A coherent null stream consistency test for gravitational wave bursts

1
A coherent null stream consistency test for
gravitational wave bursts

• Antony Searle (ANU)
• in collaboration with
• Shourov Chatterji, Albert Lazzarini, Leo Stein,
  Patrick Sutton (Caltech),Massimo Tinto
  (Caltech/JPL)

2
Motivation

• Null stream formalism tests network data for
  consistency with gravitational waves
• Y. Gürsel and M. Tinto, Phys. Rev. D 40, 3884
  (1989)
• Real interferometers have populations of
  glitches, bursts of excess power not due to
  gravitational waves
• Can the null stream be used to veto these
  glitches on the basis of their inconsistency with
  gravitational waves?
• The problem is interesting because null stream
  searches are vulnerable to single- and
  double-coincidence glitches
• This needs to be addressed before null stream
  searches can be applied to real, glitchy data
• Find a way to veto events and to make a search
  robust against glitches

3
Detecting unmodelled bursts

• For each resolvable direction on the sky (gt
  10,000)
• Postulate a gravitational wave signal from that
  direction
• Form a linear combination of three detectors that
  is orthogonal to postulated signal
• Test this null stream for excess energy
• If for any direction there is no excess energy,
  the data is consistent with a gravitational wave

4
Signal injection
There are many directions on the sky (Mollweide
projection) with low null energy, including the
true direction
DFM waveform injected onto Hanford, Livingston
and Virgo (LIGO noise curve) network with 24h
sim. noise
5
Signal injection features
Enull
Correlated energy
Eincoherent
-Ecorrelated
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False acceptance of glitches

• If any one of the three detectors does not
  exhibit excess energy, then there exist
  directions for which the network data is
  consistent with a gravitational wave
• Antenna pattern zeros of that detector, for which
  k (1, 0, 0)
• Nearby directions also affected, depending on SNR
• Background noise is consistent (with h 0)
• Equally consistent with background noise, so
  ruled out by likelihood ratio in GT and similar
  searches
• One and two detector bursts of energy are
  consistent (with h ? 0 from antenna pattern
  zeros)
• No requirement for waveform consistency
• Likelihood ratio will not rule these out without
  a more sophisticated noise model with knowledge
  of the glitch distribution
• Any veto that rejects these will also reject the
  small fraction of gravitational waves from these
  directions such a veto is not safe
• Only when there is excess energy in all three
  detectors is waveform consistency enforced over
  the whole sky

7
Glitch injection
Even for a glitch there are many directions on
the sky (Mollweide projection) with low null
energy
Waveforms injected onto Hanford, Livingston and
Virgo (LIGO noise curve) network with 24h sim.
noise
8
Glitch injection features
Enull
Correlated energy
Eincoherent
-Ecorrelated
9
Rejecting glitches

• The null stream enforces waveform consistency
  only when there is excess power to suppress
• When Eincoherent has excess energy
• Equivalently, a null stream detection is only
  significant when there is correlation
• When Ecorrelation has excess energy
• Adopting this criterion rejects
• Imperfectly correlated glitches
• Gravitational waves that at least one detector is
  insensitive to
• For each event flagged by some ETG, find the
  direction on the sky with best correlation and
  use it to decide between signal or glitch

Correlated energy
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Implementation

• MATLAB implementation xpipeline
• matapps/src/searches/burst/coherent-network
• Computes (optimal) directions for given maximum
  frequency, reads data, optionally injects signals
  and/or glitches, whitens data, computes null
  stream coefficients for each direction and
  frequency, computes time shifts for each
  direction, steps through data in overlapping 1/16
  s blocks, time-shifts data to nearest sample,
  Fourier transforms, completes time-shift with
  phase rotation, forms null stream in frequency
  domain, sums power into frequency bands, saves
  null energy (and other energies) for
  time-frequency band and direction.
• Shares some infrastructure with qpipeline.
• Runs in approximately 1/100th real time

11
Simulation

• To simulate signals
• Choose unifomly distributed sky location
• Compute time delays and antenna patterns
• Inject a particular DFM waveform into each
  detector
• To simulate glitches
• Choose unifomly distributed sky location
• Compute time delays and antenna patterns
• Inject a different (and only semi-correlated) DFM
  waveform into each detector
• Glitch population
• Would pass incoherent consistency tests
• Power, time delays physically consistent,
  frequency band overlap etc.
• A worst case (rather than a realistic) glitch
  population

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Separating populations
Inject populations of signals and glitches with
same total energy As the SNR increases the
populations become distinct The maximum
correlation for signals corresponds to low null
energy The maximum correlation for glitches
corresponds to high null energy
Correlated energy
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ROC curve

• At total energies corresponding to RMS matched
  filtering SNR of 17 in each detector, we can
• Detect most of a population of gravitational
  waves
• Reject all of a population of semi-correlated
  glitches
• The rejected gravitational waves are those that
  are weak in at least one detector

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Summary

• Null stream tests (for three interferometers)
  cannot distinguish between glitches and those
  gravitational waves coming from directions that
  members of the network are insensitive to
• Requiring correlation, or equivalently a
  particular distribution of excess power, is one
  way to distinguish between signals and
  uncorrelated glitches
• The SNR (17) at which gravitational waves and
  semi-correlated glitches can be so distinguished
  in this toy simulation is encouraging

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Future directions

• Better simulations
• Inject more waveforms and other than linear
  polarisations
• Real interferometer glitches
• How correlated? How frequent
• Different networks
• Fourth detector and second null stream invalidate
  these examples
• More theoretical work
• Current justification is ad-hoc
• Bayesian interpretations and formulations
• Distribution-free (nonparametric) correlation
  test?
• Gives known statistics for a very general noise
  model

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Review Null streams

• The whitened output di of N detectors can be
  modelled by
• Antenna patterns Fi
• Strain h
• Amplitude spectrum si
• White noise ni
• The N 2 linear combinations (Zd)j are
  orthogonal to strain and each other

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Review Null stream visualization
d1

• Consider analogy with one fewer dimension
• Detectors d1, d2
• One polarization
• Sensitivity F1, F2
• Large strain h
• Null stream Z is orthogonal to F
• Zd is white
• Fd estimates signal

Z
F
Zd
F1
d2
F2
Fd
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Review Directions

• Every direction O on the sky has different
• Null stream coefficients Z
• Delays ?ti for detector at xi
• c?ti xi O
• Sample the sky with some limited mismatch
• Template placement problem
• Affected by network geometry

• Mollweide plot of 0.6 ms resolution map for HLV
• Near-optimal
• Low density on plane of HLV baselines