Model-independent astrophysical constraints on leptophilic Dark Matter in the framework of Tsallis statistics

Abstract

We derive model-independent astrophysical constraints on leptophilic dark matter (DM), considering its thermal production in a supernova core and taking into account core temperature fluctuations within the framework of q-deformed Tsallis statistics. In an effective field theory approach, where the DM fermions interact with the Standard Model via dimension-six operators of either scalar-pseudoscalar, vector-axial vector, or tensor-axial tensor type, we obtain bounds on the effective cut-off scale Λ from supernova cooling and free-streaming of DM from supernova core, and from thermal relic density considerations, depending on the DM mass and the q-deformation parameter. Using Raffelt's criterion on the energy loss rate from SN1987A, we obtain a lower bound on Λ ≳ 3 (12) TeV corresponding to q = 1.0 (1.1) and an average supernova core temperature of 0TSN=3 MeV . From the optical depth criterion on the free-streaming of DM fermions from the outer 10% of the SN1987A core, the cooling bound is restricted to Λ ≳ 1 TeV . Both cooling and free-streaming bounds are insensitive to the DM mass mχ for mχ≲ TSN, whereas for mχ≫ TSN, the bounds weaken significantly due to the Boltzmann-suppression of the DM number density. We also calculate the thermal relic density of the DM particles in this setup and find that it imposes an upper bound on Λ4/mχ2, which together with the cooling/free-streaming bound significantly constrains light leptophilic DM.