Improved filters for gravitational waves from inspiraling compact binaries

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 inspiraling 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 $e\left(v\right)\mathrm{}$ and $f\left(v\right),$ respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of $e\left(v\right)\mathrm{}$ and $f\left(v\right)\mathrm{}$. 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 ${\mathrm{}(v/c)\mathrm{}}^5$-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.