Population Study of Gamma Ray Bursts

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Population Study of Gamma Ray Bursts

• S. D. Mohanty
• The University of Texas at Brownsville

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GRB030329Death of a massive star
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GRB050709 (and three others)Evidence for binary
NS mergers
Chandra
HETE error circle
(Fox et al, Nature, 2005)
Bottom-line The GW sources we are seeking are
visible once a day!
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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

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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

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Detection Statistic
Integration length
offset
x1k
Cross-correlation (cc) ? ?x1k x2k
x2k
Segment length
?i (max-cc)
Max. over offsets

• Final detection statistic
• ??i , i1,..,Ngrb
• Form of detection algorithm obtained depends on
  the prior knowledge used

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Analysis pipeline for S2/S3/S4

• Band pass filtering
• Phase calibration
• Whitening

H1
Maximum over offsets from GRB arrival time
Correlation coefficient with fixed integration
length of 100ms
H2
1 for on-source segment
Several (Nsegs) from off-source data
On-source pool of max-cc values
Wilcoxon rank-sum test
Empirical significance against Nsegs/Ngrbs
off-source values
LR statistic sum of max-cc values
Off-source pool
Data Quality Cut
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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

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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) / Sj(f) Sk(f)
• Let the conditional distribution of max-cc be
  p(?i ???jk i)
  
  for the ith GRB

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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

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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

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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.

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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

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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.