M.-A. Bizouard, F. Cavalier Coincidence and coherent analyses for burst search using interferometers M.-A. Bizouard, F. Cavalier on behalf of the Virgo-Orsay group Network model Results of coincidence analysis: loose and tight coincidence Results of coherent analysis Comparison of all scenarios GWDAW 8 – Milwaukee – 19/12/03

Network of detectors For burst events a single detector can’t claim for a GW discovery Need several ITF output to reject transient Coincidence with other kind of detectors (optical, ν, …) can help ITF Network: hypotheses of this study ITFs: Identical ITF sensitivity curves ITF Beam pattern and orientation Time delays between ITFs Up to 6 ITFs: Virgo, LIGO Hanford, LIGO Livingston, GEO, TAMA and AIGO Sources = Gaussian peak (width=1ms) and uniformly distributed in the sky Noise = Gaussian and white noise Filtering method: match filtering Monte Carlo simulations to estimate the efficiency versus false alarm rate curves (ROC)

Network beam patterns Fx and F+ depend on detector location Source position Polarisation angle Ψ Sky map = Ψ averaged beam pattern functions LIGO maps similar by design Virgo and GEO more or less similar due to geometrical proximity Virgo and LIGO maps are “orthogonal”

Single ITF performance (Virgo) Beam Pattern Effect Selected Events Beam pattern effect on the GW SNR Virgo detection efficiency vs the source sky location

Coincidence Definition of a time window depending on time delay between detectors The source location is not known: loose coincidence The source position is known: tight coincidence has been determined on simulation (SNR dependence): (<0.3 ms for SNR>5) for SNR>6

Virgo-LIGO coincidence (loose) Request on 1/3 Twofold coincidence Coincidence less likely: ~ 20% for the 2 LIGO ~ 30% by adding Virgo Large regions almost blind Good sky global coverage: average efficiency of 67% No more blind regions

Loose coincidence in LIGO-Virgo network SNRopt=10 Best strategy: twofold coincidences (at least 2 among 3) Twofold coincidence is dominated by the 2 LIGO network (beam pattern matching) Single detector less efficient than coincidences Threefold coincidences are rare

Full network loose coincidence SNRopt=10 Twofold coincidence quite likely even at small false alarm rate Threefold coincidences also possible Larger coincidences much rarer

Full network tight coincidence Loose vs tight coincidence: - only few % of improvement in the region “1 false alarm per hour” - 20% at very low false alarm rate For the Virgo-LIGO network very small improvement SNRopt=10

Coherent analysis Coherent statistics derived from a likelihood ratio (Pai, Bose & Dhurandhar (2001) method for coalescing binaries) General case: the source location is not known bank of N templates to cover the full sky for a Gaussian peak signal N goes 1/w2 for w=1ms and MM=0.97 N ~ 5000 whatever the configuration (up to 6 ITFs)

Virgo-LIGO coherent analysis results Significant improvement in detection efficiency with respect to the coincidence case Efficiency remains above 60% for SNRopt = 10 even at a false alarm rate of 1 per week (35% for a twofold coincidence) Still no real hope to detect a weak signal (SNRopt = 5) in the 3 interferometer Virgo-LIGO network

Full network coherent analysis Clear enhancement of detection efficiencies by going from 3 to 6 ITFs Almost certain detection for SNRopt = 10 Still more than 80% efficiency @ SNRopt = 7.5 Efficiency remains limited @ SNRopt = 5 and below

Comparison Coherent/Coincident SNR = 10, False Alarm Rate = 5. 10-7 Single detector 39% OR strategy in Virgo-LIGO 69% OR strategy in full network 97% Twofold coincidence in Virgo-LIGO 52% Twofold coincidence in full network (loose) 90% Twofold coincidence in full network (tight) 93% Threefold coincidence in Virgo-LIGO 23% Threefold coincidence in full network (loose) 73% Threefold coincidence in full network (tight) 78% Coherent in Virgo-LIGO 78% Coherent in full network 99%

This study has shown: Coincident: Coherent vs coincident: Future work: No large increase of the efficiency when using tight coincidence Virgo-LIGO network: significant enhancement of the twofold efficiency when adding Virgo! One definitely gains more with a 6 ITFs network Increase of the network size is mandatory The sensitivity of the ITF in the network is also a fundamental parameter Virgo+LH4km+LL4km  LH2km+LH4km+LL4km : Increase the false alarm rate by 2 orders of magnitude at equal efficiency! Coherent vs coincident: Coherent analysis is much more powerful than coincidence (even tight one) but is heavier to set up Future work: Improvement of the coincident analysis by introducing criteria about the main characteristics of the signal events?