Tidal deformability of dark matter admixed neutron stars

The tidal properties of a neutron star are measurable in the gravitational waves emitted from inspiraling binary neutron stars, and they have been used to constrain the neutron star equation of state. In the same spirit, we study the dimensionless tidal deformability of dark-matter-admixed neutron stars. The tidal Love number is computed in a two-fluid framework. The dimensionless tidal Love number and dimensionless tidal deformability are computed for dark-matter-admixed stars with the dark matter modeled as ideal Fermi gas or self-interactive bosons. The dimensionless tidal deformability shows a sharp change from being similar to that of a pure normal matter star to that of a pure dark matter star, within a narrow range of intermediate dark matter mass fraction. Based on this result, we illustrate an approach to study the dark matter parameters through the tidal properties of massive compact stars, making use of the self-similarity of the dimensionless tidal deformability–mass relations when the dark matter mass fraction is high.

Figure 1

Mass-radius relations for different compact stars. Pure NM neutron stars (black lines) are modeled by the APR, KDE0v1, and LNS EOSs. Fermionic DM stars (green lines) modeled by the ideal Fermi gas EOS are labeled by the particle mass $\mu$ (in GeV). Bosonic DM stars (red lines) are labeled by ${\rho }_0{\hslash }^3$ (in ${10}^{-4}{\mathrm{GeV}}^4$).

Figure 2

Tidal Love number against total mass for the same EOSs and parameters as those in Fig. 1.

Figure 3

Same as Fig. 2, but for the dimensionless tidal deformability.

Figure 4

Mass-radius relations of DM-admixed compact stars constructed with the APR EOS and $\mu =0.5\mathrm{GeV}$ fermionic DM EOS for different DM fractions $f$. The dashed line is the black hole limit.

Figure 5

Same as Fig. 4, but with the APR EOS and ${\rho }_0{\hslash }^3=2.93\times {10}^{-4}{\mathrm{GeV}}^4$ bosonic DM EOS.

Figure 6

Density profile of a configuration in Fig. 5, where $\beta =0.255$ and $f=0.1$.

Figure 7

Same as Fig. 6, but with $f=0.3$.

Figure 8

Same as Fig. 4, but with the LNS EOS and $\mu =1.0\mathrm{GeV}$.

Figure 9

Same as Fig. 4, but with the LNS EOS and $\mu =0.6\mathrm{GeV}$.

Figure 10

Same as Fig. 9, but for the tidal Love number against total mass.

Figure 11

Same as Fig. 10, but for the tidal Love number against compactness.

Figure 12

Profiles of $y(r)$ for $\beta =0.18$ and different $f$ from 0.05 to 0.40. Same setting as Fig. 11.

Figure 13

Total energy density profiles for $\beta =0.18$. Same setting as Fig. 11.

Figure 14

Same as Fig. 10, but for the dimensionless tidal deformability.

Figure 15

Same as Fig. 14, but for the KDE0v1 EOS with $\mu =1.0\mathrm{GeV}$.

Figure 16

Same as Fig. 14, but with the total mass normalized by the $M_{\max }$ of each curve.

Figure 17

$\mathrm{\Lambda }-M$ relation for bosonic DM EOSs, with $M$ normalized by the maximum mass. Black lines indicate the range of variables of the example.

Figure 18

A contour plot of maximum mass as a function of the DM fraction and ${\rho }_0{\hslash }^3$. APR EOS are assumed for NM, and bosonic DM are assumed.