It has been argued that the existence of old neutron stars excludes the possibility of non-annihilating light bosonic dark matter, such as that arising in asymmetric dark matter scenarios. If non-annihilating dark matter is captured by neutron stars, the density will eventually become sufficient for black hole formation. However, the dynamics of collapse is highly sensitive to dark-matter self-interactions. Repulsive self-interactions, even if extremely weak, can prevent black hole formation. We argue that self-interactions will necessarily be present, and estimate their strength in representative models. We also consider co-annihilation of dark matter with nucleons, which arises naturally in many asymmetric dark matter models, and which again acts to prevent black hole formation. We demonstrate how the excluded region of the dark-matter parameter space shrinks as the strength of such interactions is increased, and conclude that neutron star observations do not exclude most realistic bosonic asymmetric dark matter models.
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