We study the volume-limited and nearly mass selected (stellar mass M stars > ∼ 6 × 10 9 M ) ATLAS 3D sample of 260 early-type galaxies (ETGs, ellipticals Es and lenticulars S0s). We construct detailed axisymmetric dynamical models (JAM), which allow for orbital anisotropy, include a dark matter halo, and reproduce in detail both the galaxy images and the highquality integral-field stellar kinematics out to about 1R e , the projected half-light radius. We derive accurate total mass-to-light ratios (M/L) e and dark matter fractions f DM , within a sphere of radius r = R e centred on the galaxies. We also measure the stellar (M/L) stars and derive a median dark matter fraction f DM = 13% in our sample. We infer masses M JAM ≡ L × (M/L) e ≈ 2 × M 1/2 , where M 1/2 is the total mass within a sphere enclosing half of the galaxy light. We find that the thin two-dimensional subset spanned by galaxies in the (M JAM , σ e , R maj e ) coordinates system, which we call the Mass Plane (MP) has an observed rms scatter of 19%, which implies an intrinsic one of 11%. Here R maj e is the major axis of an isophote enclosing half of the observed galaxy light, while σ e is measured within that isophote. The MP satisfies the scalar virial relation M JAM ∝ σ 2 e R maj e within our tight errors. This show that the larger scatter in the Fundamental Plane (FP) (L, σ e , R e ) is due to stellar population effects (including trends in the stellar Initial Mass Function [IMF]). It confirms that the FP deviation from the virial exponents is due to a genuine (M/L) e variation. However, the details of how both R e and σ e are determined are critical in defining the precise deviation from the virial exponents. The main uncertainty in masses or M/L estimates using the scalar virial relation is in the measurement of R e . This problem is already relevant for nearby galaxies and may cause significant biases in virial mass and size determinations at high-redshift. Dynamical models can eliminate these problems. We revisit the (M/L) e − σ e relation, which describes most of the deviations between the MP and the FP. The best-fitting relation is (M/L) e ∝ σ 0.72 e (r-band). It provides an upper limit to any systematic increase of the IMF mass normalization with σ e . The correlation is more shallow and has smaller scatter for slow rotating systems or for galaxies in Virgo. For the latter, when using the best distance estimates, we observe a scatter in (M/L) e of 11%, and infer an intrinsic one of 8%. We perform an accurate empirical study of the link between σ e and the galaxies circular velocity V circ within 1R e (where stars dominate) and find the relation max(V circ ) ≈ 1.76 × σ e , which has an observed scatter of 7%. The accurate parameters described in this paper are used in the companion Paper XX of this series to explore the variation of global galaxy properties, including the IMF, on the projections of the MP.

We provide a census of the apparent stellar angular momentum within one effective radius of a volume‐limited sample of 260 early‐type galaxies (ETGs) in the nearby Universe, using the integral‐field spectroscopy obtained in the course of the ATLAS3D project. We exploit the λR parameter (previously used via a constant threshold value of 0.1) to characterize the existence of two families of ETGs: slow rotators which exhibit complex stellar velocity fields and often include stellar kinematically distinct cores, and fast rotators which have regular velocity fields. Our complete sample of 260 ETGs leads to a new criterion to disentangle fast and slow rotators which now includes a dependency on the apparent ellipticity ε. It separates the two classes significantly better than the previous prescription and better than a criterion based on V/σ: slow rotators and fast rotators have λR lower and larger than , respectively, where kFS= 0.31 for measurements made within an effective radius Re. We show that the vast majority of ETGs are fast rotators: these have the regular stellar rotation, with aligned photometric and kinematic axes (Paper II of this series), include discs and often bars and represent 86 ± 2 per cent (224/260) of all ETGs in the volume‐limited ATLAS3D sample. Fast rotators span the full range of apparent ellipticities from ε= 0 to 0.85, and we suggest that they cover intrinsic ellipticities from about 0.35 to 0.85, the most flattened having morphologies consistent with spiral galaxies. Only a small fraction of ETGs are slow rotators representing 14 ± 2 per cent (36/260) of the ATLAS3D sample of ETGs. Of all slow rotators, 11 per cent (4/36) exhibit two counter‐rotating stellar disc‐like components and are rather low‐mass objects (Mdyn < 1010.5 M⊙). All other slow rotators (32/36) appear relatively round on the sky (εe < 0.4), tend to be massive (Mdyn > 1010.5 M⊙), and often (17/32) exhibit kinematically distinct cores. Slow rotators dominate the high‐mass end of ETGs in the ATLAS3D sample, with only about one‐fourth of galaxies with masses above 1011.5 M⊙ being fast rotators. We show that the a4 parameter which quantifies the isophote’s disciness or boxiness does not seem to be simply related to the observed kinematics, while our new criterion based on λR and ε is nearly independent of the viewing angles. We further demonstrate that the classification of ETGs into ellipticals and lenticulars is misleading. Slow and fast rotators tend to be classified as ellipticals and lenticulars, respectively, but the contamination is strong enough to affect results solely based on such a scheme: 20 per cent of all fast rotators are classified as ellipticals, and more importantly 66 per cent of all ellipticals in the ATLAS3D sample are fast rotators. Fast and slow rotators illustrate the variety of complex processes shaping galactic systems, such as secular evolution, disc instabilities, interaction and merging, gas accretion, stripping and harassment, forming a sequence from high to low (stellar) baryonic angular...

