On the prospect of using the maximum circular velocity of halos to encapsulate assembly bias in the galaxy-halo connection

Understand

We investigate a conceptual modification of the halo occupation distribution approach, using the halos' present-day maximal circular velocity, $\vmax$, as an alternative to halo mass.

• In particular, using a semi-analytic galaxy formation model applied to the Millennium WMAP7 simulation, we explore the extent that switching to $\vmax$ as the primary halo property incorporates the effects of assembly bias into the formalism.
• We consider fixed number density galaxy samples ranked by stellar mass and examine the variations in the halo occupation functions with either halo concentration or formation time.
• We find that using $\vmax$ results in a significant reduction in the occupancy variation of the central galaxies, particularly for concentration.