Adiabatic contraction revisited: implications for primordial black holes

We simulate the adiabatic contraction of a dark matter (DM) distribution during the process of the star formation, paying particular attention to the phase space distribution of the DM particles after the contraction. Assuming the initial uniform density and Maxwellian distribution of DM velocities, we find that the number $n(r)$ of DM particles within the radius $r$ scales like $n(r) \propto r^{1.5}$, leading to the DM density profile $ρ\propto r^{-1.5}$, in agreement with the Liouville theorem and previous numerical studies. At the same time, the number of DM particles $ν(r)$ with periastra smaller than $r$ is parametrically larger, $ν(r) \propto r$, implying that many particles contributing at any given moment into the density $ρ(r)$ at small $r$ have very elongated orbits and spend most of their time at distances larger than $r$. This has implications for the capture of DM by stars in the process of their formation. As a concrete example we consider the case of primordial black holes (PBH). We show that accounting for very eccentric orbits boosts the amount of captured PBH by a factor of up to $2\times 10^3$ depending on the PBH mass, improving correspondingly the previously derived constraints on the PBH abundance.

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