The Gas–Star Formation Cycle in Nearby Star-forming Galaxies. I. Assessment of Multi-scale Variations

PHANGS–ALMA imaged the CO(2–1) emission in our targets using the ALMA 12 m, 7 m, and total power antennas. In this paper, we use a pilot sample observed during Cycle 1 (project 2012.1.00650.S; NGC 0628) and Cycle 3 (projects 2013.1.00925.S and 2013.1.00956.S; remaining galaxies except NGC 5194). We chose our target area to match the region of active star formation indicated by an intensity contour of 1 MJy sr⁻¹ in the WISE 22 μm image.

We use integrated intensity maps constructed from the data cubes delivered in PHANGS–ALMA internal data release 3.3 as our starting point. The construction of these maps is described in A. K. Leroy et al. (2019, in preparation), and their properties are summarized in Table 2. Briefly, these were imaged in CASA 5.4.0. They should be sensitive to emission on all spatial scales due to the inclusion of data from both the 12 m array and the Morita Atacama Compact Array. Four of the galaxies (NGC 3627, NGC 4254, NGC 4321, and NGC 5068) were observed in two separate large (100+ pointings) mosaics. We matched the beams of the two halves via convolution and combined them via linear mosaicking. This results in moderately different noise properties for the two halves of the map. After calibration and imaging, the resulting data cubes were convolved to have a round beam. The typical rms noise in brightness temperature units is σ_rms ≈ 0.17 K per 2.5 km s⁻¹ channel, but varies slightly between cubes.

Table 2.  Datasets and Parameters Used for CO and Hα Maps

Name	FoVCO	σCO	θCO	θbest,CO	LCO	fCO	θHα	θbest,Hα	fN ii	THα	LHα,int	SFR	fDIG	$\mathrm{log}{L}_{{\rm{H}}\alpha ,\min }$
	('' × '')	(K km s−1)	('')	(pc)	(108 K km s−1pc2)		('')	(pc)			(1041erg s−1)	(M⊙ yr−1)		(erg s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
NGC 0628	319 × 319a	0.8	1.12	60	1.85	0.72	1.73	90	0.019	0.938	0.7	0.4	0.39	37.5
NGC 3351	172 × 166a	0.7	1.46	80	0.92	0.65	1.16	60	0.209	0.972	0.6	0.3	0.56	36.5
NGC 3627	158 × 273a	0.9	1.57	90	6.14	0.91	1.44	80	0.223	0.986	1.6	0.9	0.41	36.7
NGC 4254	199 × 232a	0.4	1.71	140	11.88	0.86	1.52	130	0.235	0.979	4.8	2.6	0.40	36.6
NGC 4321	237 × 211a	0.5	1.64	130	5.67	0.76	1.28	100	0.112	0.838	1.6	0.9	0.58	36.5
NGC 4535	145 × 199a	0.5	1.56	120	2.89	0.72	1.23	100	0.168	0.915	0.8	0.4	0.49	36.6
NGC 5068	269 × 274a	1.3	1.00	30	0.06	0.31	1.34	40	0.0770	0.993	0.3	0.2	0.35	37.0
NGC 5194	280 × 180b	4.4	1.06	50	10.97	0.95	1.83	80	0.228	0.983	1.4	0.7	0.47	37.6

Notes. Summary of data products used for the CO and Hα emission as well as relevant parameters derived for each data product. The information provided for column: (1) galaxy name; (2) size of the area mapped in CO line emission; (3) characteristic 1σ sensitivity corresponding to the average rms across the integrated intensity CO map at the resolution given in column (4); (4) angular resolution refers to the round Gaussian CLEAN beam used for restoration, except for NGC 5194 where the geometric mean of the elliptical CLEAN beam is given; (5) highest native spatial resolution achieved in CO (if the resolution of the CO data sets the limiting spatial scale of our analysis, it is highlighted in bold-face); (6) integrated CO line flux present in the final maps used for our analysis (i.e., after applying a threshold at 12.6 M_⊙ pc⁻² at 140 pc resolution and artifact mask, within the common field of view); (7) fraction of integrated CO emission contained in maps used for the analysis (see column (6)) relative to integrated CO emission in the PHANGS–ALMA internal data release v3.3 cube (the delivered zeroth moment maps have a much better flux recovery (≳95%); the drop in flux between the delivered maps and our input maps is mostly due to the CO threshold, which is set by the CO map with the poorest sensitivity at 140 pc scale (NGC 5194, $3-\sigma ({{\rm{\Sigma }}}_{\mathrm{mol},140\mathrm{pc}})\sim 12.6$ M_⊙ pc⁻²)); (8) angular resolution of the Hα maps (θ_Hα) as determined on stars in the maps; (9) highest native spatial resolution achieved in Hα (if the resolution of the Hα data sets the limiting spatial scale of our analysis, it is highlighted in bold-face); (10) N ii fraction f_{N ii} as determined by taking the filter response curves into account (see the text for details); (11) transmission correction for Hα T_Hα as determined by taking the filter response curves into account (see the text for details); (12) integrated Hα line emission present in the final maps used for our analysis (i.e., within our field of view and with foreground stars masked); (13) SFR based on integrated Hα line emission (from column (13)) present in the map used for analysis; (14) contribution of diffuse ionized gas emission to total Hα emission; (15) minimum H ii region luminosity, calculated as the Hα surface brightness threshold integrated over the beam area, corresponding to our diffuse ionized gas separation strategy.

