The dependence of subhalo abundance matching on galaxy photometry and selection criteria

Abundance matching (AM) is a popular technique for assigning galaxy mass or luminosity to haloes produced in $N$-body simulations. The method works by matching the cumulative number functions of the galaxy and halo properties, and is therefore sensitive both to the precise definitions of those properties and to the selection criteria used to define the samples. Further dependence follows when AM parameters are calibrated with galaxy clustering, which is known to depend strongly on the manner in which galaxies are selected. In this paper we introduce a new parametrisation for AM and derive the best-fit AM parameters as a function of various properties of the selection of the galaxy sample and of the photometric definition, including S\'ersic vs Petrosian magnitudes, stellar masses vs $r$-band magnitudes and optical (SDSS) vs HI (ALFALFA) selection. In each case we calculate the models' goodness-of-fit to measurements of the projected two-point galaxy correlation function. In the optically-selected samples we find strong evidence that the scatter in the galaxy-halo connection increases towards the faint end, and that AM performs better with luminosity than stellar mass. The AM parameters of optically- and HI-selected galaxies are mutually exclusive, with the latter suggesting the importance of properties beyond halo mass. We provide best-fit parameters for the AM galaxy-halo connection as a function of each of our input choices, extending the domain of validity of the model while reducing potential systematic error in its use.