New estimation method for mass of an isolated neutron star using gravitational waves

We investigate the possibility of estimating the mass of an isolated rapidly rotating neutron star (NS) from a continuous gravitational wave (GW) signal emitted by the NS. When the GW passes through the gravitational potential of the NS, the GW takes a slightly longer time to travel to an observer than it does in the absence of the NS. Such a time dilation effect holds also for photons and is often referred to as the gravitational time delay (or the Shapiro time delay). Correspondingly, the phase of the GW from the NS shifts due to the Coulomb-type gravitational potential of the NS, and the resulting logarithmic phase shift depends on the mass, the spin frequency of the NS, and the distance to the NS. We show that the NS mass can, in principle, be obtained by making use of the phase-shift difference between two modes of the continuous GW such as once and twice spin frequency modes induced by a freely precessing NS or a NS containing a pinned superfluid core. We estimate the measurement accuracy of the NS mass using Monte Carlo simulations and find that the mass of the NS with its spin frequency 500 Hz and its ellipticity $10^{-6}$ at 1 kpc is typically measurable with an accuracy of 20% using the Einstein Telescope.

Figure 1

The cumulative distribution function as a function of relative error of NS mass $\mathrm{\Delta }{M}_{\mathrm{NS}}/M_{\mathrm{NS}}$ for two different spin frequencies (a) 300 Hz and (b) 500 Hz. The solid line, the dashed line, and the dashed-dotted line correspond to NSs at the distances $r=1$, 10, and 50 kpc, respectively. For NSs at the distance of $r=50$ kpc that emit GWs at the first harmonic GW mode frequency of $f_{\text{gw},1}=300$ Hz, measurement accuracy becomes more than 100%.

Figure 2

The scatter plot of relative error of NS mass $\mathrm{\Delta }{M}_{\mathrm{NS}}/M_{\mathrm{NS}}$ and inclination $\iota$ (left), misalignment angle $\theta$ (right). The GW signals are assumed to have the GW frequency 500 Hz from NSs at $r=10$ kpc.