No abstract

We investigate the relationship between H I, H 2 , and the star formation rate (SFR) using azimuthally averaged data for seven CO-bright spiral galaxies. Contrary to some earlier studies based on global fluxes, we find that Σ SFR exhibits a much stronger correlation with Σ H2 than with Σ HI , as Σ HI saturates at a value of ∼ 10 M pc −2 or even declines for large Σ SFR . Hence the good correlation between Σ SFR and the total (H I+H 2 ) gas surface density Σ gas is driven by the molecular component in these galaxies, with the observed relation between Σ SFR and Σ H2 following a Schmidt-type law of index n mol ≈0.8 if a uniform extinction correction is applied or n mol ≈1.4 for a radially varying correction dependent on gas density. The corresponding Schmidt law indices for Σ gas vs. Σ SFR are 1.1 and 1.7 for the two extinction models, in rough agreement with previous studies of the disk-averaged star formation law. An alternative to the Schmidt law, in which the gas depletion timescale is proportional to the orbital timescale, is also consistent with the data if radially varying extinction corrections are applied. We find no clear evidence for a link between the gravitational instability parameter for the gas disk (Q g ) and the SFR, and suggest that Q g be considered a measure of the gas fraction. This implies that for a state of marginal gravitational stability to exist in galaxies with low gas fractions, it must be enforced by the stellar component. In regions where we have both H I and CO measurements, the ratio of H I to H 2 surface density scales with radius as roughly R 1.5 , and we suggest that the balance between H I and H 2 is determined primarily by the midplane interstellar pressure. These results favor a "law" of star formation in quiescent disks in which the ambient pressure and metallicity control the formation of molecular clouds from H I, with star formation then occurring at a roughly constant rate per unit H 2 mass.

We show that the ratio of molecular to atomic gas in galaxies is determined by hydrostatic pressure and that the relation between the two is nearly linear. The pressure relation is shown to be good over 3 orders of magnitude for 14 galaxies, including dwarfs, H i-rich, and H 2 -rich galaxies, as well as the Milky Way. The sample spans a factor of 5 in mean metallicity. The rms scatter of individual points of the relation is only about a factor of 2 for all the galaxies, although some show much more scatter than others. Using these results, we propose a modified star formation prescription based on pressure determining the degree to which the ISM is molecular. The formulation is different in high-and low-pressure regimes, defined by whether the gas is primarily atomic or primarily molecular. This formulation can be implemented in simulations and provides a more appropriate treatment of the outer regions of spiral galaxies and molecule-poor systems, such as dwarf irregulars and damped Ly systems.

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...