Coincidences in

gravitational wave experimentsPia Astone

4th Amaldi conference

Perth July 8-13, 2001

Main coincidence analyses we have done in the past:

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 1997-1998Phys. Rev. Letters,85,2000

The IGEC analysis of the data 1997-2000 is now being done The IGEC analysis of the data 1997-2000 is now being done

Some basics figures of the coincidence analysis

• We exchange eventsevents, above given thresholds (depending on the detector sensitivitiesvarying with the time)

• Each group applies vetoing procedures, to the noise and/or to the events, before the analysis is done

• The analysis procedure is based on “the time shift procedure” (see-e.g.-Int. Journal of Modern Physics D,9,2000)

• 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

• The choice of the coincidence window

Main problems

Noiseof

ExplorerAnd

Nautilusin 1998

The y-axis expresses

thesensitivityto burst Days from 1 Jan 1997 Days from 1 Jan 1997

3 10-18

0.5 10-18

The detector sensitivities may be very different..and thus different signals could be detected

and also the event energies may be different,

Explorer -Nautilus 1996

Days from1 Jan 1994

Astrop. Phys., 10, 1999

SIGNALS-EVENTS

What is the solution ?First of all: it should be clear the difference

SIGNALS-EVENTS

Event SNR

Differentialprobability

SNR=signal to noise

ratio of the signal(here: 10, 20, 50)

The x-axis gives thesignal to noise ratio

of the eventThe y-axis gives the

differential probabilityfor the SNRof the event

Signals and events

SNR of the threshold

Probabilityof detection

SNR=signal to noise

ratio of the signal(here: 10, 20, 50)

The x-axis gives thesignal to noise ratio

of the thresholdThe y-axis gives the

probabilityof detection for a given

SNR-t

Probability of detection

Note that this effect does not depend

on thedetector bandwidth

Simulation of the efficiency of detection:delta-like signals applied to the Explorer data,

with various SNRsAstone,D’Antonio,Pizzella PRD 62 (2000)

Simulation of the efficiency of detection:delta-like signals applied to the Explorer data,

with various SNRsAstone,D’Antonio,Pizzella PRD 62 (2000)

The analysis procedure:a new selection algorithm based on the

event energies CQG, 18 (2001)

• Now we know that, for given SNR_s of the signal, there is a chance of obtaining certain SNR_e of the event

• We assume various signal values (h=10^-18-10^-17)• For each h we evaluate SNR_s (different for each detector

and for each event-it is a function of the local noise)

• We accept an event, and thus a coincidence, if the

SNR_s - 1 std < SNR_e < SNR_s + 1 std

Based on an original observation of D. Blair et al.: the distribution ofenergy ratios of the event energies of two detectors

is different for real and accidental coincidences (if non-gaussian noise)Journal of General Relativity and Gravitation (2000)

Explorer and Nautilus 1998 IGEC data

N

events

N

hoursT eff[mK]

Overlap

hoursN of overlap

Events

Ex55070 3415 40.6

227137944

NA37734 3450 19.1 24118

Bursts sensitivity h (SNR=1) : Ex= 1.6 10-18 NA= 1.1 10-18

We have applied this algorithm to theExplorer and Nautilus 1998 IGEC data

Number of

coincidences

Average number of

shifted coincidences

Common hours

of

observation

223 231.7 2271

61 50.5 2271

The use of the energy

selectionalgorithm

has reducedthe number of

accidentalcoincidences by

a factor of 4

Noselect

Energyselect

Another selection criterium:based on the detector orientation

with respect to specific sources, e.g. GC

• Since no extragalactic signals are expected, with the present sensitivity, we can select the events according to the orientation of the detectors, with respect to the GC

(sin)4

This criterium has been applied in CQG,18 (2001)

Based on the same idea, we are now testing a new procedure:coincidences (real or shifted) are weighted according to the

value of sin(teta)4 for given directions(M. Visco)

Experimental probability

Right ascension

Decl The plot represents,for each direction,the experimental

probability that theresult for real(zero delay)

coincidences isdue to noise

A new procedure for evaluation of upper limits(Astone,Pizzella: Astrop. Physics, in press 2001)

• 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 GW

Efficiency of

detection

It is smaller than unity, andthis changes the upper limit

659 d

553 d

852 d

221 d

200 d

ON times for the various detectors 1997-2001

1 detector=609 d

4 detectors=30 d

3 detectors=149 d

2 detectors=535 d

0 detectors=137 d

ON times for the 1997-2000 coincidence analysis2 detectors=714 days3 detectors=179 days

We have applied the GC algorithm to theExplorer and Nautilus 1998 IGEC data

Number of

coincidences

Average number of

shifted coincidences

Common hours

of

observation

223 231.7 2271

61 50.5 2271

19 10 450

All

Energy

GC

Time deviation and the problem of the coincidence window

• We have found that, for signals syncronized with the sampling time, the statistical time uncertainty is expressed by

= 1/(2 f) sqrt(2/SNR)

This suggests to use a

variable coincidence

window (R. Terenzi)

Simulation of the efficiency of detection andtime deviation:

delta-like signals applied to the Explorer data,with various SNRs