18/01/01GEO data analysis meeting, Golm Issues in GW bursts Detection Soumya D. Mohanty AEI Outline of the talk Transient Tests (Transient=Burst) Establishing Confidence in Detection Upper Limits Detector Characterization

18/01/01GEO data analysis meeting, Golm Transient Tests Several Tests have been developed. –No uniformly most powerful transient detector known. –Need detectors that can exploit NR waveform information. Thorough comparison required. –One such project is already underway. (SDM, Patrice Hello, Eric Chassande-Motin.) Criteria for comparison –Receiver Operating Characteristics (ROC). –Robustness against noise models. –Robustness against signal models. –Computational requirements.

18/01/01GEO data analysis meeting, Golm Establishing Confidence in Detection Confidence: –Probability of detected event being not due to noise. –1 - (False alarm probability). What should be our level of confidence? False alarms: Terrestrial burst interference, instrumental noise. Primary means of establishing confidence –Coincidence between GW interferometers. –Coincidence between GW and Astronomical observations. –Anti-coincidence with auxiliary channels.

18/01/01GEO data analysis meeting, Golm Coincidence: GW detectors (I) False alarm rate (noise) in pairwise coincidence = r 1 r 2 w. r 1, r 2 = false alarm rates in each detector. w = window size. Detection probability = Q 1 Q 2 p. –Important: p comes from time of arrival estimation error. (It is also direction dependent.) –Estimation errors are threshold independent. For given SNR, Detection probability <= p. –p can become small if w is not sufficiently greater than.

18/01/01GEO data analysis meeting, Golm Coincidence: GW Detectors (II) For transients, time of arrival estimates will not be as good as for known waveform signals. –Will not be a surprise if the error is comparable to light travel time. Need a good estimate of the time of arrival estimate error variance. –Monte Carlo simulations required for complicated tests. –Detector characteristics used in simulations change with time.

18/01/01GEO data analysis meeting, Golm Coincidence: GW Detectors (III) How does SNR in coincidence scale with number of detectors ? –Coincidence cannot beat (Number of detectors) ½ scaling of SNR in Likelihood Ratio tests. Coincidences possible in other parameters –Each extra coincidence parameter means reduction in detection probability. –Note: As before, there will be a threshold independent limit on detection probability. –Estimation error covariance matrix required for correct window volume.

18/01/01GEO data analysis meeting, Golm Bar detectors Strategy: Detect an excess in coincidences. –Considerable experience available. –Do some of the same concerns apply? Other issues –Differing detector characteristics (e.g., noise PSD). –Cross-correlation based methods: Have to rule out terrestrial sources of cross-correlation, SNR goes as N ¼. Coincidence: GW Detectors (IV)

18/01/01GEO data analysis meeting, Golm Coincidence: GW with Astro. (I) Coincidence window in time for GW and Astro. event will not be known in general. –Method under development by Soma Mukherjee and SDM that makes window size a parameter that can be searched over for the best fit to the observed rates. –Can be generalized to include positional information. Positional coincidence: Too big an error box is a problem for counterpart searches. –Could do something like ROTSE or LOTIS: Fast, wide- field optical searches by robotic telescopes. –What is the confidence level required by astronomers? –Even if a candidate is found, may need to estimate GW burst waveform to form a plausible link.

18/01/01GEO data analysis meeting, Golm Coincidence: GW and Astro. (II) Use astronomical triggers to look for GW bursts. –Reduces data duration for search and, hence, false alarm rate (increases confidence). –Analysis for Binary Inspirals by Piran (1993). Need to put a selection on triggers. –Example: Most GRBs occur at large distances. Putting a distance cutoff can enhance confidence. Statistical Detection possible. –Finn, Mohanty, Romano, –Use triggers to “chop” between background and source and check for statistical difference. –Useful quantities can be calculated such as average GW burst strength.

18/01/01GEO data analysis meeting, Golm Anti-coincidence with Aux. Channels (I) Simple analysis. –For N aux. channels per site with false alarm rate of r in each channel, probability of at least one false anti-coincidence = 2 N r w. (w is the time window). –w = 2 sec, N = 10, r = 5/hour gives 1 out of 18 GW bursts falsely dismissed. False alarm rate for aux. channels may have large error –Example: actual r could be 10/hour: 1 per 10 GW bursts lost. –Robust test: false alarm rate independent of noise models (SDM, 2000). –This could also be an issue for GW-GW coincidence since false alarm rate r 1 r 2 w goes as square of individual false alarm rate.

18/01/01GEO data analysis meeting, Golm Robust Transient Test SDM, PRD, False alarm rate is independent of noise model. Made possible by –Adopting the weakest possible criterion for a transient: Brief episode of non-stationarity. No mention of Gaussianity or non-Gaussianity here. –Check for a change in the (only) measure of (wide sense) stationarity which is the PSD. Surprisingly good performance. –Can be improved by reducing robustness (= less general criterion for a transient).

18/01/01GEO data analysis meeting, Golm Anti-coincidence with Aux. Channels (II) Clearly, a simple anti-coincidence is not enough Need to establish if an aux. channel event could have caused the GW channel transient. –May require an end-to-end simulation software as being developed in the LIGO project. –Waveform estimation tools required. –Estimation also occurs in designing a proper GW-GW coincidence scheme (eg.,time of arrival estimation error). –Estimation seems to be intimately intertwined with detection.

18/01/01GEO data analysis meeting, Golm Upper Limits Upper limit on what? –Rate at a certain SNR, in some Bandwidth, in a certain class of bursts. –Max. SNR in a certain class of bursts. –Other quantities of Astrophysical interests. –Each quantity above requires its own analysis scheme. Combining upper limits on rates with coincidence analyses. –Much to learn from the Bar detector community. Important to characterize background (rate, distribution of amplitude etc.) –One possible way: Treat all non-coincident events as part of background. Estimate rate etc., from these events.

18/01/01GEO data analysis meeting, Golm Detector Characterization Instantaneous Detector “state” required –For estimating estimation errors and performance of transient tests via simulations. –Need to study estimation tools and fix what information constitutes detector state. Characterization of rate and amplitude distribution of terrestrial bursts required for upper limit calculations. –This requires keeping track of detector history. –Analyze almost all data: Need an automated pipeline!