Compact Stars Sourced by Perfect Fluid Dark Matter Halos

TL;DR

This work investigates whether isotropic perfect-fluid dark matter halos can source non-singular, horizonless compact stars. By solving the static, spherically symmetric Einstein equations with DM density profiles from Einasto and Dehnen models, the authors construct stellar-like configurations and assess energy conditions. They demonstrate viable, DEC-satisfying solutions and prove linear stability against axial perturbations using the Regge-Wheeler framework, with a positive potential $V(r)$ for $\ell\ge2$. The study further identifies critical parameter thresholds ($\rho_{0,c}$, $k_c$, $\gamma_c$) beyond which $\rho<P$ occurs and the solutions become non-physical, highlighting potential astrophysical relevance for DM concentrations in galactic centers and motivating future gravitational-wave and shadow analyses.

Abstract

Recent studies have shown that dark matter halos can support regular black holes or compact stars by assuming an anisotropic energy-momentum tensor. In this paper, we extend the analysis to the dark matter halo as an isotropic perfect fluid. By employing galactic dark matter profiles-specifically the Einasto and Dehnen models-as the mass-energy density source, we numerically solve the Einstein field equations and find a class of non-singular, horizonless compact star solutions. Moreover, these configurations remain stable against axial perturbations while satisfying the dominant energy condition.

Figures (4)

• Figure 1: Radial profiles of the functions $N$, $-g_{tt}$, $\rho$, and $P$ for an Einasto-type density distribution. The curves correspond to different values of the central density $\rho_0$, with $n=0.5$, $0.75$, and $1$, respectively.
• Figure 2: Radial profiles of the functions $N$, $-g_{tt}$, $\rho$, and $P$ for an Dehnen-type density distribution. The curves correspond to different values of the $k$, with $\rho_0=0.1$, $a=1$, $\gamma=4$, $\alpha=0$.
• Figure 3: Radial profiles of the functions $N$, $-g_{tt}$, $\rho$, and $P$ for an Dehnen-type density distribution. The curves correspond to different values of the central density $\rho_0$, with $a=1$, $k=1$, $\gamma=4$, $\alpha=0$.
• Figure 4: Radial profiles of the functions $N$, $-g_{tt}$, $\rho$, and $P$ for an Dehnen-type density distribution. The curves correspond to different values of the $\gamma$, with $\rho_0=0.5$, $a=1$, $k=1$, $\alpha=0$.