upper limits on the stochastic background of gravitational waves from ligo
DESCRIPTION
Upper Limits on the Stochastic Background of Gravitational Waves from LIGO. Vuk Mandic Einstein2005 Conference Paris, July 20 2005. Outline. Sources and Observations Searching for Gravitational Waves with Interferometers Searching for Stochastic Background Results Outlook and Conclusions. - PowerPoint PPT PresentationTRANSCRIPT
LIGO-G050312-00-D
Upper Limits on the Stochastic Background of Gravitational Waves from
LIGO
Vuk Mandic
Einstein2005 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
3LIGO-G050312-00-D
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])
Lo
g(
0h 1
002 )
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
5LIGO-G050312-00-D
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
Y2
2
opt
i
i22
opt
0h1002 Yopt T
ˆ opt T
PI
t
60s
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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 s
pect
rum
(ar
b)
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