Statistics of structures in the gravitational potential - a possible way to constrain halo populations without reference to mass

暗物质晕的质量分布是标准宇宙学模型的核心预测之一。Press-Schechter质量函数或其变体预测了暗物质晕的质量函数。尽管基于令人怀疑的简单假设，数值模拟却以惊人的准确性证实了这一点。真正的暗物质晕的质量函数在原则上是简单的，在实践中很难测量。主要的问题是，质量并不是天文上可观测到的。质量可以从运动学或动力学观测中推断出来，如示踪剂的运动、热气体的温度或引力透镜引起的光偏转。这些可观测到的都不是质量，而是引力势的深度或其导数。质量只有在对某些体积内的局部信息进行整合后才能得到，而这些体积通常是任意定义的，其中心通常是不确定的。质量的替代物，如x射线温度或光度，实际上在一定程度上有所帮助，但在概念上并不能改善这种情况。此外，它们还引入了校准不确定度。这样就产生了一个问题：是否可以在不参考质量的情况下直接预测可观测量的分布函数？在完成了一个成功的试点研究后，我们建议研究重力势中结构的分布函数，这些结构与温度、速度色散或引力透镜效应等局部观测直接相关。足够深度和大小的潜在汇的统计数据可以从高斯随机场理论推导出来，从而可以直接预测，例如，x射线温度函数，它至少在高质量端与观测结果非常吻合。在提议的项目中，我们希望扩展和改进我们的原型方法，以便可以在所有尺度上直接预测几个可观测值的分布函数。

The distribution of dark-matter halos with mass is one of the central predictions of the standard cosmological model. The Press-Schechter mass function or variants thereof predict the mass function of dark-matter halos. Although based on questionably simple assumptions, numerical simulations confirm it with astonishing accuracy. The mass function of real dark-matter halos is in principle simple and in practice very difficult to measure. The main problem is that mass is not an astronomical observable. Mass is inferred from kinematic or dynamical observables such as the motion of tracers, the temperature of hot gas, or from light deflection by gravitational lensing. None of these observables measures mass, but rather the depth of the gravitational potential or derivatives thereof. Mass is obtained only after integrating local information within some volume which is typically arbitrarily defined, and whose centre is typically uncertain. Proxies to the mass, such as X-ray temperature or luminosity, help practically to some degree, but do not conceptually improve the situation. Besides, they introduce calibration uncertainties. The question thus arises whether distribution functions of observable quantities can directly be predicted without reference to mass. Having completed a successful pilot study, we propose to investigate distribution functions of structures in the gravitational potential, which are directly related to local observables such as temperatures, velocity dispersions or gravitational-lensing effects. The statistics of potential sinks of sufficient depth and size can be derived from the theory of Gaussian random fields, allowing the direct prediction of, e.g., X-ray temperature functions which agree very well with the observations at least at the high-mass end. Within the proposed project, we wish to extend and improve our prototype method such that distribution functions of several observables can directly be predicted on all scales.