^a12CO(J = 2 → 1) observed by ALMA; A. K. Leroy et al. (2019, in preparation). ^b12CO(J = 1 → 0) observed by IRAM; Schinnerer et al. (2013), Pety et al. (2013). ^cCTIO 1.5 m, 145 × 145 field of view, CT6586/20 filter, SINGS fifth delivery document (http://irsa.ipac.caltech.edu/data/SPITZER/SINGS/doc/sings_fifth_delivery_v2.pdf). ^dKPNO 2.1 m, 102 × 102 field of view, KP1563 filter, SINGS fifth delivery document. ^eKPNO 2.1 m, 102 × 102 field of view, KP1564 filter, SINGS fifth delivery document. ^fMPG 2.2 m/WFI, 16' × 16', 856 filter; A. Razza et al. (2019, in preparation). ^gCTIO 1.5 m, 102 × 143 field of view, MCELS6568/30 filter; Meurer et al. (2006).

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We use the integrated intensity maps delivered in the internal data release v3.3. These are constructed by applying a "broad" signal identification mask to the spectral line cube before summing all valid pixels across the observed velocity range. Specifically, the broad mask is the logical union of two signal identification masks, the first generated from the data cube at the best available resolution and the second from a version of the cube that has been smoothed to a spatial resolution of 500 pc. In both cases, we identify emission above 3.5σ in three consecutive channels of the cube, and expand it to include contiguous regions in (x, y, v) space that show emission above 2σ over two consecutive channels. The resulting "broad" integrated intensity maps have high completeness, meaning that they include most CO emission in the cube, even emission present at only modest signal-to-noise. More quantitatively, the flux recovery in the v3.3 broad integrated intensity maps (which are our input maps for the analysis) varies between 93% (NGC 4321) and 99% (NGC 3627) of the total CO flux that is present in the input best-resolution data cube (see also the discussion in Sun et al. 2018). Sensitivity estimates for these integrated intensity maps are given in Table 2. These are spatial averages of the sensitivity across each map, calculated as ${\sigma }_{\mathrm{RMS}}\times \sqrt{N}\times {\rm{\Delta }}v$, where N is the number of channels in the signal identification mask for that sightline, and Δv is the channel width. The equivalent inclination-corrected 1σ integrated molecular mass surface density sensitivity limits vary between 2.5 and 7.4 M_⊙ pc⁻² across the PHANGS galaxies, assuming a standard Galactic conversion factor of α_CO = 4.35 M_⊙ pc⁻² (K km s⁻¹)⁻¹(Bolatto et al. 2013) and a ¹²CO(J = 2 → 1) to ¹²CO(J = 1 → 0) brightness temperature ratio of R₂₁ = 0.7.

For NGC 5194 (M51), we use the 1'' resolution-integrated CO(1–0) image from PAWS (Schinnerer et al. 2013). PAWS combined observations from the IRAM PdB interferometer and 30 m single dish telescope, ensuring that the map includes emission on all spatial scales. Details of the observations and data reduction are presented in Pety et al. (2013). The PAWS map has an average 1σ sensitivity of ∼4.4 K km s⁻¹, corresponding to an integrated mass surface density sensitivity of ∼19 M_⊙ pc⁻².

We used narrowband Hα imaging to trace recent massive star formation, drawing from a mixture of new and literature data. For the literature data, we adopted the image that best matched the following criteria: (i) a field of view (FoV) sufficient to cover the CO data, (ii) angular resolution similar to the CO data, and (iii) a corresponding R-band image observed with the same telescope under similar conditions. For several galaxies where no literature data matched our criteria, we obtained new Wide-Field Imager (WFI) narrowband and R-band imaging using the MPG/ESO 2.2 m telescope. Details on the data sets used can be found in Table 2.

