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)

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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

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Detecting unmodelled bursts

• For each resolvable direction on the sky (> 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

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Signal injection

DFM waveform injected onto Hanford, Livingston and Virgo (LIGO noise curve) network with 24h sim. noise

There are many directions on the sky (Mollweide projection) with low null energy, including the true direction

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Correlated energy

Enull

Eincoherent

-Ecorrelated

Signal injection features

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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

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Glitch injection

Waveforms injected onto Hanford, Livingston and Virgo (LIGO noise curve) network with 24h sim. noise

Even for a glitch there are many directions on the sky (Mollweide projection) with low null energy

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Enull

Eincoherent

-Ecorrelated

Correlated energy

Glitch injection features

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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

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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

Correlated energy

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

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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 σi

– 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

• 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

Zd

Fd

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Review: Directions

• Every direction Ω on the sky has different

– Null stream coefficients Z

– Delays Δti for detector at xi

cΔti = –xi · Ω

• 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