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If Dark Matter (DM) is made of WIMP-like candidates, we know that it would be efficiently captured in stars, leading to observable signatures. Capture of Dark Matter in the Sun has been studied in the last 3 decades. If the DM mass larger than about 3 GeV, it can be efficiently captured in the Sun, leading to different signatures. Possible observable signatures include neutrino annihilation products or modified energy transport into the Sun.
We consider a different possibility: the capture of DM in other stars different from the Sun, in particular in Neutron Star (NS) and White Dwarfs (WD). These stars are very compact and dense, that are ideal features to have a very efficient capture. However, there are several differences w.r.t. the Sun, for which we will need, first of all, to update the formalism used for DM capture in the Sun. First, gravity in these stars is very strong, especially in NS. We will therefore need to use GR rather than Newtonian mechanics for the kinematics of the capture process.
Second, strong gravity means larger momentum transfers, so we will need to account for that and consider form factors and different types of interactions, the so called "momentum-dependent" ones, that are usually very suppressed in DD and in the Sun. We will need to use Loretnz invariant formalism as relativistic effects will play a crucial role.
Third, the target medium in NS is degenerate, as well as are electrons in WD, and we need to account for this different state of the target particles. We will see that Pauli blocking plays an important role in some mass ranges.
Finally, thanks to the compact nature of the star, some cases that usually require simulations in the case of the Sun, like Multiple scattering, can be treated well analytically or semi-analytically, and I will show some examples of that.
I will then review the possible observational signatures, focusing on the kinetic heating and its consequences.