# Brightest galaxies as halo centre tracers in SDSS DR7

## TL;DR

This study investigates the positional relationship between brightest galaxies and halo centers in SDSS DR7, revealing that the brightest galaxy is not always the central, with implications for galaxy-halo connection models.

## Contribution

It provides new constraints on the fraction of haloes where the brightest galaxy is not central, accounting for unrelaxed haloes and velocity offsets, improving previous estimates.

## Key findings

- Approximately 30% of haloes have the brightest galaxy offset from the center.
- The fraction of non-central brightest galaxies decreases with luminosity.
- The non-central fraction increases with host halo mass.

## Abstract

Determining the positions of halo centres in large-scale structure surveys is crucial for many cosmological studies. A common assumption is that halo centres correspond to the location of their brightest member galaxies. In this paper, we study the dynamics of brightest galaxies with respect to other halo members in the Sloan Digital Sky Survey DR7. Specifically, we look at the line-of-sight velocity and spatial offsets between brightest galaxies and their neighbours. We compare those to detailed mock catalogues, constructed from high-resolution, dark-matter-only $N$-body simulations, in which it is assumed that satellite galaxies trace dark matter subhaloes. This allows us to place constraints on the fraction $f_{\rm BNC}$ of haloes in which the brightest galaxy is not the central. Compared to previous studies we explicitly take into account the unrelaxed state of the host haloes, velocity offsets of halo cores and correlations between $f_{\rm BNC}$ and the satellite occupation. We find that $f_{\rm BNC}$ strongly decreases with the luminosity of the brightest galaxy and increases with the mass of the host halo. Overall, in the halo mass range $10^{13} - 10^{14.5} h^{-1} M_\odot$ we find $f_{\rm BNC} \sim 30\%$, in good agreement with a previous study by Skibba et al. We discuss the implications of these findings for studies inferring the galaxy--halo connection from satellite kinematics, models of the conditional luminosity function and galaxy formation in general.