Adapting matched filtering searches for compact binary inspirals in LSC detector data. Chad Hanna – For the LIGO Scientific Collaboration.

Introduction It is common to have single detector triggers at SNR ~1000 and millions of triggers at SNR 7. At the end of the pipeline we want only a few interesting candidates to follow To do this we tune our pipeline with injections. We try to separate injections from noise while assuring all (>99%) of injections which are detected at the onset survive the pipeline.

Outline Coincidence – timing, mass, psi, etc. Effective distance cuts – amplitude consistency Signal based vetoes – X 2, r 2 detection statistics (or how to separate the good stuff from the noise) Background estimation – time slides When applicable I will discuss the following for three different inspiral searches: Binary Neutron Star (BNS), Primordial Black Hole Binaries (PBHB), Binary Black Hole (BBH).

Coincidence parameter philosophy (BNS, PBHB, BBH) Injections are used to determine how a coincident event should be defined For BNS, PBHB, BBH we compare the end time that we inject with what we detect for a single instrument. The error in time found in the single detector establishes a coincident window we then apply to triggers between sites. (Of course the maximum GW travel time between sites is automatically accounted for.) For BNS, PBHB, we can repeat the procedure for chirp mass and  (which are both functions of the masses.) But the BBH case is more difficult, which I will explain. In all cases it is our philosophy to choose such windows generously as to not miss a detection.

Coincidence parameters (BNS,PBHB) End time We compare the end time of found injections with the injected end time in single detectors to place bounds on the coincidence windows between detectors. S3 BNS timing coincidence window 2 ms S3 PBH timing coincidence window 4 ms PBHB BNS Seconds difference

Coincidence parameters (BBH) BBH – EOB End time The BBH search is complicated by injecting several physical template families some of which produce tails in the timing distribution when detected with BCV templates. The worst case parameters are chosen. BBH – Taylor T1 S3 BBH timing window 25ms

Coincidence parameters (BNS,PBHB) Chirp mass We compare the chirp mass of found injections with the injected chirp mass in single detectors to place bounds on the chirp mass coincidence windows between detectors. S3 BNS chirp mass window.02 M סּ S3 PBHB timing window.002 Mסּ PBHB BNS

Coincidence parameters (BBH) BBH EOB  0,  3 The BBH search doesn’t tune mass but rather the BCV parameters  0,  3. These are not injection parameters and therefore the single detector scheme shown in the previous slides doesn’t work. Instead we must look at coincidences before we choose the  0,  3 coincidence windows. The BBH windows are  0 =  3 = Full range. BBH EOB

Effective Distance Cut (BNS,PBHB) Injections (and real GW signals) have effective distance ratios which are close to unity for H1 and H2 (within calibration errors). Therefore any triggers which are found to have non unity effective distances are not consistent with real GW sources and may be disregarded. BNS PBHB BNS fractional difference in effective distance cut = 0.45 PBHB fractional difference in effective distance cut = 0.50 Fractional difference in eff. distance

Signal based vetoes -  2 - (PBHB,BNS) 22 The  2 test is a waveform consistency test to separate real signals from false alarms. We actually adjust the  2 to be a function of P (the number of frequency bins),  2 (SNR_, and \ a parameter called  2. I will denote This modified  2 as  * 2.  2 should be the bank mismatch But it is tuned to not lose nearby injections.  * 2 =  2 /(P+  2  2 )

Signal Based Vetoes - r 2 - (PBHB,BNS) r2r2 See poster by Andy Rodriguez The  2 test itself is powerful but it can be refined further by examining the time A signal spends above the r 2 threshold. An injection spends little time above, whereas glitches (false alarms) spend a lot of time above. BNS r 2 =  2 /p

Detection Statistics (BNS, PBHB) Now that we have a nice waveform consistency test (  2 ), SNR alone is not the best way to separate false Coincidences from injections. There is a better statistic which involves a combination of SNR and Χ 2 Lines of constant S follow the contours of accidental coincidences quite well. The 250 is found empirically. BNS PBHB

Background Estimation / Combined Statistic (PBHB,BNS) PBHB BNS In order to differentiate between real signals and background we examine false coincidences by sliding the trigger sets of one detector with respect to another in time. A typical search has more than 50 slides where two of three detectors are slid by ~5-10 seconds each time. Using the statistic discussed earlier, in a combined way (e.g. H1S + L1S), lines of constant false alarm are approximated by the linear statistic contours between detectors.

Conclusion BNS, PBHB, and BBH searches are similar in that they must overcome messy data. Although the procedures for each search vary the philosophy remains to have a few good candidates at the end with little question about missing a detection