Differentially rotating neutron stars with dark matter cores

TL;DR

The paper develops a two-fluid equilibrium framework for neutron stars containing a dark matter core by extending the RNS code to model baryonic matter and self-interacting bosonic DM in differential rotation. Using a representative rotation law and the DD2 BM EOS alongside a bosonic DM EOS, it constructs quasi-equilibrium sequences to study how DM cores affect maximum mass, angular-momentum distribution, and stability of hypermassive remnants. Key findings include a general DM-induced reduction in $M_{max}$, DM-driven features in the BM angular-velocity profile such as a local minimum, and a Padé-resummed description of how $M_{max}$ scales with total angular momentum $J_{tot}$; higher DM angular momentum fractions can mitigate the mass loss but constrain the parameter space. The results provide a controlled link between DM microphysics and macroscopic remnant properties, with implications for interpreting post-merger gravitational-wave signals and informing future simulations that incorporate DM halos or broader DM models.

Abstract

Dark matter is expected to accumulate inside neutron stars, modifying the structure of isolated stars and influencing both the dynamics of binary mergers and the evolution of the resulting hypermassive remnants. Since differential rotation is the primary mechanism delaying the collapse of these remnants, understanding its behavior is crucial when assessing the impact of an embedded dark component. In this work, we extend the numerical code RNS to describe two gravitationally coupled fluids in differential rotation, with baryonic matter modeled by a realistic nuclear equation of state and dark matter represented as a self-interacting bosonic condensate. Within this framework, we construct equilibrium sequences for a representative differential rotation law, providing a basis to explore how dark matter may influence the global properties and rotational dynamics of binary neutron star remnants.

Figures (9)

• Figure 1: BM and DM density profiles in the yz plane of two configurations with the same baryonic central energy density $\epsilon^c_{\text{BM}} = 0.75e15\dens$ and ${f^M_{\text{DM}}} = 5\%$, ${f^J_{\text{DM}}} = 1\%$, $(\lambda_1, \lambda_2) = (2, 0.5)$.
• Figure 2: Mass vs BM central energy density sequences for the DD2 EOS and rotational parameters $\lambda_1 = 2$ and $\lambda_2 = 0.5$. The sequences have fixed total angular momentum $J_{\text{tot}}$, represented with the color gradient. Dashed lines represent solutions with ${f^M_{\text{DM}}} = 0\%$, solid lines show solutions with ${f^M_{\text{DM}}} = 5\%$ and ${f^J_{\text{DM}}} = 1\%$. Both have been computed up to $J_{\text{tot}} = 8\Junit$. Dash-dotted lines represent solutions with ${f^M_{\text{DM}}} = 5\%$ and ${f^J_{\text{DM}}} = 5\%$, computed up to $J_{\text{tot}} = 4\Junit$ and finally dotted lines solutions with ${f^M_{\text{DM}}} = 5\%$ and $\Omega_{\text{DM}} / \Omega^{\text{DM}}_{\text{K}} = 3/4$, computed up to $J_{\text{tot}} = 7\Junit$. The red symbols report the sequence maximum mass, marking the turning point beyond which models become unstable. Since a nonlinear monotonic relationship exists between central and maximum energy density for all reported models, we present the results as a function of the former, which is the parameter used to generate the models.
• Figure 3: Distribution of the angular momentum fraction in the DM component for models rotating at $75\%$ of their Kepler frequency. Blue and red bars represent the full sample and the stable models only, respectively. Dashed lines indicate the average values: ${f^J_{\text{DM}}} = 2.68\%$ for the former and ${f^J_{\text{DM}}} = 2.65\%$ for the latter. Models with ${f^J_{\text{DM}}} > 4\%$ exhibit low total angular momentum ($J_{\text{tot}} < 2\Junit$) and lie near the maximum of their respective sequence. These models are sampled uniformly along the dotted sequences shown in Fig. \ref{['fig:Me_DD2noY_(2,05)']}.
• Figure 4: Normalized gravitational mass vs square of the total angular momentum for the same configurations computed in Fig. \ref{['fig:Me_DD2noY_(2,05)']}. Colored lines are fitted with Eq. \ref{['eq:fit']}. The bottom panel shows the logarithm of the absolute value of the residuals.
• Figure 5: Central energy density of the BM component as a function of the DM deformation parameter. Lines and colors have the same meaning as in Fig. \ref{['fig:Me_DD2noY_(2,05)']}.