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We demonstrate how the properties of a galaxy depend on the mass of its hostdark matter subhalo, using two independent models of galaxy formation. For thecases of stellar mass and black hole mass, the median property value displays amonotonic dependence on subhalo mass. The slope of the relation changes forsubhalo masses for which heating by active galactic nuclei becomes important.The median property values are predicted to be remarkably similar for centraland satellite galaxies. The two models predict considerable scatter around themedian property value, though the size of the scatter is model dependent. Thereis only modest evolution with redshift in the median galaxy property at a fixedsubhalo mass. Properties such as cold gas mass and star formation rate,however, are predicted to have a complex dependence on subhalo mass. In thesecases subhalo mass is not a good indicator of the value of the galaxy property.We illustrate how the predictions in the galaxy property - subhalo mass planediffer from the assumptions made in empirical models of galaxy clustering byreconstructing the model output using a subhalo abundance matching scheme. Inits simplest form, abundance matching generally does not reproduce theclustering predicted by the models, typically resulting in an overprediction ofthe clustering signal. We show how the basic abundance matching scheme can beextended to reproduce the model predictions more faithfully, which hasimplications for the analysis of galaxy clustering, particularly for lowabundance samples.

The galaxy - dark matter halo connection: which galaxy properties are correlated with the host halo mass?