A Waveform Consistency Test for Binary Inspirals using LIGO data Andres C. Rodriguez Gabriela González (Louisiana State University) Peter Shawhan (LIGO | Caltech) Evan Oshsner (University of Maryland) LIGO Observatories I’m going to talk today about a waveform consistency test for binary inspirals using data from the LIGO interferometer. LSC Inspiral Analysis Working Group LIGO-G050236-00-Z American Physical Society April Meeting 4.16.05

American Physical Society April Meeting LIGO Observatories Hanford: two interferometers in same vacuum envelope (4km(H1), 2km(H2)) *For one of the sources of gravitational waves that could be detected by LIGO I, binary inspirals are one example. Initial LIGO (40Hz-2 KHz)will be sensitive to gravitational waves emitted as far as the VIRGO cluster for a 1.4-1.4 Msol neutron star inspiralling binary. Matched filtering is the optimal detection strategy if detector noise is stationary & white Livingston: one interferometer (4km(L1)) 4.16.05 American Physical Society April Meeting 02

Template based Matched Filtering Data stream searched using matched filtering between data & template waveform. Transform data to frequency domain : s(f) Calculate template in frequency domain: h(f) s(t) = n(t) + h(t) ~ ~ n(t), where it is assumed to be stationery The matched filter output is described by s(f): data , h*(f) : template, with a weight inversely proportional to the power spectral density of the noise, sn(f): , estimated from nearby data * Find maxima of over arrival time and phase of |z(t)| above some threshold *************************** Noise power spectrum estimated from data in each chunk; Lay out a bank of templates to catch any signal for which each component in the binary system has a mass between 1 Msol and 3 Msol 4.16.05 American Physical Society April Meeting 03

Template based Matched Filtering Signal to Noise (): 2: Where we Characterize event by signal-to-noise ratio, , Sigma: variance Check consistency of signal with expected chirp waveform By checking that the candidate signals have the expected distribution of signal power as a function of frequency: chi^2 zl(t): template filter output for a given bin, z(L): data filter output Divide template into p frequency bands which contribute equally to power, on average Currently use p=16 frequency bands Next is to define some thresholds: 4.16.05 American Physical Society April Meeting 04

Template based Matched Filtering - Thresholds Signal to Noise (): 2 : » really: So if  > * and r2 < r2* --> inspiral “trigger”  > threshold (* ) < threshold (r2*) For our search, we threshold on the output of the matched filter and demand that the SNR be above some value, SNR* * We also use a chi^2 threshold, but since Large signals to have higher c2 values, due to mismatch with discrete template bank This was also introduced to finding the siulations And introduce a weighting factor p: number of bins, delta: mismatch in bank - tunable parameter, SNR^2, to avoid losing real signals * So, let’s look at an example simulation plus data event. 4.16.05 American Physical Society April Meeting 05

Simulated Inspiral (Injection) * SNR r2* r2 SNR and r^2 time series for a: This particular injection in H1 data was a1.4-1.4 Msolar template at 8 Mpc Optimally oriented to Hanford 4km . The thresholds used for the test are denoted by the dashed green lines. We expected for 1-4*2 Msol binary optimally oriented at have a SNR 8 -2 0 +2 time (s) to inferred coalescence 4.16.05 American Physical Society April Meeting 06

time (s) to inferred coalescence Injection vs. Trigger Injection Trigger SNR r2 * On the left we have an inspiral trigger of the sample template. One obvious thing here is that there is a significant difference between the output of an injection with a trigger. This trigger did pass the snr and r^2 theshold test, we see a case of excess noise Looking further I see that there seems to be much fluctuation in r^2 series vs. signal to noise This conveys the fact earlier that any slight mismatches of template with data over short duration and excess noise could lead to ringing of the matched filter. -2 0 +2 time (s) to inferred coalescence 4.16.05 American Physical Society April Meeting 06

time (s) to inferred coalescence Injection vs. Trigger Injection Trigger r2 Chisq test does not do as well here, can we try to improve on this, as there are significant deviations prior to the trigger: * Can we find a quantitative measure of the obvious difference between our simulated event and and data event, some sort of check that the detector noise around the time of the trigger was consistent with the stationary noise assumed by the matched filter. -2 0 time (s) to inferred coalescence 4.16.05 American Physical Society April Meeting 07

