A unified approach to χ2 discriminators for searches of gravitational waves from compact binary coalescences

Sanjeev Dhurandhar, Anuradha Gupta, Bhooshan Gadre, and Sukanta Bose
Phys. Rev. D 96, 103018 – Published 21 November 2017

Abstract

We describe a general mathematical framework for χ2 discriminators in the context of the compact binary coalescence (CBC) search. We show that with any χ2 is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The χ2 is then defined as the square of the L2 norm of the data vector projected onto a finite-dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform. Any such fibre leads to a χ2 discriminator, and the full vector bundle comprising the subspaces and the base manifold constitute the χ2 discriminator. We show that the χ2 discriminators used so far in the CBC searches correspond to different fibre structures constituting different vector bundles on the same base manifold, namely, the parameter space. Several benefits accrue from this general formulation. It most importantly shows that there are a plethora of χ2’s available and further gives useful insights into the vetoing procedure. It indicates procedures to formulate new χ2’s that could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no χ2 with a reasonable number of degrees of freedom is foolproof. It could also shed light on understanding why the traditional χ2 works so well. We show how to construct a generic χ2 given an arbitrary set of vectors in the function space of data segments. These vectors could be chosen such that glitches have maximum projection on them. Further, for glitches that can be modeled, we are able to quantify the efficiency of a given χ2 discriminator by a probability. Second, we propose a family of ambiguity χ2 discriminators that is an alternative to the traditional one [B. Allen, Phys. Rev. D 71, 062001 (2005), B. Allen et al., Phys. Rev. D 85, 122006 (2012).]. Any such ambiguity χ2 makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. It is termed so because it makes significant use of the ambiguity function. We first describe the formulation with the help of the Newtonian waveform, apply the ambiguity χ2 to the spinless TaylorF2 waveforms, and test it on simulated data. We show that the ambiguity χ2 essentially gives a clean separation between glitches and signals. We indicate how the ambiguity χ2 can be generalized to detector networks for coherent observations. The effects of mismatch between signal and templates on a χ2 discriminator using general arguments and the geometrical framework are also investigated.

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  • Received 11 August 2017

DOI:https://doi.org/10.1103/PhysRevD.96.103018

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Sanjeev Dhurandhar1,*, Anuradha Gupta2,1,†, Bhooshan Gadre1,‡, and Sukanta Bose1,3,§

  • 1Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007, India
  • 2Institute for Gravitation and Cosmos, Physics Department, Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 3Department of Physics and Astronomy, Washington State University, 1245 Webster, Pullman, Washington 99164-2814, USA

  • *sanjeev@iucaa.in
  • axg645@psu.edu
  • bug@iucaa.in
  • §sukanta@iucaa.in

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Issue

Vol. 96, Iss. 10 — 15 November 2017

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