Stability of Neutron-Dark Matter Mixed Stars and Hybrid Stars

TL;DR

This work establishes a formal equivalence between radial-oscillation and critical-curve stability criteria for dark-matter–nuclear-matter mixed stars within general relativity, extending the analysis to general multi-fluid systems. It demonstrates that stable mixed-star configurations occupy a two-dimensional surface in the central-pressure–mass–radius parameter space and can include twin-star solutions with identical M and R but different interior structure. Using NS EoS SLy4 and holographic NM, along with bosonic and fermionic DM EoS, the authors show that DM properties significantly shape stability boundaries and macroscopic observables. The results offer a framework to constrain DM properties via astrophysical measurements (e.g., NICER, GW signals) and suggest directions for incorporating more complex DM models and rotation in future work.

Abstract

Concerning the stability of two-fluid star models, we prove the rigorous equivalence of two independent determining methods for mixed stars, after a brief review of the hybrid star case. Our derivations apply to general multi-fluid cases, and here we take dark matter admixed neutron star models for example, demonstrating a stability boundary distinct from the single-fluid case. Stable configurations form a surface in the three-dimensional parameter space of (either) central pressure, mass, and radius, which yields a group containing stable mixed stars. This group includes twin stars with identical masses and radii but different interior structures. These results can help interpret compact star observations and constrain dark matter properties through astrophysics.

Figures (10)

• Figure 1: Schematic diagram: two different possible structures: hybrid stars (I) and mixed stars (II).
• Figure 2: Schematic diagram: the stability turning point of the hybrid star deviates from the mass vertex.
• Figure 3: Single fluid stability analysis. Left panel (Fig.\ref{['fig:single_fluid_eigenvalue_a']}) shows fundamental eigenvalue curves as functions of central configuration for different EoS: Bosonic DM ($B_4 = 0.1$), SLy4, and Holographic NM ($\ell ^{-7}=10300$) respectively. Right panel (Fig.\ref{['fig:single_fluid_eigenvalue_b']}) displays the corresponding $M$-$R$ relation curves.
• Figure 4: Radial oscillation analysis results for the mixed star model with EoS of Holographic NM ($\ell ^{-7}=10300$) and Bosonic DM ($B_4 = 0.1$). Left panel (Fig.\ref{['fig:shooting_a']}) shows the continuous distribution of eigenvalues. Right panel (Fig.\ref{['fig:shooting_b']}) displays the distribution of stable and unstable configuration points in the central pressure parameter space, where the black curve represents configurations where the fundamental radial mode frequency vanishes and its interior indicates the stable region.
• Figure 5: Critical curves for different EoS combinations. The black curves indicate multiple stability boundaries. The units of both the horizontal and vertical axes are in astrophysical units ($p_\odot$), representing the magnitudes of central pressure for the two components. The black-and-white heatmap in the background displays the normalized cross product of the gradient directions at each point of the total mass field and the particle number field of the second component; the darker the color, the more the gradient directions of the two fields at that point tend to be parallel. $N_1\equiv N_{DM}$, represents the DM particle number.

Theorems & Definitions (4)

• Theorem 3.1
• proof
• Theorem 3.2
• proof