Determination of mass of an isolated neutron star using gravitational wave at two frequency modes: Effects of misalignment angle

A mountainous isolated neutron star (NS) would emit gravitational wave (GW) that may be detectable with KAGRA, advanced LIGO, advanced VIRGO, and proposed third generation detectors such as the Einstein telescope. GW emitted by a NS does not propagate freely, but suffers from a NS mass dependent phase shift due to the Coulomb type gravitational field of the NS itself. We have shown that we can determine mass of an isolated NS if we could detect such phase shifts in more than two frequency modes with correlated reference GW phases. Indeed, our Monte Carlo simulations have demonstrated that the mass of a NS with its ellipticity $10^{-6}$ at 1 kpc is typically measurable with precision of $20\%$ using the Einstein Telescope, if the NS is precessing or has a pinned superfluid core and emits GWs at two frequency modes both detectable. After briefly explaining our idea and results, this paper concerns with the effect of misalignment angle ("wobble angle" in the case of a precessing NS) on the mass measurement precision.