Optimal χ2 discriminator against modeled noise transients in interferometric data in searches for binary black-hole mergers

Abstract

A vitally important requirement for detecting gravitational-wave (GW) signals from compact binary coalescences (CBCs) with high significance is the reduction of the false-alarm rate of the matched-filter statistic. The data from GW detectors contain transient noise artifacts, or glitches, which adversely affect the performance of search algorithms, especially for finding short-lived astrophysical signals, by producing false alarms, often with high signal-to-noise ratio (SNR). These noise transients particularly affect the CBC searches, which are typically implemented by cross-correlating detector strain data with theoretically modeled waveform templates, chosen from a template bank that is densely populated to cover the source parameter ranges of interest. Owing to their large amplitudes, many of the glitches can produce detectably large peaks in the SNR time series—termed “triggers”—in spite of their small overlap with the templates. Such glitches contribute to the false alarms. Historically, the traditional χ2 test has proven quite useful in distinguishing triggers arising from CBC signals and those caused by glitches. In a recent paper, a unified origin for a large class of χ2 discriminators was formulated, along with a procedure to construct an optimal χ2 discriminator, especially when the glitches can be modeled. A large variety of glitches that often occur in GW detector data can be modeled as sine-Gaussians, with quality factor and central frequency, (Q,f 0), as parameters. An important feature of a sine-Gaussian glitch is that there is a lag between its time of occurrence in the GW data and the time of the trigger it produces in a templated search. Therefore, this time lag is the third parameter used in characterizing the glitch. The total number of sampled points in the glitch parameter space is associated with the degrees of freedom (d.o.f.) of the χ2. We use singular value decomposition to identify the most significant d.o.f., which helps keep the computational cost of our χ2 down. Finally, we utilize the above insights to construct a χ2 statistic that optimally discriminates between sine-Gaussian glitches and CBC signals. We also use receiver-operating characteristics to quantify the improvement in search sensitivity when it employs the optimal χ2 compared to the traditional χ2. The improvement in detection probability is by a few to several percentage points, near a false-alarm probability of a few times 10−3, and holds for binary black holes with component masses from several to a hundred solar masses. Moreover, the glitches that are best discriminated against are those that are like sine-Gaussians with Q∈[25,50] and f0∈[40,80] Hz.