Download The Virgo-bars search for bursts

An example or real data analysis:
the VIRGO-bars search for bursts
Andrea Viceré
for VIRGO – Auriga - Rog
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Motivations and outline
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Background: During Virgo Commissioning Run 7 (Sept. 2005), also
INFN resonant bars, AURIGA, EXPLORER and NAUTILUS were taking
data.
A limited amount of data (24 hours) was exchanged, to permit the
development of network analysis methods.
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Goals:
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understand the potentialities of a network of different detectors.
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Develop new techniques coping with their heterogeneous nature.
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Bring together the two DA communities and their experiences.
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Pave the way towards greater integration in the future.
Methodology:
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Search for coincident events, no assumptions on the waveforms.
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Bring in physically motivated assumptions when evaluating the
detection efficiency of the network.
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Use the assumptions to optimize the cuts on the events of each
individual detectors, without compromising the detection efficiency
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Deduce upper limits from the fact that coincidences do not exceed
background expectations.
Andrea Viceré - IHP Paris, November 13th 2006
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The VIRGO-bars network in one slide
• 24 hours of data taken
during Virgo C7 run: start
at UTC time 810774700,
(14 Sep 2005 - 23:11 27s)
• Heterogeneous Network:
• spectral sensitivity
• directional response
• Patterns for circularly
polarized signals
Andrea Viceré - IHP Paris, November 13th 2006
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More details on the study
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Goal: assess interpreted confidence intervals on the flux of
gravitational waves.
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The interpretation comes from software injections which are used
to compute the efficiency of detection for a source population
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We have restricted the study to a class of signals, the Damped
Sinusoids, and to one general direction in the sky, the Galactic Center.
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Main methodology: coincidence search on trigger lists made by
each detector. The coincident counts, divided by efficiency and
observation time, become observed rates (or upper limits on rates).
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Optimization of thresholds: for each template and each target
amplitude, the best compromise between efficiency and false alarm
rate is searched, using variable threshold for each detector.
The efficiency acts not just passively at the end of the analysis to
calibrate the results, but also actively during an optimization phase.
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Blind analysis: not to bias results by feedbacks on methods from
looking at results, a “secret” time offset was added to detector times.
Andrea Viceré - IHP Paris, November 13th 2006
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Signals and astrophysical motivation
• fgw and t are frequency and damping times
• hrss is the scale factor (we will define it precisely later)
• y and i are geometrical factors (polarization and “source plane” inclination
Such signals could be produced by a ringdown of a system excited in a l=m=2 mode
BH-BH ring-down.
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.
In this case the f-mode could produce a wave with variable frequency and
damping time; to keep this into account we did not use matched filtering.
Ferrari V. et al., Mon. Not. Roy. Astron. Soc. 342 (2003) 629
Andrea Viceré - IHP Paris, November 13th 2006
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Event Trigger Generators and Observables
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AURIGA: WaveBursts (S. Klimenko et al, LIGOT050222-00-Z) adapted to AURIGA data.
The cluster S/N (close to the optimal) was used as an
indicator of the signal magnitude.
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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.
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VIRGO: PowerFilter is the chosen trigger generator.
The logarithmic S/N was used as an indicator of the
signal magnitude.
Andrea Viceré - IHP Paris, November 13th 2006
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Assessing the background of accidentals
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To assess the significance of rates, we need an estimate of the
rate of accidentals.
Ideally one would like to have events at each detector
distributed as independent Poisson processes. The autocorrelogram of the events at each detector should be flat.
Instead, because of non-gaussianity, oscillations occur, for
instance in Virgo which is under commissioning.
However, the cross-correlogram is flat! So the coincidences can
be regarded as a Poisson process.
Andrea Viceré - IHP Paris, November 13th 2006
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A better view in the frequency domain
Andrea Viceré - IHP Paris, November 13th 2006
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Software injections details
Damped Sinusoids:
elliptic polarization
distributed signals
assumed to come from the
Galactic Center
• Several damping times
and central frequencies to
span our parameter space.
• 11 templates
• For each class, we
generated randomly:
injection times
polarization angle y
inclination angle i
• N=8640 (1/10 s)
• hrss=1e-20 - 2e-18
Hz-1/2
Andrea Viceré - IHP Paris, November 13th 2006
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Which physical parameters?
• Take just the example of Quasi Normal Modes of Black Holes, and
assume that an l=m=2 mode dominates the signal.
• Mass and ratio j = J/M2 are correlated with frequency and damping time.
• So, we are looking also at t values which are incompatible with these modes
Andrea Viceré - IHP Paris, November 13th 2006
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Events+injections @ hrss=1e-19 Hz-1/2
AURIGA
EXPLORER
N=1413
N=5614
NAUTILUS
VIRGO
N=8628
N=24241
Andrea Viceré - IHP Paris, November 13th 2006
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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
Andrea Viceré - IHP Paris, November 13th 2006
DS: f0=866 Hz tau=10ms
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Time coincidence
• We are not using matched filtering
• Time errors are therefore 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
multi-modal time error of the Virgo Power Filter
•The coincidence “window”, Tw = 40 ms
f0=914 Hz
f0=866 Hz
f0=930 Hz
tau=1ms
tau=10ms
tau=30ms
Andrea Viceré - IHP Paris, November 13th 2006
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Optimization of the thresholds (1)
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To shrink interpreted confidence interval we choose to
optimize the 2-fold coincidence searches => Better Upper
Limits
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For each configuration/template/amplitude, the magnitude
thresholds for the 2 detectors are tuned => large trial factor.
We keep this into account when calculating the statistics.
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The criterion is to maximize the ratio efficiency over the
fluctuation of the accidental coincidences.
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The efficiency is calculated on the data sets containing the
MDC injections
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The average background of accidental coincidence is
estimated by means of +/- 400 time shifts (~ +/- 7 min).
Coincidences are Poisson point processes: fluctuation is
sqrt(counts).
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The magnitude thresholds are optimized every 30 min
Andrea Viceré - IHP Paris, November 13th 2006
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Optimization (2): DS @ 914 Hz, 1ms, 1e-19 Hz-1/2
AURIGA
VIRGO
Andrea Viceré - IHP Paris, November 13th 2006
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Statistical Analysis (1)
Global confidence
• Blind Analysis: we do not open the box of zero-lag until all tunable
parameters are fixed, and the methodology to be used is chosen.
• 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
Andrea Viceré - IHP Paris, November 13th 2006
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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 in coincidence 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
• Note: 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
After approval by the Collaborations, we exchanged the secret
time offsets and we “opened the box” and…
Andrea Viceré - IHP Paris, November 13th 2006
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Results for the 2-fold coincidence searches
Upper Limits at 95% coverage
No excess of Coincidences found. Null hypothesis survives...
Andrea Viceré - IHP Paris, November 13th 2006
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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
(
) p
d
f(x
;
)
x
|


