INTERPRETATION of IGEC RESULTS

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Ernest Wiggins
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starting point: IGEC 1997-2000 results (P.Astone et al.

1 INTERPRETATION of IGEC RESULTS Lucio Baggio, Giovanni Andrea Prodi University of Trento and INFN Italy or unfolding gw source parameters starting point: IGEC results (P.Astone et al., PRD 68 (2003) ) with reference to: LIGO S1 burst gw results (B.Abbott et al., gr-qc/ )

2 IGEC COMPARISON at a GLANCE LIGO S1 systematic search over many amplitude thresholds: many data selections many data points bound of maximum false dismissal probability of detection: conservative efficiency is estimated for δ-like waveform results are upper limits on rate of detected burst gws above threshold: rate vs search threshold cumulative Lacking the unfolding to gw source parameters ( uninterpreted results) playground data to tune the search: one data selection one data point montecarlo for some specific source models: efficiency is measured vs gw amplitude for sample waveforms results are upper limits on rate of incoming burst gws: rate vs true amplitudes Source model: sample waveforms incoming at fixed amplitude + directional corrections

3 UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION Poisson rate of detected gw [year 1 ] dashed region excluded with probability 90% overcoverage search threshold signal template = -like gw from the Galactic Center direction signal amplitude H S = FT[h S ] at Hz H 21 S ~ 210 / Hz 002. M converted in burst gw at GalacticCe nter

4 UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (2) Poisson rate of detected gw [year 1 ] dashed region excluded with probability 90% overcoverage 1.8 yr -1 search threshold no coincidences found, limited by the observation time limited by accidental coincidences observation time cuts off: sensitivity cut

5 UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (3) Poisson rate of detected gw [year 1 ] search threshold analysis includes all the measured signal amplitudes search threshold result is cumulative for H M H t systematic search vs threshold H t many trials (20 /decade) almost independent results

6 Case of gw flux of constant amplitude: δ-like signal from GC Poisson rate of detected δ gw [year 1 ] search threshold correct each result for the detection efficiency as a function of gw amplitude H S convert in terms of parameters of the source model at H S H t efficiency 0.25 due to 2-fold observations at threshold at H S 2 H t efficiency = 1 enough above the threshold Poisson rate of incoming gw [year 1 ] true δ amplitude H S

7 Case of gw flux of constant amplitude: δ-like signal from GC (2) complete conservative efficiency estimation for the single data point on all data points convert from H S = FT[h S ] at Hz to template amplitude parameter e.g. for a sine-gaussian(850 Hz;Q=9) h rss = 10 Hz 0.5 H S Poisson rate of incoming gw [year 1 ] true δ amplitude H S

8 Remarks IGEC time coincidence search provides a systematic search as a function of common threshold a directional search strategy is able to deal with detectors with different sensitivities (level & bandwidths) search with templates search resctricted on the common sensitivity bandwidth detectors with different antenna patterns and locations if gw polarization is modeled or simply linear IGEC method is able to assess the false detection probability Of course, relevant improvements are possible: - provide measurements of detection efficiency Monte Carlo injection of selected templates - feed a further stage of coherent analysis - effective control of false detections of surveys

9 1,000 HOW to UNFOLD IGEC RESULTS in terms of GW FLUX at the EARTH Take a model for the distribution of events impinging on the detector H S H t (dashed line) Estimate the distribution of measured coincidences H M H t (cont.line) Compare with IGEC results to set confidence intervals on gw flux parameters rate (year 1 ) coverage search threshold 1E-21 1E-20 1E-19 H (Hz -1 t )

10 the resulting interpreted upper limit Case of gw flux of constant amplitude: δ-like signal from GC (3) convert from H S = FT[h S ] at Hz to template amplitude parameter e.g. for a sine-gaussian(850 Hz;Q=9) h rss = 10 Hz 0.5 H S Poisson rate of detected gw [year 1 ] search threshold

11 the resulting interpreted upper limit Case of gw flux of constant amplitude: comparison to LIGO convert from H S = FT[h S ] at Hz to template amplitude parameter e.g. for a sine-gaussian(850 Hz;Q=9) h rss = 10 Hz 0.5 H S Poisson rate of detected gw [year 1 ] h rss

12 Case of gw flux of constant amplitude: comparison with LIGO results IGEC sets an almost independent result per each tried threshold H t correct each result for the detection efficiency as a function of gw amplitude H S : e.g. at H S H t efficiency 0.25 due to 2-fold observations at threshold at H S 2 H t efficiency = 1 enough above the threshold Poisson rate of detected gw [year 1 ] search threshold

