We present an algorithm for inferring the dynamical mass of galaxy clusters directly from their respective phase-space distributions, i.e. the observed line-of-sight velocities and projected distances of galaxies from the cluster centre. Our method employs neural flows, a deep neural network capable of learning arbitrary high-dimensional probability distributions, and inherently accounts, to an adequate extent, for the presence of interloper galaxies which are not bounded to a given cluster, the primary contaminant of dynamical mass measurements. We validate and showcase the performance of our neural flow approach to robustly infer the dynamical mass of clusters from a realistic mock cluster catalogue. A key aspect of our novel algorithm is that it yields the probability density function of the mass of a particular cluster, thereby providing a principled way of quantifying uncertainties, in contrast to conventional machine learning approaches. The neural network mass predictions, when applied to a contaminated catalogue with interlopers, have a logarithmic residual scatter which goes down to 0.043 dex for the most massive clusters. This is nearly an order of magnitude improvement over the classical cluster mass scaling relation with the velocity dispersion, and outperforms recently proposed machine learning approaches. We also apply our neural flow mass estimator to a compilation of galaxy observations of some well-studied clusters with robust dynamical mass estimates, further substantiating the efficacy of our algorithm. Such sophisticated approaches would undoubtedly be relevant for robust and efficient dynamical mass inference from upcoming surveys covering unprecedented volumes of the sky.

中文翻译：

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具有神经流的星系团的动力学质量推断

我们提出了一种算法，用于直接从它们各自的相空间分布推断星系团的动力学质量，即观察到的视线速度和星系距星系团中心的投影距离。我们的方法采用神经流，一种能够学习任意高维概率分布的深度神经网络，并且在足够程度上固有地说明了不限于给定星团的闯入星系的存在，这是动力质量的主要污染物测量。我们验证并展示了我们的神经流方法的性能，以从现实的模拟集群目录中稳健地推断集群的动态质量。我们新算法的一个关键方面是它产生特定簇质量的概率密度函数，从而提供了一种量化不确定性的原则方法，与传统的机器学习方法相反。神经网络质量预测，当应用于具有闯入者的受污染目录时，具有对数残差散布，对于最大规模的集群，其下降至 0.043 dex。这比经典的簇质量缩放关系与速度色散的关系提高了近一个数量级，并且优于最近提出的机器学习方法。我们还将我们的神经流质量估计器应用于一些经过充分研究的星系团的星系观测汇编，并具有强大的动态质量估计，进一步证实了我们算法的有效性。