Inferring Neutron Star Properties via r-mode Gravitational Wave Signals

Abstract: We present two frameworks to infer some of the properties of neutron stars from their electromagnetic radiation and the emission of continuous gravitational waves due to r-mode oscillations. In the first framework, assuming a distance measurement via electromagnetic observations, we infer three neutron star properties: the moment of inertia, a parameter related to the r-mode saturation amplitude, and the component of magnetic dipole moment perpendicular to the rotation axis. Unlike signals from mountains, r-mode oscillations provide additional information through a parameter (\kappa) that satisfies a universal relation with the star's compactness. In the second framework, we utilize this and the relation between the moment of inertia and compactness, in addition to assuming an equation of state and utilizing pulsar frequency measurements, to directly measure the neutron star's distance along with the aforementioned parameters. We employ a Fisher information matrix-based approach for quantitative error estimation in both frameworks. We find that the error in the distance measurement dominates the errors in the first framework for any reasonable observation time. In contrast, due to the low errors in pulsar frequency measurements, parameters can be inferred accurately via the second framework but work only in a restricted parameter space. We finally address potential ways to overcome critical drawbacks of our analyses and discuss directions for future work.