13 amplitude (Hz ) DIRECTIONAL SEARCH: sensitivity modulation time (hours) amplitude (Hz ) sin 2 ϑgc amplitude directional sensitivity sin 2 ϑ time (hours) GC

14 Resampling statistics by time shifts amplitude (Hz ) time (hours) We can approximately resample the stochastic process by time shift. in the shifted data the gw sources are off, along with any correlated noise Ergodicity holds at least up to timescales of the order of one hour. The samples are independent as long as the shift is longer than the maximum time window for coincidence search (few seconds)

15 Setting confidence intervals IGEC approach is frequentistic in that it computes the confidence level or coverage as the probability that the confidence interval contains the true value unified in that it prescribes how to set a confidence interval automatically leading to a gw detection claim or an upper limit based on maximum likelyhood confidence intervals (different from Feldman & Cousins) false dismissal is under control (but detection efficiency is only lowerbounded) estimation of the probability of false detection (many attempts made to enhance the chances of detection)

16 TESTING the NULL HYPOTHESIS N gw search threshold [10-21 /Hz] many trials! all upper limits but one: NULL HYPOTHESIS WELL IN AGREEMENT WITH THE OBSERVATIONS testing the null hypothesis overall false alarm probability 33% for 0.95 coverage 56% for 0.90 coverage at least one detection in the set in case NO GW are in the data

17 FALSE ALARM RATES false alarm rate [yr -1 ] E-3 1E-4 1E-5 AL-AU AL-AU-NA dramatic improvement by increasing the detector number: 3-fold or more would allow to identify the gw candidate 1E-6 2E-21 1E-20 common search threshold [Hz -1 ] mean rate of events [ yr -1 ] mean timing [ms]

18 UPPER LIMIT on the RATE of BURST GW from the GALACTIC CENTER DIRECTION (3) Poisson rate of detected gw [year 1 ] search threshold analysis includes all the measured signal amplitudes search threshold result is cumulative for H M H t systematic search vs threshold H t many trials (20 /decade) almost independent results

19 MULTIPLE DETECTOR ANALYSIS network is needed to estimate (and reduce) the false alarms time coincidence search among exchanged triggers time window is set according to timing uncertainties by requiring a conservative false dismissal t t k σ + σ false dismissal 2 2 i j i j false alarms k maximize the chances of detection i.e. the ratio 1 k 2 by Tchebyscheff inequality efficiency of detection fluctuations of false alarms measure the false alarms: time shifts resampling the stochastic processes so that: gw sources are off (as well as any correlated noise) statistical properties are preserved (max shift ~ 1 h) independent samples (min shift > largest time window ~ few s)

20 DIRECTIONAL SENSITIVITY The achieved sensitivity of bar detectors limits the observation range to sources in the Milky Way. The almost parallel orientation of the detectors guarantees a good coverage of the Galactic Center Sin 2 (θ) ALLEGRO AURIGA -EXPLORER NAUTILUS NIOBE amplitude directional Time (h) sensitivity factor vs sideral time (hours)

21 Fourier amplitude of burst gw h() t = H δ ( t t ) TARGET GW SIGNALS 0 arrival time Detectable signals: transients with flat Fourier amplitude at the detector frequencies (900 Hz) each detector applies an exchange threshold on measured H OBSERVATION TIME (days) threshold on burst gw

$fraction of time in monthly bins threshold on burst gw > 610 Hz 21 1 3 6 10 Hz 21 1 < 310$

22 EXCHANGED PERIODS of OBSERVATION ALLEGRO AURIGA EXPLORER NAUTILUS NIOBE fraction of time in monthly bins threshold on burst gw > 610 Hz Hz 21 1 < 310 Hz 21 1

23 AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS normalized to each detector threshold for trigger search 1 1 relative counts relative counts AMP/THR ALLEGRO 1 10 AMP/THR AURIGA 1 10 AMP/THR EXPLORER 1 10 AMP/THR NAUTILUS 1 10 AMP/THR NIOBE typical trigger search thresholds: SNR 3 ALLEGRO, NIOBE SNR 5 AURIGA, EXPLORER, NAUTILUS The amplitude range is much wider than expected: non modeled outliers dominate at high SNR

24 POISSON STATISTICS of ACCIDENTAL COINCIDENCES Poisson fits of accidental concidences: χ 2 test sample of EX-NA background one-tail probability = 0.71 histogram of one-tail χ 2 probabilities for ALL two-fold observations agreement with uniform distribution coincidence times are random

