SDSS-IV MaNGA: Stellar population correlates with stellar root-mean-square velocity $V_{\rm rms}$ gradients or total-density-profile slopes at fixed effective velocity dispersion $\sigma_{\rm e}$

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.