在暗物质搜索的背景下Eddington类反演方法的剖析
Anatomy of Eddington-like inversion methods in the context of dark matter searches
摘要：
无论暗物质（DM）的候选人，几个潜在的可观察到的签名来自晕，特别是在银河系（MW）晕DM的速度分布。例子包括直接搜索弱相互作用的大质量粒子（WIMP），$p$波抑制或Sommerdom增强的湮灭信号，原始黑洞（PBH）的微透镜事件，{ \em等}。目前大多数预言都是基于麦克斯韦近似，这不仅在有界系统中理论上不一致，而且也没有得到宇宙学模拟的支持。在直接WIMP搜索的计算中，有时会使用一种更一致的方法，即所谓的爱丁顿反演方法，该方法将DM相空间分布函数（DF）与其质量密度分布和系统的总引力势联系起来。这种方法最初建立在各向同性假设的基础上，可以扩展到各向异性系统。我们调查这些反演方法的背景下，银河DM搜索，动机的事实，MW是一个强约束系统，应该更是如此与正在进行的盖亚调查。我们仍然得出适用于一般情况的结论。特别是，我们说明了如何忽略DM晕的径向边界导致理论上的不一致。我们还表明，几个现实的配置DM晕和MW重子内容需要不明确的DF，显着限制这些反演方法可以应用的配置空间。我们对这些问题提出了一致的解决方案。最后，我们计算了几个观测推断从约束银河系质量模型相关DM搜索（WIMP或PBH），{ \em例如}。DM速度和相对速度分布的矩和反矩。
英文摘要：
Irrespective of the dark matter (DM) candidate, several potentially observable signatures derive from the velocity distribution of DM in halos, in particular in the Milky Way (MW) halo. Examples include direct searches for weakly-interacting massive particles (WIMPs), $p$-wave suppressed or Sommerfeld-enhanced annihilation signals, microlensing events of primordial black holes (PBHs), {\em etc}. Most current predictions are based on the Maxwellian approximation which is not only theoretically inconsistent in bounded systems, but also not supported by cosmological simulations. A more consistent method sometimes used in calculations for direct WIMP searches relies on the so-called Eddington inversion method, which relates the DM phase-space distribution function (DF) to its mass density profile and the total gravitational potential of the system. Originally built upon the isotropy assumption, this method can be extended to anisotropic systems. We investigate these inversion methods in the context of Galactic DM searches, motivated by the fact that the MW is a strongly constrained system, and should be even more so with the ongoing Gaia survey. We still draw conclusions that apply to the general case. In particular, we illustrate how neglecting the radial boundary of the DM halo leads to theoretical inconsistencies. We also show that several realistic configurations of the DM halo and the MW baryonic content entail ill-defined DFs, significantly restricting the configuration space over which these inversion methods can apply. We propose consistent solutions to these issues. Finally, we compute several observables inferred from constrained Galactic mass models relevant to DM searches (WIMPs or PBHs), {\em e.g.} moments and inverse moments of the DM speed and relative speed distributions.
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