Compact stars made of fermionic dark matter

Abstract

Compact stars consisting of fermions with arbitrary masses and interaction strengths are studied by solving the structure equation of general relativity, the Tolman-Oppenheimer-Volkoff equations. Scaling solutions are derived for a free and an interacting Fermi gas and tested by numerical calculations. We demonstrate that there is a unique mass-radius relation for compact stars made of free fermions which is independent of the fermion mass. For sufficiently strong interactions, the maximum stable mass of compact stars and its radius are controlled by the parameter of the interaction, both increasing linearly with the interaction strength. The mass-radius relation for compact stars made of strongly interacting fermions shows that the radius remains approximately constant for a wide range of compact star masses.