Specifically, we used data from the Spitzer Infrared Nearby Galaxies Survey (SINGS) ancillary survey (Kennicutt et al. 2003) for NGC 0628, NGC 3351, NGC 4254, NGC 4321, and NGC 5194. Details of the observations, including the associated R-band data used for continuum subtraction, can be found in the SINGS fifth delivery document.²⁴ The continuum R-band data reach a depth of 25 mag arcsec⁻² with a signal-to-noise of ∼10. The Hα narrowband filter data were observed for 1800 s.

NGC 5068 was observed in the Hα narrowband and R band as part of the Survey for Ionization in Neutral Gas Galaxies (SINGG; Meurer et al. 2006) at the CTIO. NGC 5068 was also observed for 1800 s in the narrowband, and 360 s in the R band.

For NGC 3627 and NGC 4535, the literature data were not of sufficient quality to match our criteria. Therefore, we used data from a new survey of PHANGS targets using the WFI instrument on the MPG/ESO 2.2 m telescope at La Silla Observatory. This survey obtained both the narrowband Hα and Rc band using the WFI. The galaxies were placed in a single CCD, avoiding chip gaps, allowing an uninterrupted FoV of 16' × 16'. These data were astrometrically and photometrically calibrated using Gaia DR2 catalogs cross-matched to all stars in the full FoV of the WFI images. Full details of this survey, including observations, reduction, calibration, and sky subtraction can be found in A. Razza et al. (2019, in preparation).

2.2.1. Sky Subtraction

2.2.2. Seeing and Astrometry

2.2.3. Continuum Subtraction

2.2.4. Correction for Transmission, [N ii] Contamination, and Galactic Extinction

2.2.5. Filtering Out Emission from Diffuse Ionized Gas

2.2.6. No Correction for Internal Extinction

We threshold both the CO and Hα images before comparing them. This fixes the total flux used in the analysis across scale. It also ensures that we have high confidence that all emission entering the analysis corresponds to real high-mass star formation or massive concentrations of molecular gas.

The total CO and Hα fluxes after thresholding within the common FoV of our 140 pc resolution images are tabulated in Table 2. For Hα, our threshold is set by our DIG removal strategy (see Section 2.2.5). For CO, we impose a mass surface density threshold that allows us to work exclusively with securely detected pixels across all our CO maps. For the CO emission, we do not impose any filtering analogous to what we used to subtract the DIG (from the Hα maps). Our reasoning is that while "diffuse" CO emission has been identified in galaxies (e.g., Pety et al. 2013; Caldú-Primo et al. 2015; Roman-Duval et al. 2016), the physical nature of this gas remains unclear. Extended CO emission still does indicate the presence of molecular gas, which may very well be in marginally bound clouds and available for star formation. This is not symmetric to the DIG, which represents emission not associated with local massive star formation. This is an important topic for future exploration, but in the interests of maintaining a simple, physically motivated, and reproducible approach, we do not filter the CO emission.

For reference, our adopted CO threshold is roughly equivalent to a cut of A_V ≈ 1 mag (e.g., Bohlin et al. 1978). This is close to the limit of A_V = 2 mag used by Heiderman et al. (2010) to define the boundaries of local molecular clouds in highly resolved maps. That is, our CO threshold already identifies only pixels where the emission averaged over a 140 pc beam matches that seen within highly resolved local GMCs.

Typically, this threshold retains about 75% of the total flux in the input CO data cube, but this drops to 30% in the case of the low-mass galaxy NGC 5068.

We compare the distributions of CO and Hα at a series of common spatial resolutions up to 1.5 kpc. The best physical resolution shared by our entire sample is 140 pc, which is set by the resolution of our CO map of NGC 4254. We adopt 140 pc as the fiducial measurement scale for our analysis.

To convolve the data, we smooth the thresholded images using Gaussian convolution kernels. For each convolved map, we sort the map pixels by intensity (from brightest to faintest), and reject the faintest pixels that together contribute 2% of the total flux. We verify that this additional clipping level is sufficient to remove faint halos that are convolution artifacts. This step sets a large amount of area to have zero intensity at each scale without significantly affecting the flux in the analysis. We test that other reasonable rejection criteria (between 1% and 5%) do not affect our conclusions.

Finally, we note that, while we apply the same methodology to the CO and Hα maps, the output depends on the intrinsic distribution of the emission in the input map. Faint emission located next to a bright peak in the input map will tend to be recovered in the lower-resolution map, for example, while isolated faint emission is more likely to fall beneath the 2% clipping threshold in the lower-resolution maps. In this sense, our smooth-and-clip strategy is likely to impact our CO and Hα maps differently. Our method for DIG removal often results in high-brightness regions being surrounded by zero-valued pixels. On the other hand, the mass surface density threshold applied to construct our CO maps tends to yield contiguous regions of relatively faint emission. We note this as another potential area for improvement.

