1. LIGO-G050312-00-D Upper Limits on the Stochastic Background of Gravitational Waves from LIGO Vuk Mandic Einstein2005 Conference Paris, July 20 2005

2. LIGO-G050312-00-D 2 Outline Sources and Observations Searching for Gravitational Waves with Interferometers Searching for Stochastic Background Results Outlook and Conclusions

3. LIGO-G050312-00-D 3 Stochastic Background of Gravitational Waves Energy density: Characterized by log- frequency spectrum: Related to the strain spectrum: Strain scale:

4. LIGO-G050312-00-D 4 -16-14-12-10-8-6-4-202468 -14 -12 -10 -8 -6 -4 -2 0 Log(f [Hz]) Log (W 0 h 100 2 ) f ~ H 0 - one oscillation in the lifetime of the universe f ~ 1/Plank scale – red shifted from the Plank era to the present time -1810 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 ~ 10 9 GeV Landscape LIGO S1, 2 wk data Ω 0 h 100 2 < 23 PRD 69(2004)122004 Initial LIGO, 1 yr data Expected Sensitivity ~ 2x10 -6 Advanced LIGO, 1 yr data Expected Sensitivity ~ 7x10 -10

5. LIGO-G050312-00-D 5 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: »E in = E 0 x e i*  *cos(  t) Output voltage is demodulated »Pound-Drever-Hall lock-in. Time

6. LIGO-G050312-00-D 6 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 MIT 3002 km (L/c = 10 ms) Livingston, LA Hanford, WA

7. LIGO-G050312-00-D 7 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

8. LIGO-G050312-00-D 8 Detection Strategy Cross-correlation estimator Theoretical variance Optimal Filter Overlap Reduction Function

9. LIGO-G050312-00-D 9 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 PIPI t 60s

10. LIGO-G050312-00-D 10 Stationarity Cut For each segment, require:

11. LIGO-G050312-00-D 11 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

12. LIGO-G050312-00-D 12 S3 Run: 31 Oct 2003 – 9 Jan 2004 H1-L1 Pair, Exposure of 218 hours S3 Results Power lawFreq. Range at 100Hz Upper Limit α=069-156Hz α=273-244Hz α=376-329Hz h 100 =0.72

13. LIGO-G050312-00-D 13 S3 Results Ω gw  10 3 Cumulative Analysis Time (hr) Running Point EstimateCross-Correlation Spectrum Ω gw  10 3 CC spectrum (arb) Frequency (Hz) (α=0)

14. LIGO-G050312-00-D 14 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