  Dark matter (DM) can be captured in celestial bodies after scattering and
losing sufficient energy to become gravitationally bound. We derive a general
framework that describes the current DM distribution inside celestial objects,
which self-consistently includes the effects of concentration diffusion,
thermal diffusion, gravity, and capture accumulation. For DM with sufficient
interactions, we show that a significant DM population can thermalize and sit
towards the celestial-body surface. This floating distribution allows for new
phenomenology for DM searches in a wide range of celestial bodies, including
the Sun, Earth, Jupiter, Brown Dwarfs, and Exoplanets.
