Galaxy Clustering Topology in the Sloan Digital Sky Survey Main Galaxy Sample: a Test for Galaxy Formation Models

We measure the topology of the main galaxy distribution using the Seventh Data Release of the Sloan Digital Sky Survey, examining the dependence of galaxy clustering topology on galaxy properties. The observational results are used to test galaxy formation models. A volume-limited sample defined by $M_r<-20.19$ enables us to measure the genus curve with amplitude of $G=378$ at $6h^{-1}$Mpc smoothing scale, with 4.8\% uncertainty including all systematics and cosmic variance. The clustering topology over the smoothing length interval from 6 to $10 h^{-1}$Mpc reveals a mild scale-dependence for the shift ($\Delta\nu$) and void abundance ($A_V$) parameters of the genus curve. We find substantial bias in the topology of galaxy clustering with respect to the predicted topology of the matter distribution, which varies with luminosity, morphology, color, and the smoothing scale of the density field. The distribution of relatively brighter galaxies shows a greater prevalence of isolated clusters and more percolated voids. Even though early (late)-type galaxies show topology similar to that of red (blue) galaxies, the morphology dependence of topology is not identical to the color dependence. In particular, the void abundance parameter $A_V$ depends on morphology more strongly than on color. We test five galaxy assignment schemes applied to cosmological N-body simulations of a $\Lambda$CDM universe to generate mock galaxies: the Halo-Galaxy one-to-one Correspondence model, the Halo Occupation Distribution model, and three implementations of Semi-Analytic Models (SAMs). None of the models reproduces all aspects of the observed clustering topology; the deviations vary from one model to another but include statistically significant discrepancies in the abundance of isolated voids or isolated clusters and the amplitude and overall shift of the genus curve. (Abridged)