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.

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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 - 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

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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.

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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.

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

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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
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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
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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

f0914 Hz tau1ms
f0866 Hz tau10ms
f0930 Hz tau30ms
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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

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Optimization (2) DS _at_ 914 Hz, 1ms, 1e-19 Hz-1/2
AURIGA
VIRGO
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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
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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
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Results for the 2-fold coincidence searches
Upper Limits at 95 coverage
Preliminary
No excess of Coincidences found. Null hypothesis
survives...
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Confidence Belt Coverage
physical unknown
confidence interval
coverage
experimental data
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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 hrss10-20 Hz-1/2 would correspond to 10-3
Mo radiated at 10kpc
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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.

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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.