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Search implementation for the gravitational wave stochastic background applied to the

Search implementation for the gravitational wave stochastic background applied to the S1 LIGO I Science Run Albert Lazzarini for the LIGO Scientific Collaboration 06 May 2003 LIGO Science Seminar at Caltech

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Search implementation for the gravitational wave stochastic background applied to the

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  1. Search implementation for the gravitational wave stochastic background applied to the S1 LIGO I Science Run Albert Lazzarini for the LIGO Scientific Collaboration 06 May 2003 LIGO Science Seminar at Caltech SGWB Working Group WWW SITE: http://feynman.utb.edu/~joe/research/stochastic/upperlimits/ Lazzarini - LIGO Science Seminar

  2. Outline of Talk • Stochastic GW background • LIGO S1 run summary • Search technique, implementation • Details of analysis • Results • Conclusions Lazzarini - LIGO Science Seminar

  3. The Stochastic GW Background • The stochastic GW background arises from an incoherent superposition of unresolved sources of gravitational radiation bathing Earth. • Measure: rGW -- energy density in Universe associated with GWs • Wgw(f) -- frequency distribution of energy • Cosmological sources • GW can probe the very early universe • Inhomogeneities near Planck time, inflation • Phase transitions • Cosmological defects • Astrophysical sources • NS/NS, WD/WD, periodic sources, SNe • Wgw(f) < 10-8 in LIGO band (Maggiore, gr-qc/0008027) Lazzarini - LIGO Science Seminar

  4. Relationship between cosmological quantities and measurable quantities • Power spectrum, Sgw(f): • Wgw(f) in terms of Sgw(f): • Strain for constant W: Lazzarini - LIGO Science Seminar

  5. Allen & Koranda, PhysRevD Lommen, astro-ph/0208572 Kolb & Turner, TheEarlyUniverseAddisonWesley1990 2 What is known about the stochastic background? Lazzarini - LIGO Science Seminar

  6. Stochastic GW Background Detection • Cross-correlate the output of two (independent) detectors with a suitable filter kernel: • Requires: (i) Two detectors must have overlapping frequency response functions i.e., (ii) Detectors sensitive to same polarization state (+, x) of radiation field, hgw. (iii) Baseline separation must be suitably “short”: • Limits of detection (1 year integration): • LIGO I: Wgw< 10-5 • Advanced LIGO: Wgw< 5 x 10-9 Lazzarini - LIGO Science Seminar

  7. Stochastic GW Background Detection • Correlation kernel weighting function -> optimal filter • SNR is maximized for: Lazzarini - LIGO Science Seminar

  8. Overlap Reduction Factor, g(f) • Overlap reduction function, g(f), is a function of detector geometries, orientations and detector separations Lazzarini - LIGO Science Seminar

  9. WA - WA == 1 • LA - WA shown • g(0) ~ -1 because of WA-LA interferometer orientations: LHO LLO Overlap Reduction Factor, g(f)

  10. H1: 235 hrs H2: 298 hrs L1: 170 hrs In-Lock Data Summary from S1Red lines: integrated up timeGreen bands (w/ black borders): epochs of lock • August 23 – September 9, 2002: 408 hrs (17 days). • Individual interferometers: • H1 (4km): duty cycle 57.6% ; Total Locked time: 235 hrs • H2 (2km): duty cycle 73.1% ; Total Locked time: 298 hrs • L1 (4km): duty cycle 41.7% ; Total Locked time: 170 hrs • Double coincidences: • L1 & H1 : duty cycle 28.4%; Total coincident time: 116 hrs • L1 & H2 : duty cycle 32.1%; Total coincident time: 131 hrs • H1 & H2 : duty cycle 46.1%; Total coincident time: 188 hrs • Triple Coincidence: L1, H1, and H2 : duty cycle 23.4% ; • Total coincident time: 95.7 hrs For this analysis: L1-H1: Valid data: 75 hrs Quiet Data: 75 hrs Calibrated Data: 64 hrs Net uptime: 15.7% L1-H2: Valid data: 81 hrs Quiet Data: 66 hrs Calibrated Data: 51 hrs Net uptime: 12.5% H1-H2: Valid data: 134 hrs Quiet Data: 119 hrs Calibrated Data: 100 hrs Net uptime: 24.5% Lazzarini - LIGO Science Seminar

