天体暗物质蒸发
Evaporation of dark matter from celestial bodies
摘要：
银河系暗物质（DM）粒子与天体成分的散射可能导致它们在这些物体内积累。然而，介质的有限温度设定了DM粒子为了保持被捕获而必须具有的最小质量，即蒸发质量。低于该质量的DM粒子很可能以高于逃逸速度的速度散射，因此它们会被踢出捕获物体并逃逸。在这里，我们计算DM蒸发质量的所有球形天体流体静力平衡，跨越质量范围$[10^{-10} - 10^2]~M_\odot$，恒定的散射截面和$s$波湮灭。我们说明了蒸发率的指数尾部的关键重要性，这在最近的文献中并不总是得到赞赏，并获得了一个强大的结果：对于散射截面的几何值和与核子的相互作用，在局部星系位置，流体静力平衡下所有球形天体的DM蒸发质量近似为$E_c/T_χ\sim 30$，其中$E_c$是物体核心处DM粒子的逃逸能量，$T_χ$是它们的温度。在这种情况下，DM蒸发质量的最小值，$m_{\rm evap} \simeq 0.7$ GeV的超超新星和棕矮星。对于散射截面的其他值，DM蒸发质量在$10^{-41}~\textrm{cm}^2 \leq σ_p \leq 10^{-31}~\textrm{cm}^2$范围内仅变化小于3的因子，其中$σ_p$是自旋无关的DM核子散射截面。它依赖于银河DM密度和速度等参数，或者散射和湮灭截面只是对数，天体密度和温度分布的细节也有很小的影响。
英文摘要：
Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range $[10^{-10} - 10^2]~M_\odot$, for constant scattering cross sections and $s$-wave annihilations. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, at the local galactic position, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by $E_c/T_χ\sim 30$, where $E_c$ is the escape energy of DM particles at the core of the object and $T_χ$ is their temperature. In that case, the minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, $m_{\rm evap} \simeq 0.7$ GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor smaller than three within the range $10^{-41}~\textrm{cm}^2 \leq σ_p \leq 10^{-31}~\textrm{cm}^2$, where $σ_p$ is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic, and details on the density and temperature profiles of celestial bodies have also a small impact.
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