LIGO-G050312-00-D

Upper Limits on the Stochastic Background of Gravitational Waves from

LIGO

Vuk Mandic

Einstein2005 Conference

Paris, July 20 2005

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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])

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