Predicting Images for the Dynamics Of stellar Clusters (π-DOC): a deep learning framework to predict mass, distance and age of globular clusters

Abstract

Dynamical mass estimates of simple systems such globular clusters (GCs) still suffer from up to a factor of 2 uncertainty. This is primarily due to the oversimplifications of standard dynamical models that often neglect the effects of the long-term evolution of GCs. Here, we introduce a new approach to measure the dynamical properties of GCs, based on the combination of a deep-learning framework and the large amount of data from direct $N$-body simulations. Our algorithm, $\texttt{$π$-DOC}$ ($\textit{Predicting Images for the Dynamics Of stellar Clusters}$) is composed of two convolutional networks, trained to learn the non-trivial transformation between an observed GC luminosity map and its associated mass distribution, age, and distance. The training set is made of V-band luminosity and mass maps constructed as mock observations from $N$-body simulations. The tests on $\texttt{$π$-DOC}$ demonstrate that we can predict the mass distribution with a mean error per pixel of 27%, and the age and distance with an accuracy of 1.5 Gyr and 6 kpc, respectively. In turn, we recover the shape of the mass-to-light profile and its global value with a mean error of 12%, which implies that we efficiently trace mass segregation. A preliminary comparison with observations indicates that our algorithm is able to predict the dynamical properties of GCs within the limits of the training set. These encouraging results demonstrate that our deep-learning framework and its forward modelling approach can offer a rapid and adaptable tool competitive with standard dynamical models.