MaNGA DynPop - III. Stellar dynamics versus stellar population relations in 6000 early-type and spiral galaxies: Fundamental Plane, mass-to-light ratios, total density slopes, and dark matter fractions

We present dynamical scaling relations, combined with the stellar population properties, for a subsample of about 6000 nearby galaxies with the most reliable dynamical models extracted from the full Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) sample of 10 000 galaxies. We show that the inclination-corrected mass plane for both early-type galaxies (ETGs) and late-type galaxies (LTGs), which links dynamical mass, projected half-light radius R_e, and the second stellar velocity moment σ_e within R_e, satisfies the virial theorem and is even tighter than the uncorrected one. We find a clear parabolic relation between $\lg (M/L)_{\rm e}$, the total mass-to-light ratio (M/L) within a sphere of radius R_e, and $\lg \sigma _{\rm e}$, with the M/L increasing with σ_e and for older stellar populations. However, the relation for ETGs is linear and the one for the youngest galaxies is constant. We confirm and improve the relation between mass-weighted total density slopes $\overline{\gamma _{_{\rm T}}}$ and σ_e: $\overline{\gamma _{_{\rm T}}}$ become steeper with increasing σ_e until $\lg (\sigma _{\rm e}/{\rm km\, s^{-1}})\approx 2.2$ and then remain constant around $\overline{\gamma _{_{\rm T}}}\approx 2.2$. The $\overline{\gamma _{_{\rm T}}}\!-\!\sigma _{\rm e}$ variation is larger for LTGs than ETGs. At fixed σ_e the total density profiles steepen with galaxy age and for ETGs. We find generally low dark matter fractions, median f_DM(<R_e) = 8 per cent, within a sphere of radius R_e. However, we find that f_DM(<R_e) depends on σ_e better than stellar mass: dark matter increases to a median f_DM(<R_e) = 33 per cent for galaxies with $\sigma _{\rm e}\lesssim 100$ km s^-1. The increased f_DM(<R_e) at low σ_e explains the parabolic $\lg (M/L)_{\rm e}\!-\!\lg \sigma _{\rm e}$ relation.