Physical Correlations of the Scatter between Galaxy Mass, Stellar
  Content, and Halo Mass
  We use the UniverseMachine to analyze the source of scatter between the
central galaxy mass, the total stellar mass in the halo, and the dark matter
halo mass. 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,
the cen+N mass suffers less from projection effects in the UniverseMachine
model. The cen+N mass is therefore a viable low scatter halo mass estimator,
and should be considered an important tool to constrain cosmology with upcoming
spectroscopic data from DESI. We analyze 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 halos
have had more time to grow via accretion. If the UniverseMachine model is
correct, accurate galaxy-halo modeling of mass selected samples therefore needs
to consider halo age in addition to mass.
