论文标题
暗物质 - 巴里昂散射的确切背景碰撞玻尔兹曼方程的数值解
Numerical solution of the exact background collisional Boltzmann equation for dark matter-baryon scattering
论文作者
论文摘要
线性宇宙学可观察物可用于用重子探测暗物质（DM）的弹性散射。高精度数据的可用性需要对可能影响约束准确性的任何假设进行严格的重新评估。限制DM-Baryon散射前组合的标准形式主义是基于假设DM的Maxwell-Boltzmann（MB）速度分布。此假设并不总是合理的，除了与重子的相互作用之外，不允许探测DM自我互动。提升MB假设需要解决高度不平凡的完整碰撞玻尔兹曼方程（CBE）。较早的工作提出了更容易处理的Fokker-Planck（FP）近似CBE，但其准确性尚不清楚。在这项工作中，我们在均匀扩展的背景下首次在数字上解决了确切的CBE。我们认为DM-Baryon散射横截面是相对速度的正幂。在各向同性差分散射的情况下，我们得出了碰撞算子的分析表达式。然后，我们通过数值求解CBE，并将我们的解决方案用于DM速度分布来计算DM-Baryon热交换速率，我们将其与使用MB假设和FP近似值获得的速率进行比较。在广泛的DM与巴里亚质量比率上，我们发现FP近似值导致最大误差为17％，明显好于MB假设引入的最多160％的误差。虽然我们的结果严格仅适用于背景演变，但FP近似的准确性可能会导致扰动。这促使其实施到宇宙学玻尔兹曼代码中，在那里它可以取代较少准确的MB假设，并允许对DM与Baryons和Baryons和本身进行更一般的探索。
Linear cosmological observables can be used to probe elastic scattering of dark matter (DM) with baryons. Availability of high-precision data requires a critical reassessment of any assumptions that may impact the accuracy of constraints. The standard formalism for constraining DM-baryon scattering pre-recombination is based on assuming a Maxwell-Boltzmann (MB) velocity distribution for DM. This assumption is not always justified and does not allow for probing DM self-interactions in addition to its interactions with baryons. Lifting the MB assumption requires solving the full collisional Boltzmann equation (CBE), which is highly non-trivial. Earlier work proposed a more tractable Fokker-Planck (FP) approximation to the CBE, but its accuracy remained unknown. In this work, we numerically solve the exact CBE for the first time, in a homogeneous expanding background. We consider DM-baryon scattering cross-sections that are positive power-laws of relative velocity. We derive analytical expressions for the collision operator in the case of isotropic differential scattering cross-sections. We then solve the background CBE numerically and use our solution for the DM velocity distribution to compute the DM-baryon heat-exchange rate, which we compare against those obtained with the MB assumption and FP approximation. Over a broad range of DM-to-baryon mass ratios, we find that the FP approximation leads to a maximum error of 17%, significantly better than the up to 160% error introduced by the MB assumption. While our results strictly apply only to the background evolution, the accuracy of the FP approximation is likely to carry over to perturbations. This motivates its implementation into cosmological Boltzmann codes, where it can supersede the much less accurate MB assumption, and allow for a more general exploration of DM interactions with baryons and with itself.
