Can a conditioning on stellar mass explain the mutual information between morphology and environment?

Recent studies with SDSS have shown that a statistically significant non-zero mutual information between morphology and environment persists up to several tens of Mpc, which awaits an explanation. Galaxies in different environments acquire their stellar mass through accretion and merger and the stellar mass function of galaxies is known to depend on both environment and morphology. Naturally, stellar mass can be an important link between morphology and environment which may explain the non-zero mutual information between the two. Measuring the mutual information between morphology and environment by conditioning the stellar mass would allow us to test this possibility. We employ here a volume and stellar mass limited sample from the $16^{th}$ data release (DR16) of the SDSS and find a non-zero conditional mutual information throughout the entire length scales probed. We compare the results with three different semi-analytic models implemented on the Millennium simulation and find their predictions to be in fairly good agreement with SDSS on smaller length scales ( $\lesssim 30 h^{-1}$ Mpc ), with a clear discrepancy observed at larger length scales ( $\gtrsim 30 h^{-1}$ Mpc ) where the models predict significantly lower conditional mutual information than the SDSS. Our analysis therefore suggests that only environmental and morphology dependence of stellar mass are inadequate in explaining the observed mutual information between morphology and environment and that physical processes which alters morphology may not necessarily have an impact on the stellar mass of galaxies and vice versa.