From Halos to Galaxies. VI. Improved halo mass estimation for SDSS groups and measurement of the halo mass function

In $\Lambda$CDM cosmology, galaxies form and evolve in their host dark matter (DM) halos. Halo mass is crucial for understanding the halo-galaxy connection. The abundance matching (AM) technique has been widely used to derive the halo masses of galaxy groups. However, quenching of the central galaxy can decouple the coevolution of its stellar mass and DM halo mass. Different halo assembly histories can also result in significantly different final stellar mass of the central galaxies. These processes can introduce substantial uncertainties in the halo masses derived from the AM method, particularly leading to a systematic bias between groups with star-forming centrals (blue groups) and passive centrals (red groups). To improve, we developed a new machine learning (ML) algorithm that accounts for these effects and is trained on simulations. Our results show that the ML method eliminates the systematic bias in the derived halo masses for blue and red groups and is, on average, $\sim1/3$ more accurate than the AM method. With careful calibration of observable quantities from simulations and observations from SDSS, we apply our ML model to the SDSS Yang et al. groups to derive their halo masses down to $10^{11.5}\mathrm{M_\odot}$ or even lower. The derived SDSS group halo mass function agrees well with the theoretical predictions, and the derived stellar-to-halo mass relations for both red and blue groups matches well with those obtained from direct weak lensing measurements. These new halo mass estimates enable more accurate investigation of the galaxy-halo connection and the role of the halos in galaxy evolution.