INTERPRETATION of IGEC RESULTS Lucio Baggio Giovanni Andrea

INTERPRETATION of IGEC RESULTS Lucio Baggio, Giovanni Andrea Prodi University of Trento and INFN Italy or unfolding gw source parameters starting point: • IGEC 1997 -2000 results (P. Astone et al. , PRD 68 (2003) 022001) with reference to: • LIGO S 1 burst gw results (B. Abbott et al. , gr-qc/0312056)

COMPARISON at a GLANCE IGEC 1997 -2000 LIGO S 1 • systematic search over many amplitude thresholds: many data selections many data points • playground data to tune the search: one data selection one data point • bound of maximum false dismissal probability of detection: conservative efficiency is estimated for -like waveform • montecarlo for some specific source models: efficiency is measured vs gw amplitude for sample waveforms 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) results are upper limits on rate of incoming burst gws: rate vs true amplitudes Source model: sample waveforms incoming at fixed amplitude + directional corrections…

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 HS= FT[h. S ] at 2 900 Hz

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

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 HM Ht • systematic search vs threshold Ht many trials (20 /decade) almost independent results

Case of gw flux of constant amplitude: -like signal from GC Poisson rate of detected gw [year – 1] correct each result for the detection efficiency as a function of gw amplitude HS convert in terms of parameters of the source model search threshold at HS Ht efficiency 0. 25 due to 2 -fold observations at threshold at HS 2 Ht efficiency = 1 enough above threshold Poisson rate of incoming gw [year – 1] true amplitude HS

Case of gw flux of constant amplitude: -like signal from GC (2) • complete conservative efficiency estimation for the single data point • … on all data points • convert from HS= FT[h. S ] at 2 900 Hz to template amplitude parameter e. g. for a sine-gaussian(850 Hz; Q=9) hrss= 10 Hz 0. 5 HS Poisson rate of incoming gw [year – 1] true amplitude HS

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

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 HS Ht (dashed line) • Estimate the distribution of measured coincidences HM Ht (cont. line) • Compare with IGEC results to set confidence intervals on gw flux parameters coverage rate (year – 1) search threshold Ht (Hz -1 )

Case of gw flux of constant amplitude: -like signal from GC (3) • the resulting interpreted upper limit • convert from HS= FT[h. S ] at 2 900 Hz to template amplitude parameter e. g. for a sine-gaussian(850 Hz; Q=9) hrss= 10 Hz 0. 5 HS Poisson rate of detected gw [year – 1] search threshold

Case of gw flux of constant amplitude: comparison to LIGO • the resulting interpreted upper limit • convert from HS= FT[h. S ] at 2 900 Hz to template amplitude parameter e. g. for a sine-gaussian(850 Hz; Q=9) hrss= 10 Hz 0. 5 HS Poisson rate of detected gw [year – 1] hrss

Case of gw flux of constant amplitude: comparison with LIGO results • IGEC sets an almost independent result per each tried threshold Ht • correct each result for the detection efficiency as a function of gw amplitude HS: e. g. at HS Ht efficiency 0. 25 due to 2 -fold observations at threshold at HS 2 Ht efficiency = 1 Poisson rate of detected gw [year – 1] search threshold enough above threshold

amplitude (Hz-1· 10 -21) DIRECTIONAL SEARCH: sensitivity modulation amplitude (Hz-1· 10 -21) time (hours) amplitude directional sensitivity time (hours)

amplitude (Hz-1· 10 -21) Resampling statistics by time shifts 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)

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)

TESTING the NULL HYPOTHESIS many trials ! all upper limits but one: NULL HYPOTHESIS WELL IN AGREEMENT WITH THE OBSERVATIONS Þ 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

FALSE ALARM RATES dramatic improvement by increasing the detector number: 3 -fold or more would allow to identify the gw candidate mean rate of events [ yr -1] mean s timing [ms]

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 HM Ht • systematic search vs threshold Ht many trials (20 /decade) almost independent results

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 by Tchebyscheff inequality false alarms k maximize the chances of detection i. e. the ratio 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)

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 ALLEGRO AURIGA -EXPLORER –NAUTILUS NIOBE amplitude directional sensitivity factor vs sideral time (hours)

TARGET GW SIGNALS Fourier amplitude of burst gw Detectable signals: transients with flat Fourier amplitude at the detector frequencies (900 Hz) each detector applies arrival time an exchange threshold on measured H OBSERVATION TIME 1997 -2000 (days) threshold on burst gw

EXCHANGED PERIODS of OBSERVATION 1997 -2000 ALLEGRO AURIGA EXPLORER NAUTILUS NIOBE fraction of time in monthly bins threshold on burst gw

AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS normalized to each detector threshold for trigger search · 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

POISSON STATISTICS of ACCIDENTAL COINCIDENCES Poisson fits of accidental concidences: 2 test sample of EX-NA background one-tail probability = 0. 71 histogram of one-tail 2 probabilities for ALL two-fold observations agreement with uniform distribution coincidence times are random

Data selection at work A major false alarm reduction is achieved by excluding low amplitude events. amplitude (Hz-1· 10 -21) Duty time is shortened at each detector in order to have efficiency at least 50% time (hours)

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

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

UPGRADE of the AURIGA resonant bar detector Previous set-up during 1997 -1999 observations current set-up for the upcoming II run • beginning cool down phase • at operating temperature by November

AURIGA II run LHe 4 vessel Al 2081 holder Electronics wiring support Main Attenuator Thermal Shield Sensitive bar Compression Spring Transducer

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

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

FUTURE PROSPECTS we are aiming at

DUAL detectors estimated sensitivity at SQL: Science with HF GW • BH and NS mergers and ringdown • NS vibrations and instabilities • Eo. S of superdense matter • Exp. Physics of BH Mo Dual 16. 4 ton height 2. 3 m Ø 0. 94 m Si. C Dual 62. 2 ton height 3 m Ø 2. 9 m 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) 1020 XX in press PRL 87 (2001) 031101

New concepts - new technologies: • No resonant transducers: measure differential motion of massive cylindrical resonators • Mode selective readout: measured quantity: X = x 1+x 2 -x 3 -x 4 • High cross section materials (up to 100 times larger than Al 5056 used in bars)

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 p 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

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:

Dual Detector with √Shh~10 -23/√Hz in 1 -5 k. Hz range Molybdenum Silicon Carbide (Si. C) • Q/T>2 x 108 K-1 - Mass = 16 tons • Q/T > 2 x 108 K-1 - Mass = 62 tons • R = 0. 47 m • R = 1. 44 m - height = 2. 3 m - height = 3 m Feasibility issues Detector: Readout: • Massive resonators ( > 10 tons ) • Selective measurement strategy • Cooling • Quantum limited • Suspensions • Wide area sensor • Low loss and high cross-section materials • Displacement sensitivity

R&D on readouts: status • Requirement: ~ 5 x 10 -23 m/√Hz • Present AURIGA technology: 10 -19 m/√Hz with: optomechanical readout - based on Fabry-Perot cavities capacitive readout - based on SQUID amplifiers Foreseen limits of the readout sensitivity: ~ 5 x 10 -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.

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.