Coincidences
in
gravitational wave experiments
Pia 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 1997-1998
Phys. Rev. Letters,85,2000
The IGEC analysis of the data 1997-2000 is now being done
Some basics figures of the coincidence analysis
• We exchange events, above given thresholds
(depending on the detector sensitivitiesvarying
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)
Main problems
• 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
The detector sensitivities may be very different..
and thus different signals could be detected
3 10-18
Noise
of
Explorer
And
Nautilus
in 1998
The y-axis
expresses
the
sensitivity
to burst
0.5 10-18
Days from 1 Jan 1997
Days from 1 Jan 1997
and also the event energies may be different,
Explorer Nautilus 1996
Astrop. Phys., 10, 1999
Days from
1 Jan 1994
What is the solution ?
First of all: it should be clear the difference
SIGNALS-EVENTS
SIGNALS-EVENTS
Signals and events
Differential
probability
SNR=signal to noise
ratio of the signal
(here: 10, 20, 50)
The x-axis gives the
signal to noise ratio
of the event
The y-axis gives the
differential probability
for the SNR
of the event
Event SNR
Probability of detection
Probability
of detection
SNR=signal to noise
ratio of the signal
(here: 10, 20, 50)
Note that this effect
does
notgives
depend
The x-axis
the
signal on
to noise
the ratio
of the threshold
detector
bandwidth
The y-axis gives the
probability
of detection for a given
SNR-t
SNR of the threshold
Simulation of the efficiency of detection:
delta-like signals applied to the Explorer data,
with various SNRs
Astone,D’Antonio,Pizzella PRD 62 (2000)
Simulation of the efficiency of detection:
delta-like signals applied to the Explorer data,
with various SNRs
Astone,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 of
energy 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
Overlap N of
N
N
T eff
overlap
hours
events hours [mK]
Events
Ex
55070 3415 40.6
37944
2271
NA
37734 3450
19.1
Bursts sensitivity h (SNR=1) :
24118
Ex= 1.6 10-18
NA= 1.1 10-18
We have applied this algorithm to the
Explorer and Nautilus 1998 IGEC data
Number of
coincidences
No
select
Energy
select
Average
number of
shifted
coincidences
Common hours
of
The use of the
observation
energy
223
231.7
selection
algorithm
has reduced
2271
the number of
accidental
coincidences by
61
50.5
a factor of
2271
4
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
S=So (sinq)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
The plot represents,
for each direction,
the experimental
probability that the
result for real
(zero delay)
coincidences is
due to noise
Decl
Right ascension
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 )
described in Amaldi et al, A&A, 216 (1989)
Problems
Signals-events
Efficiency of
detection
The energy of the event
is not the energy of the GW
It is smaller than unity, and
this changes the upper limit
is
ON times for the various detectors 1997-2001
200 d
221 d
852 d
553 d
659 d
ON times for the 1997-2000 coincidence analysis
2 detectors=714 days
3 detectors=179 days
4 detectors=30 d
3 detectors=149 d
2 detectors=535 d
1 detector=609 d
0 detectors=137 d
We have applied the GC algorithm to the
Explorer and Nautilus 1998 IGEC data
Average number Common hours
Number of
of
of
coincidences shifted
observation
coincidences
All
Energy
GC
223
231.7
2271
61
50.5
2271
19
10
450
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
s
= 1/(2 p Df) sqrt(2/SNR)
This suggests to use a
variable coincidence
window (R. Terenzi)
Simulation of the efficiency of detection and
time deviation:
delta-like signals applied to the Explorer data,
with various SNRs