A 50 pc Scale View of Star Formation Efficiency across NGC 628

Our ALMA observations map CO (2–1) line emission across the central 3' × 4' (8.5 × 11.3 kpc²) star-forming disk (Figure 1). They include 12 m, 7 m, and total power observations to recover emission on all scales, achieve 1'' (47 pc) resolution, and reach an rms noise of 0.15 K over 2.5 km s⁻¹ and (1σ) sensitivity to the integrated line intensity of 1.1 K km s⁻¹ (7.5 M_⊙ pc⁻²) over 20 km s⁻¹.

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We assume a fixed Milky Way CO-to-H₂ conversion factor of ${\alpha }_{\mathrm{CO}}^{1-0}=4.4\,{M}_{\odot }$ pc⁻² (K km s⁻¹)⁻¹ (Leroy et al. 2011; Blanc et al. 2013a; Sandstrom et al. 2013), which includes a factor of 1.36 to account for heavy elements. We assume a CO (2–1)/(1-0) brightness temperature ratio of R₂₁ = 0.61 as measured by Cormier et al. (2018).

We identify 738 GMCs using CPROPS (Rosolowsky & Leroy 2006), an algorithm that identifies emission peaks and determines their macroscopic properties; we refer to E. Rosolowsky et al. (2018, in preparation) for further details. We find median cloud masses of 5.8 × 10⁵ M_⊙ and median radii of 75 pc.

We obtained MUSE observations at 1'' seeing (Figure 1) that achieve 02 astrometric accuracy (calibrated off Sloan Digital Sky Survey (SDSS) r-band imaging; Kreckel et al. 2017), and use LZIFU (Ho et al. 2016) to simultaneously fit the stellar continuum and emission lines. We reach a 3σ surface brightness sensitivity for Hα of 1.5 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻².

We correct for dust obscuration using the Balmer decrement assuming case B recombination, an electron temperature of 10⁴ K, a Fitzpatrick (1999) extinction curve, and a Milky Way value of R_V = 3.1 for all regions. This method shows good (∼5%) systematic agreement at high Σ_SFR with a hybrid Hα+24 μm dust correction, suggesting that no star-forming regions are completely obscured. Hα is detected across 95% of the map; however, Hβ is only detected in ∼50% of pixels (corresponding to morphologically diffuse Hα emission). We assume a fixed A_V = 1.3 mag where Hβ is not detected, consistent with typical H ii region values (0.5–1.5 mag) and ∼1 kpc integrated diffuse regions. We note that our results are not sensitive to this choice, as most of this more diffuse emission is subtracted from our SFR maps (Section 2.3).

We construct a catalog of 1502 H ii regions using HIIPhot (Thilker et al. 2000). We detect minimum Hα luminosities of 3 × 10³⁶ erg s⁻¹, with median luminosities of 10³⁷ erg s⁻¹ (comparable to the ionizing flux produced by a single O8V star; Schaerer & de Koter 1997) and radii of 35 pc (only marginally resolved). For each we calculate the gas-phase oxygen abundance using the theoretical strong line N2S2 diagnostic of Dopita et al. (2016).

We convert our Hα luminosities into SFR estimates following Murphy et al. (2011) as

$$\begin{eqnarray}&&\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})=5.37\times {10}^{-42}L({\rm{H}}\alpha )(\mathrm{erg}\,{{\rm{s}}}^{-1}).\end{eqnarray} \tag{ 1 }$$

We caution that on the scale of individual regions likely dominated by a single stellar population, the concept of a continuous SFR begins to break down (potentially leading to systematic underestimation of SFR by a factor of 2–3; Faesi et al. 2014).

The treatment of "diffuse" CO emission is an open, unsolved issue. While the existence of faint, spatially extended 12CO emission in some galaxies has been clearly established (Pety et al. 2013; Roman-Duval et al. 2016), the detailed structure and physical properties (e.g., density) of this gas—and its dependence on properties of the host galaxy—is less clear. In external galaxies, one cannot easily distinguish between a truly diffuse CO-emitting molecular phase and a uniform distribution of small clouds that are separated by less than the beam size. As the goal of this analysis is to compare the SF with the available molecular gas reservoir, we do not attempt to remove a diffuse CO gas component from our data.