Using the pairs of matching resolution CO and Hα maps, we classify each pixel into one of four categories.

• 1.  
  CO only—only CO emission is present; Hα emission is not detected at this position and scale.
• 2.  
  Hα only—only Hα emission is present; CO emission is not detected at this position and scale.
• 3.  
  Overlap—both CO and Hα emission are present.
• 4.  
  Empty—neither CO nor Hα emission is present.

This classification is scale-dependent, e.g., a pixel may be classed as empty at high resolution, CO only at intermediate resolution, and overlap at low resolution. At high resolution, a non-negligible fraction (on average around 60%–70%) of pixels falls in the last category (see Figure 2), indicating that large areas of galaxy disks are not directly filled with star-forming interstellar medium (ISM). At coarse resolution, the number of empty pixels decreases significantly, giving the impression that the star-forming ISM is ubiquitous. The differences among distributions of empty pixels among galaxy disks is thus a potentially interesting diagnostic of ISM evolution and galaxy morphology. In this paper, however, we are most interested in the impact of host galaxy properties and observing scale on the relative configuration of the molecular and ionized gas phases, so we do not analyze the fraction of empty pixels in detail.

At each spatial scale after removing the empty pixels, we calculate the fraction of pixels in each of the first three categories, i.e., with a detection of CO, Hα, or both. At fixed scale, these fractions may be plotted as a pie chart (Section 4.1). The evolution of these fractions as a function of scale can be illustrated using a bar graph (Section 4.2).

To assess the uncertainty on our measurements, we repeated our analysis while varying the thresholds for CO and Hα flux. We tested varying the CO threshold between 10 and 15M_⊙ pc⁻² at 140 pc scale, and thresholding at the native resolution of the CO maps using signal-to-noise criteria (i.e., 3 and 5σ cuts in integrated intensity). We also varied the unsharp masking parameters used for DIG removal, varying the size of the smoothing kernels by 25%, the gain in the first subtraction step by 25%, and the signal-to-noise threshold of the mask by ±1σ. We adopted the minimum and maximum values of the pixel fractions obtained from this suite of tests as an indication in the uncertainty of our measurements.

Figure 2 shows results for all galaxies at 140 pc resolution in map form. Table 3 summarizes the statistics for these maps, and Figure 3 visualizes these statistics as pie charts. Following Section 3, the error bars in Table 3 show the effect of varying our CO and Hα detection thresholds across their plausible ranges.

Table 3.  Line-of-sight Fractions at 140 pc Scale

Name	CO only	Hα only	overlap
	(%)	(%)	(%)
NGC 0628	${42}_{27}^{54}$	${19}_{12}^{32}$	${38}_{34}^{42}$
NGC 3351	${15}_{8}^{35}$	${66}_{63}^{81}$	${19}_{13}^{24}$
NGC 3627	${40}_{33}^{47}$	${17}_{10}^{25}$	${43}_{37}^{49}$
NGC 4254	${52}_{39}^{67}$	${11}_{6}^{17}$	${37}_{28}^{43}$
NGC 4321	${41}_{29}^{53}$	${27}_{18}^{40}$	${32}_{23}^{38}$
NGC 4535	${46}_{37}^{61}$	${23}_{13}^{38}$	${31}_{26}^{37}$
NGC 5068	${2}_{1}^{7}$	${86}_{73}^{90}$	${12}_{10}^{20}$
NGC 5194	${55}_{52}^{59}$	${6}_{4}^{8}$	${38}_{35}^{39}$
Median	42	23	37
Mean	37	32	31

Note. Fraction of sightlines with CO emission only, Hα emission only, and both CO and Hα emission. These fractions represent the numbers corresponding to the pie charts shown in Figure 3. The sub- and superscripts correspond to the minimum and maximum values obtained when different thresholds for positive detection of CO emission and DIG suppression are used (see the text). The mean (median) values reported in the final row are the means (medians) of our fiducial measurements reported for a given sightline category. Note that the medians are not re-normalized, thus the sum will not add up to 100%.

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At this resolution, emission from one or both of these tracers is typically present across 50% or more of our survey area. Of the detected sightlines, CO only sightlines (dark blue) are the most common detections in more than half of our targets (namely NGC 0628, NGC 4254, NGC 4321, NGC 4535, NGC 5194). In two targets Hα only sightlines dominate (NGC 3351 and NGC 5068). NGC 3627—the most inclined galaxy in our sample with i ∼ 55°—is our only target where sightlines with overlapping CO and Hα emission are the most common.

