Rotating Proto-Neutron Stars Admixed with Mirror Dark Matter: A two fluid approach

TL;DR

The paper investigates whether mirror dark matter (DM) embedded in rotating proto-neutron stars (PNSs) can modify their structure and thermal evolution across evolution from lepton-rich to cold catalyzed neutron stars. It develops a two-fluid EoS framework with baryonic matter described by relativistic mean-field theory using the DDME2 parameterization and a mirror DM EoS mirroring the visible sector, coupled only by gravity, and solves rotating two-fluid equilibria with a modified "rns" code while treating DM as non-rotating. Key findings are that rotation enlarges stars and increases the maximum mass up to the Kepler limit, whereas DM admixture increases compactness, raises polar redshift $Z_p$, and heats the interior by deepening the gravitational potential; DM can reduce stability thresholds for rapid rotation but increases $M_{ m tot}$ for fixed baryon mass. These results imply that neutron-star observations—mass-radius measurements, redshifts, and rotational signatures—could constrain DM properties indirectly by detecting deviations from cold-star universal relations, especially in the presence of DM-induced heating and gravitation-driven compaction.

Abstract

This work investigates the impact of mirror dark matter (DM) on the global properties of rotating neutron stars (NSs) across evolutionary stages, from hot, lepton-rich protoneutron stars (PNSs) to cold, catalyzed NSs along the Kelvin-Helmholtz timescale. The baryonic matter (BM) is modeled using a relativistic mean-field (RMF) approach with density-dependent couplings, while the dark sector mirrors the visible sector with analogous thermodynamic conditions. Using a two-fluid formalism with purely gravitational DM-BM interaction, we find that rotation enlarges the star, whereas DM admixture increases compactness and enhances gravitational stability. However, increased compactness due to DM lowers the threshold for rotational instabilities, making DM-admixed stars more susceptible. Rotation decreases {central temperature behavior} by redistributing thermal energy over a larger volume and reducing central density, while DM raises temperatures by deepening the gravitational potential and increasing thermal energy. Stars become more prone to collapse and rotational instabilities as frequency ($ν$) rises and the polar-to-equatorial radius ratio ($r_p/r_e$) decreases, especially near the Keplerian limit ($ν_K$). DM-admixed stars also show higher surface gravitational redshifts due to their compactness. Our results qualitatively agree with universal relations primarily derived for rotating cold stars. These findings highlight competing effects of rotation and DM on NS thermal evolution, structure, and observables, potentially offering indirect probes of DM within NSs.

Figures (6)

• Figure 1: The plot shows the relationship between the equatorial radius $R_e$ and the total mass, $M_{\rm tot}$ of the DMANS at different stages of PNS evolution, up to the final stage when the star becomes cold and catalyzed. For the $T=0$ panel, the steel blue area indicates the constraints obtained from the binary components of GW170817, with their respective 90% and 50% credible intervals. Additionally, the plot includes the 1 $\sigma$ (68%) CI for the 2D mass-radius posterior distributions of the millisecond pulsars PSR J0030 + 0451 (in cyan and yellow color) riley2019Miller:2019cac and PSR J0740 + 6620 (in orange and peru color)riley2021Miller:2021qha, based on NICER X-ray observations. Furthermore, we display the latest NICER measurements for the mass and radius of PSR J0437-4715 Choudhury:2024xbk (lilac color). The supernova remnant HESS J1731$-$347 2022NatAs...6.1444D is shown in red, with the outer contour representing the 90% CL and the inner contour representing the 50% CL. The points mark stars with fixed baryon masses of $M_b = 1.55\,M_\odot$ (lower) and $M_b = 2.30\,M_\odot$ (upper); star symbols denote DM-admixed models, while bullet points indicate no-DM cases.
• Figure 2: The plots show central temperatures for isentropic models as a function of total mass for different evolutionary stages of rotating PNS admixed with dark matter.
• Figure 3: Gravitational mass ($M_\mathrm{tot}$) as a function of rotational frequency ($\nu$) for neutron stars under different thermal and lepton conditions: $s_B = 1,\ Y_{l} = 0.4$ (top left), $s_B = 2,\ Y_{l} = 0.2$ (top right), $s_B = 2,\ Y_{\nu_e} = 0$ (bottom left), and $T=0$ (bottom right). Solid lines denote stars without dark matter, while dashed lines include a 5% dark matter core. Symbols represent varying rotational deformation characterized by polar-to-equatorial radius ratios $r_p/r_e \in \{0.9, 0.8, 0.7, 0.6, 0.5\}$. The color gradient encodes the ratio $\Omega/\Omega_K$.
• Figure 4: The absolute percent deviation, $|Dev(Q)|$, of the equatorial radius, $R_{eB}$, the polar to equatorial ratio, $R_{pB}/R_{eB}$, and total mass, $M_{tot}$ are shown in violin plots. The data that were produced by the various EoS in this work are visualized as black dots. The curved shape of the violin plot visualizes the data distribution.
• Figure 5: Baryonic moment of inertia ($I_{\rm BM}$) as a function of gravitational mass ($M_{\rm tot}$) for rotating neutron star configurations under different thermal and lepton conditions. Panels correspond to $s_B = 1,\ Y_{l} = 0.4$ (top left), $s_B = 2,\ Y_{l} = 0.2$ (top right), $s_B = 2,\ Y_{\nu_e} = 0$ (bottom left), and $T=0$ (bottom right). Solid lines represent stars without DM, while dashed lines correspond to configurations with 5% dark matter content. Each color denotes a different rotation rate, defined by the polar-to-equatorial radius ratio $r_p/r_e = \{0.9,\,0.8,\,0.7,\,0.6\}$. Overlaid error bars represent observational constraints from the following pulsars: Red: J0437$-$4715, Blue: J0751+1807, Green: J1713+0747, Orange: J1802$-$2124, Purple: J1807$-$2500B, Brown: J1909$-$3744, Pink: J2222$-$0137, Gray: J0740+6620 (NICER), Li_2022 Olive: J0030+0451 (NICER), Silva:2020acr Cyan: J0737$-$3039A (Double Pulsar). Kumar:2019xgpPhysRevD.105.063023Bejger:2005jy.