ALEXANDER L. URBAN LEONARD E. PARKER CENTER FOR GRAVITATION, COSMOLOGY & ASTROPHYSICS NEVER IGNORE A COINCIDENCE ENHANCING LIGO SENSITIVITY TO COMPACT BINARY MERGERS WITH GRB COUNTERPARTS 23 RD MIDWEST RELATIVITY MEETING
INTRODUCTION In building phase at the moment, Advanced LIGO will see first light in 2015 Advanced Virgo not long after that (2016) EM followup of gravitational waves will play an important science role in the era of the first detections For example, correlating GW candidates with known EM triggers can boost detection confidence in the former 2
INTRODUCTION In the early advanced era, we know little specifically about what to look for... 3
INTRODUCTION In the early advanced era, we know little specifically about what to look for......but short, hard gamma-ray bursts give us a pretty good feeling 3
WHY SHORT GRBs? sgrb progenitors likely to be compact binary systems with at least one NS NS-NS and NS-BH signals lie snuggly within aligo sensitivity band NS-BH are more energetic, but NS-NS are better-modeled Several space-borne eyes on the sky continually on the lookout for sgrb 4 Aasi et al., http://arxiv.org/abs/1304.0670 (2013)
WHY SHORT GRBs? Ingest events from Swift Gamma- Ray Explorer and Fermi Gamma- Ray Space Telescope Candidates land in our database within seconds of an event, trigger a low-latency coincidence search Swift BAT: better sky localization Fermi GBM: more sky coverage 5
WHY A COINCIDENCE SEARCH? At a noisy cocktail party... In a GW search... Your ears hear familiar tones at several frequencies Interferometers detect GW signals from CBC Your eyes resolve a small stereo speaker Telescopes see a transient at roughly the same time You quickly conclude the two are related Do a likelihood calculation, infer if they are related 6
WHY A COINCIDENCE SEARCH? At a noisy cocktail party... Your ears hear familiar tones at several frequencies In a GW search... Isotropic detector, loud background, matched filter search Interferometers detect GW signals from CBC Your eyes resolve a small stereo speaker Telescopes see a transient at roughly the same time You quickly conclude the two are related Do a likelihood calculation, infer if they are related 6
WHY A COINCIDENCE SEARCH? At a noisy cocktail party... Your ears hear familiar tones at several frequencies Your eyes resolve a small stereo speaker In a GW search... Isotropic detector, loud background, matched filter search Better localization, very little background Interferometers detect GW signals from CBC Telescopes see a transient at roughly the same time Do a likelihood calculation, infer if they are related You quickly conclude the two are related 6
WHY A COINCIDENCE SEARCH? At a noisy cocktail party... Your ears hear familiar tones at several frequencies In a GW search... Isotropic detector, loud background, matched filter search Your eyes resolve a small stereo speaker Better localization, very little background You quickly conclude the two are related Boost significance of the initial detection 6 Interferometers detect GW signals from CBC Telescopes see a transient at roughly the same time Do a likelihood calculation, infer if they are related
WHY A COINCIDENCE SEARCH? At a noisy cocktail party... Your ears hear familiar tones at several frequencies In a GW search... Isotropic detector, loud background, matched filter search Your eyes resolve a small stereo speaker Better localization, very little background You quickly conclude the two are related Boost significance of the initial detection Interferometers detect GW signals from CBC Telescopes see a transient at roughly the same time Do a likelihood calculation, infer if they are related How efficient is such a search? Do a simulation to find out 6
STRUCTURE OF SIMULATION http://www.laeff.cab.inta-csic.es/bootes/ing/grb/grb4.htm Assume isotropic emission, high detection efficiency, very high SNR Inspiral Merger Ringdown Inject into Gaussian noise http://inspirehep.net/record/811348 7
STRUCTURE OF SIMULATION number of injections 1000 800 600 400 Also assume difference in arrival time between GRB and GW signals is uniformly distributed over a [-1, +5]-second window (to not favor any emission mechanism, and to account for galactic extinction) 200 0 1 0 1 2 3 4 5 t (s) 8
