Compact Stars as Portals to Extra-Dimensional Dark Matter

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 $0.3, \rm{GeV/cm^3}$.

💡 Research Summary

The paper investigates the hydrostatic configurations of asymmetric fermionic dark matter (DM) that is allowed to propagate in d ≥ 2 large extra spatial dimensions (X‑dims), while Standard Model fields remain confined to the usual three dimensions. The authors first derive how the presence of extra dimensions modifies the equation of state (EoS) of a non‑relativistic degenerate Fermi gas. In three dimensions the polytropic index is γ = 5/3, but when momentum states in the extra dimensions become populated (once the Fermi energy exceeds the excitation energy E★ = 1/(2 m R★²)), the effective number of degrees of freedom increases and the index softens to γ = (5 + d)/(3 + d). For d ≥ 3 this index drops below the critical value 4/3, signalling a gravitational instability even for non‑relativistic particles.

Using the standard 3‑D hydrostatic equilibrium equations (pressure gradient balanced by gravity) together with the modified EoS, the authors solve the Lane‑Emden problem for two limiting scenarios: (I) the DM sphere self‑gravitates, and (II) the DM sphere is dominated by the background neutron star density. In both cases a critical mass appears when the central density reaches the threshold ρ★ at which extra‑dimensional modes are filled. For self‑gravitating configurations the critical mass is M_SG^crit ≈ 8 M_Pl³ m⁻² ρ★^{1/2} m², while for background‑dominated configurations it is M_NSG^crit ≈ 9 √3 π^{3/2} M_Pl³ m⁻² ρ★ ρ_n^{3/2}/m³. When the accumulated DM mass exceeds these values, the adiabatic index is ≤ 4/3 and the configuration becomes linearly unstable, leading to collapse.

The collapse produces a black hole (BH). The authors require that the collapsing mass exceeds the higher‑dimensional Planck mass M_* = (M_Pl² R★^d)^{1/(2+d)} so that a horizon can form. The resulting BH radius, R_BH =