1. Analysis techniques for data from resonant-mass detectors Pia Astone www.roma1.infn.it/rog www.roma1.infn.it/rog/astone SPIE conference, Waikoloa, Hawaii, 24 Aug. 2002

2. M ; T ; Q The Eq of geodetic deviation is the basis for all the experiments to detect g.w. Thermal noise, T=300mK, D L=3 10 -18 m They play a role that is similar to L ; P ; F for interferometers

3. 896 d 766d 852 d 221 d 200 d ON times of detectors Jan 1997-May,21, 2002 NI AU AL NA EX

4. The expected signal h is a short pulse ( a few ms). Bars can look for: The expected value on Earth, if 1% of M o is converted into g.w. in the GC, is of the order of 10 -18 Bursts

5. http://igec.lnl.infn.it

6. Bars can look for: Signals from rotating neutron stars, stars in binary systems Continuous signals

7. Noise, produced from a high number of uncorrelated events Cosmological origin: it is the result of processes that happened immediately after the Big-Bang. If measured, it will allow to discriminate various cosmological models Astrophysical origin: it is the result of more recent event (redshift z order of 2-5). It is due to unresolved processes of gravitational collapses. It will provide information on star formation rates, supernova rates, black holes...... Bars can look for: Stochastic background

8. Gamma-ray detectors Neutrino detectors Cosmic ray detectors, near the g.w. bar Bars can look for: Coincidences with Astro-Particle detectors

9. Explorer and Nautilus 2001 EXPLORER (CERN) ON from Mar to Dec Bandwidth = 9 Hz T=2.6 K Duty Cycle=267/294 =91% Average sensitivity h=4.5 10 -19  1.2 10 -4 M 0 in GC NAUTILUS (LNF) ON from Jan to Dec Bandwidth=0.4 Hz T=1.5 K Duty Cycle=291/365 =80% Average sensitivity h=5. 7 10 -19  2 10 -4 M 0 in GC Coincident operation for 213.5 days

10. Explorer and Nautilus 2001 90 days of coincident operation at the best ever reached sensitivity for the detection of bursts (of time duration 1 ms), h < 6 x 10 -19

11. THE DAGA2_HF FILTERS P.Astone, S.D’Antonio, S.Frasca, M.A. Papa The detection of bursts The problem is the detection of small signals, embedded in noise. To increase SNRs, for known shape signals: filter the data, using Matched filters BUT…………..

12. ....the filter coefficients must vary to take into account the fact that the noise is not stationary. - The basis of an adaptive filter design are the adaptive algorithm and the criterium of selection among the various filters. - adaptive filters are designed to obtain the maximum SNR for the signal we are looking for.

13. The improvement in SNR o obtained by filtering the data (SNR m ) can be expressed in terms of a reduction of the equivalent temperature T e to the effective temperature T eff : h = 7.97 x 10 -18 Sqrt(T eff ) for 1 ms bursts

14. E = 57.89 K. 87 TeV. The value of the merit factor, estimated from the signal, is Q = 1.7 10 5. Unfiltered signal (V 2 ) The signal after the filtering (kelvin) A big event E=58 K (the energy released in the bar is 87 TeV)

15. The adaptive algorithm is the method to estimate a new spectrum from the data. it is not possible to find an unique optimum method of estimation In theory the best spectral estimation is obtained using as much data as possible, in pratics various scenarious of non stationary noise are possible: Presence of spurious peaks in the spectra. Presence of “short” time disturbances in the unfiltered data. Presence of “long” time disturbances in the unfiltered data.

16. To face with these problems, we have implemented three different method to estimate the spectra and hence to build up the filters. WHOLE CLEAN ADAPTED (or varying memory)

17. The CLEAN does not use the periodograms whose integral is over the threshold: the spectral estimation is not degraded. The WHOLE uses all the periodograms the spectra estimation is degraded. The CLEAN filter is better than the WHOLE, when the disturbance is over Presence of “short” time disturbances in the data 7.5 8 8.5 hours

18. The integral of the periodograms is over the threshold for about 40 min and the clean filter does not adjourn itself… Presence of “long” time disturbances in the data 23 2 hours of data 25

19. CONCLUSION - The best filter is the one that, properly normalized, gives the lower T eff - Calibration signals, added to the noise of the detector, will be used to compare the filters, to evaluate the experimental efficiency of detection and all the event parameters. The calibration signals will be one channel of our acquisition system, DAGA2-HF

20. Coincidence analyses: Allegro-Explorer : Jun-Dec 1991 (180 days) Phys. Rev D 59, 1999 Explorer-Nautilus-Niobe : Dec 1994-Oct 1996 (Explorer –Nautilus: 57 days. Explorer-Niobe: 56 days) Astrop. Phys. 10, 1999 IGEC 1997-1998, Phys. Rev. Letters, 85, 2000 Explorer-Nautilus 1998 : CQG, 18, 2001 The IGEC analysis of the data 1997-2000 is now being done Preliminary results: CQG 19, 2002

21. The sensitivity of each detector varies with time The sensitivities of the various detectors are different The same signal generates events with energies different for each detector Practical problems, in a coincidence analysis Use of Energy filters and the Antenna pattern

