Abstract
Dark matter particles may be captured by a star and then thermalized in the star's core. At the end of its life a massive star collapses suddenly and a compact object is formed. The dark matter particles redistribute accordingly. In the inelastic dark matter model, an extended dense dark matter mini-halo surrounding the neutron star may be formed. Such mini-halos may be common in the Galaxy. The electron/positron flux resulting in the annihilation of dark matter particles, however, is unable to give rise to observable signal unless a nascent mini-halo is within a distance \sim a few 0.1 pc from the Earth.
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