Scalar and vector dark matter admixed neutron stars with linear and quadratic couplings

Abstract

We investigate the effects of dark scalar- and vector-mediated interactions on dark matter admixed neutron stars, employing the two-fluid formalism. We adopt three different nuclear equations of state -- BSk22, MPA1 and APR4 -- to describe the baryonic sector, while the dark component consists of fermionic particles within a relativistic mean field framework. We consider both linear and quadratic scalar interactions with the dark fermion, including a quartic self-interaction in the latter case. The parameters of the dark matter models are inferred via a Bayesian analysis that incorporates data from NICER observations and binary neutron star merger detections. The neutron star configurations obtained from the selected model parameters develop dark matter cores, leading to more compact objects with smaller masses and radii. Our findings suggest that scalar interactions generally have a weaker impact on the stellar structure compared to vector-mediated ones, though quantitative differences arise. In particular, quadratic scalar couplings suppress the net attractive interaction, allowing for larger dark matter fractions to be accreted. We also compute the sound speed of DM, finding that the scalar and quadratic interactions modify the stiffness of the dark equation of state while respecting causality: vector repulsion enhances the sound speed, whereas scalar attraction tends to soften it. We compare our results with GW1708017, GW190425 and NICER data and constrain DM couplings and mass.

Figures (12)

• Figure 1: Pressure-energy density (left panel) and mass-radius (right panel) relations for the nuclear EoSs that we adopt to describe the baryonic sector. BSk22 is the softest, with a lower maximum mass than MPA1 and a greater $R_\mathrm{TOV}$ than APR4. MPA1 is stiffer than APR4 at densities typically reach inside a NS ($\rho \leq 1400 \; \mathrm{MeV/fm^3} \simeq 2.5 \times 10^{15} \; \mathrm{g/cm^3}$).
• Figure 2: Variation of $\langle \overline{\Psi} \Psi \rangle$ as function of the Fermi momentum $k_f$ of the DM particle. $\langle \overline{\Psi} \Psi \rangle \gtrsim 300~\mathrm{MeV^3}$ as $k_f \gtrsim 20$ MeV, meaning that our ground state is $\phi_0$.
• Figure 3: Posterior distributions of the DM parameters in the linear scalar coupling scenario when the dark sector is combined with BM described by the APR4 EoS. The contour levels in the corner plots, shaded from lighter to darker red, correspond to the 50%, 86%, and 99% confidence regions; whereas the dashed lines in the 1D marginal distributions represent the 68% credible interval. No significant correlations arise among the DM parameters.
• Figure 4: Posterior distributions of the DM parameters in the quadratic scalar coupling scenario when the dark sector is combined with BM described by the APR4 EoS. The experimental data and the credible regions/intervals are the same of FIG. \ref{['fig:bayesian_linear_APR4']}.
• Figure 5: The sound speed $c_s^2$ as a function of energy density $\rho$ for both the baryonic and the dark fluids in the linear (left panel) and in the quadratic (right panel) scenarios. The purple vertical strip represents the 95% range estimation of the larger central density inside an NS. The brown dashed line denotes the conformal limit $c_s^2/3$, while cyan/dark blue curves represent the same EoS when varying the scalar/vector coupling, while gray/green curves represent the same EoS when varying the vector/$\lambda$ coupling. The details are given in the main text.