  Asymmetric dark matter under certain conditions could form compact star-like
objects, which can be searched either through gravitational lensing or by
observation of gravitational waves from binaries involving such compact
objects. In this paper we analyze possible signatures of such dark stars made
of asymmetric dark matter with a portal to the Standard Model. We argue that
compact dark stars could capture protons and electrons from the interstellar
medium, which then accumulate in the core of the dark star, forming a very hot
gas that emits X-rays or $\gamma$-rays. For dark matter parameters compatible
with current laboratory constraints, compact dark stars could be sufficiently
luminous to be detected at the Earth as point sources in the X-ray or
$\gamma$-ray sky.
