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

We demonstrate how the properties of a galaxy depend on the mass of its host dark matter subhalo, using two independent models of galaxy formation. For the cases of stellar mass and black hole mass, the median property value displays a monotonic dependence on subhalo mass. The slope of the relation changes for subhalo masses for which heating by active galactic nuclei becomes important. The median property values are predicted to be remarkably similar for central and satellite galaxies. The two models predict considerable scatter around the median property value, though the size of the scatter is model dependent. There is only modest evolution with redshift in the median galaxy property at a fixed subhalo mass. Properties such as cold gas mass and star formation rate, however, are predicted to have a complex dependence on subhalo mass. In these cases 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 plane differ from the assumptions made in empirical models of galaxy clustering by reconstructing the model output using a subhalo abundance matching scheme. In its simplest form, abundance matching generally does not reproduce the clustering predicted by the models, typically resulting in an overprediction of the clustering signal. We show how the basic abundance matching scheme can be extended to reproduce the model predictions more faithfully, which has implications for the analysis of galaxy clustering, particularly for low abundance samples.