constraints• Astone et al, 2002, 2004

18 Dec 2004 GWDAW9

Objective

Explore ways to improve the sensitivity of FMRFMR 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

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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

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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.

18 Dec 2004 GWDAW9

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)

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CORRGRAM

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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

18 Dec 2004 GWDAW9

Extend to Multiple triggers

• Unknown time of arrival and duration for each trigger

• Max LR statistic :

• Final statistic : Sum of individual maxima

GRBii

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18 Dec 2004 GWDAW9

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

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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

18 Dec 2004 GWDAW9

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

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90%

mean

Confidence belt

Mean

Mean UL

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Comparison

MULTICFTFMR

•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

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•Total segment length = 2 sec@1024Hz•Sine-Gaussian: 256Hz, =0.05 sec•Number of GRBs = 100•Integration lengths: 100 msec

Comparison cont …

FMRMAX CORRGRAMSingle integration length

18 Dec 2004 GWDAW9

Comparison cont …

•Total segment length = 10 sec@1024Hz•Sine-Gaussian: 256Hz, =0.05 sec•Number of GRBs = 100•Integration lengths: 100 msec

FMRMAX CORRGRAMSingle integration length

18 Dec 2004 GWDAW9

Comparison cont…

•Total segment length = 30 sec@1024Hz•Sine-Gaussian: 256Hz, =0.05 sec•Number of GRBs = 100•Integration lengths: 100 msec

FMRMAX CORRGRAMSingle integration length

18 Dec 2004 GWDAW9

Comparison cont …

•Total segment length = 10 sec@1024Hz•Sine-Gaussian: 256Hz, =0.05 sec•Number of GRBs = 100•Integration lengths: 100 msec

FMRSINGLE MAX CORRGRAMSingle integration length

18 Dec 2004 GWDAW9

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