1. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 261 Gravitational-wave data analysis and supernovae Shourov K. Chatterji INFN Sezione di Roma / Caltech LIGO Laboratory LSC/Virgo burst group ILIAS workshop on supernovae, neutrinos, and gravitational waves 2008 November 26 Cascina, Italy

2. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 262 Unmodeled burst search Signals lasting between ~1 millisecond and ~1 second Signals in the frequency band from ~50 Hz to ~2+ kHz Waveforms not sufficiently accurate or complete to permit a matched filter search Search for statistically significant coincident events Targeted sources Asymmetric core collapse supernovae Merger phase of binary compact objects* Gamma ray burst progenitors Neutron star instabilities Cosmic string cusps* The unexpected * Knowledge of waveforms also permits some matched filter searches

3. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 263 Unmodeled burst search (cont.) “Eyes wide open” search philosophy Make as few assumptions on signal as possible Search as wide a parameter space as possible Characterize performance on many sets of waveforms Ad-hoc waveforms Gaussians, sine-Gaussians, white noise bursts Distributed over targeted signal space Astrophysical waveforms Supernovae, black hole merger simulation catalogs Time (ms) Gaussian pulse 235Hz Sine Gaussian 50M  BBH merger Supernova ( from ZM catalog) Time (ms) -5 520 -20150 30 70

4. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 264 Unmodeled burst search (cont.) Typical approach is time-frequency “excess power” search: Whiten data Project whitened data onto basis covering target signal space Threshold on projected magnitude to identify events with statistically significant excess signal energy Cluster events that are nearby in signal space Test for coincident events between multiple detectors Test for signal consistency between multiple detectors Evaluate false detection rate by time-shifting detector data Evaluate sensitivity of search to isotropic populations for a variety of simulated waveforms Eyes wide open approach leads to multiple choice of bases Consider one such example search algorithm…

5. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 265 Example burst search QPipeline is a multi-resolution time-frequency search method Projects whitened data onto basis of sinusoidal Gaussians Evaluated for a discrete set of highly overlapping basis functions spaced to constrain the signal loss due to mismatch Equivalent to a templated matched filter search for waveforms that are sinusoidal Gaussians after whitening Naturally yields tilings of the time-frequency plane similar to dyadic wavelet transforms The time-frequency plane is tiled for multiple values of Q (frequency to bandwidth ratio)

6. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 266 Example burst search (cont.)

7. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 267 Example burst search (cont.) QPipeline view of simulated binary neutron star inspiral signal

8. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 268 Parameterization of bursts Center time, center frequency, duration, and bandwidth Characteristic amplitude at Earth Matched filter signal to noise ratio,  0 Order of magnitude energy estimates assuming isotropic emission and Gaussian enveloped sinusoidal waveforms The detectability of supernovae waveforms can be quickly estimated using the above quantities and published search results

9. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 269 Sensitivity to supernovae Simulated waveforms not sufficiently accurate or complete to permit matched filter search, but are useful to evaluate the sensitivity of the unmodeled burst search Catalogs of simulated waveforms: Zwerger and Mueller; Dimmelmeier, Font, and Mueller; Ott and Burrows; more recent? Waveform morphologies: core bounce, rotational instabilities, acoustic modes

10. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2610 Sensitivity to supernovae (cont.) Detectable range depends on waveform morphology Rough estimate from LIGO’s fourth science run (see Abbott, et al., Class. Qaunt. Grav. 24 (2007)): Range at which half of supernovae would be detected Assume isotropic distribution in direction and orientation Range between 0.2 and 8 kpc, depending on waveform Anticipate factor of ~2 increase in sensitivity for joint analysis of LIGO’s fifth science run and Virgo’s first science run Detectable event rate is on the order of the galactic core-collapse supernovae rate of ~1 per 100 years for initial LIGO/Virgo. C. D. Ott has estimated the optimal SNR for different supernovae waveform components and mechanisms…

11. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2611 Sensitivity to supernovae (cont). From C. D. Ott, 2008 November 25, CaJAGWR seminar Optimal single detector SNR due to core bounce waveform component

12. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2612 Sensitivity to supernovae (cont). From C. D. Ott, 2008 November 25, CaJAGWR seminar Optimal single detector SNR due to core rotational instability waveform component

13. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2613 Sensitivity to supernovae (cont). From C. D. Ott, 2008 November 25, CaJAGWR seminar Optimal single detector SNR due to acoustic mechanism waveform component

14. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2614 Supernovae targeted searches Sensitivity of search limited by false detections False detection rate depends on parameter space of search May be able to do better than the eyes wide open burst search How to narrow the parameter space? “Externally triggered” search Based on optical or neutrino observations observations Known time of supernova Search a limited window in time Known position of supernova Search a limited region on the sky How much can optical and neutrino observations restrict the parameter space of the search? Restrict space of waveforms Search for waveforms with specific features Optical follow-up of gravitational-wave triggers is also planned

15. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2615 Sky position recovery A number of methods exist to estimate sky position Timing based approaches use accurate measurements of the observed signal delay between pairs of detectors to triangulate the position on the sky Coherent approaches also take into account the response of the detectors to both gravitational wave polarizations, and identify the regions of greatest likelihood on the sky Bayesian coherent approaches determine a posteriori probability distributions for the source location on the sky All of the approaches are currently being evaluated on simulated signals to determine the accuracy of position reconstruction The goal is to have sky position estimation for interesting events within 10 to 30 minutes during the next joint science run starting in Spring of 2009 Searches that target a single source on the sky are also planned

16. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2616 Time based position reconstruction F. Beauville, et al. Class.Quant.Grav. 25 (2008) Simulated recovery of sky position for 1 ms Gaussian pulses using LIGO/Virgo network using Gaussian matched filter search. ~1 degree resolution Impulsive core collapse feature approximated by short duration Gaussian pulse.

17. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2617 Coherent burst search Full solution of the “inverse problem” requires three or more non- aligned detectors. Data from two detectors can be used to predict the signal in the third detector For each direction on the sky, use a linear combination of time shifted signals from two detectors to predict the signal in the third detector Compute the prediction error Find the direction on the sky where the prediction error is minimized Yields best fit sky position Also yields both polarizations of gravitational waveforms This is equivalent to the maximum likelihood approach Can be generalized to more than three detectors…

18. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2618 Coherent burst search (cont.) Coherent sum: Find linear combinations of detector data that maximize signal to noise ratio Null sum: Linear combinations of detector data that cancel the signal provide useful consistency tests. data = response x signal + noise coherent sum N-2 dimensional null space detector data coherent null 2 dimensional signal space Naturally handles arbitrary networks of detectors Analysis repeated as a function of frequency and sky position Produces significance and consistency sky maps Gursel and Tinto, PRD 40 (1989) 3884 Klimenko, et al., PRD 72 (2005) 122002 Rakhmanov, CQG 23 (2006) S673 Wen and Schutz, CQG 22 (2005) S1321 Chatterji, et al. PRD 74 (2006) 082005

19. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2619 Collocated detectors Special easy to understand case of coherent methods Applicable to the two LIGO Hanford detectors Subset of the general case Produce hybrid ‘H’ detector than makes optimal use of H1 and H2 Exhibits many of the same features as the general case Optimal combination to maximize detectability Null combination to test for consistency But there are some differences Coherent combinations are independent of source direction Computationally much cheaper than general case Cannot fully recover source information Forms the first stage of a hierarchical coherent search

20. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2620 Collocated detectors example H+ yields ~10 percent increase in SNR H- consistent with detector noise H2H1 H+ H- Simulated inspiral signal

21. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2621 Collocated detectors example (cont.) Significant H- content indicates inconstistency H1H2 H+ H- Coincident H1H2 glitch In time-shifted data set

22. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2622 Simulated consistency test Simulated (A1B3G3) supernovae signal from Dimmelmeier et al. A&A 393 (2002) 523 Injected with SNR of 20 into simulated design sensitivity H1, L1, and V1 detector noise Figure from PRD 74 (2006) 082005 Interference fringes from combining signal in two detectors form rings along locus of constant time delay True source location at intersection of rings has  2 per degree of freedom of ~1 Color indicates  2 per degree of freedom of the coherent null sum as a function of sky position Test the coherent null stream for consistency with detector noise as a function of sky position

23. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2623 Simulated consistency test (cont.) Simulated gravitational-wave burst (consistent supernovae waveforms) Simulated coincident glitch (inconsistent supernovae waveforms) Figures from PRD 74 (2006) 082005 Consistency tests useful for distinguishing coincident detector glitches from real signals Simulated (A1B3G3) supernovae signal from Dimmelmeier et al. A&A 393 (2002) 523 Injected into simulated design sensitivity H1, L1, and V1 detector noise Detector glitches do not exhibit the ring features with reduced null sum energy that are observed for consistent signals Color indicates fraction of available signal energy remaining in null stream

24. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2624 Simulated waveform recovery Given a best guess sky position, estimate the signal h from x = Fh + n by identifying the psuedo-inverse R such that RF = I. Simulated (A4B1G4) supernovae from Dimmelmeier et al. A&A 320 (1997) 209 Injected with SNR 40 into simulated H1, L1, and G1 detector noise Signal injected only into h+ polarization Recovered h+ signal (blue) is a noisy, band-passed version of the injected signal (red) Recovered hx signal (green) is just due to noise.

25. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2625 Restricting the siganl space It is possible to decompose simulated supernovae waveform catalogs into minimal set of orthogonal waveforms P. Brady and S. Ray-Majumder, Class. Qaunt. Grav 21 (2004) considered Gram-Schmidt orthogonalization S. Heng, in preparation, arXiv:0810.5707v1, considers a principal component analysis decomposition Used catalog from Dimmelmeier, et al. Phys. Rev. Lett 98 (2007) Successfully reduced the catalog to ~10 orthogonal waveforms, indicating a good degree of similarity between the waveforms The resulting basis can be used to construct a template bank for a more targeted search

26. G08XXXX-00-Z S. Chatterji, Cascina, Italy, 2008 November 2626 Restricting the signal space (cont.) S. Heng, in preparation, arXiv:0810.5707v1 Number of waveforms required to achieve a specified worst case match to all waveforms in the catalog