Unified χ² Discriminators for Gravitational Wave Searches from Compact Coalescing Binaries

By : Sanjeev Dhurandhar

Page No: 1-25

Abstract
Gravitational Wave (GW) signals of astrophysical origin are typically weak. This is because gravity is a weak force, weakest among the four forces we know of. In order to detect GW signals, one must make differential measurements of effective lengths less than thousand-th of the size of a proton. In spite of the detectors achieving extraordinary sensitivity, the detector noise typically overwhelms the signal, so that GW signals are deeply buried in the data. The challenge to the data analyst is of extracting the GW signal from the noise, that is, first deciding whether a signal is present or not then if present, measuring its parameters. However, in the search for Coalescing Compact Binary (CBC) signals, shortduration non-Gaussian noise transients (glitches) in the detector data significantly affect the search sensitivity. χ² discriminators are therefore employed to mitigate their effect. We show that the underlying mathematical structure of any χ²  is a vector bundle over the signal manifold P, that is, the discriminator and the full vector bundle comprising the subspaces S and the base manifold P constitute the χ² discriminator. We show that this structure paves the way for constructing effective χ² discriminators against different morphologies of glitches. Here we specifically demonstrate our method on blip glitches, which can be modelled as sine-Gaussians, which then generates an optimal χ² statistic for blip glitches. manifold traced out by the signal waveforms in the Hilbert space of data segments D. The χ² is then defined as the square of the L_² norm of the data vector projected onto a finite-dimensional subspace S (fibre) of D chosen orthogonal to the triggered template waveform. Any such fibre leads to a χ² discriminator and the full vector bundle comprising the subspaces S and the base manifold P constitute the χ² discriminator. We show that this structure paves the way for constructing effective χ² discriminators against different morphologies of glitches. Here we specifically demonstrate our method on blip glitches, which can be modelled as sine-Gaussians, which then generates an optimal χ² statistic for blip glitches.

Author
Sanjeev Dhurandhar: Inter University Centre for Astronomy and Astrophysics, Pune, India.
 

DOI: https://doi.org/10.32381/IAPQRT.2026.50.01.1