The search for a stochastic background of gravitational radiation Part II

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The search for a stochastic background of
gravitational radiation Part II

• LIGO/LSC Numerical Algorithms Library (LAL)
  Development

Charlie W. Torres Jr., D. Auzmus, M. Casquette,
R.M. Luna, M.C. Diaz, J.D. Romano and J.T. Whelan
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LAL

• LIGO/LSC Numerical Algorithms Library
• Coding standard for gravitational wave detection
• Contributors from all over the world
• Routines to search for different gravitational
  wave sources
• Binary inspiral Neutron stars and/or Black Holes
• Burst sources Supernova
• Periodic sources Rotating Neutron Stars
• Stochastic background Random Signal left over
  from Big Bang

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LAL Stochastic Search Modules

• Cross-Correlation Statistic
• Optimal Filter Function
• Overlap Reduction Function
• Noise Power Spectrum
• Stochastic Signal Spectrum
• Monte Carlo Simulations

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Optimal Filtering

• Cross-correlation statistic

• Qj-k Optimal Filter Function
• Qj-k maximizes the signal-to-noise-ratio
• Qj-k depends on
• location and orientation of detectors
• type of stochastic background signal
• noise in the detectors

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Overlap Reduction Function ?(f)

• Quantifies the reduction in sensitivity due to
• Separation of the two detectors
• Non-parallel alignment of the arms of the two
  detectors
• Equals 1 for coincident and coaligned detectors
• Decreases below 1 when detectors are shifted
  apart or rotated out of coalignment

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Stochastic Background Spectrum ? gw(f)

• Proportional to power spectrum of the stochastic
  signal in a single detector
• Depends on type of stochastic signal we want to
  search for
• For simplicity, consider power law spectra
• Code being written by Alberto Vecchio and Carlo
  Ungarelli

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Noise Power Spectrum P(f)

• Indicates how power in detector noise is
  distributed in frequency
• Large noise power means poor sensitivity to
  gravitational wave signals
• Three major sources of noise for interferometric
  detectors
• Seismic vibration of earth
• Thermal vibration of molecules
• Shot random arrival of photons on mirrors

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Monte Carlo Simulations

• Once code has been written, need to verify
  correctness
• Simulate a stochastic background signal in the
  presence of detector noise
• Test detection efficiency of a stochastic
  background signal

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Conclusion

• Described one of the LAL stochastic background
  module, that we have been working on
• Many more modules currently under development
• Hope to finish major parts of the code by next
  spring to participate in engineering data runs
  prior to science data runs in 2002

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