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. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #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. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #3 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

4. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #4 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

5. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #5 Correlated energy E null E incoherent -E correlated Signal injection features

6. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #6 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. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #7 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

8. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #8 E null E incoherent -E correlated Correlated energy Glitch injection features

9. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #9 Rejecting glitches The null stream enforces waveform consistency only when there is excess power to suppress –When E incoherent has excess energy Equivalently, a null stream detection is only significant when there is correlation –When E correlation 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

10. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #10 Implementation M ATLAB 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 1/100 th real time

11. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #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

12. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #12 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

13. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #13 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

14. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #14 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

15. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #15 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

16. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #16 Review: Null streams The whitened output d i of N detectors can be modelled by –Antenna patterns F i –Strain h –Amplitude spectrum σ i –White noise n i The N – 2 linear combinations (Zd) j are orthogonal to strain and each other

17. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #17 F1F1 d1d1 d2d2 F2F2 F Z Review: Null stream visualization Consider analogy with one fewer dimension –Detectors d 1, d 2 –One polarization –Sensitivity F 1, F 2 –Large strain h Null stream Z is orthogonal to F –Zd is white –Fd estimates signal Zd Fd

18. GWDAW 10 16/12/2005 A coherent null stream consistency test for gravitational wave bursts, A Searle G050636-00-Z #18 Review: Directions Every direction Ω on the sky has different –Null stream coefficients Z –Delays Δt i for detector at x i cΔt i = –x i · 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