The SAMI Galaxy Survey: gravitational potential and surface density
  drive stellar populations -- I. early-type galaxies
  The well-established correlations between the mass of a galaxy and the
properties of its stars are considered evidence for mass driving the evolution
of the stellar population. However, for early-type galaxies (ETGs), we find
that $g-i$ color and stellar metallicity [Z/H] correlate more strongly with
gravitational potential $\Phi$ than with mass $M$, whereas stellar population
age correlates best with surface density $\Sigma$. Specifically, for our sample
of 625 ETGs with integral-field spectroscopy from the SAMI Galaxy Survey,
compared to correlations with mass, the color--$\Phi$, [Z/H]--$\Phi$, and
age--$\Sigma$ relations show both smaller scatter and less residual trend with
galaxy size. For the star formation duration proxy [$\alpha$/Fe], we find
comparable results for trends with $\Phi$ and $\Sigma$, with both being
significantly stronger than the [$\alpha$/Fe]-$M$ relation. In determining the
strength of a trend, we analyze both the overall scatter, and the observational
uncertainty on the parameters, in order to compare the intrinsic scatter in
each correlation. These results lead us to the following inferences and
interpretations: (1) the color--$\Phi$ diagram is a more precise tool for
determining the developmental stage of the stellar population than the
conventional color--mass diagram; and (2) gravitational potential is the
primary regulator of global stellar metallicity, via its relation to the gas
escape velocity. Furthermore, we propose the following two mechanisms for the
age and [$\alpha$/Fe] relations with $\Sigma$: (a) the age--$\Sigma$ and
[$\alpha$/Fe]--$\Sigma$ correlations arise as results of compactness driven
quenching mechanisms; and/or (b) as fossil records of the
$\Sigma_{SFR}\propto\Sigma_{gas}$ relation in their disk-dominated progenitors.
