The sensitivity of pulsar timing arrays

Simple analytic expressions are derived for the sensitivity curve of a pulsar timing array (PTA) to both a monochromatic source of gravitational waves and an isotropic stochastic background of gravitational waves. These derivations are performed in both frequentist and Bayesian frameworks and the results verified with numerical injections and recovery in mock PTA datasets. The consistency of the frequentist and Bayesian approaches is demonstrated and the results are used to emphasise the fact that the sensitivity curve of a PTA depends not only on the properties of the PTA itself, but also on the properties of the gravitational wave source being observed. (paper)