Improved filters for gravitational waves from inspiralling 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 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.

Figures (12)

• Figure 1: Schematic illustration of our methodology to compute improved templates.
• Figure 2: Exact energy functions (a) $\hat{e}(v)$ and (b) $\hat{E}'(v),$ in the test mass case and $T$- and $P$-approximants in the comparable mass (with $\eta=1/4$) case. Note that the comparable mass case $T$-approximant and $P$-approximant, are smooth deformations of the test mass function.
• Figure 3: Newton-normalized gravitational wave luminosity in the test particle limit: (a) $T$-approximants and (b) $P$-Approximants.
• Figure 4: Newton-normalized factored gravitational wave luminosity in the test particle limit: (a) $T$-approximants and (b) $P$-Approximants.
• Figure 5: Newton-normalized energy functions in the comparable mass case. We compare the convergence of the $T$-approximants and $P$-approximants. Observe that the $P$-approximants converge much faster to the fiducial exact energy than the standard approximants.