From Capture to Collapse: Revisiting Black Hole formation by Fermionic Asymmetric Dark Matter in Neutron Stars

TL;DR

This study re-evaluates constraints on fermionic asymmetric dark matter (ADM) captured in neutron stars by incorporating a relativistic neutron-star equation of state, Pauli blocking, NS cooling, and refined black hole (BH) formation and accretion physics. By solving the four-step process—capture, thermalization, self-gravitation, and collapse to a BH—with improved modeling of optical depth, multi-scattering capture, and quantum effects on accretion and evaporation, the authors show that prior bounds can be relaxed by 2–3 orders of magnitude. They find a lower threshold for ADM mass relevant to BH formation around $m_{\\chi} \sim 10^5$–$10^7$ GeV depending on the operator and NS properties, and demonstrate that light ADM is less constrained than previously thought due to suppressed capture rates and revised Chandrasekhar-like limits. A memory-burden–induced suppression of Hawking evaporation can further extend viable ADM parameter space by up to a factor of ~100, making NSs especially powerful probes for very heavy DM and complementary to direct-detection searches for high-mass ADM.

Abstract

Fermionic asymmetric dark matter (ADM) can be captured in neutron stars (NSs) via scatterings with the star constituents. The absence of dark matter annihilation due to its asymmetric nature leads to ADM accumulation in the NS core, potentially reaching densities sufficient to exceed the Chandrasekhar limit and trigger its gravitational collapse into a black hole (BH), eventually consuming the NS from within. Therefore, the existence and observation of old neutron stars provide a means to constrain the properties of ADM. We revisit previous constraints on the mass and scattering cross section off neutrons of fermionic ADM across a class of models. We critically examine common simplifying approximations used in the literature to derive these limits. Our analysis includes improved treatments of dark matter capture, thermalization, BH formation, accretion, and evaporation. We find that previous results can be relaxed by a few orders of magnitude once these effects are properly accounted for.

Figures (8)

• Figure 1: The cooling of an isolated non-rotating neutron star: Solid and dashed curves core ($T_c$) and effective ($T_{\rm eff}$) temperature evolution with time of the three benchmark NS masses that we work with.
• Figure 2: Capture rate as a function of the DM-neutron cross section for a $1M_\odot$ NS and DM of mass $m_\chi =1{\rm \,TeV}$ (top) and $m_\chi =10^8{\rm \,GeV}$ (bottom) with scalar-scalar interactions with quarks (D1), assuming the equation of state QMC. The vertical dot-dashed blue line denotes the threshold cross section for DM-neutron scattering, which marks out the transition from the optically thin to the optically thick regime. For comparison, we show the saturation cross sections commonly used in the literature.
• Figure 3: Thermalization time as a function of the DM mass for DM-neutron cross sections such that $d\sigma_{n\chi}\propto t^n$, $n=0,1,2$. The cross section on the surface is set to $\sigma_{n\chi}=10^{-45}{\rm \,cm}^2$, and the equilibrium temperature at the center of a $1M_\odot$ NS with EoS QMC to $T_{\rm eq}=10^4{\rm \,K}$.
• Figure 4: Top: Region in the $m_\chi - \sigma_{n\chi}$ plane in which DM does not thermalize (magenta shaded region) for $d\sigma_{n\chi}\propto t^0$, i.e., $t_{\rm therm}^{(n=0)}>t_\star$. In the white region, the captured DM fully thermalizes, whereas in the light blue shaded region, a fraction of total captured DM thermalizes. The orange dashed curve represents the thermalization results from Ref. Garani:2018kkd. Bottom: Cross section for no thermalization for our different NS benchmarks for $d\sigma_{n\chi}\propto t^n$, $n=0,1,2$.
• Figure 5: Accretion rates of neutrons in a $1.5M_\odot$ NS with EoS QMC. The dot-dashed orange line denotes the BH mass for which $R_\text{Sch}(M_\text{BH})=1/p_{F,n}$.