LIKELIHOOD RATIO FORMULATION joint = p(g, I 1) p(g, I 0) = p(i 1) p(i 0) p(g 1) p(g 0) Z S 2 µ EM ( )µ GW ( ) d = EM GW corr 9
LIKELIHOOD RATIO FORMULATION joint = p(g, I 1) p(g, I 0) = p(i 1) p(i 0) p(g 1) p(g 0) = EM GW corr Probability of reporting a coincidence given that there is one Z S 2 µ EM ( )µ GW ( ) d 9
LIKELIHOOD RATIO FORMULATION joint = p(g, I 1) p(g, I 0) = p(i 1) p(i 0) p(g 1) p(g 0) = EM GW corr Probability of reporting a coincidence given that there is one Probability of reporting a coincidence given that there is NOT one Z S 2 µ EM ( )µ GW ( ) d 9
LIKELIHOOD RATIO FORMULATION joint = p(g, I 1) p(g, I 0) = p(i 1) p(i 0) p(g 1) p(g 0) = EM GW corr Probability of reporting a coincidence given that there is one Probability of reporting a coincidence given that there is NOT one Z S 2 µ EM ( )µ GW ( ) d Idea: calculate likelihood ratio for each GW-EM coincidence Apply different threshold values, compare them on a ROC curve How do false alarm rates compare to an all-sky search? 9
RESULTS 35 Detected coincidence 30 25 BAYESTAR 60 75 log( joint/ EM) 20 15 45 Known false alarm 30 15 0 15 30 10 h 8 h 6 h 4 h 2 h 0 h -2 h -4 h -6 h -8 h -10 h 10 5 injections background 45 60 75 6 7 8 9 10 11 12 13 c 0 1 2 3 4 5 10 4 prob. per deg 2 Combined SNR across a 2-detector LIGO network 10
RESULTS Define joint p 2ln joint 120 100 background injections 1.0 0.8 P (< joint ) 80 Hits 0.6 60 40 20 Misses Correct rejections False alarms 0 0 5 10 15 20 joint 0.4 0.2 C acc (> joint ) background injections 0.0 0 5 10 15 20 joint 11
RESULTS Define joint p 2ln joint 120 100 background injections 1.0 0.8 P (< joint ) 80 Hits 0.6 60 40 20 Misses Correct rejections False alarms 0 0 5 10 15 20 joint 0.4 0.2 C acc (> joint ) background injections 0.0 0 5 10 15 20 joint Spurious coincidences are random on the sky, so ~75% of background has vanishing likelihood ratio 11
RESULTS Background and foreground distributions have only minor overlap, so the ROC curve is near-optimal: 1.0 0.8 Detection probability 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 False alarm probability 12
RESULTS Background and foreground distributions have only minor overlap, so the ROC curve is near-optimal: PRELIMINARY 1.0 0.8 Detection probability 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 False alarm probability 12
RESULTS False Alarm Rate (FAR) < 10-4 Hz... By how much is this be improved? 10 9 FAR trig FAR all-sky = T ṄsGRBC acc ( joint ) T =6s Ṅ sgrb ' 1 month 1 ) FAR trig FAR all-sky ' 2.48 10 6 C acc ( joint ) FARtrig (s 1 ) 10 10 10 11 10 12 Because sgrb are rare, and coincidence window is short, FAR decreases by 6 orders of magnitude just by searching for coincidences in time alone Correlating sky locations can give at least another factor of 4, up to two more orders of magnitude 10 13 0 1 2 3 4 5 joint 13
CONCLUSIONS Gain A LOT of power in GW searches Much more powerful than an all-sky search, and ~4 times as powerful or more than time coincidence by itself Boost in horizon distance by ~4 times Recent analyses (e.g. Siellez et al., in preparation) are hopeful about rates Metzger & Berger, http://iopscience.iop.org/0004-637x/746/1/48 (2012) Fermi GBM detections need to be included for the sake of completeness Higher-latency, coherent GRB searches also planned (as was done in initial LIGO; see e.g. Predoi & Hurley (2011)) 14
CONCLUSIONS Gain A LOT of power in GW searches Much more powerful than an all-sky search, and ~4 times as powerful or more than time coincidence by itself Boost in horizon distance by ~4 times Recent analyses (e.g. Siellez et al., in preparation) are hopeful about rates Metzger & Berger, http://iopscience.iop.org/0004-637x/746/1/48 (2012) Fermi GBM detections need to be included for the sake of completeness Higher-latency, coherent GRB searches also planned (as was done in initial LIGO; see e.g. Predoi & Hurley (2011)) Above all, never ignore a coincidence!* 14 *Unless you re busy, in which case, always ignore a coincidence.
Thank-you for your attention QUESTIONS? 15