Satellite Kinematics II: The Halo Mass-Luminosity Relation of Central Galaxies in SDSS

TL;DR

This study uses satellite galaxy kinematics from SDSS to precisely determine the halo mass-luminosity relation of central galaxies, revealing that scatter in this relation is independent of halo mass and consistent with galaxy formation models.

Contribution

It provides the first detailed measurement of the scatter in the halo mass-luminosity relation, accounting for selection effects, and confirms the independence of this scatter from halo mass.

Findings

Brighter centrals reside in more massive haloes.

Scatter in halo mass increases with luminosity.

The stochasticity in galaxy formation is well constrained and independent of halo mass.

Abstract

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass-luminosity relation (MLR) of their corresponding central galaxies. In this paper we select a large sample of centrals and satellites from the Sloan Digital Sky Survey (SDSS) and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the $r$-band luminosity of the central galaxies. Using the analytical framework presented in Paper I, we use these data to infer {\it both} the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity, $\sigma_{\log M}$, also increases with increasing luminosity. As we demonstrate, this is consistent with $\sigma_{\log L}$, which reflects the scatter in the conditional probability function $P(L_c|M)$, being independent of halo mass. Our analysis of the satellite kinematics yields $\sigma_{\log L}=0.16\pm0.04$, in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by $\sigma_{\log L}$, is well constrained, is independent of halo mass, and is in good agreement with current models of galaxy formation.