Filtering post-Newtonian gravitational waves from coalescing binaries

TL;DR

This paper demonstrates that including first post-Newtonian corrections in gravitational wave signals from coalescing binaries does not increase the effective number of parameters needed for matched filtering, simplifying data analysis.

Contribution

It shows that the parameter space dimensionality remains unchanged with first post-Newtonian corrections by choosing appropriate signal parameters.

Findings

Number of search templates remains manageable with post-Newtonian corrections.

Effective parameter space dimensionality does not increase with first post-Newtonian terms.

Simplifies gravitational wave data analysis for inspiralling binaries.

Abstract

Gravitational waves from inspiralling binaries are expected to be detected using a data analysis technique known as {\it matched filtering.} This technique is applicable whenever the form of the signal is known accurately. Though we know the form of the signal precisely, we will not know {\it a priori} its parameters. Hence it is essential to filter the raw output through a host of search templates each corresponding to different values of the parameters. The number of search templates needed in detecting the Newtonian waveform characterized by three independent parameters is itself several thousands. With the inclusion of post-Newtonian corrections the inspiral waveform will have four independent parameters and this, it was thought, would lead to an increase in the number of filters by several orders of magnitude---an unfavorable feature since it would drastically slow down data analysis. In this paper I show that by a judicious choice of signal parameters we can work, even when the first post-Newtonian corrections are included, with as many number of parameters as in the Newtonian case. In other words I demonstrate that the effective dimensionality of the signal parameter space does not change when first post-Newtonian corrections are taken into account.