  Dark Matter (DM) can become captured, deposit annihilation energy, and hence
increase the heat flow in exoplanets and brown dwarfs. Detecting such a
DM-induced heating in a population of exoplanets in the inner kpc of the Milky
Way thus provides potential sensitivity to the galactic DM halo parameters. We
develop a Bayesian Hierarchical Model to investigate the feasibility of DM
discovery with exoplanets and examine future prospects to recover the spatial
distribution of DM in the Milky Way. We reconstruct from mock exoplanet
datasets observable parameters such as exoplanet age, temperature, mass, and
location, together with DM halo parameters, for representative choices of
measurement uncertainty and the number of exoplanets detected. We find that
detection of $\mathcal{O}(100)$ exoplanets in the inner Galaxy can yield
quantitative information on the galactic DM density profile, under the
assumption of 10% measurement uncertainty. Even as few as $\mathcal{O}(10)$
exoplanets can deliver meaningful sensitivities if the DM density and inner
slope are sufficiently large.