22. Explorer and Nautilus during 2001 Burst sensitivity h=3-6*10 -19 Explorer 2001 h=2*10 -19 h=5*10 -19

23. A new procedure for evaluation of upper limits (Astone,Pizzella: Astrop. Physics, 16, 2002) The procedure used in the past (e.g. Allegro-Explorer 1991, IGEC 1997-1998 ) is described in Amaldi et al, A&A, 216 (1989) Problems Signals-events The energy of the event is not the energy of the g.w. Efficiency of detection It is smaller than unity, and this changes the upper limit The procedure is based on a Bayesian approach and some criticism on reporting results as C.L. is expressed

24. Likelihood, rescaled to the asymptotic limit, where the experimental sensitivity is lost (G. D’ Agostini, Nuclear Physics B 109B, 2002) http://www-zeus.roma1.infn.it/~agostini/prob+stat.html - The information in the data should be presented in the most power and unbiased way - The results should not depend on weather one believes that there is no effect, or that something has been found - The pieces of evidence coming from different experiments should be combined in the most efficient way - If many independent data sets each provide a little evidence in favor of the searched-for signal, the combination of all data should enhance the hypothesis - If the indications are incoherent, their combination should provide a strong constraint against the hypothesis

25. Rotating neutron stars They emit g.w. if the mass distribution is non axis-simmetric along the rotation axis. About 10 9 NEUTRON STARS are expected to exist in the Galaxy, but only ~ 1000 have been detected, most as PULSARS. The search for continuous waves

26. Rotating neutron stars About 10 9 NEUTRON STARS are expected to exist in the Galaxy, but only ~ 1000 have been detected, most as PULSARS. The blind search requires high computing power and hierarchical search strategies The search for continuous waves

27. The search method is based on a hierarchical method. – Short FFT data base –Construction of Time Frequency maps –Hough Transform (inchoerent, no phase information is used) –Candidate Selection –Coherent search in the selected frequency ranges (Zooming, Doppler correction, FFT…..) –New iteration The search of continuous signals see S. Frasca grwavsf.roma1.infn.it/pss

28. Short periodograms and short FFT data base What is the maximum time length of an FFT such that a Doppler shifted sinusoidal signal remains in a single bin ? (the variation of the frequency increases with this time and the bin width decreases with it) t <= 8.7 * 10 / Sqrt(f) s 4 For Explorer at 921.38, we have chosen: t = 39.7 min ( df bin =0.419 mHz; df Doppler =0.215 mHz)

29. - Scheduled tests in Rome ROG + VIRGO (S. Frasca, C. Palomba, L. Pontisso, F. Ricci, ROG) –Method applied to the data of EXPLORER and NAUTILUS. The data are taken in a small bandwidth around the two peaks in the 900 Hz region. ROG and VIRGO agreement:

30. PSS_astro User Guide (P. Astone, S. D’ Antonio)

32. Continuous wave analysis Overall sky search (2 days,Df=0.8Hz) of data is now running and will end by the summer: the analysis will put limits at the level of h c =3*10 –23 (the procedure is in Astone, Borkowsky, Jaranowsky, Krolak, PRD, 65,042003, 2002)

35. submitted to PRD, July 2002

36. Why do we need two g.w. detectors ? - The algorithm is based on the cross-correlation of the output of two independent g.w. detectors, in a time window centered at the arrival time of the GRB - If simultaneous g.w. signals arise in both Explorer and Nautilus, no matter when, respect to the GRB (but within the chosen time window) we should find a larger value of the cross-correlation function at t=0 - To increase SNR, we need Ro, the average the cross-correlation using many GRB: in fact we expect, associated to each GRB, a g.w. signal of the order of h = 3* 10-22

37. Probability density function f (h | Eo ) 2 - Eo, the measured energy, is proportional to Sqrt(Ro); - P.d.f. of g.w. energy E, or of amplitude h, can be inferred using the Bayes’s theorem: f(h|Eo )  f(Eo |h) x fo(h) 2 =0.56*10-18 ;  =0.35*10-18 2

38. Upper limit, p(h) < h Probabilistic results depend on the chosen prior: those firmly convinced that g.w. h values are in the 10-22 region would never allow a 5% chance to h above 1.2 x 10-18 thus…….

39. Relative belief updating ratio, as a function of the dimensionless amplitude of g.w.’s -Up to a fraction of 10-18 the experiment does not change our believes; -Values much larger than 10-18 are ruled out. -The region of transition from 1 to 0 identified the sensitivity bound R=0.5 s.s.b.=1.3 x 10-18 R=0.05 s.s.b.=1.5 x 10-18

40. EXPLORER and NAUTILUS Feb. 1997 Crosscorrelation measurement of stochastic g.w. background with two resonant detectors (Astr. Astroph 351,1999) (see also Phys. Lett. B, 385, 1996) 12 hours of data Bandw.=0.1 Hz Omega_gw < 6*10 10 -42 10 -38 10 -40 S h Hz -1 905 925 Hz

41. CONCLUSIONS I have presented a general idea of some analysis tools we have developed to analyze data from resonant detectors. In the paper, I have referenced only to a few papers, I invite you to refer also to the references therein. Detection of g.w.'s is a very important task in frontier research physics and collaboration with the entire g.w. community is essential to reach the goal, for which we are all so hardly working.

42. Web sites, of resonant detectors: Allegro gravity.phys.lsu.edu Auriga www.auriga.lnl.infn.it Explorer, www.roma1.infn.it/rog Nautilus Niobe www.gravity.phys.edu.au