  11. S1 Sensitivities • Spectra taken just before run • Cross correlation technique allows one to “dig” signal below noise floor in individual instruments • Dashed lines show expected 90% confidence bounds one could set: • 100 hrs of observation with H2km +L4km (W=10) • 150 hrs of observation with H2km + H4km (W=1) • Limits from theoretical SNR equation Lazzarini - LIGO Science Seminar

  12. IJ Implementation of analysis • Analysis performed in data intervals of 900s (15 min) • For each 900s interval, I : • Average power spectrum, mid point calibration used for entire interval • Ten 90s segments are analyzed separately • Provides 10 independent estimates, statistics of estimates • For each 90s segment J, estimate: • resample data to 1024 samples/s (512 Hz Nyquist) • 90% of SNR comes below f~300Hz • FFT, window data • Calculate estimate YIJ • Average n = 45 frequency bins to obtain cross-correlation spectra with Df = 0.25 Hz • Average 10 values of YIJ to obtain interval average, YI, sample variance, sI2 Lazzarini - LIGO Science Seminar

  13. Implementation of analysis • Results for 900s intervals combined to obtain run averaged answer (“point estimate”). • Weights sI2 are obtained from the power spectra for each interval,I. • Measures data quality -- how quiet the interferometer pair was during interval I • Overall statistical error for the estimate derived from individual interval variances Lazzarini - LIGO Science Seminar

  14. Pipeline analysis flow Lazzarini - LIGO Science Seminar

  15. sWindow sData T = 90s Windowing Effects • Sources of spectral leakage: • Analysis of data in finite segments • Redness of spectrum (seismic wall) • Narrow band features • Will be removed by notching, need to make sure their effect is contained in a few frequency bins • Studied different window widths • Used a Tukey window • Flat top plus smooth fall-off at ends: • 0.5s + 89s + 0.5s 1/2 THann Lazzarini - LIGO Science Seminar

  16. End-to-end pipeline validationSW and HW injection of simulated stochastic backgrounds • Generate time series of correlated random noise with same properties as SGWB • Injected in hardware during S1 run at several amplitudes • Inject post run for further verification Lazzarini - LIGO Science Seminar

  17. Extractions consistent with injections Extraction of injected signals • c2 with 2 D.O.F: time offset, amplitude • Theoretical curve determined by power spectra, P1(f), P2(f) • Points obtained by performing a time-shift analysis of data • Analysis sensitive to relative timing of data streams • 270 ms offset consistent with post-run GPS measurements Lazzarini - LIGO Science Seminar

  18. Survey of cross-spectral coherences, G12(f) • Narrowband coherences persist over long integration times • n x 60 Hz (H1-H2) line harmonics • n x16 Hz (all pairs) GPS-synchronized clocking electronics for data acquisition system • 250 Hz (?) • Lines excised by excluding them from the integration over frequency to obtain estimates, YIJ Lazzarini - LIGO Science Seminar

  19. IJ Time-frequency map of cross-correlationstatistics YIJfor entire S1 run H1-H2 Lazzarini - LIGO Science Seminar

  20. Data Quality -- Variability in noise floor during S1 • Variations in statistical weights, sI2, with which individual measurements are combined • Horizontal lines correspond to “representative” power spectra shown earlier • Variability shown is on 900s scale, taken into account by weights • Variability on <900s leads to source of error in estimate beyond statistical errors • H1-H2: sPSD nonstationarity~ 0.1 • H1-L1: sPSD nonstationarity ~ 0.3 • H2-L1: sPSD nonstationarity ~ 9.3 • Effect estimated by rerunning analysis with a finer granularity Lazzarini - LIGO Science Seminar

  21. Data Quality --Variations in calibrations during S1Example :H2-L1 (H2 interferometer) • 900s midpoint calibrations used • 60s trends in calibration were acquired • Variability on <900s leads to source of error in estimate beyond statistical errors • H1-H2: scalibration~ 0.2 • H1-L1: scalibration ~ 0.4 • H2-L1: scalibration ~ 1.2 • Re-ran analysis on finer granularity to assess effect of varying R Lazzarini - LIGO Science Seminar