Across the sample, the median fraction of detected sightlines that contain CO only emission is ∼40%. This is comparable to the fraction of overlap sightlines (∼40%), while the fraction of Hα only sightlines is typically only ∼20%. The clear separation of the CO and Hα emission at our high working resolution (i.e., the lower overlap fraction compared to sightlines with one tracer only), and the detection of widespread CO emission above 12.6 M_⊙ pc⁻² without associated Hα emission (typically CO only sightlines are more than 2× more abundant than Hα only ones) are two main results of this paper.

Table 4 (see also Figure 9) shows the results when we consider how the CO and Hα fluxes (rather than the number of sightlines) are distributed between different categories, i.e., instead of the number of pixels in each category, we consider their respective contribution to the total CO or Hα flux. On average, we find that ∼40% of the CO flux at 140 pc resolution remains unassociated with bright Hα emission. This is lower than the ∼60% of CO only sightlines, but implies the same qualitative conclusion that there is a significant mass fraction of CO-traced molecular gas without Hα emission.

We find a greater discrepancy between the distributions of flux and sightlines for Hα. At our fiducial 140 pc scale, the median overlap fraction for Hα-emitting sightlines is about two-thirds across our sample. These same regions contribute a median of ∼80% of the total Hα flux. These results indicate that these overlap sightlines, which show both CO and Hα, tend to have higher Hα intensity than sightlines probing Hα only emission. This agrees with a visual inspection of the maps. Since these overlap regions are by definition co-spatial with CO-emitting molecular gas, they likely suffer from dust attenuation that we do not account for in the processing of our Hα maps (see Sections 2.2.4 and 2.2.6). The true flux contribution of these regions is thus probably higher than the ∼80% that we measure.

Galaxy centers can contribute significantly to the total flux while covering only a few sightlines. Figures 1 and 2 show that the galaxy centers in our sample tend to have overlapping high intensity CO and Hα emission. In the Appendix, we test the degree to which the centers drive the discrepancies between our flux- and sightline-based measurements. To do this, we repeat the calculation considering only the main galaxy disks, i.e., excluding the region within a radius of 1 kpc of the reference position listed in Table 1 for all galaxies. For NGC 3351, we follow Sun et al. (2018), who adopted a larger radius of 1.5 kpc so that the visually distinct inner disk is entirely inside the central region of NGC 3351. The regions that we define as central are indicated by yellow ellipses in Figure 2. Excluding the central regions from our analysis improves the agreement between the flux- and sightline-based measurements for NGC 3351, but does not significantly alter our results for other galaxies.

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Relation to morphology. In most galaxies, the CO-emitting sightlines form coherent, kiloparsec-scale structures such as spiral arms, bars, or rings in the disk. The sightlines probing Hα emission appear more irregular and patchy than the CO emission, though they generally trace out the same galactic structures as the CO. Overlap sightlines with both CO and Hα emission appear prevalent in the centers of almost all targets (indicated by the yellow ellipse in Figure 2) and along the major galactic structures traced by CO emission.

In several galaxies with strong spiral arms, we find a pronounced offset between sightlines probing Hα emission and those with CO only. This is most evident along the spiral arms of NGC 0628, NGC 4321, and NGC 5194, but the same pattern can be seen in NGC 4254, and NGC 4535. The sense of the offset is that the sightlines with Hα (both overlap and Hα only) tend to lie along the convex side of the arm, offset from the CO only ones. Assuming that the spiral arms are trailing, this implies that the Hα only and overlap sightlines appear offset downstream from the CO only sightlines (when observing them inside their co-rotation).

The overlap in the central regions appears strong for the barred galaxies NGC 3351, NGC 3627, NGC 4321, and NGC 4535. In several of these targets, we see overlapping CO and Hα in the central region, and then again in the region outside the stellar bar. Along the bar itself, we see predominantly CO only emission, though this emission is not always present along the full length of the bar (e.g., see NGC 3351). A similar feature appears in NGC 5194, with CO only sightlines appearing along segments of the inner spiral arms (features associated with strong streaming motions by Meidt et al. 2013).

Here and throughout our analysis, NGC 5068 shows a distinct morphology: a patchy, incoherent distribution of CO- and Hα-emitting regions. This galaxy has the lowest stellar mass, lowest metallicity, and latest Hubble type in our sample. It resembles M33, NGC 300 and the Large Magellanic Cloud (LMC), where similar observations have found tracers of gas and star formation to be incoherent on small scales (Kawamura et al. 2009; Onodera et al. 2010; Schruba et al. 2010; Gratier et al. 2012; Faesi et al. 2014). Those studies have postulated that star formation in dwarf spirals proceeds in a stochastic way, without any large-scale organization.