American Physical Society April Meeting The Test Use the r2 time series as a method to search for excess noise Impose a “looser” r2 threshold than the search employs » Count the number of time samples above a given threshold in a time interval before inferred coalescence » Count the number of threshold crossings Time interval “window” chosen to be 2 seconds Do my triggers behave like software, hardware injections? » yes ->> keep » no ->> veto Design 2 tests A crossing is defined as an instance of the r^2(t) time series crossing over a given threshold r^2*, in an upward going direction. One way to decide on thesholds is to look at the distributions: 4.16.05 American Physical Society April Meeting 08

American Physical Society April Meeting 2 , r2 distribution log10(counts) * One way to decide thresholds is to look at the distribution of r^2. Blue : rho^2 and r^2 time series for a segment of data: 128 seconds. Red: gaussian detector noise simulation, variance of 32. 200 r2 70 2 4.16.05 American Physical Society April Meeting 09

American Physical Society April Meeting 2 , r2 distribution log10(counts) In the case of the r^2 time series,We see already at around 6, there seems to be fluctuations in noise of the detector, there could be a good place to start. 40 r2 12 2 4.16.05 American Physical Society April Meeting 09

American Physical Society April Meeting Injection vs. Trigger Crossings = 0 Time above Threshold = 0 sec Crossings = 52 Time above Threshold = 0.9 sec r2 looser r2 threshold So, let’s go back to my first example and see how this test does? * Show only 1 threshold, rsq = 6 Crossings, Time above #’3 So, what would we see if we were to apply this to the simulations and playground triggers in S3 H1 data? 4.16.05 American Physical Society April Meeting 10

Preliminary Results for H1 Injections + Playground Data r2 threshold = 10 window H1 Injections Time above r2 threshold (ms) This plot shows the distribution of injection and playground triggers for the time spent above threshold vs signal to noise. * I also plot an approximate linear fit to the injections. It it is clear here to see that the character of the time spent above my given looser threshold of r^2 = 10, shows a significant difference in lower values of SNR, where all the playground triggers lie. If I was to use this fit as a possible threshold, then many of the triggers that passed the first step in the pipeline for a single ifo could be discarded. Also note that the injections with the highest SNR have < 2 crossings, which says that I could possibly use a combination of time above threshold and threshold crossings. These triggers passed the first  4.16.05 American Physical Society April Meeting 11

Preliminary Results for H1 Injections + Playground Data r2 threshold = 10 H1 Injections Time above r2 threshold (ms) This plot shows the distribution of injection and playground triggers for the time spent above threshold vs signal to noise. * I also plot an approximate linear fit to the injections. It it is clear here to see that the character of the time spent above my given looser threshold of r^2 = 10, shows a significant difference in lower values of SNR, where all the playground triggers lie. If I was to use this fit as a possible threshold, then many of the triggers that passed the first step in the pipeline for a single ifo could be discarded. Also note that the injections with the highest SNR have < 2 crossings, which says that I could possibly use a combination of time above threshold and threshold crossings. These triggers passed the first  4.16.05 American Physical Society April Meeting 11

Preliminary Results: H1 Injections + Playground Data possibly vetoed r2 threshold = 10 Crossings < 2 H1 Injections Triggers Time above r2 threshold (ms) This plot shows the distribution of injection and playground triggers for the time spent above threshold vs signal to noise. * I also plot an approximate linear fit to the injections. It it is clear here to see that the character of the time spent above my given looser threshold of r^2 = 10, shows a significant difference in lower values of SNR, where all the playground triggers lie. If I was to use this fit as a possible threshold, then many of the triggers that passed the first step in the pipeline for a single ifo could be discarded. Also note that the injections with the highest SNR have < 2 crossings, which says that I could possibly use a combination of time above threshold and threshold crossings. These triggers passed the first  4.16.05 American Physical Society April Meeting 11

American Physical Society April Meeting Summary and Plans Preliminary testing r2 thresholds set to 6, 8, & 10. The test would be able to eliminate many of our loudest false triggers --> reduces false alarm rate. Additional tuning using S3 Hardware Injections and testing on S3 playground data from L1,H2. Will be incorporated into S3, S4 BNS search, and future online analysis. 4.16.05 American Physical Society April Meeting 12