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
Gamma Ray Bursts
Black Hole
accreting rapidly
Relativistic ejecta
• Internal and/or
• external shocks
Gamma Ray Burst
Central Engine
Possible progenitors
•Core collapse of massive,
high angular momentum
stars
•Merger of NS stars
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•Beamed Gamma Ray
emission
•Followed by afterglow
Intrinsic delay depends on where
shocks form
• Gravitational wave emission
•formation, activity and decay of
central engine
•Neutrino etc.
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 = 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
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Objective
Explore ways to improve the sensitivity of FMR
FMR works by
• Cross-correlating pairs of segments for every GRB trigger
(on-source sample) …
N 1
x ,x
1
2
  x1[ j ] x2 [ j ]
j 0
• 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.
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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
z[k , M ] 
k  M 1
 x [ j] x [ j]
j k
1
2
• CORRGRAM (Mohanty et al, Proc GWDAW8; R-statistic /
CORRPOWER, Cadonati, Marka, Poster, this conference)
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CORRGRAM
x1
x2
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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
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Extend to Multiple triggers
• Unknown time of arrival and duration for each
trigger
• Max LR statistic :
max  zi[k , M ], i  1,, NGRB
(i )
(i )
i
• Final statistic : Sum of individual maxima
 max z [k , M
(i )
i
i
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(i )
]
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)
max
zi [ k , M ], i  1, , N GRB
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
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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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Confidence belt
Mean UL
90%
mean
Mean
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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
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Comparison cont …
FMR
MAX CORRGRAM
Single integration length
•Total segment length =
2 sec@1024Hz
•Sine-Gaussian: 256Hz, =0.05 sec
•Number of GRBs = 100
•Integration lengths: 100 msec
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Comparison cont …
FMR
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
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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
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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
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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
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