As shown in Kreckel et al. (2016), a significant fraction (∼20%–50%) of the Hα emission in NGC 628 arises from a diffuse ionized gas (DIG) component, but its association with SF is not clear (Zurita et al. 2000; Zhang et al. 2017). We choose here to model and subtract the DIG emission from our SF calculations, with the caveat that we could be systematically underestimating the SFR on large scales.

We leverage the [S ii]/Hα> 0.5 line ratio to identify 10% of the total Hα flux (41% of the pixels) as pure DIG emission in our extinction-corrected Hα line map (Kreckel et al. 2016). We interpolate across the entire map, and subtract this DIG model from our extinction-corrected Hα map (Figure 1). This removes 16% of the flux at the location of cataloged H ii regions, and results in a total diffuse fraction of 36%.

The tight correlation between SFR surface density and molecular gas surface density observed on >kpc scales in galaxies (Bigiel et al. 2008, 2011; Leroy et al. 2013; Utomo et al. 2017) breaks down on smaller scales due to stochastic sampling of the evolution of individual molecular clouds and SF regions (Onodera et al. 2010; Schruba et al. 2010; Kruijssen & Longmore 2014; Jameson et al. 2016). This is apparent in NGC 628 (Figure 1) by the clear displacement of the Hα and CO emission due to time evolution combined with the motion of the spiral pattern around the disk (Schinnerer et al. 2017). Figure 2 explores how the inferred depletion times and their scatter change over 50–500 pc scales. Individual data points show the surface density in (Nyquist sampled) apertures detected in both tracers uniformly sampling the emission maps at signal-to-noise ratio (S/N) > 3. The inset histograms show that a significant number of regions (50%–75%) are detected in only one tracer.

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We measure median gas depletion times of 1–3 Gyr, consistent with what was previously found for NGC 628 on ∼400 pc (Rebolledo et al. 2015) and 750 pc (Bigiel et al. 2008; Leroy et al. 2008, 2013) scales. At scales below 300 pc the molecular gas and SFR surface densities are largely uncorrelated (Spearman's rank correlation coefficient ρ ≈ 0.3), and even on larger scales the correlation remains weak (ρ ≈ 0.5). This weak correlation, combined with the large number of regions detected in only one tracer, implies that there is only a short overlap phase between molecular gas and young stars.

We observe an increased scatter in the depletion time (σ ≈ 0.4 dex) on small (<300 pc) scales, consistent with what has been observed in M51 (Blanc et al. 2009), M33 (Schruba et al. 2010), and the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC; Jameson et al. 2016). By combining our results on small scales with complementary measurements for NGC 628 from the HERA CO-Line Extragalactic Survey (HERACLES) survey (Leroy et al. 2013), we can trace the change in scatter from 50 pc to 2.4 kpc scales (Figure 3), observing a flattening in the scatter below ∼300 pc.

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If neighboring star-forming regions are independent and uncorrelated, with evolutionary cycling as the only source of scatter, then we naively expect this relation to follow a simple power law (σ ∝ R⁻¹; Leroy et al. 2013). However, accounting for additional scatter from the cloud or H ii region mass spectrum, flux evolution within a single evolutionary phase, and sensitivity limits, we expect uncorrelated SF to result in a flattening at the smallest spatial scales (Kruijssen & Longmore 2014; Kruijssen et al. 2018). Similarly, the smallest apertures contain on average only a single GMC and H ii region, which causes the scatter to decrease. The observed trend agrees qualitatively with the predictions of the Kruijssen & Longmore (2014) model (Figure 3), where for reference we show a curve of the model assuming standard parameter values, specifically measured within NGC 628 when possible (Chevance et al. 2018).

Given our large sample of 738 GMCs and 1502 H ii regions, we expect some fraction of these will currently exist in a short overlap phase (Kawamura et al. 2009). To compare with cloud-based studies in the Milky Way and Local Group galaxies, we crossmatch all GMC and H ii region centers (crossmatch tolerance of 05 ≈ 20 pc) and find 74 matches (Figure 4, left). By eye, >90% of these look like associated objects and not chance alignments in crowded regions. The small fraction of overlapping regions implies that there is a quick time evolution between molecular gas clouds and young stars.

