  Galaxy properties are known to correlate most tightly with the galaxy
effective stellar velocity dispersion $\sigma_{\rm e}$. Here we look for {\em
additional} trends at fixed $\sigma_{\rm e}$ using 1339 galaxies ($M_\ast
\gtrsim 6\times10^9$ M$_\odot$) with different morphologies in the MaNGA (DR14)
sample with integral-field spectroscopy data. We focus on the gradients
($\gamma_{\rm rms} \equiv \sigma(R_{\rm e}/4)/\sigma_{\rm e}$) of the stellar
root-mean-square velocity ($V_{\rm rms} \equiv \sqrt{V^2 + \sigma^2}$), which
we show traces the total mass density gradient $\gamma_{\rm tot}$ derived from
dynamical models and, more weakly, the bulge fraction. We confirm that
$\gamma_{\rm rms}$ increases with $\sigma_{\rm e}$, age and metallicity. We
additionally find that these correlations still exist at fixed $\sigma_{\rm
e}$, where galaxies with larger $\gamma_{\rm rms}$ are found to be older and
more metal-rich. It means that mass density gradients contain information of
the stellar population which is not fully accounted for by $\sigma_{\rm e}$.
This result puts an extra constraint on our understanding of galaxy quenching.
We compare our results with galaxies in the IllustrisTNG hydrodynamical
simulations and find that, at fixed $\sigma_{\rm e}$, similar trends exist with
age, the bulge fraction, and the total mass density slope but, unlike
observations, no correlation with metallicity can be detected in the
simulations.
