Abstract
We calculate the number of dark matter particles that a neutron star
accumulates over its lifetime as it rotates around the center of a galaxy, when
the dark matter particle is a self-interacting boson but does not
self-annihilate. We take into account dark matter interactions with baryonic
matter and the time evolution of the dark matter sphere as it collapses within
the neutron star. We show that dark matter self-interactions play an important
role in the rapid accumulation of dark matter in the core of the neutron star.
We consider the possibility of determining an exclusion region of the parameter
space for dark matter mass and dark matter interaction cross sections based on
the observation of old neutron stars with strong dark matter self-interactions.
We show that for a dark matter density of $~10^3$ GeV/cm$^3$ and dark matter
mass $m_\chi10$ GeV, there is a potential exclusion region for dark
matter interactions with nucleons that is three orders of magnitude more
stringent than without self-interactions, and for dark matter self-interactions
that is many orders of magnitude stronger than the current Bullet Cluster
limit.
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