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

Abstract

Light dark matter($\simeq 1-30\mathrm{MeV}$) particles pair produced in electron-positron annihilation $e^{-}{e}^{+}\stackrel{\gamma }{⟶}\chi \bar{\chi }$ 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 $T_{SN}=30\mathrm{MeV}$) and using the Raffelt's criterion on the emissivity for any new channel $\dot{\epsilon }(e^{+}{e}^{-}\to \chi \overline{\chi })\le 10^{19}erg{g}^{-1}{s}^{-1}$, 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 $m_{\chi }=30\mathrm{MeV}$. Using the optical depth criteria on the free streaming of the dark matter fermion, we find the lower bound on $\Lambda \sim 10^8\mathrm{TeV}$ for $m_{\chi }=30\mathrm{MeV}$. In a scenerio,where the dark matter fermions are pair produced in the outermost sector of the supernova core (with radius $0.9R_c\le r\le R_c$, $R_c(=10\mathrm{km})$ 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.

24 pages and 22 figures

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