Much of our knowledge of galaxies comes from analysing the radiation emitted by their stars, which depends on the present number of each type of star in the galaxy. The present number depends on the stellar initial mass function (IMF), which describes the distribution of stellar masses when the population formed, and knowledge of it is critical to almost every aspect of galaxy evolution. More than 50 years after the first IMF determination, no consensus has emerged on whether it is universal among different types of galaxies. Previous studies indicated that the IMF and the dark matter fraction in galaxy centres cannot both be universal, but they could not convincingly discriminate between the two possibilities. Only recently were indications found that massive elliptical galaxies may not have the same IMF as the Milky Way. Here we report a study of the two-dimensional stellar kinematics for the large representative ATLAS(3D) sample of nearby early-type galaxies spanning two orders of magnitude in stellar mass, using detailed dynamical models. We find a strong systematic variation in IMF in early-type galaxies as a function of their stellar mass-to-light ratios, producing differences of a factor of up to three in galactic stellar mass. This implies that a galaxy's IMF depends intimately on the galaxy's formation history.

The ATLAS3D project is a multiwavelength survey combined with a theoretical modelling effort. The observations span from the radio to the millimetre and optical, and provide multicolour imaging, two‐dimensional kinematics of the atomic (H i), molecular (CO) and ionized gas (Hβ, [O iii] and [N i]), together with the kinematics and population of the stars (Hβ, Fe5015 and Mg b), for a carefully selected, volume‐limited (1.16 × 105 Mpc3) sample of 260 early‐type (elliptical E and lenticular S0) galaxies (ETGs). The models include semi‐analytic, N‐body binary mergers and cosmological simulations of galaxy formation. Here we present the science goals for the project and introduce the galaxy sample and the selection criteria. The sample consists of nearby (D < 42 Mpc, |δ− 29°| < 35°, |b| > 15°) morphologically selected ETGs extracted from a parent sample of 871 galaxies (8 per cent E, 22 per cent S0 and 70 per cent spirals) brighter than MK < −21.5 mag (stellar mass M★≳ 6 ×109 M⊙). We analyse possible selection biases and we conclude that the parent sample is essentially complete and statistically representative of the nearby galaxy population. We present the size–luminosity relation for the spirals and ETGs and show that the ETGs in the ATLAS3D sample define a tight red sequence in a colour–magnitude diagram, with few objects in the transition from the blue cloud. We describe the strategy of the SAURON integral field observations and the extraction of the stellar kinematics with the ppxf method. We find typical 1σ errors of ΔV≈ 6 km s−1, Δσ≈ 7 km s−1, Δh3≈Δh4≈ 0.03 in the mean velocity, the velocity dispersion and Gauss–Hermite (GH) moments for galaxies with effective dispersion σe≳ 120 km s−1. For galaxies with lower σe (≈40 per cent of the sample) the GH moments are gradually penalized by ppxf towards zero to suppress the noise produced by the spectral undersampling and only V and σ can be measured. We give an overview of the characteristics of the other main data sets already available for our sample and of the ongoing modelling projects.