Data analysis of continuous gravitational wave: All sky search and study of templates

TL;DR

This paper analyzes the all-sky search for continuous gravitational waves with known waveforms, focusing on template matching, fitting factors, and the exponential increase in templates needed for higher accuracy.

Contribution

It introduces a detailed analysis of template requirements and the symmetry in source parameters, advancing methods for gravitational wave data analysis.

Findings

Symmetry observed in template parameters $ heta_T$ and $_T$

Number of templates increases exponentially with higher fitting factors

Higher FF demands significantly more templates for accurate detection

Abstract

We have studied the problem of all sky search in reference to continuous gravitational wave particularly for such sources whose wave-form are known in advance. We have made an analysis of the number of templates required for matched filter analysis as applicable to these sources. We have employed the concept of {\it fitting factor} {\it (FF)}; treating the source location as the parameters of the signal manifold and have studied the matching of the signal with templates corresponding to different source locations. We have investigated the variation of FF with source location and have noticed a symmetry in template parameters, $\theta_T$ and $\phi_T$. It has been found that the two different template values in source location, each in $\theta_T$ and $\phi_T$, have same {\it FF}. We have also computed the number of templates required assuming the noise power spectral density $S_n(f)$ to be flat. It is observed that higher {\it FF} requires exponentially increasing large number of templates.