Improved filters for gravitational waves from inspiralling compact binaries

TL;DR

This paper introduces P-approximants, a new class of gravitational wave filters based on Pade approximation, which significantly improve detection accuracy and efficiency for inspiralling compact binaries compared to standard methods.

Contribution

The paper develops P-approximants using Pade approximation and new energy and flux functions, enhancing effectualness, faithfulness, and convergence over traditional Taylor approximants.

Findings

P-approximants achieve over 96.5% overlap with exact waveforms.

More than 90% of potential events are detectable with P-approximants.

Standard approximants detect only 10-15% of events.

Abstract

The order of the post-Newtonian expansion needed, to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiralling compact binaries, is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) The introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of Pade approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available O(v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5% implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10-15 % that would be detectable using standard post-Newtonian approximants.