Tighter dark-matter constraints from the projected mass method: A neural-network-enhanced method for galaxy groups and clusters

Measuring the total mass of the Milky Way and nearby galaxy groups is difficult because (i) classical dynamical estimators rely on assumptions about satellite orbital geometry that are rarely satisfied in practice and (ii) few satellite galaxies are typically available as kinematic tracers. We present a new framework that corrects the well-known projected-mass estimator (PME) using a residual neural network trained on thousands of simulated galaxy groups from the IllustrisTNG cosmological simulation. Separate networks were trained for each satellite sample size, ranging from five to 50 satellites, so that the correction automatically accounted for the statistical noise that dominates when only a small number of tracers is available. In tests on simulated halos, the classical PME systematically overestimated halo masses by factors of M_ ̊m proj /M_ ̊m true = 1.30^ +0.72 _ -0.62 (using the 2D distance) and 1.46^ +0.97 _ -0.72 (using the 3D distance), with root-mean-square errors (RMSEs) of 0.29 and 0.32 dex, respectively. The neural-network correction reduced this to M_ ̊m proj /M_ ̊m true = 1.02^ +0.30 _ -0.26 , with an RMSE of 0.13 dex. When applied to the Milky Way, the method yielded a total mass of M_ ̊m MW = 1.144^ +0.399 _ -0.296 12 ,M_⊙, with estimates based on the brightest five to ten satellites favoring a somewhat lower range of $(0.8-0.95) ,M_⊙$. The modified PME gives a tighter constraint on the virial masses and the inferred dark-matter content of galaxy groups and clusters. 12