Galaxy Rotation Curve Fitting Using Machine Learning Tools

Galaxy rotation curve (RC) fitting is an important technique which allows the placement of constraints on different kinds of dark matter (DM) halo models. In the case of non-phenomenological DM profiles with no analytic expressions, the art of finding RC best-fits including the full baryonic $+$ DM free parameters can be difficult and time-consuming. In the present work, we use a gradient descent method used in the backpropagation process of training a neural network, to fit the so-called Grand Rotation Curve of the Milky Way (MW) ranging from $\sim$1 pc all the way to $\sim$$10^5$ pc. We model the mass distribution of our Galaxy including a bulge (inner $+$ main), a disk, and a fermionic dark matter (DM) halo known as the Ruffini-Arg\"uelles-Rueda (RAR) model. This is a semi-analytical model built from first-principle physics such as (quantum) statistical mechanics and thermodynamics, whose more general density profile has a dense core -- diluted halo morphology with no analytic expression. As shown recently and further verified here, the dark and compact fermion-core can work as an alternative to the central black hole in SgrA* when including data at milliparsec scales from the S-cluster stars. Thus, we show the ability of this state-of-the-art machine learning tool in providing the best-fit parameters to the overall MW RC in the $10^{-2}$--$10^5$ pc range, in a few hours of CPU time.