Ix
confidence
interval I x

I
x
experimental data
Andrea Viceré - IHP Paris, November 13th 2006
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Interpretation of the found limits
We go back to the signal model
The hrss is just a spectral scale of the signall
The definition of the energy flux distribution over angle and frequency
With the signal model, the total radiated energy is easily computed
as
With the signal model, the total radiated energy is easily computed as
An hrss=10-20 Hz-1/2 would correspond to ~ 10-3 Mo radiated at 10kpc
Andrea Viceré - IHP Paris, November 13th 2006
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Next Steps
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The 2-fold coincidences 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
amplitudes (i.e. 1e-18, 5e-19 and 1e-19 Hz-1/2. ), the best
compromise between efficiency and FAR is searched, using variable
thresholds for each detector with ½ hour bins in order to reach the
target level of background.
The zero-delay will be analyzed 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.
Andrea Viceré - IHP Paris, November 13th 2006
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Conclusions
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Because of the limitations on the observation time, the
Virgo-bars study does not yield stringent limits
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It is however a good example of the different ingredients
of the analysis
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Efficient event search: to see as much as possible
with “open eyes” in the data.
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Careful statistical analysis. Take into account that If
you look long enough, you see anything you want.
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Power of the coincidence method. As well known
from IGEC and LIGO experience, the network brings
difficult statistics to more manageable ones
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Need of good theoretical glasses. We may not need
waveforms to catch all classes of signals. But we need
them to assess the significance and constrain physical
parameters.
Andrea Viceré - IHP Paris, November 13th 2006
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