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Dark Matter Densities during the Formation of the First Stars and in Dark Stars

The first stars in the universe form inside $\sim 10^6 M_\odot$ dark matter (DM) haloes whose initial density profiles are laid down by gravitational collapse in hierarchical structure formation scenarios. During the formation of the first stars in the universe, the baryonic infall compresses the dark matter further. The resultant dark matter density is presented here, using an algorithm originally developed by Young to calculate changes to the profile as the result of adiabatic infall in a spherical halo model; the Young prescription takes into account the non-circular motions of halo particles. The density profiles obtained in this way are found to be within a factor of two of those obtained using the simple adiabatic contraction prescription of Blumenthal et al. Our results hold regardless of the nature of the dark matter or its interactions and rely merely on gravity. If the dark matter consists of weakly interacting massive particles, which are their own antiparticles, their densities are high enough that their annihilation in the first protostars can indeed provide an important heat source and prevent the collapse all the way to fusion. In short, a ``Dark Star'' phase of stellar evolution, powered by DM annihilation, may indeed describe the first stars in the universe.