Transcript IGECresults

Results of the 1997-2000 Search for Burst Gw by IGEC
G.A.Prodi - INFN and Università di Trento, Italy
International Gravitational Event Collaboration
http://igec.lnl.infn.it
GWDAW 2002
ALLEGRO group:
ALLEGRO (LSU)
http://gravity.phys.lsu.edu
Louisiana State University, Baton Rouge - Louisiana
AURIGA group:
AURIGA (INFN-LNL)
http://www.auriga.lnl.infn.it
INFN of Padova, Trento, Ferrara, Firenze, LNL
Universities of Padova, Trento, Ferrara, Firenze
IFN- CNR, Trento – Italia
NIOBE group:
NIOBE (UWA)
http://www.gravity.pd.uwa.edu.au
University of Western Australia, Perth, Australia
ROG group:
EXPLORER (CERN)
http://www.roma1.infn.it/rog/rogmain.html
NAUTILUS (INFN-LNF)
INFN of Roma and LNF
Universities of Roma, L’Aquila
CNR IFSI and IESS, Roma - Italia
GWDAW 2002
OUTLINE
 overview of the EXCHANGED DATA SET 1997-2000
sensitivity and observation time
candidate burst gw events
 multiple detector DATA ANALYSIS
directional search strategy
search as a function of amplitude threshold
false dismissal or detection efficiency
estimation of accidental coincidences by time shifts
methods  L.Baggio tomorrow
 RESULTS
accidental coincidences are Poisson r.v.
compatibility with null hypothesis
upper limit on the rate of detected gw
…unfolding the sources (not yet)
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DETECTOR LOCATIONS
almost parallel detectors
LIGHT TRAVEL
TIME (ms)
AL-NI
41.8
EX-NI
39.0
NA-NI
39.0
AU-NI
38.7
AL-AU
20.5
AL-EX
20.0
AL-NA
19.7
EX-NA
2.4
AU-EX
1.6
AU-NA
1.3
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EXCHANGED PERIODS of OBSERVATION 1997-2000
ALLEGRO
AURIGA
NAUTILUS
EXPLORER
NIOBE
fraction of time in monthly bins
exchange threshold
 6  1021 Hz 1
3  6  1021 Hz 1
 3  1021 Hz 1
Fourier amplitude of burst gw
h(t )  H 0   (t  t0 )
arrival time
GWDAW 2002
amplitude (Hz-1)
DIRECTIONAL SEARCH
10
9
8
7
6
5
4
3
2
1
0
0
6
12
18
24
30
36
42
48
54
60
amplitude (Hz-1)
time (hours)
1.0
5
10
0.9
9
amplitude
directional
sensitivity
0.8
8
4
7
0.7
6
0.6
3
sin 2 GC
0.5
5
sin 2 GC
0.4
4
2
0.3
3
2
0.2
1
1
0.1
0
0.0
0
6
12
18
24
30
36
42
48
48
54
54
60
60
time (hours)
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amplitude (Hz-1)
DATA SELECTION
10
9
8
7
6
5
4
3
2
1
0
0
6
12
18
24
30
36
42
48
54
60
time (hours)
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OBSERVATION TIME 1997-2000
total time when exchange threshold has been lower than gw amplitude
amplitude of burst gw
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amplitude (Hz-1)
DATA SELECTION
10
9
8
7
6
5
4
3
2
1
0
0
6
12
18
24
30
36
42
48
54
60
amplitude (Hz-1)
time (hours)
10
9
8
7
6
5
4
3
2
1
0
0
6
12
18
24
30
36
42
48
54
60
time (hours)
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RESULTING PERIODS of OBSERVATION and EVENTS
no directional search
time (hours)
directional search
time (hours)
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AMPLITUDE DISTRIBUTIONS of EXCHANGED EVENTS
normalized to each detector threshold for trigger search
1
1
-1
relative counts
10
-2
-2
10
10
-3
-3
10
relative counts
-1
10
10
-4
-4
10
10
-5
-5
10
10
1
10 AMP/THR
ALLEGRO
1
10 AMP/THR
AURIGA
1
10 AMP/THR
EXPLORER
1
10 AMP/THR
NAUTILUS
1
10 AMP/THR
NIOBE

typical SNR of trigger search thresholds:
 3 ALLEGRO, NIOBE
 5 AURIGA, EXPLORER, NAUTILUS
·
amplitude range much wider than expected:
non modeled outliers dominating at high SNR
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FALSE ALARM REDUCTION
by thresholding events
amplitude
time
natural consequence:
AMPLITUDE CONSISTENCY of SELECTED EVENTS
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FALSE DISMISSAL PROBABILITY
• data selection as a function of the common search threshold Ht
keep the observation time when false dismissal is under control
keep events above threshold
