LIGO-G050312-00-D Upper Limits on the Stochastic Background of Gravitational Waves from LIGO Vuk Mandic Einstein2005 Conference Paris, July 20 2005
Jan 06, 2018
LIGO-G050312-00-D
Upper Limits on the Stochastic Background of Gravitational Waves from
LIGO
Vuk MandicEinstein2005 Conference
Paris, July 20 2005
2LIGO-G050312-00-D
Outline
Sources and Observations Searching for Gravitational Waves with
Interferometers Searching for Stochastic Background Results Outlook and Conclusions
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Stochastic Background of Gravitational Waves
Energy density:
Characterized by log-frequency spectrum:
Related to the strain spectrum:
Strain scale:
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-16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8
-14
-12
-10
-8
-6
-4
-2
0
Log (f [Hz])
Log
(0h
1002 )
f ~ H0 - one oscillation in the lifetime of the universe
f ~ 1/Plank scale – red shifted from the Plank era to the present time
-18 10
Laser Interferometer Space Antenna - LISA
Inflation
Slow-roll
Cosmic strings
Pre-big bang model
EW or SUSY Phase transition
Cyclic model
CMB
Pulsar Nucleosynthesis
Horizon size GW redshifted into LIGO band were produced at T ~ 109 GeV
Landscape LIGO S1, 2 wk data Ω0h100
2 < 23 PRD 69(2004)122004
Initial LIGO, 1 yr data Expected Sensitivity
~ 2x10-6
Advanced LIGO, 1 yr data Expected Sensitivity~ 7x10-10
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Interferometers as Gravitational Wave Detectors
Gravitational wave stretches one arm while compressing the other.
Interferometer measures the arm-length difference.» All masses are free.
Fabry-Perot cavities effectively magnify the arm lengths.
Input field is phase modulated:» Ein = E0 x ei**cos(t)
Output voltage is demodulated» Pound-Drever-Hall lock-in.
Time
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LIGO Observatories
3 interferometers:» H1: 4 km at Hanford, WA» H2: 2 km at Hanford, WA» L1: 4 km at Livingston, WA
Correlating interferometers significantly improves the sensitivity.» Assuming instrumental
correlations are negligible.
Caltech
MIT3002 km
(L/c = 10 ms)
Livingston, LA
Hanford, WA
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LIGO Sensitivity
Fundamental sensitivity limitations:» Seismic noise: <30 Hz» Thermal noise: 30-150 Hz» Shot noise: >150 Hz
In practice, many other sources:» Intensity and frequency noise of the
laser» Auxiliary feedback loops
Rapidly approaching design sensitivity
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Detection Strategy Cross-correlation estimator
Theoretical variance
Optimal Filter
Overlap Reduction Function
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Analysis Details
60-sec segments Sliding Point Estimate
» Avoid bias» Allows stationarity cut
Data manipulation:» Down-sample to 1024 Hz» Notch: 16 Hz, 60 Hz, simulated
pulsar lines» High-pass filter
50% overlapping Hann windows
ii
iii Y
Y 2
2
opt
i
i22
opt
0h1002 Yopt T
ˆ opt T
PI
t60s
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Stationarity Cut
For each segment, require: %201
i
ii
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Hardware and Software Injections
Hardware Injections:» Performed by physically moving
the test-masses» Successfully recovered» Ultimate test of the analysis code
Software injections» Performed by adding a stochastic
time-series in the analysis code» By repeating many times can
check the theoretical variance
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S3 Run: 31 Oct 2003 – 9 Jan 2004 H1-L1 Pair, Exposure of 218 hours
S3 Results
Power law Freq. Range
at 100Hz
Upper Limit Upper Limit
α=0 69-156Hz
α=2 73-244Hz
α=3 76-329Hz
4^^
10
gw
410gw2/1232/1 10 HzSgw
0.70.6
2.77.4
2.60.4
4.8
21009.4 Hzf
31008.1 Hzf 2.1
211001.2 fHz
231001.2 fHz
h100=0.72
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S3 Results
Ωgw
1
03
Cumulative Analysis Time (hr)
2
Running Point Estimate Cross-Correlation Spectrum
Ωgw
1
03C
C sp
ectru
m (a
rb)
Frequency (Hz)
2
(α=0)
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Outlook and Conclusions
Run S4» 1 month (Feb-Mar 2005)» Expect ~10 times better sensitivity for
the H1-L1 pair Year long run expected to start in
the fall» Design sensitivity» Another factor of ~10 expected
H1-H2 pair even more sensitive» But also more susceptible to site-
related correlations AdvLIGO: ~1000x improvement in
sensitivity