Compact stars as dark matter probes

Compact stars - neutron stars and white dwarfs - can capture and accumulate dark matter. Even though only a tiny fraction of the star mass can be accumulated in realistic conditions, this may lead to dramatic consequences such as the star collapse into a black hole. Thus, mere existence of neutron stars and white dwarfs sets constraints on DM models where this phenomenon occurs. Alternatively, if only a fraction of NS is converted into black holes, these may be identified with the gravitational wave detectors: the masses of such BH are around one solar mass, while stellar evolution does not lead to BH lighter than ~2 solar masses. We will discuss in detail two examples: the DM composed of primordial black holes, and asymmetric DM with self-interactions.