We investigate the well‐known correlations between the dynamical mass‐to‐light ratio (M/L) and other global observables of elliptical (E) and lenticular (S0) galaxies. We construct two‐integral Jeans and three‐integral Schwarzschild dynamical models for a sample of 25 E/S0 galaxies with SAURON integral‐field stellar kinematics to about one effective (half‐light) radius Re. They have well‐calibrated I‐band Hubble Space Telescope WFPC2 and large‐field ground‐based photometry, accurate surface brightness fluctuation distances, and their observed kinematics is consistent with an axisymmetric intrinsic shape. All these factors result in an unprecedented accuracy in the M/L measurements. We find a tight correlation of the form (M/L) = (3.80 ± 0.14) × (σe/200 km s−1)0.84±0.07 between the M/L (in the I band) measured from the dynamical models and the luminosity‐weighted second moment σe of the LOSVD within Re. The observed rms scatter in M/L for our sample is 18 per cent, while the inferred intrinsic scatter is ∼13 per cent. The (M/L)–σe relation can be included in the remarkable series of tight correlations between σe and other galaxy global observables. The comparison of the observed correlations with the predictions of the Fundamental Plane (FP), and with simple virial estimates, shows that the ‘tilt’ of the FP of early‐type galaxies, describing the deviation of the FP from the virial relation, is almost exclusively due to a real M/L variation, while structural and orbital non‐homology have a negligible effect. When the photometric parameters are determined in the ‘classic’ way, using growth curves, and the σe is measured in a large aperture, the virial mass appears to be a reliable estimator of the mass in the central regions of galaxies, and can be safely used where more ‘expensive’ models are not feasible (e.g. in high‐redshift studies). In this case the best‐fitting virial relation has the form (M/L)vir= (5.0 ± 0.1) ×Reσ2e/(LG), in reasonable agreement with simple theoretical predictions. We find no difference between the M/L of the galaxies in clusters and in the field. The comparison of the dynamical M/L with the (M/L)pop inferred from the analysis of the stellar population, indicates a median dark matter fraction in early‐type galaxies of ∼30 per cent of the total mass inside one Re, in broad agreement with previous studies, and it also shows that the stellar initial mass function varies little among different galaxies. Our results suggest a variation in M/L at constant (M/L)pop, which seems to be linked to the galaxy dynamics. We speculate that fast‐rotating galaxies have lower dark matter fractions than the slow‐rotating and generally more‐massive ones. If correct, this would suggest a connection between the galaxy assembly history and the dark matter halo structure. The tightness of our correlation provides some evidence against cuspy nuclear dark matter profiles in galaxies.

We present the emission‐line fluxes and kinematics of 48 representative elliptical and lenticular galaxies obtained with our custom‐built integral‐field spectrograph, SAURON, operating on the William Herschel Telescope. Hβ, [O iii]λλ4959,5007 and [N i]λλ5198,5200 emission lines were measured using a new procedure that simultaneously fits both the stellar spectrum and the emission lines. Using this technique we can detect emission lines down to an equivalent width of 0.1 Å  set by the current limitations in describing galaxy spectra with synthetic and real stellar templates, rather than by the quality of our spectra. Gas velocities and velocity dispersions are typically accurate to within 14 and 20 km s−1, respectively, and at worse to within 25 and 40 km s−1. The errors on the flux of the [O iii] and Hβ lines are on average 10 and 20 per cent, respectively, and never exceed 30 per cent. Emission is clearly detected in 75 per cent of our sample galaxies, and comes in a variety of resolved spatial distributions and kinematic behaviours. A mild dependence on the Hubble type and galactic environment is observed, with higher detection rates in lenticular galaxies and field objects. More significant is the fact that only 55 per cent of the galaxies in the Virgo cluster exhibit clearly detected emission. The ionized‐gas kinematics is rarely consistent with simple coplanar circular motions. However, the gas almost never displays completely irregular kinematics, generally showing coherent motions with smooth variations in angular momentum. In the majority of the cases, the gas kinematics is decoupled from the stellar kinematics, and in half of the objects this decoupling implies a recent acquisition of gaseous material. Over the entire sample however, the distribution of the mean misalignment values between stellar and gaseous angular momenta is inconsistent with a purely external origin. The distribution of kinematic misalignment values is found to be strongly dependent on the apparent flattening and the level of rotational support of galaxies, with flatter, fast rotating objects hosting preferentially corotating gaseous and stellar systems. In a third of the cases, the distribution and kinematics of the gas underscore the presence of non‐axisymmetric perturbations of the gravitational potential. Consistent with previous studies, the presence of dust features is always accompanied by gas emission while the converse is not always true. A considerable range of values for the [O iii]/Hβ ratio is found both across the sample and within single galaxies. Despite the limitations of this ratio as an emission‐line diagnostic, this finding suggests either that a variety of mechanisms is responsible for the gas excitation in E and S0 galaxies or that the metallicity of the interstellar material is quite heterogeneous.

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.

We use the ATLAS 3D sample of 260 early-type galaxies to study the apparent kinematic misalignment angle, , defined as the angle between the photometric and kinematic major axes. We find that 71 per cent of nearby early-type galaxies are strictly aligned systems ( ≤ 5 • ), an additional 14 per cent have 5 • < ≤ 10 • and 90 per cent of galaxies have ≤ 15 • . Taking into account measurement uncertainties, 90 per cent of galaxies can be considered aligned to better than 5 • , suggesting that only a small fraction of early-type galaxies (∼10 per cent) are not consistent with the axisymmetry within the projected half-light radius. We identify morphological features such as bars and rings (30 per cent), dust structures (16 per cent), blue nuclear colours (6 per cent) and evidence of interactions (8 per cent) visible on ATLAS 3D galaxies. We use KINEMETRY to analyse the mean velocity maps and separate galaxies into two broad types of regular and non-regular rotators. We find 82 per cent of regular rotators and 17 per cent of non-regular rotators, with two galaxies that we were not able to classify due to the poor data quality. The non-regular rotators are typically found in dense regions and are massive. We characterize the specific features in the mean velocity and velocity dispersion maps. The majority of galaxies do not have any specific features, but we highlight here the frequency of the kinematically distinct cores (7 per cent of galaxies) and the aligned double

We present a generalization of surface photometry to the higher-order moments of the line-ofsight velocity distribution of galaxies observed with integral-field spectrographs. The generalization follows the approach of surface photometry by determining the best-fitting ellipses along which the profiles of the moments can be extracted and analysed by means of harmonic expansion. The assumption for the odd moments (e.g. mean velocity) is that the profile along an ellipse satisfies a simple cosine law. The assumption for the even moments (e.g. velocity dispersion) is that the profile is constant, as it is used in surface photometry. We test the method on a number of model maps and discuss the meaning of the resulting harmonic terms. We apply the method to the kinematic moments of an axisymmetric model elliptical galaxy and probe the influence of noise on the harmonic terms. We also apply the method to SAURON observations of NGC 2549, NGC 2974, NGC 4459 and NGC 4473 where we detect multiple co-and counter-rotating (NGC 2549 and NGC 4473, respectively) components. We find that velocity profiles extracted along ellipses of early-type galaxies are well represented by the simple cosine law (with 2 per cent accuracy), while possible deviations are carried in the fifth harmonic term which is sensitive to the existence of multiple kinematic components, and has some analogy to the shape parameter of photometry. We compare the properties of the kinematic and photometric ellipses and find that they are often very similar, but a study on a larger sample is necessary. Finally, we offer a characterization of the main velocity structures based only on the kinemetric parameters which can be used to quantify the features in velocity maps.