Estimating the sensitivity of pulsar timing arrays

TL;DR

This paper calculates the sensitivity curves of pulsar timing arrays for different sources using Bayesian and frequentist methods, highlighting how sensitivity depends on both data and source properties.

Contribution

It provides a comprehensive comparison of Bayesian and frequentist approaches and clarifies the dependence of sensitivity curves on source and data characteristics.

Findings

Bayesian and frequentist results are consistent

Analytic and numerical methods agree well

Sensitivity depends on source and data properties

Abstract

The sensitivity curve of a canonical pulsar timing array is calculated for two types of source: a monochromatic wave and a stochastic background. These calculations are performed in both a Bayesian and frequentist framework, using both analytical and numerical methods. These calculations are used to clarify the interpretation of the sensitivity curves and to illustrate the sometimes overlooked fact that the sensitivity curve depends not only on the properties of the pulse time-of-arrival data set but also on the properties of the source being observed. The Bayesian and frequentist frameworks were found to give consistent results and the analytic and numerical calculations were also found to be in good agreement.