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Trend with galactocentric radius. Visual inspection of the maps in Figure 2 suggests that many of the Hα only sightlines occur toward the outer edges of our maps. We quantify this in Figure 4, where we plot the CO only, Hα only and overlap fractions in annuli of width 0.2R₂₅. Indeed in all galaxies except NGC 5068, there is a clear trend for the Hα only fraction to increase with increasing galactocentric radius. This increase seems more pronounced in barred galaxies (plotted with circles and solid lines in Figure 4). At the same time the radial distribution of the CO sightlines (both CO only and overlap) shows on average a stronger (decreasing) trend for barred galaxies than for the three non-barred ones, although also with a much wider spread in values. A possible explanation for these trends is the fact that photoionization bubbles expand more quickly in low-density media because the Strömgren radius scales as ρ^−2/3, thus larger H ii regions are expected at larger radii where the gas surface density is presumably lower. Conversely, this decrease in gas surface density should lead to more isolated patches of molecular gas. As many other galaxy parameters vary with galactocentric radius, e.g., metallicity, a secure interpretation of these trends requires further investigation using a larger sample with better sampling of galaxy morphological type and stellar mass.

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Figures 5 and 6 illustrate the spatial distribution of CO and Hα emission as we vary the resolution of the maps (showing maps at 140, 300, 500, and 1000 pc). In Figures 7 and 8, we plot the covering fractions of CO only, Hα only, and overlap regions as a function of spatial scale (from 140 pc up to 1.5 kpc in steps of 100 pc starting at 200 pc).

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From 140 to 500 pc resolution. As we blur the maps from 140 to 500 pc resolution, sightlines where CO and Hα emission coincide become more prevalent in all galaxies. By 500 pc resolution, overlapping sightlines dominate (>60%) while CO only sightlines make up <25% of the emitting sightlines in all targets. For most targets, we see a significant slow-down in the increase of the fraction of CO only sightlines at spatial scales of ∼150–200 pc. The exceptions are NGC 4254 and NGC 5194, where the CO only fraction continuously decreases from 140 pc to larger scales.

Most of the evolution of overlap fraction and structure of CO only emission occurs over this range, 140–500 pc. As the resolution degrades, the detailed morphology visible at high resolution evolves toward a simple, amorphous geometry. Structures that were prominent at sharper resolution, such as spiral arms and bars, disappear and emission fills in the region between galactic structures. As this occurs, the region covered by overlapping CO and Hα emission grows from patches to form coherent structures along spiral arms and stellar bars. Over this range, in all but two galaxies (NGC 3351 and NGC 5068) the Hα only covering fraction shows less significant evolution than the CO only or overlap fraction. Three-quarters of our sample show no variation in Hα only covering fraction for scales of 300 pc and larger. In these cases, the Hα only regions often appear as mostly isolated, compact regions, often located at large galactocentric radius.

Beyond 500 pc resolution. As we blur the maps to resolutions greater than 500 pc, the overlap sightlines tend to become unified structures that include the galaxy nucleus. By 1.0 kpc resolution, the CO only (dark blue) sightlines tend to no longer trace galactic structures, but rather appear spread across the galaxy. This heavy overlap between CO and Hα emission at coarse resolution agrees with numerous previous studies showing a tight correlation between these quantities at this resolution (e.g., Bigiel et al. 2008; Leroy et al. 2008, 2013; Liu et al. 2011; Bolatto et al. 2017).

Overall, the changes in morphology and covering fraction beyond 500 pc resolution appear less pronounced than those between 140 and 500 pc. For the majority of our sample, the most significant changes in the fraction of overlapping (lavender) sightlines occur between 140 and 500 pc resolution. The fact that this overlap emerges only after averaging agrees with previous observations of increasing scatter in the correlation between molecular gas and star formation tracers with decreasing spatial scale (e.g., Bigiel et al. 2008; Onodera et al. 2010; Schruba et al. 2010; Leroy et al. 2013; Kruijssen et al. 2019).

The relative contributions of CO only, Hα only, and overlap sightlines vary dramatically with spatial scale. At ∼140 pc resolution, we find a roughly equal number of CO-emitting sightlines (at and above our H₂ surface density threshold of 12.6 M_⊙ pc⁻²) with and without associated Hα emission in our sample galaxies. The CO only sightlines contribute ∼40% of the total CO flux above this threshold. This implies the presence of a significant reservoir of quiescent molecular gas.

