A machine learning approach for dynamical mass measurements of galaxy clusters

Abstract

We present a modern machine learning (ML) approach for cluster dynamical mass measurements that is a factor-of-two improvement over using a conventional scaling relation. Different methods are tested against a mock cluster catalog constructed using halos with mass $\geqslant {{10}^{14}}\, {{M}_{\odot }}{{\text{h}}^{-1}}$ from Multidark's publicly available N-body MDPL halo catalog. In the conventional method, we use a standard M(σv) power-law scaling relation to infer cluster mass, M, from line of sight (LOS) galaxy velocity dispersion, σv. The resulting fractional mass error distribution is broad, with width ${\Delta}\epsilon \approx 0.87$ (68% scatter), and has extended high-error tails. The standard scaling relation can be simply enhanced by including higher-order moments of the LOS velocity distribution. Applying the kurtosis as a correction term to ${\rm log} ({{\sigma }_{v}})$ reduces the width of the error distribution to ${\Delta}\epsilon \approx 0.74$ (16% improvement). ML can be used to take full advantage of all the information in the velocity distribution. We employ the Support Distribution Machines (SDMs) algorithm that learns from distributions of data to predict single values. SDMs trained and tested on the distribution of LOS velocities yield ${\Delta}\epsilon \approx 0.46$ (47% improvement). Furthermore, the problematic tails of the mass error distribution are effectively eliminated. Decreasing cluster mass errors will improve measurements of the growth of structure and lead to tighter constraints on cosmological parameters.