# Physical Correlations of the Scatter between Galaxy Mass, Stellar Content, and Halo Mass

## TL;DR

This paper investigates the sources of scatter in galaxy and halo mass relations using the UniverseMachine, proposing a new halo mass estimator, cen+N, that performs well in redshift space and highlights the importance of halo age in galaxy-halo modeling.

## Contribution

It introduces the cen+N mass estimator as a low scatter, redshift-space robust tool and emphasizes the role of halo age in galaxy mass correlations.

## Key findings

- cen+N mass has competitive scatter with richness estimators in real space.
- cen+N mass is less affected by projection effects in redshift space.
- Central stellar mass depends on both halo mass and halo age.

## Abstract

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.