1. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Modeling the Performance of Networks of Gravitational-Wave Detectors in Bursts Search Maria Principe 1, Patrick Sutton 2 1 University of Sannio, Benevento, Italy 2 LIGO-CALTECH

2. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas GW Bursts Search GWBs are generated by systems such as core-collapse supernovae, black-hole mergers and gamma-ray bursters Poor theoretical knowledge of the source and of the resulting GW signal Multiple-detector search is required, but »Different noise spectra »Different alignment »Different algorithms »Non-Gaussian, non-stationary data It’s not obvious how to use the different detectors optimally We wrote a Network Simulator for helping the tuning of GWB searches

3. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Multiple-Detector Searches GW search codes typically have a single threshold (e.g. on SNR or significance) which is varied after trigger generation to tune the analysis. Multi-detector GWB searches can be tuned according Neyman- Pearson criterion Achieve maximum probability of detection while not allowing the probability of false alarm to exceed a certain value

4. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Target of the work Develop a software tool in Matlab to find the optimal tuning of analyses in actual network GWB search »Input: –Lists of triggers from raw data and from injected signals »Output: –Optimal trigger threshold for each detector to satisfy N-P criterion –Network efficiency –Predicted false alarm rate »Available on CVS archive Such a tool could be also useful »to simulate the behavior of GW detectors in trigger-based searches for GW bursts (GWBs) »to estimate sensitivity to populations of signals other than those directly tested in the search »to estimate the effect of uncertainties in the properties of the individual detectors (calibration,..)

5. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas The idea Single-IFO Event Generation: »Get trigger from ETG (Q-pipeline, Excess Power, TFClusters, …) »Select trigger threshold for each IFO Single-Detector False Alarm Rate: »Estimate for selected threshold Network False Alarm Rate: »Estimate after –Time Coincidence test in all IFOs. –Frequency, amplitude comparisons. Single-Detector Efficiency: »Compute efficiency to optimally oriented sources for chosen trigger threshold Network Efficiency: »Measure based on known single-detector efficiencies Best trigger threshold set, satisfying N-P criterion: »Threshold set with best network efficiency and FAR below desired value

6. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Test: LIGO-Virgo Simulated Data We demonstrate the Network Simulator using Q-pipeline (S. Chatterji) triggers from the LIGO-Virgo project 1B simulated data »With burst injections »Gaussian noise at LIGO/Virgo design sensitivity Injected simulated signals: »linearly polarized Gaussian-modulated sinusoids »fixed amplitude h rss = 5 x 10 -22 Hz -1/2 »Q = 2π f c  = 15 »central frequency f c = 235 Hz »Duration  = 10 ms

7. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Detector False Alarm Rate Estimate single-detector time FAR »Based on trigger list and total observation time »Background noise is modeled as a Poisson process H1 Rate of background noise events occurring above selected threshold

8. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Network False Alarm Rate Actual GWB searches require a candidate GWB to be observed simultaneously by all detectors, to minimize the probability of falsely claiming a GW detection. Also often require similar measured frequency and/or amplitude. Network Simulator can estimate the false rate after any of these coincidence tests: »time coincidence »frequency coincidence (optional) »amplitude coincidence (optional, applied only to user-specified detectors) Expected network FAR is given by NTFAR: Rate at which background noise events occur simultaneously in all detectors NFFAP: Probability for background noise events to occur in frequency coincidence in all detectors NAFAP: Probability for background noise events (that are frequency coincident) to occur with approximately the same amplitude in specified detectors

9. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Time coincidence R t_nw - NTFAR Time Coincidence test: »a, w t ij user-specified quantities »A set of event triggers is defined to be in coincidence if each pair is in coincidence The expected network background rate for a set of N detectors with rates R i is estimated by Monte Carlo method [1] t i - peak time of the event i w t ij - coincidence window for the pair (i, j) Δt i - duration of the event i N det = 2 N det = 3 [1] L. Baggio et al. 2002 Classical and Quantum Gravity 19 T obs

10. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Frequency and Amplitude Coincidence P f_nw – NFFAP Frequency Coincidence condition: »a, w f ij user-specified quantities Compute fraction of noise events which satisfy coincidence condition by Monte Carlo P h_nw – NAFAP Amplitude Coincidence condition: »w h ij user-specified quantities »Usually applied only to aligned detectors Compute fraction of noise events (frequency coincident) which satisfy coincidence condition by Monte Carlo f i - central frequency of the event i w f ij - coincidence window for the pair (i, j) Δf i - frequency bandwidth of the event i H = log(h) h = observed amplitude w h ij - coincidence window for the pair (i, j)

11. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Single-Detector Efficiency Compute time coincidences between triggers and injections Tolerance for timing errors (~10 ms) Use sigmoid fitting function (Blackburn & Chatterji) Compute ‘optimally oriented’ efficiency curve, as function of h obs = h rss |F+| (linearly polarized signals only) …as expected, efficiency gets worse increasing threshold H1 ρ

12. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Network Efficiency cos(θ), φ and ψ dimensions are sampled uniformly or user can specify an arbitrary sampling map Possibility to choose an arbitrary distribution (under process) Sigmoid fitting function turns out ok also for network efficiency curves Solving by Monte Carlo H1 H2 L1 V1 H1-H2-L1-V1 [7 7 7 7] [7 7 7 10]

13. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Optimal tuning set Fix a target network FAR Choose a grid of trial threshold sets For each set compute network FAR For sets with FAR below target value compute network efficiency curve Optimal threshold set is the set with 50% efficiency at the lowest signal amplitude

14. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas LIGO-Virgo example target FAR: 3.1688e-010 (1/century) detector threshold (normalized energy) range: [9.5, 10], step : 0.1 Computed optimal set: [9.7 9.7 9.7 9.7] Achieved network FAR: 3.1623e-010 H1 H2 L1 V1 all

15. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Future plans Further improving and testing of optimal threshold set functions »Interpolation to find FAR=constant surface »Clustering for non-Poisson events Apply Network Simulator to real triggers sets »S2 Excess Power triggers »Possibly tuning online Excess Power search

16. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Acnowledgments LIGO–CALTECH and Summer Undergraduate Research Fellowship program Shourov Chatterji and the LIGO-Virgo joint working group for providing the Q-pipeline triggers we used to demonstrate the Network Simulator. I.M. Pinto and Wavesgroup of University of Sannio

17. M. Principe, GWDAW-10, 16th December 2005, Brownsville, Texas Thank you for your attention Any questions?