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We investigate a conceptual modification of the halo occupation distributionapproach, using the halos' present-day maximal circular velocity, $\vmax$, asan alternative to halo mass. In particular, using a semi-analytic galaxyformation model applied to the Millennium WMAP7 simulation, we explore theextent that switching to $\vmax$ as the primary halo property incorporates theeffects of assembly bias into the formalism. We consider fixed number densitygalaxy samples ranked by stellar mass and examine the variations in the halooccupation functions with either halo concentration or formation time. We findthat using $\vmax$ results in a significant reduction in the occupancyvariation of the central galaxies, particularly for concentration. Thesatellites occupancy variation on the other hand increases in all cases. Wefind effectively no change in the halo clustering dependence on concentration,for fixed bins of $\vmax$ compared to fixed halo mass. Most crucially, wecalculate the impact of assembly bias on galaxy clustering by comparing theamplitude of clustering to that of a shuffled galaxy sample, finding that thelevel of galaxy assembly bias remains largely unchanged. Our results suggestthat while using $\vmax$ as a proxy for halo mass diminishes some of occupancyvariations exhibited in the galaxy-halo relation, it is not able to encapsulatethe effects of assembly bias potentially present in galaxy clustering. The useof other more complex halo properties, such as $\vpeak$, the peak value of$\vmax$ over the assembly history, provides some improvement and warrantsfurther investigation.

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