This apparently quiescent molecular gas could have several distinct physical origins. It may be genuinely non-star-forming, due to large-scale dynamical effects that stabilize the gas (e.g., Meidt et al. 2013, 2019) or the disruptive effect of stellar feedback (e.g., Krumholz & McKee 2005; Ostriker et al. 2010). Alternatively, it could be forming stars that are not massive enough to generate the ionizing photons needed for significant Hα emission. High-mass stars could be forming behind a screen of dust that obscures Hα photons (see Table 2). Or the gas could still be in the process of collapsing, reflecting recently formed molecular clouds that have not yet "ramped up" star formation (e.g., Lee et al. 2016).

Quiescent gas and spatial scale. This quiescent molecular gas is only accessible thanks to the high physical resolution of our data. For our adopted CO and Hα thresholds, the fraction of CO only sightlines decreases from ∼40% at 140 pc resolution to ≲15% at 500 pc. Our adopted fiducial scale of 140 pc is a pragmatic choice, not a physical one. For five galaxies in our sample, the best-matching spatial resolution of our data is 90 pc or better, allowing us to test whether the fraction of CO only sightlines in galaxies is larger at higher physical resolution. We repeated the analysis described in Section 3 for the CO and Hα maps of these galaxies at 90 pc resolution, using a threshold of 19.5 M_⊙ pc⁻² (i.e., the 3σ mass surface density sensitivity of our NGC 5194 data at 90 pc resolution). We find that the fraction of CO only sightlines in all galaxies shows a relative increase of 5%–20% as the resolution improves from 140 to 90 pc. The fraction of Hα only sightlines typically shows a similar relative increase, while the fraction of overlap sightlines shows a relative decrease of ∼30% as the resolution improves.

At coarser resolution than 140 pc, the quiescent CO emission rapidly vanishes as the resolution is degraded. The rapid decrease in CO only sightlines between 140 and 500 pc resolution is accompanied by a significant increase in the fraction of overlap sightlines (from ∼30% to ∼65%) across this range of scales.

For most of our sample, the visible morphology of CO emission also changes over this spatial range: as the resolution degrades, the initially sparse, patchy overlap sightlines become more common, while the overlap regions spread out, replacing the CO only regions and covering the main morphological features of the galaxy. Scale-dependent variations in the fraction and spatial distribution of the Hα only sightlines are less marked in our current, small sample of galaxies. This is because the Hα only regions tend to be relatively isolated, distinct regions toward the outer parts of our maps.

At resolution coarser than ∼500 pc, the overlap sightlines cover most of the mapped area in all targets. At these scales, differences in the morphology of the CO and Hα emission disappear. Even major morphological features of galaxies (e.g., prominent spiral arms, very luminous H ii regions in outer disks) start to "wash out" and are mostly indistinguishable on spatial scales above ≳1.0 kpc.

Our results agree with previous observations showing how star formation scaling relations—i.e., the power law scaling between the molecular gas and SFR surface density, where SFR is typically traced by Hα emission—vary with spatial scale. Several studies have demonstrated that the scatter in the molecular gas depletion time decreases as the spatial scale of the molecular gas and SFR surface density measurements increases. These works include high-resolution studies of individual galaxies (e.g., Blanc et al. 2009; Onodera et al. 2010; Schruba et al. 2010; Kreckel et al. 2018; Kruijssen et al. 2019) and coarser-resolution studies of larger galaxy samples (Bigiel et al. 2008; Leroy et al. 2013). To our knowledge, our work here represents the best combination of resolution (140 pc across the sample) and sample size (eight galaxies) to date.

Under the assumption of simple steady-state cycling, every star-forming unit progresses from a cold gas cloud that is not yet forming stars (CO only) to one that is actively forming massive stars (overlap regions), to a region of massive young stars from which the cold gas has been entirely dispersed (Hα only). In this case, the covering fractions that we measure are a reflection of the time spent by a star-forming region in each of these different evolutionary phases.

Versions of this steady-state cycling heuristic have been used by Kawamura et al. (2009) to estimate the lifetimes of molecular clouds in the LMC, and by Gratier et al. (2012) and Corbelli et al. (2017) to characterize the cloud life-cycle in M33. Recently, Battersby et al. (2017) applied a similar approach to Milky Way observations to determine the timescales for dense molecular gas structures (i.e., clumps) to evolve from starless to star-forming. Schruba et al. (2010) invoked a similar cycling scenario to explain the scatter and bias in the molecular gas depletion time measured at high spatial resolution in M33. Feldmann et al. (2011) also considered this phenomenon in terms of the scatter (see also Leroy et al. 2013). Building on this work, Kruijssen & Longmore (2014) and Kruijssen et al. (2018) developed a general formalism to derive the evolutionary timescales of star-forming regions from concentric apertures centered on peaks identified at different wavelengths. This formalism has been applied to CO and Hα maps of the spiral galaxy NGC 300, an M33 analog, in order to estimate the typical lifetime of molecular clouds and characteristic duration of star formation feedback in that galaxy (Kruijssen et al. 2019). Analogous arguments have been used to infer timescales in other fields, including, e.g., to measure the life cycle of protostars (e.g., see the review in Dunham et al. 2014). All these methods require an externally calibrated fiducial clock, e.g., the time t_Hα over which an H ii region is visible, to translate between population/mass/area statistics and an absolute timescale.

