A coherent method for the detection and estimation of continuous gravitational wave signals using a pulsar timing array

TL;DR

This paper introduces a likelihood-based method for detecting and estimating continuous gravitational wave signals from supermassive black hole binaries using pulsar timing arrays, explicitly accounting for pulsar terms and constraints.

Contribution

It presents a novel detection and estimation technique that avoids previous approximations by explicitly including pulsar terms and using Particle Swarm Optimization.

Findings

Method effectively detects monochromatic gravitational waves

Explicitly accounts for pulsar terms in the signal

Utilizes Particle Swarm Optimization for parameter estimation

Abstract

The use of a high precision pulsar timing array is a promising approach to detecting gravitational waves in the very low frequency regime ($10^{-6} -10^{-9}$ Hz) that is complementary to the ground-based efforts (e.g., LIGO, Virgo) at high frequencies ($\sim 10 -10^3$ Hz) and space-based ones (e.g., LISA) at low frequencies ($10^{-4} -10^{-1}$ Hz). One of the target sources for pulsar timing arrays are individual supermassive black hole binaries that are expected to form in galactic mergers. In this paper, a likelihood based method for detection and estimation is presented for a monochromatic continuous gravitational wave signal emitted by such a source. The so-called pulsar terms in the signal that arise due to the breakdown of the long-wavelength approximation are explicitly taken into account in this method. In addition, the method accounts for equality and inequality constraints involved in the semi-analytical maximization of the likelihood over a subset of the parameters. The remaining parameters are maximized over numerically using Particle Swarm Optimization. Thus, the method presented here solves the monochromatic continuous wave detection and estimation problem without invoking some of the approximations that have been used in earlier studies.