Gamma-ray constraints on the first stars from annihilation of light WIMPs

We calculate the limits on the fraction of viable dark matter minihalos in the early universe to host Population III.1 stars, surviving today as dark matter spikes in our Milky Way halo. Motivated by potential hints of light dark matter from the DAMA and CoGeNT direct dark matter searches, we consider thermal relic WIMP dark matter with masses of 5, 10, and 20 GeV, and annihilation to μ+μ-, τ+τ-, and qq¯. From this brief study we conclude that, if dark matter is light, either the typical black hole size is ≲100Msun (i.e. there is no significant Dark Star phase), and/or dark matter annihilates primarily to μ+μ- or other final states that result in low gamma-ray luminosity, and/or that an extremely small fraction of minihalos in the early universe that seem suitable to host the formation of the first stars actually did.