25 Data selection at work Duty time is shortened at each detector in order to have efficiency at least 50% A major false alarm reduction is achieved by excluding low amplitude events. amplitude (Hz ) time (hours)

26 FALSE ALARM REDUCTION by amplitude selection of events amplitude A consequence: selected events have consistent amplitudes time

27 Auto- and cross-correlation of time series (clustering) Auto-correlation of time of arrival on timescales ~100s No cross-correlation

28 UPGRADE of the AURIGA resonant bar detector Previous set-up during observations current set-up for the upcoming II run beginning cool down phase at operating temperature by November

29 AURIGA II run Al2081 holder LHe4 vessel Main Attenuator Electronics wiring support Sensitive bar Thermal Shield Compression Spring Transducer

30 AURIGA II run: upgrades new mechanical suspensions: attenuation > 360 db at 1 khz new capacitive transducer: two-modes (1 mechanical+1 electrical) new amplifier: double stage SQUID new data analysis: C++ object oriented code FEM modelled optimized mass 200 energy resolution frame data format

31 initial goal of AURIGA II: improving amplitude sensitivity by factor 10 over IGEC results

32 FUTURE PROSPECTS we are aiming at

33 DUAL detectors estimated sensitivity at SQL: Science with HF GW BH and NS mergers and ringdown NS vibrations and instabilities EoSof superdense matter Exp. Physics of BH Mo Dual 16.4 ton height 2.3 m Ø 0.94m SiC Dual 62.2 ton height 3 m Ø 2.9m T~0.1 K, Standard Quantum Limit Only very few noise resonances in bandwidth. Sensitive to high frequency GW in a wide bandwidth. PRD 68 (2003) 1020XX in press PRL 87 (2001)

34 New concepts - new technologies: No resonant transducers: measure differential motion of massive cylindrical resonators Mode selective readout: measured quantity: X = x1+x2-x3-x4 High cross section materials (up to 100 times larger than Al5056 used in bars)

resonator is driven below resonance phase difference of π In the differential measurement: the signals sum up

35 Dual detector: the concept 2 nested masses: below both resonances: the masses are driven in-phase phase difference is null Intermediate frequency range: the outer resonator is driven above resonance, the inner resonator is driven below resonance phase difference of π In the differential measurement: the signals sum up the readout back action noise subtracts above both resonances: the masses are driven out-of-phase phase difference is null

36 Differential measurement strategy Average the deformation of the resonant masses over a wide area: reduce thermal noise contribution from high frequency resonant modes which do not carry the gravitational signal Readout with quadrupolar symmetry: geometrically selective readout that rejects the non-quadrupolar modes bandwidth free from acoustic modes not sensitive to gw. Example: - capacitive readout - The current is proportional to:

37 Dual Detector with S hh ~10-23 / Hz in 1-5 khz range Molybdenum Q/T>2x10 8 K -1 - Mass = 16 tons R = 0.47 m - height = 2.3 m Silicon Carbide (SiC) Q/T > 2x10 8 K -1 - Mass = 62 tons R = 1.44 m - height = 3 m Feasibility issues Detector: Massive resonators ( > 10 tons ) Cooling Suspensions Low loss and high cross-section materials Readout: Selective measurement strategy Quantum limited Wide area sensor Displacement sensitivity

38 R&D on readouts: status Requirement: ~ 5x10-23 m/ Hz Present AURIGA technology: m/ Hz with: optomechanical readout - based on Fabry-Perot cavities capacitive readout - based on SQUID amplifiers Foreseen limits of the readout sensitivity: ~ 5x10-22 m/ Hz. Critical issues: optomechanical push cavity finesse to current technological limit together with Watts input laser power capacitive push bias electric field to the current technological limit Develop non-resonant devices to amplify the differential deformation of the massive bodies.

39 Idea to relax requirements on readout sensitivity: mechanical amplifiers based on the elastic deformation of monolithic devices well known for their applications in mechanical engineering. GOAL: Amplify the differential deformations of the massive bodies over a wide frequency range. Requirements: * Gain of at least a factor 10. * Negligible thermal noise with respect to that of the detector.

Search for gravitational wave bursts by the network of resonant detectors

INSTITUTE OF PHYSICSPUBLISHING Class. Quantum Grav. 9 (2002) 367 375 CLASSICAL ANDQUANTUM GRAVITY PII: S0264-938(02)30777-9 Search for gravitational wave bursts by the network of resonant detectors PAstone,