  22. Data Quality --Variations in timing during S1Example :H2-L1 • Timing offsets of acquisition system changed during S1 • Hardware reboots • Variability over run leads to source of systematic error in estimate beyond statistical errors • Scale factor, ftime, in estimate • H1-H2: ftime~ 1 (not signifcant) • H1-L1: ftime ~ 1 (not signifcant) • H2-L1: ftime ~ 1.05 • +200 ms shift • Include in final result as a scaling up of estimate Lazzarini - LIGO Science Seminar

  23. < > Frequency, time dependence ofcross correlation kernels • Run-averaged kernels • Integrals correspond to estimates of Weff Lazzarini - LIGO Science Seminar

  24. Time evolution over S1 of estimates • Running estimates of Weff over run • End points correspond to estimates of Weff: • Bottom panels show probability of observing running estimate at each time, T, if underlying process is zero-mean Gaussian noise +/- 1.65s Lazzarini - LIGO Science Seminar

  25. Statistics of estimates • Normal deviates of 90s estimates from average values are Gaussian RVs: • <XIJ> = 0 • s2= 1 Lazzarini - LIGO Science Seminar

  26. Time shift analysis of final results • H2-L1, H1-L1 consistent with random excursions from point to point • H1-H2 exhibits time variations not consistent with random noise • Influence of residual instrumental correlations present • Time series not consistent with SNR=10 signal due to W=const. Lazzarini - LIGO Science Seminar

  27. S1 results • H1-H2: W0(h100)2 + Winstrumental = (-11 +/- 2) + 20% • H1-L1: W0(h100)2 < 70 + 20% • H2-L1: W0(h100)2 < 23+ 20% Lazzarini - LIGO Science Seminar

  28. S2 -> Stochastic Gravitational Wave Background“Landscape” Lazzarini - LIGO Science Seminar

  29. Summary and conclusions H2-L1 provides the best upper limit from S1 Measurement BW Df = 274 Hz: 40Hz , f < 314 Hz Within 2x of expectation at beginning of run (~10 vs ~23) 64 hrs vs 100 hrs -> 1.25x calibration variation, overall uncertainty non-stationarity of noise floors timing offsets 2x - 3x better than previous (narrowband, Df = 1 Hz) direct measurement with bars @ 1 kHz

  30. Summary and conclusions H1-H2 was not usable, even though it would have had 10x sensitivity Statistical error is as expected, ~ 1 Bias (-10s) was not foreseen (could have been expected) Correlations exhibit instrumental features WA-LA: narrowband GPS synchronization of data acquisition systems 250 Hz feature of presently unknown nature WA-WA : narrowband and broadband 60 Hz mains and harmonics, upconversion broadening Acoustic couplings within corner station between detection systems Broadband 200 - 300 Hz

  31. Summary and conclusions (2) • PlansforS2 andbeyond • Take calibration variability, non-stationarity into account on the finest possible time scales • Improve on calibration uncertainty • Identifyandeliminate or remove correlatednoisesourcesforH-H2 • Review, improvedataanalysispipelineeghigh-passfilteringlineremovalfrequency rangewindowing • SetupinfrastructureforALLEGRO-LLOGEO-LIGOcorrelations • ALLEGRO - LLO correlation may allow identification of instrumental biases vs signal • ALLEGRO can be rotated, allowing for an improved analysis (Finn & Lazzarini, PRD 15 October 2001) • Restructureanalysiscodeformoreefficienttime-shiftanalysis, simulations • ExpectedS2 upper-limitW(h100)2 <10-2 for H2-L1 • Ultimate LIGO I (1 yr integration): W(h100)2 <10-5 H2-L1 Lazzarini - LIGO Science Seminar

  32. FINIS Lazzarini - LIGO Science Seminar

  33. Lazzarini - LIGO Science Seminar

  34. Lazzarini - LIGO Science Seminar

  35. H1 - H2 Lazzarini - LIGO Science Seminar

  36. H2 - L1 Lazzarini - LIGO Science Seminar

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