Effects of dark matter on the in-spiral properties of the binary neutron stars

Abstract

Using the relativistic mean-field model, we calculate the properties of binary neutron star (BNS) in the in-spiral phase. Assuming the dark matter (DM) particles are accreted inside the neutron star (NS) due to its enormous gravitational field, the mass $M$, radius $R$, tidal deformability $\hat{I}»$ and dimensionless tidal deformability $\hat{I}›$ are calculated at different DM fractions. The value of $M$, $R$, $\hat{I}»$ and $\hat{I}›$ decreases with the increase of DM percentage inside the NS. The in-spiral phase properties of the BNS are explored within the post-Newtonian (PN) formalism, as it is suitable up to the last orbits in the in-spiral phase. We calculate the strain amplitude of the polarization waveform $h_{+}$ and $h_{\times }$, (2,2) mode waveform $h_{22}$, orbital phase $\hat{I}¦$, frequency of the gravitational wave $f$ and PN parameter $x$ with DM as an extra candidate inside the NS. The magnitude of $f$, $\hat{I}¦$ and $x$ are almost the same for all assumed forces; however, the in-spiral time duration in the last orbit is different. We find that the BNS with soft equation of state and a high fraction of DM sustains more time in their in-spiral phase. We suggest that one should take DM inside the NS when they modelling the in-spiral waveforms for the BNS systems.

9 pages, 7 figures, 2 tables, accepted for publication in MNRAS