Star-forming and Quiescent Central Galaxies Cluster Similarly: Implications for the Galaxy-Halo Connection

We measure the clustering of low-redshift SDSS galaxies as a function of stellar mass ($10.0<\log(M_*/M_\odot)<11.5$) and specific star formation rate (sSFR) and compare the results to models of the galaxy--halo connection. We find that the auto-correlation functions of central galaxies exhibit little dependence on sSFR, with the well-known stronger clustering of quiescent galaxies mainly attributable to satellites. Because halo assembly history is known to affect distinct halo clustering, this result implies that there is little net correlation between halo assembly history and central galaxy sSFR. However, cross-correlations with satellites are stronger for quiescent centrals than star-forming centrals, consistent with quiescent centrals having more satellites in their haloes at fixed $M_*$, as found in SDSS group catalogues. We model the galaxy--halo connection in an $N$-body simulation by assigning sSFRs to central galaxies in three different ways. Two of the models depend on halo assembly history (being based on halo accretion rate or concentration), while the third is independent of halo assembly history (being based on peak halo circular velocity, $V_\text{peak}$, a proxy for halo mass). All three models replicate the observed auto-correlations of central galaxies, while only the $V_\text{peak}$ model reproduces the observed cross-correlations with satellites. This further suggests that the effects of halo assembly history may not be easily seen in auto-correlations of centrals and implies that a more complete understanding of central galaxy clustering may require more than auto-correlations of centrals alone. Additionally, the good agreement with the $V_\text{peak}$ model supports the idea that quiescent galaxies reside in more massive haloes than star-forming galaxies at fixed $M_*$.