Gravitational waves from spinning neutron stars as not-quite-standard sirens

As is well known, gravitational wave detections of coalescing binaries are standard sirens, allowing a measurement of source distance by gravitational wave means alone. In this paper we explore the analogue of this capability for continuous gravitational wave emission from individual spinning neutron stars, whose spin-down is driven purely by gravitational wave emission. We show that in this case, the distance measurement is always degenerate with one other parameter, which can be taken to be the moment of inertia of the star. We quantify the accuracy to which such degenerate measurements can be made. We also discuss the practical application of this method to scenarios where one or other of distance or moment of inertia is constrained, breaking this degeneracy and allowing a measurement of the remaining parameter. We consider a broad range of possible unknown parameters, as well as we present results for the aLIGO and Einstein Telescope sensitivities. Our results will be of use following the eventual detection of a neutron star spinning down through such gravitational wave emission.