用Tsallis统计近似暗物质晕的本动速度分布
Approximating the peculiar velocity distribution of dark matter halos with Tsallis statistics
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中文总结 AI 辅助
该研究用Tsallis模型结合N体模拟，近似暗物质晕本动速度分布，其在z=0-2、速度低于1000 km/s时精度达5%，可作为宇宙学参数探针，单个Tsallis函数近似已足够准确。
中文摘要 AI 辅助
承载星系和星系团的暗物质晕的本动速度远非热平衡状态。表征该速度分布的非线性和非高斯特征，有助于深化对宇宙网引力演化的理解，并为相关宇宙学应用提供支撑。我们致力于建立晕的本动速度分布与非平衡统计力学之间的联系，目标是获得一个既简洁又适用于实际应用的模型。我们从大型N体模拟中提取晕样本，并使用源自非广延统计力学的双参数Tsallis模型对本动速度分布进行最大似然拟合。理论上，我们通过基于伽马分布的广义Gram-Charlier展开，在超统计框架下重新表述了晕的分布。对于低于1000 km/s的晕本动速度，Tsallis模型在红移z=0至2范围内达到5%的精度，且在较低红移时性能提升。我们的结果表明，随着时间推移，晕速度分布变得愈发非高斯，且进一步偏离平衡态。最佳拟合参数对质量的依赖较弱，不过低质量晕表现出略强的非高斯性。这两个参数，尤其是速度弥散，有望作为宇宙学参数的探针。理论上，我们发现晕本动速度分布函数通常可表示为一系列Tsallis分布函数的叠加，而模拟结果表明，零阶近似即单个Tsallis函数已能达到足够的精度。
英文摘要
Dark matter halos, which host galaxies and galaxy clusters, have peculiar velocities far from thermal equilibrium. Characterizing the nonlinear and non-Gaussian features of this velocity distribution improves our understanding of the gravitational evolution of the cosmic web and supports related cosmological applications. We endeavor to establish a connection between the peculiar velocity distribution of halos and nonequilibrium statistical mechanics, with the objective of obtaining a model that is both concise and accurate for practical applications. We extracted halo samples from large N-body simulations and performed maximum-likelihood fits to the peculiar velocity distributions using a two-parameter Tsallis model, derived from non-extensive statistical mechanics. On the theoretical side, we reformulated the halo distribution in the superstatistics framework by means of a generalized Gram-Charlier expansion based on the gamma distribution. For halo peculiar velocities below 1000 km/s, the Tsallis model achieves 5 percent accuracy over z=0-2, with performance improving toward lower redshifts. Our results show that the halo velocity distribution becomes increasingly non-Gaussian and departs further from equilibrium over time. The best-fit parameters depend only weakly on mass, though low-mass halos exhibit slightly stronger non-Gaussianity. The two parameters, especially the velocity dispersion, offer promising probes of cosmological parameters. Theoretically, we find that in general the halo peculiar velocity distribution function is expressible as a superposition of a series of Tsallis distribution functions, while simulation results demonstrate that the zeroth-order approximation, namely a single Tsallis function, already achieves sufficient accuracy.
