The distribution of inelastic dark matter in the Sun

If dark matter is composed of new particles, these may become captured after scattering with nuclei in the Sun, thermalize through additional scattering, and finally annihilate into neutrinos that can be detected on Earth. If dark matter scatters inelastically into a slightly heavier (O(10-100)keV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {O}} (10-100)\,\hbox {keV}$$\end{document}) state it is unclear whether thermalization occurs. One issue is that up-scattering from the lower mass state may be kinematically forbidden, at which point the thermalization process effectively stops. A larger evaporation rate is also expected due to down-scattering. In this work, we perform a numerical simulation of the capture and thermalization process in order to study the evolution of the dark matter distribution. We then calculate and compare the annihilation rate with that of the often assumed Maxwell–Boltzmann distribution. We also check if equilibrium between capture and annihilation is reached. We find that, unless the mass splitting is very small (≲50keV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lesssim 50\,\hbox { keV}$$\end{document}) and/or the dark matter has a sub-dominant elastic cross section, the dark matter distribution does not reach a stationary state, it is not isothermal, annihilation is severely suppressed, and equilibrium is generally not reached. We also find that evaporation induced by down-scattering is not effective in reducing the total dark matter abundance.