Introducing decorated HODs: modelling assembly bias in the galaxy–halo connection

The connection between galaxies and dark matter haloes is often inferred from data using probabilistic models, such as the halo occupation distribution (HOD). Conventional HOD formulations assume that <it>only</it> halo mass governs the galaxy–halo connection. Violations of this assumption, known as <it>galaxy assembly bias</it>, threaten the HOD programme. We introduce <it>decorated HODs</it>, a new, flexible class of models designed to account for assembly bias. Decorated HODs minimally expand the parameter space and maximize the independence between traditional and novel HOD parameters. We use decorated HODs to quantify the influence of assembly bias on clustering and lensing statistics. For SDSS-like samples, the impact of assembly bias on galaxy clustering can be as large as a factor of 2 on <it>r</it> ∼ 200 kpc scales and ∼15 per cent in the linear regime. Assembly bias can either enhance or diminish clustering on large scales, but generally increases clustering on scales <it>r</it> ≲ 1 Mpc. We performed our calculations with <scp>halotools</scp>, an open-source, community-driven <scp>python</scp> package for studying the galaxy–halo connection (<inter-ref locator="http://halotools.readthedocs.org" locator-type="url">http://halotools.readthedocs.org</inter-ref>). We conclude by describing the use of decorated HODs to treat assembly bias in otherwise conventional likelihood analyses.