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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H1-H2 Coherence• Well behaved after frequency

masking.

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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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