A probabilistic deep learning model to distinguish cusps and cores in dwarf galaxies

Numerical simulations within a cold dark matter (DM) cosmology form halos with a characteristic density profile with a logarithmic inner slope of -1. Various methods, such as Jeans and Schwarzschild modelling, have been used in an attempt to determine the inner density of observed dwarf galaxies, in order to test this theoretical prediction.Here, we develop a mixture density convolutional neural networks (MDCNNs) to derive a posterior distribution of the inner density slopes of DM halos. We train the MDCNN on a suite of simulated galaxies from the NIHAO and AURIGA projects, inputting line-of-sight velocities and 2D spatial information of the stars within simulated galaxies. The output of the MDCNN is a probability density function representing the posterior probability of a certain slope to be the correct one, thus producing accurate and complex information on the uncertainty of the predictions.The model recovers accurately the correct inner slope of dwarfs: around 82% of the galaxies have a derived inner slope within ±0.1 of their true value, while around 98% within ±0.3.We then apply our model to four Local Group dwarf spheroidal galaxies and find similar results to those obtained with the Jeans modelling based code GravSphere.