We study the global star formation law -the relation between gas and star formation (SF) rates in a sample of 181 local galaxies with infrared (IR) luminosities spanning almost five orders of magnitude (10 7.8 − 10 12.3 L ⊙ ), which includes 115 normal spiral galaxies and 66 (ultra)luminous IR galaxies [(U)LIRGs, L IR ≥ 10 11 L ⊙ ]. We derive their atomic, molecular gas and dense molecular gas masses using newly available HI, CO and HCN data from the literature, and SF rates are determined both from total IR (8 − 1000 µm) and 1.4 GHz radio continuum (RC) luminosities. In order to derive the disk-averaged surface densities of gas and SF rates, we have taken a novel approach and used high-resolution RC observations to measure the radio sizes for all 181 galaxies. In our sample, we find that the surface density of dense molecular gas (as traced by HCN) has the tightest correlation with that of SF rates (Σ SFR ), and is linear in log − log space (power-law slope of N = 1.01 ± 0.02) across the full galaxy sample. The correlation between surface densities of molecular gas (Σ H2 ,traced by CO) and Σ SFR is sensitive to the adopted value of the CO-to-H 2 conversion factor (α CO ) used to infer molecular gas masses from CO luminosities. For a fixed Galactic value of α CO , a power law index of 1.14 ± 0.02 is found. If instead we adopt values for α CO of 4.6 and 0.8 for disk galaxies and (U)LIRGs, respectively, we find the two galaxy populations separate into two distinct Σ SFR versus Σ H2 relations. Finally, applying a continuously varying α CO to our sample, we recover a single Σ SFR -Σ H2 relation with slope of 1.60 ± 0.03. The Σ SFR is a steeper function of total gas Σ gas (molecular gas with atomic gas) than that of molecular gas Σ H2 , and are tighter among low-luminosity galaxies. We find no correlation between global surface densities of SFRs and atomic gas (H I).

As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project we present an estimate of the mass of the supermassive black hole (SMBH) in the nearby fast-rotating early-type galaxy NGC4429, that is barred and has a boxy/peanut-shaped bulge. This estimate is based on Atacama Large Millimeter/submillimeter Array (ALMA) cycle-2 observations of the 12 CO(3-2) emission line with a linear resolution of ≈13 pc (0. 18 × 0. 14). NGC4429 has a relaxed, flocculent nuclear disc of molecular gas that is truncated at small radii, likely due to the combined effects of gas stability and tidal shear. The warm/dense 12 CO(3-2) emitting gas is confined to the inner parts of this disc, likely again because the gas becomes more stable at larger radii, preventing star formation. The gas disc has a low velocity dispersion of 2.2 +0.68 −0.65 km s −1 . Despite the inner truncation of the gas disc, we are able to model the kinematics of the gas and estimate a mass of (1.5±0.1 +0.15 −0.35 ) ×10 8 M for the SMBH in NGC4429 (where the quoted uncertainties reflect the random and systematic uncertainties, respectively), consistent with a previous upper limit set using ionised gas kinematics. We confirm that the V-band mass-to-light ratio changes by ≈30% within the inner 400 pc of NGC4429, as suggested by other authors. This SMBH mass measurement based on molecular gas kinematics, the sixth presented in the literature, once again demonstrates the power of ALMA to constrain SMBH masses.

We present a systematic survey of multiple velocity-resolved H 2 O spectra using Herschel/Heterodyne Instrument for the Far Infrared (HIFI) toward nine nearby actively star-forming galaxies. The ground-state and low-excitation lines (E up 130 K) show profiles with emission and absorption blended together, while absorption-free mediumexcitation lines (130 K E up 350 K) typically display line shapes similar to CO. We analyze the HIFI observation together with archival SPIRE/PACS H 2 O data using a state-of-the-art 3D radiative transfer code that includes the interaction between continuum and line emission. The water excitation models are combined with information on the dust and CO spectral line energy distribution to determine the physical structure of the interstellar medium (ISM). We identify two ISM components that are common to all galaxies: a warm10 10 cm 3 ), more extended phase is present. It outputs the emission in the low-excitation H 2 O lines and typically also produces the prominent line absorption features. For the two ULIRGs in our sample (Arp 220 and Mrk 231) an even hotter and more compact (R s 100 pc) region is present, which is possibly linked to AGN activity. We find that collisions dominate the water excitation in the cold gas and for lines with  E 300 up K and  E 800 up K in the warm and hot component, respectively. Higher-energy levels are mainly excited by IR pumping.