efficiency of detection depends on signal amplitude, direction, polarization …
e.g. > 50% with amplitude > Ht at each detector
• time coincidence search
time window is set requiring a conservative false dismissal
robust and general method: Tchebyscheff inequality
1
ti  t j  k  i2   2j  false dismissal  2
k
false alarms  k
• amplitude consistency check: gw generates events with correlated amplitudes
testing Ai  Aj  A (same as above)
 efficiency of detection versus false alarms:
fraction of found gw coincidences
maximize the ratio
fluctuations of accidental background
best balance in our case: time coincidence max false dismissal 5%  30%
no rejection based on amplitude consistency test
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POISSON STATISTICS of ACCIDENTAL COINCIDENCES
Poisson fits of accidental concidences: 2 test
sample of EX-NA background
one-tail probability = 0.71
agreement with uniform distribution
histogram of one-tail 2
probabilities for
ALL two-fold observations
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SETTING CONFIDENCE INTERVALS
unified & frequentistic approach
 tomorrow talk by L. Baggio
References:
1. B. Roe and M. Woodroofe, PRD 63, 013009 (2000)
most likely confidence intervals ensuring a given coverage (our choice)
2. G.J.Feldman and R.D.Cousins, PRD 57, 3873 (1998)
3. Recommendations of the Particle Data Group: http://pdg.lbl.gov/2002/statrpp.pdf
see also the review: F.Porter, Nucl. Instr. Meth A 368 (1996)
COVERAGE: probability that the confidence interval contains the true value
unified treatment of UPPER LIMIT  DETECTION
freedom to chose the confidence of goodness of the fit tests independently from
the confidence of the interval
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SETTING CONFIDENCE INTERVALS / 2
GOAL: estimate the number of gw which are detected with amplitude  Ht
Example: confidence interval with coverage  95%
“upper limit” : true value outside
with probability  95%
18
16
14
12
Ngw
10
8
6
Ht
4
2
0
1.0
10.0
search threshold [10-21/Hz]
100.0
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SETTING CONFIDENCE INTERVALS / 3
18
16
systematic search on thresholds
many trials !
14
12
Ngw
10
8
all upper limits but one:
6
testing the null hypothesis
4
2
0
1.0
overall false alarm probability
33%
search threshold [10-21/Hz]
at least one detection in case
PDG recommendation NO GW are in the data
10.0
100.0
A potential difficulty with unified intervals arises if, for example, one constructs
such
an interval for a Poisson
parameter
s of some
yet toIN
be discovered signal process
NULL
HYPOTHESIS
WELL
with,
AGREEMENT WITH THE
say, 1 -  = 0:9. If the true signal
parameter is zero, or in any case much less than
OBSERVATIONS
the
expected background, one will usually obtain a one-sided upper limit on s. In a
certain
fraction of the experiments, however, a two-sided interval for s will result. Since,
however, one typically chooses 1 -  to be only 0:9 or 0:95 when searching for a
GWDAW 2002
UPPER LIMIT /1
on RATE of BURST GW from the GALACTIC CENTER DIRECTION
with measured amplitude  search threshold
no model is assumed for the sources, apart from being a random time series
1,000
rate
year -1
100
0.60
0.80
0.90
0.95
10
1
1E-21
1E-20
ensured
minimum
coverage
1E-19
search threshold
Hz -1
true rate value is under the curves with a probability = coverage
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UPPER LIMIT /2
on RATE of BURST GW without performing a directional search
measured amplitude  search threshold
(amplitudes of gw are referred to the direction of detectors)
no model is assumed for the sources, apart from being a random time series
1,000
rate
year -1
100
0.60
0.80
0.90
0.95
ensured
minimum
coverage
10
1
1E-21
1E-20
1E-19
search threshold
Hz -1
true rate value is under the curves with a probability = coverage