Adiabatic contraction revisited: implications for primordial black holes

Understand

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 $\rho\propto r^{-1.5}$, in agreement with the Liouville theorem and previous numerical studies.
• At the same time, the number of DM particles $\nu(r)$ with periastra smaller than $r$ is parametrically larger, $\nu(r) \propto r$, implying that many particles contributing at any given moment into the density $\rho(r)$ 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.