1. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 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/

2. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 2 Outline of Talk Stochastic GW background LIGO S1 run summary Search technique, implementation Details of analysis Results Conclusions

3. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 3 The stochastic GW background arises from an incoherent superposition of unresolved sources of gravitational radiation bathing Earth. »Measure:  GW -- energy density in Universe associated with GWs  gw (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  gw (f) < 10 -8 in LIGO band (Maggiore, gr-qc/0008027) The Stochastic GW Background

4. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 4 Relationship between cosmological quantities and measurable quantities Power spectrum, S gw (f):  gw (f) in terms of S gw (f): Strain for constant  :

5. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 5 2 Allen & Koranda, Phys  Rev  D  Lommen, astro-ph/0208572 Kolb & Turner, The  Early  Universe  Addison  Wesley  1990 What is known about the stochastic background?

6. LIGO-G030242-01-E 06 May 2003Lazzarini - 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, h gw. (iii) Baseline separation must be suitably “short”: Limits of detection (1 year integration): »LIGO I:  gw < 10 -5 »Advanced LIGO:  gw < 5 x 10 -9

7. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 7 Correlation kernel weighting function -> optimal filter SNR is maximized for: Stochastic GW Background Detection

8. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 8 Overlap Reduction Factor,  (f) Overlap reduction function,  (f), is a function of detector geometries, orientations and detector separations

9. LIGO-G030242-01-E Overlap Reduction Factor,  (f) WA - WA == 1 LA - WA shown  (0) ~ -1 because of WA-LA interferometer orientations: LHO LLO

10. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 10 In-Lock Data Summary from S1 In-Lock Data Summary from S1 Red lines: integrated up time Green 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 H1: 235 hrsH2: 298 hrs L1: 170 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%

11. LIGO-G030242-01-E 06 May 2003Lazzarini - 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 (  =10) »150 hrs of observation with H2km + H4km (  =1) »Limits from theoretical SNR equation

12. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 12 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 Y IJ –Average n = 45 frequency bins to obtain cross-correlation spectra with  f = 0.25 Hz »Average 10 values of Y IJ to obtain interval average, Y I, sample variance, s I 2 Implementation of analysis IJ

13. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 13 Implementation of analysis Results for 900s intervals combined to obtain run averaged answer (“point estimate”). Weights  I 2 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

14. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 14 Pipeline analysis flow

15. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 15 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 Windowing Effects  Window  Data T = 90s 1/2 T Hann

16. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 16 End-to-end pipeline validation SW 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

17. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 17 Extraction of injected signals  2 with 2 D.O.F: time offset, amplitude Theoretical curve determined by power spectra, P 1 (f), P 2 (f) Points obtained by performing a time- shift analysis of data Extractions consistent with injections Analysis sensitive to relative timing of data streams 270  s offset consistent with post-run GPS measurements

18. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 18 Survey of cross-spectral coherences,  12 (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, Y IJ

19. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 19 Time-frequency map of cross-correlation statistics Y IJ for entire S1 run H1-H2 IJ

20. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 20 Data Quality -- Variability in noise floor during S1 Variations in statistical weights,  I 2, 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:  PSD nonstationarity ~ 0.1 H1-L1:  PSD nonstationarity ~ 0.3 H2-L1:  PSD nonstationarity ~ 9.3 Effect estimated by rerunning analysis with a finer granularity

21. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 21 Data Quality -- Variations in calibrations during S1 Example :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:  calibration ~ 0.2 H1-L1:  calibration ~ 0.4 H2-L1:  calibration ~ 1.2 Re-ran analysis on finer granularity to assess effect of varying R

22. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 22 Data Quality -- Variations in timing during S1 Example :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,  time, in estimate H1-H2:  time ~ 1 (not signifcant) H1-L1:  time ~ 1 (not signifcant) H2-L1:  time ~ 1.05 +200  s shift Include in final result as a scaling up of estimate

23. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 23 Frequency, time dependence of cross correlation kernels Run-averaged kernels Integrals correspond to estimates of  eff

24. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 24 Time evolution over S1 of estimates Running estimates of  eff over run End points correspond to estimates of  eff : Bottom panels show probability of observing running estimate at each time, T, if underlying process is zero-mean Gaussian noise +/- 1.65 

25. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 25 Statistics of estimates Normal deviates of 90s estimates from average values are Gaussian RVs: » = 0 »    = 1

26. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 26 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  =const. Time shift analysis of final results

27. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 27 S1 results H1-H2:   (h 100 ) 2 +  instrumental = (-11 +/- 2) + 20% H1-L1:   (h 100 ) 2 < 70 + 20% H2-L1:   (h 100 ) 2 < 23 + 20%

28. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 28 Stochastic Gravitational Wave Background “Landscape” S2 ->

29. LIGO-G030242-01-E Summary and conclusions H2-L1 provides the best upper limit from S1 Measurement BW  f = 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,  f = 1 Hz) direct measurement with bars @ 1 kHz

30. LIGO-G030242-01-E Summary and conclusions H1-H2 was not usable, even though it would have had 10x sensitivity »Statistical error is as expected, ~ 1 »Bias (-10  ) 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. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 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   (h 100 ) 2 <  10 -2 for H2-L1 »Ultimate LIGO I (1 yr integration):   (h 100 ) 2 <  10 -5 H2-L1

32. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 32 FINIS

33. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 33

34. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 34

35. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 35 H1 - H2

36. LIGO-G030242-01-E 06 May 2003Lazzarini - LIGO Science Seminar 36 H2 - L1