We measure the star formation efficiency (SFE), the star formation rate per unit gas, in 23 nearby galaxies and compare it to expectations from proposed star formation laws and thresholds. We use H I maps from THINGS and derive H 2 maps from CO measured by HERACLES and BIMA SONG. We estimate the star formation rate by combining GALEX FUV maps and SINGS 24µm maps, infer stellar surface density profiles from SINGS 3.6µm data, and use kinematics from THINGS. We measure the SFE as a function of: the free-fall and orbital timescales; midplane gas pressure; stability of the gas disk to collapse (including the effects of stars); the ability of perturbations to grow despite shear; and the ability of a cold phase to form. In spirals, the SFE of H 2 alone is nearly constant at 5.25 ± 2.5 × 10 −10 yr −1 (equivalent to an H 2 depletion time of 1.9 × 10 9 yr) as a function of all of these variables at our 800 pc resolution. Where the ISM is mostly H I, on the other hand, the SFE decreases with increasing radius in both spiral and dwarf galaxies, a decline reasonably described by an exponential with scale length 0.2-0.25 r 25 . We interpret this decline as a strong dependence of GMC formation on environment. The ratio of molecular to atomic gas appears to be a smooth function of radius, stellar surface density, and pressure spanning from the H 2 -dominated to H I-dominated ISM. The radial decline in SFE is too steep to be reproduced only by increases in the free-fall time or orbital time. Thresholds for large-scale instability suggest that our disks are stable or marginally stable and do not show a clear link to the declining SFE. We suggest that ISM physics below the scales that we observe -phase balance in the H I, H 2 formation and destruction, and stellar feedback -governs the formation of GMCs from H I.

We present a comprehensive analysis of the relationship between star formation rate surface density, Σ SFR , and gas surface density, Σ gas , at sub-kpc resolution in a sample of 18 nearby galaxies. We use high resolution H i data from THINGS, CO data from HERACLES and BIMA SONG, 24 µm data from the Spitzer Space Telescope, and UV data from GALEX. We target 7 spiral galaxies and 11 late-type/dwarf galaxies and investigate how the star formation law differs between the H 2 -dominated centers of spiral galaxies, their H i-dominated outskirts and the H i-rich late-type/dwarf galaxies. We find that a Schmidt-type power law with index N = 1.0 ± 0.2 relates Σ SFR and Σ H2 across our sample of spiral galaxies, i.e., that H 2 forms stars at a constant efficiency in spirals. The average molecular gas depletion time is ∼ 2 · 10 9 years. The range of Σ H2 over which we measure this relation is ∼ 3 − 50 M ⊙ pc −2 , significantly lower than in starburst environments. We find the same results when performing a pixel-by-pixel analysis, averaging in radial bins, or when varying the star formation tracer used. We interpret the linear relation and constant depletion time as evidence that stars are forming in GMCs with approximately uniform properties and that Σ H2 may be more a measure of the filling fraction of giant molecular clouds than changing conditions in the molecular gas. The relationship between total gas surface density (Σ gas ) and Σ SFR varies dramatically among and within spiral galaxies. Most galaxies show little or no correlation between Σ HI and Σ SFR . As a result, the star formation efficiency (SFE), Σ SFR /Σ gas , varies strongly across our sample and within individual galaxies. We show that this variation is systematic and consistent with the SFE being set by local environmental factors: in spirals the SFE is a clear function of radius, while the dwarf galaxies in our sample display SFEs similar to those found in the outer optical disks of the spirals. We attribute the similarity to common environments (low-density, low-metallicity, H i-dominated) and argue that shear (which is typically absent in dwarfs) cannot drive the SFE. In addition to a molecular Schmidt law, the other general feature of our sample is a sharp saturation of H i surface densities at Σ HI ≈ 9 M ⊙ pc −2 in both the spiral and dwarf galaxies. In the case of the spirals, we observe gas in excess of this limit to be molecular.

