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The Virgo-bars search for bursts

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Title: The Virgo-bars search for bursts


1
An example or real data analysisthe VIRGO-bars
search for bursts
Andrea Viceré for VIRGO Auriga - Rog
2
Motivations and outline
  • 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.
  • Goals
  • understand the potentialities of a network of
    different detectors.
  • Develop new techniques coping with their
    heterogeneous nature.
  • Bring together the two DA communities and their
    experiences.
  • Pave the way towards greater integration in the
    future.
  • Methodology
  • Search for coincident events, no assumptions on
    the waveforms.
  • Bring in physically motivated assumptions when
    evaluating the detection efficiency of the
    network.
  • Use the assumptions to optimize the cuts on the
    events of each individual detectors, without
    compromising the detection efficiency
  • Deduce upper limits from the fact that
    coincidences do not exceed background
    expectations.

3
The VIRGO-bars network in one slide
  • 24 hours of data taken during Virgo C7 run
    start at UTC time 810774700,
  • (14 Sep 2005 - 2311 27s)
  • Heterogeneous Network
  • spectral sensitivity
  • directional response
  • Patterns for circularly polarized signals

4
More details on the study
  • Goal assess interpreted confidence intervals on
    the flux of gravitational waves.
  • The interpretation comes from software injections
    which are used to compute the efficiency of
    detection for a source population
  • We have restricted the study to a class of
    signals, the Damped Sinusoids, and to one general
    direction in the sky, the Galactic Center.
  • 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).
  • 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.
  • Blind analysis not to bias results by feedbacks
    on methods from looking at results, a secret
    time offset was added to detector times.

5
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 lm2 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

6
Event Trigger Generators and Observables
  • AURIGA WaveBursts (S. Klimenko et al,
    LIGO-T050222-00-Z) 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
    Wiener-Kolmogorov 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.

7
Assessing the background of accidentals
  • 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 auto-correlogram 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.

8
A better view in the frequency domain
9
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 ? inclination
    angle ?
  • N8640 (1/10 s)
  • hrss1e-20 - 2e-18
  • Hz-1/2

10
Which physical parameters?
  • Take just the example of Quasi Normal Modes of
    Black Holes, and assume that an lm2 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

11
Eventsinjections _at_ hrss1e-19 Hz-1/2
AURIGA N1413
EXPLORER N5614
VIRGO N24241
NAUTILUS N8628
12
Efficiency
DS f0930 Hz tau30ms
  • Single detector efficiencies
  • For VIRGO, 7 hrs out of 24 have been excluded
    by epoch vetoes
  • gt Asymptotic 70

DS f0866 Hz tau10ms
DS f0914 Hz tau1ms
13
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

f0914 Hz tau1ms
f0866 Hz tau10ms
f0930 Hz tau30ms
14
Optimization of the thresholds (1)
  • To shrink interpreted confidence interval we
    choose to optimize the 2-fold coincidence
    searches gt Better Upper Limits
  • For each configuration/template/amplitude, the
    magnitude thresholds for the 2 detectors are
    tuned gt large trial factor. We keep this into
    account when calculating the statistics.
  • 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). Coincidences are Poisson point
    processes fluctuation is sqrt(counts).
  • The magnitude thresholds are optimized every 30
    min

15
Optimization (2) DS _at_ 914 Hz, 1ms, 1e-19 Hz-1/2
AURIGA
VIRGO
16
Statistical Analysis (1)
  • 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 gt 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 gt
    the single trial confidence is tuned in order to
    reach a total false claim of 99

Global confidence
Single trial confidence
17
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
18
Results for the 2-fold coincidence searches
Upper Limits at 95 coverage
Preliminary
No excess of Coincidences found. Null hypothesis
survives...
19
Confidence Belt Coverage
physical unknown
confidence interval
coverage
experimental data
20
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 hrss10-20 Hz-1/2 would correspond to 10-3
Mo radiated at 10kpc
21
Next Steps
  • The 2-fold coincidences have a high level of
    accidental background, single detection not
    possiblegt 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.

22
Conclusions
  • Because of the limitations on the observation
    time, the Virgo-bars study does not yield
    stringent limits
  • It is however a good example of the different
    ingredients of the analysis
  • Efficient event search to see as much as
    possible with open eyes in the data.
  • Careful statistical analysis. Take into account
    that If you look long enough, you see anything
    you want.
  • Power of the coincidence method. As well known
    from IGEC and LIGO experience, the network brings
    difficult statistics to more manageable ones
  • 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.
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