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 -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 -ray sky.

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