  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.
