The effectiveness of exoplanets and Brown Dwarfs as sub-GeV Dark Matter detectors

In this work we demonstrate that Dark Matter (DM) evaporation severely hinders the effectiveness of exoplanets and Brown Dwarfs as sub-GeV DM probes. Moreover, we find useful analytic closed form approximations for DM capture rates for arbitrary astrophysical objects, valid in four disticnt regions in the $\sigma-m_X$ parameter space. As expected, in one of those regions the Dark Matter capture saturates to its geometric limit, i.e. the entire flux crossing an object. As a consequence of this region, which for many objects falls within the parameter space not excluded by direct detection experiments, we point out the existence of a DM parameter dependent critical temperature ($T_{crit}$), above which astrophysical objects lose any sensitivity as Dark Matter probes. For instance, Jupiters at the Galactic Center have a $T_{crit}$ ranging from $700$ K (for a $3 M_J$ Jupiter) to $950$ K (for $14 M_J$). This limitation is rarely (if ever) considered in the previous literature of indirect Dark Matter detection based on observable signatures of captured Dark Matter inside celestial bodies.