1. 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

2. 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)

3. 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”

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

5. 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

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

7. 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

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

9. 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

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= N ~ 5000 whatever the configuration
(up to 6 ITFs)

11. 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

12. 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% SNRopt = 7.5
Efficiency remains SNRopt = 5 and below

13. Comparison Coherent/Coincident
SNR = 10, False Alarm Rate =
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%

14. 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?