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Evaporation of dark matter from celestial bodies

Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range $[10^{-10} - 10^2]~M_\odot$, for constant scattering cross sections and $s$-wave annihilations. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, at the local galactic position, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by $E_c/T_χ\sim 30$, where $E_c$ is the escape energy of DM particles at the core of the object and $T_χ$ is their temperature. In that case, the minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, $m_{\rm evap} \simeq 0.7$ GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor smaller than three within the range $10^{-41}~\textrm{cm}^2 \leq σ_p \leq 10^{-31}~\textrm{cm}^2$, where $σ_p$ is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic, and details on the density and temperature profiles of celestial bodies have also a small impact.