Impact of Evaporation Barriers on Solar-Captured Dark Matter Distributions and Evaporation Mass

TL;DR

The paper addresses how an in-medium evaporation barrier, quantified by the central strength parameter $\beta$, alters the distributions of dark matter captured by the Sun. It solves the linear Boltzmann equation in the bound-orbit space $(E,L)$ using a Markov-chain Monte Carlo method to obtain the steady-state distribution $f_\chi(E,L)$ under gravity with and without the barrier, enabling extraction of the capture rate $C_\odot$, evaporation rate $E_\odot$, and effective annihilation volume $V_{\rm eff}$ with compact fits across DM mass $m_\chi$ and $\beta=0,1,2,3$. The barrier deepens the potential, raises the local escape speed, and shifts the distribution toward low $E$ and $L$, leading to higher $C_\odot$, exponential suppression of $E_\odot$, and a mild reduction of $V_{\rm eff}$, which moves the evaporation mass $m_{\rm evap}$ to smaller values. The study provides regime maps in the $(m_\chi, \sigma_p)$ plane and delivers practical fits for $C_\odot$, $E_\odot$, and $V_{\rm eff}$ that can be used directly in solar neutrino flux calculations and broader DM phenomenology, while outlining future work to relate $\beta$ to mediator properties and to incorporate channel-dependent yields.

Abstract

We study the non-thermal distributions of dark matter captured by the Sun by solving the linear Boltzmann equation with a Markov-chain Monte Carlo scheme in the space of orbital energy and angular momentum. From the resulting steady-state distribution, we derive the capture rate, the evaporation rate, and the effective annihilation volume, and provide compact fitting formulas across the studied mass ranges for several values of the potential-depth parameter beta. The presence of an in-medium potential deepens the total solar potential and raises the local escape speed, compressing the phase space toward lower specific energy and angular momentum. As a result, the capture rate increases, the evaporation rate is exponentially suppressed, the effective annihilation volume is mildly reduced, and the evaporation mass shifts to smaller values. Maps in the plane of dark-matter mass and scattering cross section quantify these trends, with the evaporation mass indicated on the maps. The results are presented in a form directly applicable to solar-neutrino flux calculations and related dark-matter phenomenology.

Figures (8)

• Figure 1: The equilibrium distribution $f_\chi(E,L)$ for $m_\chi=2.5~\mathrm{GeV}$ at $\beta=0$ (left) and $\beta=1$ (right). The energy $E$ and angular momentum $L$ are expressed in units of $GM_\odot/R_\odot$ and $\sqrt{GM_\odot R_\odot}$, respectively. Only the colored parameter region corresponds to bound states.
• Figure 2: The integrated distribution function in velocity $v_\chi$ for $\beta=0$ in orbit $(E=-1.175,\ L=0.1223)$, and for $\beta=1,2,3$ in orbit $(E=-1.567,\ L=0.1223)$.
• Figure 3: The integrated distribution function in radius $r$ for $\beta=0$ in orbit $(E=-1.175,\ L=0.1223)$, and for $\beta=1,2,3$ in orbit $(E=-1.567,\ L=0.1223)$.
• Figure 4: The ratio of the non-thermal to the approximated thermal distribution for $\beta=0$ at $m_\chi=1.5,\ 2.0,\ 2.5,\ 3.0,\ 3.5,$ and $4.0~\mathrm{GeV}$.
• Figure 5: The ratio of the non-thermal to the approximated thermal distribution for $\beta=1$ at $m_\chi=0.5,\,1.0,\,1.5,\,2.0,\,2.5,\,3.0,\,3.5,$ and $4.0~\mathrm{GeV}$.