Transmutation Timescales for Dark Matter Induced Collapse of Compact Stars into Black Holes

Abstract

Ultra-heavy asymmetric dark matter (DM) particles captured by compact stars can thermalize, self-gravitate, and collapse to form an endoparasitic black hole (EBH), whose subsequent growth may transmute the host star into a black hole. The continued existence of old millisecond pulsars (MSPs) and white dwarfs (WDs) thus places powerful constraints on the DM particle mass $m_χ$ and the DM-nucleon scattering cross-section $σ_{\rm nχ}$. We derive an analytical expression for the transmutation timescale by solving the EBH growth equation, consistently accounting for Bondi accretion of stellar matter, Hawking evaporation, and sustained DM feeding of the EBH in a steady-state capture regime. We also incorporate quantum effects in baryonic accretion when the hydrodynamic description breaks down, providing a unified treatment of EBH growth across both particle and fluid regimes. Adopting a physically transparent collapse criterion for fermionic and bosonic asymmetric DM, we compute EBH transmutation timescales for representative MSPs and WDs in environments with different DM densities. Although the physical ingredients are broadly similar to previous studies, this work derives updated constraints through a closed-form analytical treatment of EBH growth and an adopted prescription for the EBH formation timescale, yielding a lower critical EBH mass for sustained growth and revised transmutation timescales. Requiring the transmutation time to exceed $\sim 1$ Gyr for MSPs and $\sim 10$ Gyr for WDs, we derive revised constraints on $σ_{\rm nχ}$ over $m_χ\sim 10^{6}$--$10^{14}$ GeV, and show that EBHs with initial masses as small as $\sim 4\times10^{4}$ kg can undergo sustained growth, extending the region of DM parameter space probed by compact stars.