q-deformed statistics and the role of a light fermionic dark matter in the supernova SN1987A cooling

TL;DR

This paper investigates how q-deformed statistics affect constraints on light fermionic dark matter from supernova SN1987A cooling, deriving bounds on the dark matter interaction scale based on energy loss and free streaming criteria.

Contribution

It introduces a q-deformed statistical framework to analyze supernova cooling constraints on light fermionic dark matter, providing new bounds on the interaction scale for different deformation parameters.

Findings

Bounds on the dark matter interaction scale vary with the deformation parameter q.

For q=1.0, the lower bound on Λ is 3.3×10^6 TeV; for q=1.1, it is 3.2×10^7 TeV.

The bounds from SN cooling and free streaming are comparable for dark matter masses 10-30 MeV.

Abstract

Light dark matter($\simeq 1-30~\rm{MeV}$) particles pair produced in electron-positron annihilation $ e^-e^+ \stackrel{\gamma}{\longrightarrow} \chi \bar{\chi}$ inside the supernova core can take away the energy released in the supernova SN1987A explosion. Working within the formalism of $q$-deformed statistics (with the average value of the supernovae core temperature(fluctuating) being $T_{SN} = 30~\rm{MeV}$) and using the Raffelt's criterion on the emissivity for any new channel $\dot{\varepsilon}(e^+ e^- \to \chi \overline{\chi}) \le 10^{19}~{erg~g^{-1}s^{-1}}$, we find that as the deformation parameter $q$ changes from $1.0$ (undeformed scenario) to $1.1$(deformed scenario), the lower bound on the scale $\Lambda$ of the dark matter effective theory varies from $3.3\times 10^6$ TeV to $3.2 \times 10^7$ TeV for a dark matter fermion of mass $m_\chi = 30~\rm{MeV}$. Using the optical depth criteria on the free streaming of the dark matter fermion, we find the lower bound on $\Lambda \sim 10^{8}~\rm{TeV}$ for $m_\chi = 30~\rm{MeV}$. In a scenerio,where the dark matter fermions are pair produced in the outermost sector of the supernova core (with radius $0.9 R_c \le r \le R_c$, $R_c (=10~\rm{km})$ being the supernova core radius or the radius of proto-neutron star), we find that the bound on $\Lambda$ ($\sim 3 \times 10^7$ TeV)obtained from SN cooling criteria (Raffelt's criteria) is comparable with the bound obtained from free streaming (optical depth criterion) for light fermion dark matter of mass $m_{\chi}=10 - 30$ MeV.