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 $[10^{-10} - 10^2]~M_odot$. 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, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by $E_c/T_chi sim 30$, where $E_c$ is the escape energy of DM particles at the core of the object and $T_chi$ is the DM temperature. 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 of two or less within the range $10^{-41}~textrm{cm}^2 leq sigma_p leq 10^{-31}~textrm{cm}^2$, where $sigma_p$ is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the local galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic.
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