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We present the HERA CO-Line Extragalactic Survey (HERACLES), an atlas of CO emission from 18 nearby galaxies that are also part of The H I Nearby Galaxy Survey (THINGS) and the Spitzer Infrared Nearby Galaxies Survey (SINGS). We used the HERA multi-pixel receiver on the IRAM 30-m telescope to map the CO J = 2 → 1 line over the full optical disk (defined by the isophotal radius r 25 ) of each target, at 13 ′′ angular resolution and 2.6 km s −1 velocity resolution. Here we describe the observations and reduction of the data and show channel maps, azimuthally averaged profiles, integrated intensity maps, and peak intensity maps. The implied H 2 masses range from 7 × 10 6 to 6 × 10 9 M ⊙ , with four low metallicity dwarf irregular galaxies yielding only upper limits. In the cases where CO is detected, the integrated H 2 -to-H I ratios range from 0.02 -1.13 and H 2 -to-stellar mass ratios from 0.01 to 0.25. Exponential scale lengths of the CO emission for our targets are in the range 0.8 -3.2 kpc, or 0.2 ± 0.05 r 25 . The intensity-weighted mean velocity of CO matches that of H I very well, with a 1σ scatter of only 6 km s −1 . The CO J = 2 → 1/J = 1 → 0 line ratio varies over a range similar to that found in the Milky Way and other nearby galaxies, ∼ 0.6-1.0, with higher values found in the centers of galaxies. The typical line ratio, ∼ 0.8, could be produced by optically thick gas with an excitation temperature of ∼ 10 K.

We compare molecular gas traced by 12 CO(2-1) maps from the HERACLES survey, with tracers of the recent star formation rate (SFR) across 30 nearby disk galaxies. We demonstrate a first-order linear correspondence between Σ mol and Σ SFR but also find important second-order systematic variations in the apparent molecular gas depletion time, τ mol dep = Σ mol /Σ SFR . At the 1 kpc common resolution of HERACLES, CO emission correlates closely with many tracers of the recent SFR. Weighting each line of sight equally, using a fixed alpha CO equivalent to the Milky Way value, our data yield a molecular gas depletion time, τ mol dep = Σ mol /Σ SFR ≈ 2.2 Gyr with 0.3 dex 1σ scatter, in very good agreement with recent literature data. We apply a forward-modeling approach to constrain the power-law index, N , that relates the SFR surface density and the molecular gas surface density, Σ SFR ∝ Σ N mol . We find N = 1 ± 0.15 for our full data set with some scatter from galaxy to galaxy. This also agrees with recent work, but we caution that a power law treatment oversimplifies the topic given that we observe correlations between τ mol dep and other local and global quantities. The strongest of these are a decreased τ mol dep in low-mass, low-metallicity galaxies and a correlation of the kpc-scale τ mol dep with dust-to-gas ratio, D/G. These correlations can be explained by a CO-to-H 2 conversion factor (α CO ) that depends on dust shielding, and thus D/G, in the theoretically expected way. This is not a unique interpretation, but external evidence of conversion factor variations makes this the most conservative explanation of the strongest observed τ mol dep trends. After applying a D/G-dependent α CO , some weak correlations between τ mol dep and local conditions persist. In particular, we observe lower τ mol dep and enhanced CO excitation associated with nuclear gas concentrations in a subset of our targets. These appear to reflect real enhancements in the rate of star formation per unit gas and although the distribution of τ dep does not appear bimodal in galaxy centers, τ dep does appear multivalued at fixed Σ mol , supporting the the idea of "disk" and "starburst" modes driven by other environmental parameters.

We combine data from The H I Nearby Galaxy Survey and the GALEX Nearby Galaxy Survey to study the relationship between atomic hydrogen (H I) and far-ultraviolet (FUV) emission outside the optical radius (r 25 ) in 17 spiral and 5 dwarf galaxies. In this regime, H I is likely to represent most of the ISM and FUV emission to trace recent star formation with little bias due to extinction, so that the two quantities closely trace the underlying relationship between gas and star formation rate (SFR). The azimuthally averaged H I and FUV intensities both decline with increasing radius in this regime, with the scale length of the FUV profile typically half that of the H I profile. Despite the mismatch in profiles, there is a significant spatial correlation (at 15 ′′ resolution) between local FUV and H I intensities; near r 25 this correlation is quite strong, in fact stronger than anywhere inside r 25 (where H I is not a good tracer for the bulk of the ISM), and shows a decline towards larger radii. The star formation efficiency (SFE) -defined as the ratio of FUV/H I and thus the inverse of the gas depletion time -decreases with galactocentric radius across the outer disks, though much shallower than across the optical disks. On average, we find the gas depletion times to be well above a Hubble time (∼ 10 11 yr). We observe a clear relationship between FUV/H I and H I column in the outer disks, with the SFE increasing with increasing H I column. Despite observing systematic variations in FUV/H I, we find no clear evidence for step-function type star formation thresholds, though we emphasize that it may not be realistic to expect them. When compared with results from inside r 25 , we find outer disk star formation to be distinct in several ways: it is extremely inefficient (depletion times of many Hubble times which are also long compared to either the free fall or orbital timescale) with column densities and SFRs lower than found anywhere inside the optical disks. It appears that the H I column is one of, perhaps even the key environmental factor in setting the SFR in outer galaxy disks.

