The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

TL;DR

This paper develops analytic methods for evaluating large order Bessel functions in gravitational wave signals from pulsars, improving computational efficiency and accuracy in astrophysical data analysis.

Contribution

It introduces asymptotic expansion strategies for large order Bessel functions in gravitational wave signal analysis, addressing computational challenges in high-performance contexts.

Findings

Enhanced evaluation techniques for large order Bessel functions

Improved accuracy in Fourier Transform computations of GW signals

Broader applicability to related problems in physics and applied mathematics

Abstract

In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic expansions in evaluation of such Bessel functions which also happen to have large argument. Large order Bessel functions also arise in the Peters-Mathews model of binary inspiralling stars emitting GW and several problems in potential scattering theory. Other applications also arise in a variety of problems in Applied Mathematics as well as in the Natural Sciences and present a challenge for High Performance Computing(HPC).