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We infer integrated cloud-scale depletion times (M_GMC/SFR) of 1–10 Gyr, with a median value (3 Gyr) that is slightly longer than the depletion times that we measure over larger scales (Figure 2). As each GMC may collapse to form multiple stars and star clusters, all additional H ii regions within the GMC footprint are also included in calculating the associated SFR. We note that GMCs that are not fully decomposed could bias us to longer depletion times.

As the typical GMC size is larger than the typical H ii region (75 versus 35 pc in radius, Figure 1), we perform a second catalog match by loosening the requirement that the selected GMCs must have H ii region counterparts within 05, and instead sum up all H ii regions where the center falls within a given GMC's footprint. By selecting for peaks in the molecular gas distribution and measuring the associated SFR, an approach that biases us to longer depletion times (∼10 Gyr), we find 162 GMCs with associated SF (Figure 4, right), of which 40% have two or more associated H ii regions.

Milky Way studies (Lada et al. 2010; Murray 2011; Evans et al. 2014; Vutisalchavakul et al. 2016) show systematically shorter (100 Myr to 1 Gyr) depletion times (Figure 4), with over two orders of magnitude scatter (partly driven by methodological differences between studies). We find good agreement when extrapolating the trend identified by Vutisalchavakul et al. (2016), though our clouds are an order of magnitude more massive. Few such cloud-scale studies are available for external galaxies. Ochsendorf et al. (2017) observed long (∼1 Gyr) depletion times as a function of GMC mass in the LMC. Targeting H ii regions in NGC 300, Faesi et al. (2014) measured significantly short (230 Myr) depletion times on 250 pc scales. We note that studies preselecting only star-forming regions biases their results to shorter depletion times (Kruijssen et al. 2018), just as our preselection of GMCs (Figure 4, right panel) biases us to longer depletion times.

We observe ∼0.3 dex scatter in τ_dep on large scales. In M51, Meidt et al. (2013) and Leroy et al. (2017) found such variations to correlate with the apparent gravitational boundedness of the gas, while theories focused on the gravitational free-fall time predict correlations between τ_dep and the local mean cloud density. We test for such variations by calculating τ_dep at 500 pc scales and then correlating this with the local mass-weighted mean properties of the molecular gas. This methodology (Leroy et al. 2016) tests how the mean cloud-scale properties affect the depletion time.

In Figure 5 we consider trends with the molecular gas, SFR, and stellar surface densities. The latter is modeled from Spitzer imaging and cleaned of non-stellar emission (Querejeta et al. 2015). We also explore the impact of local physical conditions, including the molecular gas boundedness ($B\equiv {{\rm{\Sigma }}}_{\mathrm{mol}}/{\sigma }_{v}^{2}$, where σ_v is the line equivalent width), gas-phase metallicity measured within H ii regions, and H ii region clustering (parameterized by n₃, the average projected distance to the three nearest neighbors).

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We observe the strongest correlation with SFR surface density; however, this parameter covers a wider dynamic range than the molecular gas surface density (which shows no correlation). Random sampling of the CO surface densities does not change the strength of this correlation, suggesting that it is purely driven through the inverse relationship with τ_dep. The central star-forming ring (at high stellar-mass surface densities) shows systematically longer depletion times (4–8 Gyr), though the reported decrease in CO-to-H₂ conversion factor in the center implies an overestimation by up to a factor of two (Blanc et al. 2013a; Sandstrom et al. 2013) but cannot fully account for the offset that we see. Gas that is more bound (larger B) was found in M51 to exhibit a shorter depletion time (Leroy et al. 2017); however, we observe no such correlation in NGC 628. This suggests that the key driver for long depletion times in M51 is not simply the virial parameter of the molecular gas, but rather large-scale dynamical effects as suggested by Meidt et al. (2013). Other trends in NGC 628 are only tentative (ρ ≤ 0.3), but suggest shorter depletion times occur in the outer disk (lower stellar-mass surface densities) where H ii regions are more clustered (lower n₃). A larger sample of galaxies is needed to expand the parameter space explored here.