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暗物质晕的质量函数。虽然基于令人怀疑的简单假设，但数值模拟以惊人的准确性证实了这一点。真实的暗物质晕的质量函数在原理上是简单的，但在实践中却很难测量。主要的问题是质量不是天文学上的可观测量。质量可以从运动学或动力学的可观测量中推断出来，例如示踪物的运动，热气体的温度，或者引力透镜引起的光偏转。这些观测量都不是测量质量，而是测量引力势或其导数的深度。只有在将局部信息整合到通常任意定义的体积内之后才能获得质量，并且其中心通常不确定。质量的近似值，如X射线温度或光度，在某种程度上实际上有帮助，但在概念上并不能改善这种情况。此外，它们引入校准不确定性。这样就产生了一个问题，即可观测量的分布函数是否可以在不考虑质量的情况下直接预测。在完成了一个成功的试点研究，我们建议调查的分布函数的结构在引力势，这是直接相关的局部观测，如温度，速度色散或引力透镜效应。足够深度和大小的潜在汇的统计数据可以从高斯随机场的理论导出，从而允许直接预测，例如，至少在高质量端，X射线温度函数与观测值吻合得很好。在拟议的项目中，我们希望扩展和改进我们的原型方法，使几个观测值的分布函数可以直接预测所有尺度。

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.