Compact Stars as Portals to Extra-Dimensional Dark Matter

TL;DR

The paper explores how fermionic dark matter that propagates in extra spatial dimensions within a neutron-star environment alters the internal balance of pressure and gravity. By deriving a density-dependent, higher-dimensional equation of state and analyzing hydrostatic stability, the authors show that for d >= 3 the softened EoS drives an instability (⟨Γ⟩ ≤ 4/3) that can lead to the formation of higher-dimensional black holes inside neutron stars, potentially consuming the star and producing solar-mass BHs. They develop a full framework for DM capture, thermalization, and BH evolution (accretion vs evaporation) in this context, yielding constraints on DM mass m, nucleon cross section, and the size/number of extra dimensions from old neutron-star observations. The results provide a novel probe of both dark-sector properties and spacetime dimensionality, with NSs constraining DM candidates and extra-dimensional parameters in regions distinct from terrestrial experiments. Overall, old neutron stars emerge as sensitive laboratories for extra-dimensional dark matter and the dimensionality of space.

Abstract

We investigate hydrostatic configurations of asymmetric dark matter (DM) spheres in scenarios where fermionic DM can propagate into extra spatial dimensions, while Standard Model fields remain confined to ordinary three dimensions. As the number of extra dimensions increases, the effective equation of state for non-relativistic matter softens, making even modest DM accumulation inside neutron stars susceptible to gravitational collapse into extra-dimensional black holes. These black holes are longer lived than their $3$ dimensional counterparts and can accrete enough material to consume an entire neutron star, ultimately producing solar-mass black holes. For geometric cross sections, DM with masses above $\mathcal{O}(10\,{\rm TeV})$ may already be excluded for more than two extra dimensions of size ${\mathcal{O}(\rm fm})$ -- sharply contrasting with the standard $3$ dimensional case, where comparable limits only appear for masses $\gtrsim 10^{5}$ TeV at typical halo densities of $0.3\, \rm{GeV/cm^3}$.

Figures (6)

• Figure 1: Adiabatic index as a function of density for various cases of extra spatial dimensions for $m R_\star = 10^4$.
• Figure 2: Mass--Radius relation obtained by solving 3D hydrostatic equations with Xdims adiabatic indices. The $\textcolor{red}{\bigstar}$ marks values of central density, $\rho_0=\rho_{\star}$ (eq. \ref{['eq:rhostar']}). The thick curves correspond to configurations in which DM cloud self-gravitates (case I). The thin lines correspond to cases in which DM cloud is non-self gravitating, dominated by the background neutrons (case II). Here, $\bar{M}=M/\left(M_{\text{Pl}}^3/m^2\right)$ and $\bar{R} =R/\left(M_{\text{Pl}}/m^2\right)$.
• Figure 3: Constraints from old NS for scenarios with three Xdims. In the red regions, the dark matter cloud is destabilized by propagation in Xdims, forming a BH that consumes the NS. Green regions correspond to BHs light enough to evaporate within $\rm Gyrs$. Solid yellow curves show current LZ limits LZ:2024zvo, while dashed yellow lines indicate the neutrino fog OHare:2021utq. White regions are unconstrained, either because collapse criteria are not met or DM does not thermalize with neutron matter. Region ${\bf I}$ corresponds to self-gravitating NR collapse; Region ${\bf II}$ corresponds to perturbatively unstable configurations but does not necessarily lead to collapse; and region ${\bf III}$ to relativistic collapse. Left panel: DM–neutron cross section vs DM mass for $d=3$ and $R_\star =1~{\rm fm}$. Right panel: For saturation cross section and $d=3$, constraints on $R_\star$ vs. DM mass; black shading marks parameters for which the DM cloud is unstable before onset of degeneracy.
• Figure E1: Averaged adiabatic index as a function of central density of hydrostatic configurations corresponding to fig. (\ref{['fig:M-R_LM_d']}). The $\bigstar$ marks the critical density $\rho_{\star}$, eq. \ref{['eq:rhostar']}.
• Figure S1: Evolution of a dark matter sphere in NSs as the extra-dimensional phase space becomes accessible. After thermalization, DM particles become degenerate; when their density exceeds $\rho_\star$ (eq. \ref{['eq:rhostar']}) the Xdims are populated. Further accumulation of particles triggers instability and collapse to a BH of mass $M_{\rm crit}$, given by eq. \ref{['eq:Mcrit_sg']}.