We use the IRAM HERACLES survey to study CO emission from 33 nearby spiral galaxies down to very low intensities. Using 21 cm line atomic hydrogen (H i) data, mostly from THINGS, we predict the local mean CO velocity based on the mean H i velocity. By re-normalizing the CO velocity axis so that zero corresponds to the local mean H i velocity we are able to stack spectra coherently over large regions. This enables us to measure CO intensities with high significance as low as, an improvement of about one order of magnitude over previous studies. We detect CO out to galactocentric radii r gal ∼ r 25 and find the CO radial profile to follow a remarkably uniform exponential decline with a scale length of ∼0.2 r 25 . Here we focus on stacking as a function of radius, comparing our sensitive CO profiles to matched profiles of H i, Hα, far-UV (FUV), and Infrared (IR) emission at 24 μm and 70 μm. We observe a tight, roughly linear relationship between CO and IR intensity that does not show any notable break between regions that are dominated by molecular gas (Σ H 2 > Σ H i ) and those dominated by atomic gas (Σ H 2 < Σ H i ). We use combinations of FUV + 24 μm and Hα + 24 μm to estimate the recent star formation rate (SFR) surface density, Σ SFR , and find approximately linear relations between Σ SFR and Σ H 2 . We interpret this as evidence of stars forming in molecular gas with little dependence on the local total gas surface density. While galaxies display small internal variations in the SFR-to-H 2 ratio, we do observe systematic galaxy-to-galaxy variations. These galaxy-to-galaxy variations dominate the scatter in relationships between CO and SFR tracers measured at large scales. The variations have the sense that less massive galaxies exhibit larger ratios of SFR-to-CO than massive galaxies. Unlike the SFR-to-CO ratio, the balance between atomic and molecular gas depends strongly on the total gas surface density and galactocentric radius. It must also depend on additional parameters. Our results reinforce and extend to lower surface densities, a picture in which star formation in galaxies can be separated into two processes: the assembly of star-forming molecular clouds and the formation of stars from H 2 . The interplay between these processes yields a total gas-SFR relation with a changing slope, which has previously been observed and identified as a star formation threshold.

We combine new sensitive, wide-field CO data from the HERACLES survey with ultraviolet and infrared data from GALEX and Spitzer to compare the surface densities of H 2 , Σ H2 , and the recent star formation rate, Σ SFR , over many thousands of positions in 30 nearby disk galaxies. We more than quadruple the size of the galaxy sample compared to previous work and include targets with a wide range of galaxy properties. Even though the disk galaxies in this study span a wide range of properties, we find a strong, and approximately linear correlation between Σ SFR and Σ H2 at our common resolution of 1 kpc. This implies a roughly constant median H 2 consumption time, τ H2 Dep = Σ H2 /Σ SFR , of ∼ 2.35 Gyr (including heavy elements) across our sample. At 1 kpc resolution, there is only a weak correlation between Σ H2 and τ H2 Dep over the range Σ H2 ≈ 5-100 M ⊙ pc −2 , which is probed by our data. We compile a broad set of literature measurements that have been obtained using a variety of star formation tracers, sampling schemes and physical scales and show that overall, these data yield almost exactly the same results, although with more scatter. We interpret these results as strong, albeit indirect evidence that star formation proceeds in a uniform way in giant molecular clouds in the disks of spiral galaxies.