Dark matter effects on tidal deformabilities and moment of inertia in a hadronic model with short-range correlations

In this work, we study the outcomes related to dimensionless tidal deformability ($\mathrm{\Lambda }$) obtained through a relativistic mean-field (RMF) hadronic model including short-range correlations (SRCs) and dark matter (DM) content [Phys. Rev. D 105, 023008 (2022)]. As a dark particle candidate, we use the lightest neutralino interacting with nucleons through the Higgs boson exchange. In particular, we test the model against the constraints regarding the observation of gravitational waves from the binary neutron star merger event GW170817 provided by the LIGO/Virgo Collaboration (LVC). We show that $\mathrm{\Lambda }$ decreases as the dark particle Fermi momentum ($k_F^{\mathrm{DM}}$) increases. This feature favors the RMF-SRC-DM model used here to satisfy the limits of ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$ ($\mathrm{\Lambda }$ of a $1.4M_{\odot }$ neutron star), and $\tilde{\mathrm{\Lambda }}=300_{-230}^{+420}$ given by the LVC. We also show that as $k_F^{\mathrm{DM}}$ increases, ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$, namely, the tidal deformabilities of the binary system, are also moved in the direction of the GW170817 observational data. Finally, we verify that the inclusion of DM in the system does not destroy the $I$-Love relation (correlation between $\mathrm{\Lambda }$ and the dimensionless moment of inertia, $\overline{I}$). The observational data for ${\overline{I}}_{\star }\equiv \overline{I}(M_{\star })=11.10_{-2.28}^{+3.68}$, with $M_{\star }=1.338M_{\odot }$, is obtained by the RMF-SRC-DM model.

Figure 1

(a) $\mathrm{\Lambda }$ as a function of $M/M_{\odot }$. Full circle: result of ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$ obtained in Ref. [41]. (b) Dimensionless tidal deformabilities for the case of high-mass (${\mathrm{\Lambda }}_1$) and low-mass (${\mathrm{\Lambda }}_2$) components of the GW170817 event. Confidence lines, namely, 90% and 50%, are also taken from Ref. [41]. For both panels, the dark matter content is characterized by $k_F^{\mathrm{DM}}=0$ (no DM: gray bands), 0.02 GeV (red bands) and 0.03 GeV (blue bands).

Figure 2

${\mathrm{\Lambda }}_{1.4}$ as a function of (a) $L_0$ and (b) $J$ for different values of $k_F^{\mathrm{DM}}$. The range of $L_0$ is defined in Eq. (20). Green dotted horizontal lines: boundaries of ${\mathrm{\Lambda }}_{1.4}=190_{-120}^{+390}$ [41].

Figure 3

$\tilde{\mathrm{\Lambda }}$ as a function of (a) $L_0$ and (b) $J$ for different values of $k_F^{\mathrm{DM}}$. The range of $L_0$ is defined in Eq. (20). Dashed lines: range of $\tilde{\mathrm{\Lambda }}=300_{-230}^{+420}$ determined by LVC [42].

Figure 4

Dimensionless moment of inertia as a function of (a) the dimensionless tidal deformability, and (b) the ratio $M/M_{\odot }$. Dashed curve: fitting curve obtained in Ref. [87]. The circle with error bars represents an indirect prediction of $\overline{I}(M=1.338M_{\odot })$ made in Ref. [87] by considering the observational data of the dimensionless tidal deformability (see text for more details).