An elliptical tiling method to generate a 2-dimensional set of templates for gravitational wave search

TL;DR

This paper introduces an elliptical tiling method for efficiently generating template sets in gravitational wave searches, optimizing detection while minimizing computational costs.

Contribution

It presents a novel geometrical approach to cover parameter space with ellipses, improving template bank design for gravitational wave data analysis.

Findings

Effective coverage of parameter space with fewer templates

Enhanced detection efficiency for damped sine signals

Applicable to black hole ringdown and supernova signals

Abstract

Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated to a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the de-excitation phase of black holes -- the so-called 'ringdown' signals -- and are also encountered in some numerically computed supernova signals.