Computational Resources to Filter Gravitational Wave Data with P-approximant Templates

TL;DR

This paper calculates the number of templates and computational resources needed for gravitational wave detection using P-approximant waveforms, revealing an increase compared to standard PN templates but with promising robustness at 2-PN order.

Contribution

It introduces the first calculation of template numbers for P-approximant waveforms in gravitational wave data analysis, expanding previous methods to include these new templates.

Findings

P-approximant templates require more templates than standard PN templates, up to a factor of 3.

The increase in templates depends on the PN order and mass range considered.

At 2-PN order, the increase is small and benefits from the robustness of P-approximant templates.

Abstract

The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expanding the post-Newtonian waveforms to 2.5-PN order and secondly, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.