The WIMP capture process for dark stars in the early universe

The first stars to form in the universe may have been dark stars, powered by dark matter annihilation instead of nuclear fusion. The initial amount of dark matter gathered by the star gravitationally can sustain it only for a limited period of time. It has been suggested that capture of additional dark matter from the environment can prolong the dark star phase even to the present day. Here we show that this capture process is ineffective to prolong the life of the first generation of dark stars. We construct a Monte-Carlo simulation that follows each Weakly Interacting Massive Particle (WIMP) in the dark matter halo as its orbit responds to the formation and evolution of the dark star, as it scatters off the star's nuclei, and as it annihilates inside the star. A rapid depletion of the WIMPs on orbits that cross the star causes the demise of the first generation of dark stars. We suggest that a second generation of dark stars may in principle survive much longer through capture. We comment on the effect of relaxing our assumptions.