On mini-halo encounters with stars

We study, analytically and numerically, the energy input into dark matter mini-haloes by interactions with stars. We find that the fractional energy input in simulations of Plummer spheres agrees well with the impulse approximation for small and large impact parameters, with a rapid transition between these two regimes. Using the impulse approximation, the fractional energy input at large impact parameters is fairly independent of the mass and density profiles of the mini-halo; however, low-mass mini-haloes experience a greater fractional energy input in close encounters. We formulate a fitting function which encodes these results and use it to estimate the disruption time-scales of mini-haloes, taking into account the stellar velocity dispersion and mass distribution. For mini-haloes with mass formula on typical orbits which pass through the disc, we find that the estimated disruption time-scales are independent of mini-halo mass, and are of the order of the age of the Milky Way. For more massive mini-haloes, the estimated disruption time-scales increase rapidly with increasing mass.