The ATLAS3D project - XX. Mass-size and mass-Σ distributions of early-type galaxies: bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function

In the companion Paper XV of this series, we derive accurate total mass-to-light ratios (M/L)(JAM) approximate to (M/L)(r = R-e) within a sphere of radius r = R-e centred on the galaxy, as well as stellar (M/L)(stars) (with the dark matter removed) for the volume-limited and nearly mass-selected (stellar mass M-star greater than or similar to 6 x 10(9) M-circle dot) ATLAS(3D) sample of 260 early-type galaxies (ETGs, ellipticals Es and lenticulars S0s). Here, we use those parameters to study the two orthogonal projections (M-JAM, sigma(e)) and (M-JAM, R-e(maj)) of the thin Mass Plane (MP) (M-JAM, sigma(e), R-e(maj)) which describes the distribution of the galaxy population, where M-JAM = L x (M/L)(JAM) approximate to M-star. The distribution of galaxy properties on both projections of the MP is characterized by: (i) the same zone of exclusion (ZOE), which can be transformed from one projection to the other using the scalar virial equation. The ZOE is roughly described by two power laws, joined by a break at a characteristic mass M-JAM approximate to 3 x 10(10) M-circle dot, which corresponds to the minimum R-e and maximum stellar density. This results in a break in the mean M-JAM-sigma(e) relation with trends M-JAM proportional to sigma(2.3)(e) and M-JAM proportional to sigma(4.7)(e) at small and large sigma(e), respectively; (ii) a characteristic mass M-JAM approximate to 2 x 10(11) M-circle dot which separates a population dominated by flat fast rotator with discs and spiral galaxies at lower masses, from one dominated by quite round slow rotators at larger masses; (iii) below that mass the distribution of ETGs' properties on the two projections of the MP tends to be constant along lines of roughly constant sigma(e), or equivalently along lines with R-e(maj) proportional to M-JAM, respectively (or even better parallel to the ZOE: R-maj(e) proportional to M-JAM(0.75)); (iv) it forms a continuous and parallel sequence with the distribution of spiral galaxies; (v) at even lower masses, the distribution of fast-rotator ETGs and late spirals naturally extends to that of dwarf ETGs (Sph) and dwarf irregulars (Im), respectively. We use dynamical models to analyse our kinematic maps. We show that Sigma(e) traces the bulge fraction, which appears to be the main driver for the observed trends in the dynamical (M/L)(JAM) and in indicators of the (M/L)(pop) of the stellar population like H beta and colour, as well as in the molecular gas fraction. A similar variation along contours of Sigma(e) is also observed for the mass normalization of the stellar initial mass function (IMF), which was recently shown to vary systematically within the ETGs' population. Our preferred relation has the form log(10)[(M/L)(stars)/(M/L)(Salp)] = a + b x log(10)(sigma(e)/130 km s(-1)) with a = -0.12 +/- 0.01 and b = 0.35 +/- 0.06. Unless there are major flaws in all stellar population models, this trend implies a transition of the mean IMF from Kroupa to Salpeter in the interval log(10)(sigma(e)/km s(-1)) approximate to 1.9-2.5 (or sigma e approximate to 90-290 km s-1), with a smooth variation in between, consistently with what was shown in Cappellari et al. The observed d205 (or sigma e istribution of galaxy properties on the MP provides a clean and novel view for a number of previously reported trends, which constitute special two-dimensional projections of the more general four-dimensional parameters trends on the MP. We interpret it as due to a combination of two main effects: (i) an increase of the bulge fraction, which increases Sigma(e), decreases R-e, and greatly enhance the likelihood for a galaxy to have its star formation quenched, and (ii) dry merging, increasing galaxy mass and R-e by moving galaxies along lines of roughly constant Sigma(e) (or steeper), while leaving the population nearly unchanged.