基于广义轮廓预测暗物质晕质量与可观测量之间的标度关系 I：运动学示踪子
Predicting the Scaling Relations between the Dark Matter Halo Mass and Observables from Generalised Profiles I: Kinematic Tracers
AI总结：
本研究通过解析晕模型与Jeans方程通解，推导暗物质晕质量与孔径速度弥散的标度关系，量化参数敏感性，发现晕结构与运动学轮廓对质量估计的不确定度影响较小，为光谱巡天的晕质量测量提供参考。
摘要：
我们研究了暗物质晕的质量轮廓与其引力势内运动学示踪子的速度弥散测量值之间的关系。通过预测晕质量与孔径速度弥散的标度关系$M_\mathrm{vir} - σ_\mathrm{ap}$，我们在解析晕模型中给出了该晕质量示踪子的预期形式及其对物理参数的依赖关系：模型参数包括晕的内区对数密度负斜率$α$、集中度参数$c$以及速度各向异性参数$β$。针对这些理想化晕，我们得到了Jeans方程的通解，将其沿视线方向投影并在孔径内取平均，得到对应的孔径速度弥散轮廓。通过量纲分析，我们利用这些孔径速度弥散轮廓的解析界明确构建了$M_\mathrm{vir} - σ_\mathrm{ap}$标度关系，从而能够在合理的参数选择下对该关系施加约束。我们预测了$M_{200} - σ_\mathrm{ap}$和$M_{500} - σ_\mathrm{ap}$标度关系，两者的不确定度分别为60.5%和56.2%。研究发现，这些晕质量估计值对晕的集中度和质量标度的敏感性较弱，对测量孔径速度弥散的孔径半径大小、晕内区斜率的最大值以及速度各向异性的最小值和最大值最为敏感。我们的结果表明，晕的结构和运动学轮廓对其质量估计仅造成较小的不确定度。因此，旨在利用运动学示踪子约束晕质量的光谱巡天可以聚焦于表征其他更复杂的不确定度来源和观测系统误差。
英文摘要：
We investigate the relationship between a dark matter halo's mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - σ_\mathrm{ap}$, we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo's negative inner logarithmic density slope, $α$, its concentration parameter, $c$, and its velocity anisotropy parameter, $β$. For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - σ_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - σ_\mathrm{ap}$ and $M_{500} - σ_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$, respectively. These halo mass estimates are found to be weakly sensitive to the halo's concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo's inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo's structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics.
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