The three hundred project. A machine learning method to infer clusters of galaxy mass radial profiles from mock Sunyaev–Zel’dovich maps

We develop a machine learning algorithm to infer the three-dimensional cumulative radial profiles of total and gas masses in galaxy clusters from thermal Sunyaev–Zel’dovich effect maps. We generate around 73 000 mock images along various lines of sight using 2522 simulated clusters from THE THREE HUNDRED project at redshift z < 0.12 and train a model that combines an auto-encoder and a random forest. Without making any prior assumptions about the hydrostatic equilibrium of the clusters, the model is capable of reconstructing the total mass profile as well as the gas mass profile, which is responsible for the Sunyaev–Zel’dovich effect. We show that the recovered profiles are unbiased with a scatter of about 10 per cent, slightly increasing towards the core and the outskirts of the cluster. We selected clusters in the mass range of 1013.5 ≤ M200/(h−1 M) ≤ 1015.5, spanning different dynamical states, from relaxed to disturbed haloes. We verify that both the accuracy and precision of this method show a slight dependence on the dynamical state, but not on the cluster mass. To further verify the consistency of our model, we fit the inferred total mass profiles with a Navarro–Frenk–White model and contrast the concentration values with those of the true profiles. We note that the inferred profiles are unbiased for higher concentration values, reproducing a trustworthy mass–concentration relation. The comparison with a widely used mass estimation technique, such as hydrostatic equilibrium, demonstrates that our method recovers the total mass that is not biased by non-thermal motions of the gas.