A Search for the Stochastic GWBackground with the LIGO
Hanford-Hanford PairNickolas Fotopoulos (for the LIGO Scientific Collaboration)
The 7th Edoardo Amaldi Conference on Gravitational WavesSydney, Australia
2007-07-13
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Look at what LIGO could win!
Grand prize: H1-H2 can theoretically makea 10x deeper SGWB search than H1-L1
First runner up prize: H1-H2 sensitive tohigh frequencies (S4 H1-H2 was ~50xmore sensitive than S4 LLO-Allegro)
Bottom line: H1-H2 trounces the competition if we can ever believe its results (also applies to LCGT)
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Our Tools
We have two complementary techniques to identify non-gravitational contributions to H1-H2 coherence:
IFO-PEM Coherence*:Look at environmental coupling directly
IFO-IFO Timeshift:Look at everything narrow-band (non-SGWB)
* Class. Quantum Grav. 23 (2006) S693-S704
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Method Summary
Veto egregiously bad frequencies Run the search on surviving frequencies Subtract ΩPEM estimated from this band Estimate the uncertainty introduced
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Determine Veto (1) PEM coherence:
» Calculate γ12 = maxi (γ1i γ2i), where iruns through all PEM channels
» This estimates linear environmentalcontribution to H1-H2 coherence
» Could be broadband
Time-shift:» Shift H1 w.r.t. H2 by ±1,or 2 sec» Narrow-band instrumental features
should survive the time-shift» Insensitive to broad-band correlations
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Determine Veto (2)
Start with 40-240 Hz band Notch out 60 Hz harmonics Notch out structures where two
veto methods agree Most of the regions 68-102 Hz
and 126-160 Hz preserved.
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Non-stationarity
Feature at 138-143Hz shutoff fairly abruptly
Visible, but washed out overwhole dataset
Possible Solutions:» Always look at instrumental
coherence estimates on multiplesub-epochs
» Split whole search into multipleepochs with independent vetoes
[ Time-frequency Coherence map ]
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Subtract Broadband PEMContribution
Use γPEM to estimate YPEM(f).
PEM contribution not large (~1σ). [ Will omit x axis ]
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Uncertainty on ΩPEM
Statistical error negligible. Some uncertainty in definition ofγPEM
Systematic error» Assessed using vetoed (i.e.
environmentally dominated)frequency bands
» Systematic error seems to be~50%
Further study necessary
[ This is data that does notget integrated into the result,so should be safe to show. ]
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Closing Words IFO-PEM coherence and time-shift methods agree well in identifying
compromised frequency bands. IFO-PEM coherence method also offers a way to estimate broad-band
correlations.» Statistical error in ΩPEM is negligible - error is all systematic
Future work:» Investigate non-stationarity» Finalize estimate of uncertainty on ΩPEM» Recover hardware and software injections
We need feedback! Let us know if you have suggestionsfor other checks, uncertainty estimates etc.
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Stochastic Background ofGravitational Waves
Energy density:
Characterized by log-frequency spectrum:
Related to the strain powerspectrum:
Strain scale:
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Detection Strategy Cross-correlation estimator
Theoretical variance
Optimal Filter
Overlap Reduction Function
For template:
Choose N such that:
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Analysis Details Data divided into segments:
» Yi and σi calculated for eachinterval i.
» Weighed average performed. Sliding Point Estimate:
» Avoid bias in point estimate» Allows stationarity (Δσ) cut
|σi±1 – σi| / σi < ζ Data manipulation:
» Down-sample to 1024 Hz» High-pass filter (~40 Hz cutoff)
50% overlapping Hann windows:» Overlap in order to recover the
SNR loss due to windowing.
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