lower at higher redshift. The derived SHM relation is used to predict the stellar mass dependent galaxy CF and bias at high redshift. Our model predicts that not only are massive galaxies more biased than low mass ones at all redshifts, but the bias increases more rapidly with increasing redshift for massive galaxies than for low mass ones. We present convenient fitting functions for the SHM relation as a function of redshift, the conditional mass function, and the bias as a function of stellar mass and redshift.'
author:
- 'Benjamin P. Moster, Rachel S. Somerville, Christian Maulbetsch, Frank C. van den Bosch, Andrea V. Macciò, Thorsten Naab, and Ludwig Oser'
title: Constraints on the relationship between stellar mass and halo mass at low and high redshift
---

Introduction {#s:introduction}
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In the standard Cold Dark Matter (CDM) paradigm, the formation of galaxies is driven by the growth of the large-scale structure of the Universe and the formation of dark matter halos. Galaxies form by the cooling and condensation of gas in the centers of the potential wells of extended virialized dark matter halos [@whiterees78; @fallefstathiou1980; @blumenthal1984]. In this picture, galaxy properties, such as luminosity or stellar mass, are expected to 