  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 is slightly smaller, although it 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 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.
