Determination of mass of an isolated neutron star using continuous gravitational waves with two frequency modes: an effect of a misalignment angle

A rapidly spinning neutron star (NS) would emit a continuous gravitational wave (GW) detectable by the advanced LIGO, advanced Virgo, KAGRA and proposed third generation detectors such as the Einstein Telescope (ET). Such a GW does not propagate freely, but is affected by the Coulomb-type gravitational field of the NS itself. This effect appears as a phase shift in the GW depending on the NS mass. We have shown that mass of an isolated NS can, in principle, be determined if we could detect the continuous GW with two or more frequency modes. Indeed, our Monte Carlo simulations have demonstrated that mass of a NS with its ellipticity $10^{-6}$ at 1 kpc is typically measurable with precision of 20% using the ET, if the NS is precessing or has a pinned superfluid core and emits GWs with once and twice the spin frequencies. 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.