VIRGO-bars joint data analysis
Francesco Salemi
for the VIRGO-bars Collaboration
Francesco Salemi - London, October 26th - 27th, 2006
1
Summary
•
•
•
•
•
•
INTRO
• Target Signals
• Sensitivity Curves
Exchanged data
MDC injections
• Time errors
2-fold Coincidence Analysis
• Optimization of the thresholds
• Background & Efficiency
• Statistical Analysis
Preliminary Results
TODO
• 3-fold Coincidence Analysis
Francesco Salemi - London, October 26th - 27th, 2006
2
Outline
•
VIRGO-bars Network: AURIGA, EXPLORER, NAUTILUS and VIRGO
•
Goal: assess interpreted confidence intervals on the flux of gravitational
waves (damped sinusoids, DS) coming from the galactic center (GC).
The interpretation comes from software injections (MDC) which are
used to compute the efficiency of detection for a source population
•
•
Main methodology: coincidence search on trigger lists provided by
each detector. The coincident counts, divided by the efficiency and by the
observation time, become observed rates (or upper limits on rates).
•
Optimization of thresholds: for each template and each given target
amplitude, the best compromise between efficiency and FAR is searched,
using variable threshold for each detector with ½ hour bins.
The efficiency acts not just passively at the end of the analysis to
calibrate the results, but also actively during an optimization phase.
•
•
Blind analysis: in order not to bias results by feedbacks on methods
from looking at results, a “secret” time offset has been added to detector
times.
Francesco Salemi - London, October 26th - 27th, 2006
3
The VIRGO-bars network
• 24 hours of data taking
during C7, starting from
UTC time 810774700,
(14 Sep 2005 - 23:11 27s)
• Heterogeneous Network:
• spectral sensitivity
• directional response
Francesco Salemi - London, October 26th - 27th, 2006
4
Software injections details
Damped Sinusoids:
elliptic polarization
distributed signals as it is
expected for binary
systems at GC
• Several damping times
and central frequency to
span our parameter space.
• 11 templates
• For each class, we
generated randomly:
injection times
polarization angle 
inclination angle 
• N=8640 (1/10 s)
• hrss=1e-20 - 2e-18
Hz-1/2
Francesco Salemi - London, October 26th - 27th, 2006
5
Single detector ETG and Observables
•
AURIGA: WaveBursts (S. Klimenko et al, LIGOT050222-00-Z) was succesfully adapted to AURIGA
data. The cluster S/N (close to the optimal) was used
as an indicator of the signal magnitude.
•
NAUTILUS and EXPLORER: a single linear WienerKolmogorov filter matched to the impulse
response is applied to the output data. The impulse
S/N was used as an indicator of the signal
magnitude.
•
VIRGO: PowerFilter is the chosen trigger generator.
The logarithmic S/N was used as an indicator of the
signal magnitude.
Francesco Salemi - London, October 26th - 27th, 2006
6
Exchanged Data (correlograms)
Francesco Salemi - London, October 26th - 27th, 2006
7
Exchanged data: triggers+MDC @ 1e-19 Hz-1/2
AURIGA
EXPLORER
N=1413
N=5614
NAUTILUS
VIRGO
N=8628
N=24241
Francesco Salemi - London, October 26th - 27th, 2006
8
Efficiency
• Single detector efficiencies
DS: f0=930 Hz tau=30ms
• For VIRGO, ~ 7 hrs out of 24
have been excluded by epoch
vetoes
=> Asymptotic 70%
DS: f0=914 Hz tau=1ms
Francesco Salemi - London, October 26th - 27th, 2006
DS: f0=866 Hz tau=10ms
9
Time coincidence
• Our ETGs are not “matched” to DS
• Time errors are dominated by systematic biases.
• The narrower the bandwidth, the greater the signal is distorted
• Example : AURIGA – VIRGO coincidences. The double peak is due to the
multimodal time error by PF
•The coincidence “window”, Tw = 40 ms
f0=914 Hz
f0=866 Hz
f0=930 Hz
tau=1ms
tau=10ms
tau=30ms
Francesco Salemi - London, October 26th - 27th, 2006
10
Optimization (1)
•
To shrink the interpreted confidence interval we choose to optimize
the 2-fold coincidence serches => Better Upper Limits
•
For each configuration/template/amplitude, the magnitude
thresholds for the 2 detectors are tuned => large trial factor
•
The criterion is to maximize the ratio efficiency over the fluctuation
of the accidental coincidences.
•
The efficiency is calculated on the data sets containing the MDC
injections
•
The average background of accidental coincidence is estimated by
means of +/- 400 time shifts (~ +/- 7 min). Poisson point process:
fluctuation is sqrt(counts).
•
The magnitude thresholds are optimized every 30 min
Francesco Salemi - London, October 26th - 27th, 2006
11
Optimization (2): DS @ 914 Hz, 1ms, 1e-19 Hz-1/2
AURIGA
VIRGO
Francesco Salemi - London, October 26th - 27th, 2006
12
Statistical Analysis (1)
Global confidence
• Blind Analysis: we don’t “open the box” of the zero-lag until we have
fixed all the tunable parameters and chosen the methodology to be
used.
