Physical correlations of the scatter between galaxy mass, stellar content, and halo mass

We use the UniverseMachine to analyse the source of scatter between the central galaxy mass, the total stellar mass in the halo, and the dark matter halo mass, for massive (M_vir > 10¹³ M☉) haloes. We also propose a new halo mass estimator, the cen+N mass: the sum of the stellar mass of the central and the N most massive satellites. We show that, when real space positions are perfectly known, the cen+N mass has scatter competitive with that of richness-based estimators. However, in redshift space, using a simple cluster finder, the cen+N mass suffers less from projection effects in the UniverseMachine model. The cen+N mass is therefore a potential candidate to constrain cosmology with upcoming spectroscopic data from DESI. We analyse the scatter in stellar mass at fixed halo mass and show that the total stellar mass in a halo is uncorrelated with secondary halo properties, but that the central stellar mass is a function of both halo mass and halo age. This is because central galaxies in older haloes have had more time to grow via accretion. If the UniverseMachine model is correct, this implies that haloes selected using the centrals stellar mass will be biased old and that accurate galaxy-halo modelling of mass selected samples therefore needs to consider halo age in addition to mass.