An Efficient Approximation to the Likelihood for Gravitational Wave Stochastic Background Detection Using Pulsar Timing Data

TL;DR

This paper presents a computationally efficient approximation to the likelihood function for detecting stochastic gravitational wave backgrounds with pulsar timing arrays, maintaining accuracy and unbiased parameter estimates.

Contribution

It introduces a new approximation method that reduces computational complexity while accurately reproducing results of the full likelihood in gravitational wave detection.

Findings

Approximate likelihood matches full likelihood results in simulations.

The method provides unbiased parameter estimates for realistic background amplitudes.

Computational savings scale with the square of the number of pulsars.

Abstract

Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime ($10^{-7}$ Hz -- $10^{-9}$ Hz), we expect that a superposition of gravitational waves from many sources will manifest itself as an isotropic stochastic gravitational wave background. Currently, a number of techniques exist to detect such a signal; however, many detection methods are computationally challenging. Here we introduce an approximation to the full likelihood function for a pulsar timing array that results in computational savings proportional to the square of the number of pulsars in the array. Through a series of simulations we show that the approximate likelihood function reproduces results obtained from the full likelihood function. We further show, both analytically and through simulations, that, on average, this approximate likelihood function gives unbiased parameter estimates for astrophysically realistic stochastic background amplitudes.