• Large trial factor => multiple tests performed, increase of the false
claim probability
• to reduce the trial factor, for each template/amplitude, we analyze only
on the best couples of detectors (72).
• The effective global probability is empirically estimated over the 400
time shifted data sets => the single trial confidence is tuned in order to
reach a total false claim of 99%
Single trial confidence
Francesco Salemi - London, October 26th - 27th, 2006
13
Statistical Analysis (2)
• The confidence intervals were set according to the confidence belt
already used by IGEC1 (see L. Baggio and G.A. Prodi, “Setting
confidence intervals incoincidence search analysis" in Statistical
problems in particle physics, astrophysics and cosmology, R.Mount,
L.Lyonsand and R.Reitmeyer editors, Stanford (2003) 238)
• When the null hypothesis test is fulfilled, than the confidence
interval is simply an Upper Limit
• Notice that: a rejection of the null is a claim for an excess
correlation in the observatory at the true time, not taken into
account in the measured noise background at different time lags.
Whether these correlations are true GW or just correlated noise
signals is not known.
• A Virgo-note was produced to discuss the methodology:
VIR-NOT-FIR-1390-328
Last Friday we exchanged the secret time offsets and we “opened the
box” and…
Francesco Salemi - London, October 26th - 27th, 2006
14
Results for the 2-fold coincidence searches
Upper Limits at 95% coverage
No excess of Coincidences was found. The null hypothesis survives...
Francesco Salemi - London, October 26th - 27th, 2006
15
Next Steps
•
The 2-fold coincidence searches have a high level of accidental
background, single detection not possible=> 3-fold coincidence
searches
•
Goal: to be able to issue a claim at 99.5% confidence on a single
observed triple coincidence.
In the next weeks, we plan to try the 3-fold coincidence search. The
methodology and all the key parameters have been decided before
“opening the box” of the double coincidence searches.
•
•
•
•
Optimization of thresholds: for each template and some MDC
amplitudes (i.e. 1e-18, 5e-19 and 1e-19 Hz-1/2. ), the best compromise
between efficiency and FAR is searched, using variable threshold for each
detector with ½ hour bins in order to reach the target level of
background.
The zero-delay will be analysed with the optimization for the minimal
signal amplitude which allows at least a level of efficiency of 40%.
Configurations of detectors/template, which do not reach such minimal
level for any of the chosen amplitudes, will be discarded.
Given the chosen 99.5% of confidence level, to be compared with the
99% (~1% spread) for the 2-fold coincidence searches, performing the
3-fold coincidence searches will slightly affect the global
confidence.
Francesco Salemi - London, October 26th - 27th, 2006
16
EXTRA SLIDES
Francesco Salemi - London, October 26th - 27th, 2006
17
Software injections details (1)
We chose a family of DS with several damping times and central
frequency combination in order to span evenly our parameter space.
For all the classes, we set hrss = 10−23Hz −1/2 (this can be changed simply rescaling all the
signals).
• For each class, we generated a series of injection times (signal arrival at the center of the
Earth), spaced by 10s + uniform random jitter of +/- 0.5s.
• For each class and for each injection time we generated a random polarization angle  in
[0, 2], and a random inclination angle  such that cos  is distributed uniformly in [−1,1];
frequency
VIRGOcentral
- DS(930Hz;10ms)
projected
decay
time amplitudes
[10-23Hz-1/2]
14
850
870
890
910
930
12
0.1
950
970
990
optimal  alignment
10
8
6
4
0.01
2
0.001
22:21
20:31
18:52
17:09
15:22
13:28
11:48
9:56
8:09
6:26
4:33
2:55
1:08
23:23
0
t (ms)
Df (Hz)
N°
1
64
3
3
32
5
10
16
13
30
8
22
100
4
38
time [h:min]
Francesco Salemi - London, October 26th - 27th, 2006
18
Astrophysical motivations:
The chosen signals can be produced by:
BH-BH ring-down.
In this case the energy release to make a detection realistic
should be about 10-3 - 10-4 Mo for a galactic event.
Andersson N. and Kokkotas K., Mon. Not. Roy. Astron. Soc. 299 (1998)
Kokkotas K.D. and Schmidt B.G., http://www.livingreviews.org/lrr-1999-2 (1999)
f-mode of neutron stars.
Here too the energy release must be high. Moreover,
the f-mode could produce a wave with variable frequency and
damping time, which anyway should sweep inside the observed
frequency band.
Ferrari V. et al., Mon. Not. Roy. Astron. Soc. 342 (2003) 629
The wave polarisation should be linear for SN explosions, but elliptic for BHBH
coalescenses (V. Ferrari, private communication).
Francesco Salemi - London, October 26th - 27th, 2006
19
Confidence Belt & Coverage
For each outcome x one should be able to determine a confidence interval Ix
For each possible , the measures x  I  which lead to a confidence interval consistent
with the true value have probability C(), i.e. 1-C() is the false dismissal probability
physical
unknown
coverage
C() 

pdf ( x ; )
x|I x
confidence
interval I x

I
x
experimental data
Francesco Salemi - London, October 26th - 27th, 2006
20