A Universal fundamental plane and the $M_{dyn}-M_{\star}$ relation for galaxies with CALIFA and MaNGA

We use the stellar kinematics for $2458$ galaxies from the MaNGA survey to explore dynamical scaling relations between the stellar mass $M_{\star}$ and the total velocity parameter at the effective radius, $R_e$, defined as $S_{K}^{2}=KV_{R_e}^{2}+\sigma_{\star_e}^{2}$, which combines rotation velocity $V_{R_e}$, and velocity dispersion $\sigma_{\star_e}$. We confirm that spheroidal and spiral galaxies follow the same $M_{\star}-S_{0.5}$ scaling relation with lower scatter than the $M_{\star}-V_{R_e}$ and $M_{\star}-\sigma_{\star_e}$ ones. We also explore a more general Universal Fundamental Plane described by the equation $log(\Upsilon_{e}) = log (S_{0.5}^{2}) - log (I_{e}) - log (R_{e}) + C$, which in addition to kinematics, $S_{0.5}$, and effective radius, $R_e$, it includes surface brightness, $I_e$, and dynamical mass-to-light ratio, $\Upsilon_e$. We use sophisticated Schwarzschild dynamical models for a sub-sample of 300 galaxies from the CALIFA survey to calibrate the so called Universal Fundamental Plane. That calibration allows us to propose both: (i) a parametrization to estimate the difficult-to-measure dynamical mass-to-light ratio at the effective radius; and (ii) a new dynamical mass proxy consistent with dynamical models within $0.09\ dex$. We reproduce the relation between the dynamical mass and the stellar mass in the inner regions of galaxies. We use the estimated dynamical mass-to-light ratio from our analysis, $\Upsilon_{e}^{fit}$, to explore the Universal Fundamental Plane with the MaNGA data set. We find that all classes of galaxies, from spheroids to disks, follow this Universal Fundamental Plane with a scatter significantly smaller $(0.05\ dex)$ than the one reported for the $M_{\star}-S_{0.5}$ relation $(0.1\ dex)$, the Fundamental Plane $(\sim 0.09\ dex)$ and comparable with Tully-Fisher studies $(\sim 0.05\ dex)$, but for a wider range of galaxy types.