Here we apply a simple version of this approach to molecular gas that is visible above a fixed surface density threshold, treating individual pixels as discrete star-forming units. The lifetime of the cold molecular gas in a star-forming unit is then

$$\begin{eqnarray}&&{t}_{\mathrm{gas}}={t}_{{\rm{H}}\alpha }\times \displaystyle \frac{{f}_{\mathrm{CO} \mbox{-} \mathrm{only}}+{f}_{\mathrm{overlap}}}{{f}_{{\rm{H}}\alpha \mbox{-} \mathrm{only}}+{f}_{\mathrm{overlap}}}={t}_{{\rm{H}}\alpha }\times {f}_{\mathrm{scale}},\end{eqnarray} \tag{ 1 }$$

where f_CO-only is the fraction of CO only sightlines, f_Hα-only the fraction of Hα only sightlines, and f_overlap the fraction of overlap sightlines. Then f_scale represents the scaling factor to translate from the fiducial timescale, here t_Hα, to the lifetime for a cold gas structure.

5.2.1. Timescales

Table 5 reports the results of Equation (1) applied to our sample at various scales using the numbers derived in Section 4. As the resolution improves (i.e., the spatial scale decreases), regions with overlapping Hα and CO emission tend to occupy a diminishing fraction of sightlines (see Figure 8). The ratio f_scale thus tends to increase for galaxies where CO only sightlines are prominent, while it decreases rapidly for galaxies where Hα only sightlines dominate (i.e., NGC 3351 and NGC 5068). If we were to improve upon our 140 pc resolution, we would expect these trends to continue. This highlights some natural next steps to improve on the current data treatment (see Section 5.5).

Table 5.  Inferred Relative Gas Cycling Timescales by Sightlines at Various Scales

Name	${f}_{\mathrm{scale}}=\tfrac{{f}_{\mathrm{CO} \mbox{-} \mathrm{only}}+{f}_{\mathrm{overlap}}}{{f}_{{\rm{H}}\alpha \mbox{-} \mathrm{only}}+{f}_{\mathrm{overlap}}}$
	140 pc	300 pc	500 pc	1000 pc
NGC 0628	1.4	1.2	1.0	0.9
NGC 3351	0.4	0.6	0.7	0.8
NGC 3627	1.4	1.1	1.0	0.9
NGC 4254	1.8	1.2	1.0	0.9
NGC 4321	1.3	1.0	0.9	0.8
NGC 4535	1.4	1.3	1.1	0.9
NGC 5068	0.1	0.5	0.7	0.8
NGC 5194	2.1	1.4	1.2	1.0
Median	1.4	1.2	1.0	0.9
Mean	1.2	1.0	1.0	0.9

Note. The reported values are derived using Equation (1) and need to be multiplied by the assumed t_Hα, i.e., the time an H ii region is visible above our thresholds. See the text for a discussion of reasonable values for t_Hα.

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For most of our targets, these measurements imply a median CO visibility timescale of 1.4× the Hα visibility timescale t_Hα at 140 pc resolution. Typical estimates for the visibility time of Hα are 5–10 Myr.²⁶ Binaries, extinction, and other effects may complicate the picture, but taking these numbers at face value, Table 5 suggests molecular cloud lifetimes of ∼10–15 Myr at our best resolution of 140 pc.

While there is a clear dependence on scale (and the data have some limitations, see Section 5.5), these short timescales are in reasonable agreement with measurements of molecular cloud lifetimes in other galaxies in the literature (see above). For the specific galaxies in our sample besides NGC 5068 and NGC 3351, our estimates also agree within a factor of ∼2 with cloud timescale estimates obtained by Chevance et al. (2019) applying the formalism of Kruijssen et al. (2018) to these systems. This robustness to adopted methodology suggests that both sets of results do indeed reflect the true underlying cycling times.

The order of magnitude of t_gas also agrees well with theoretical estimates of the timescale for star formation. It is comparable to the crossing or freefall time for individual molecular clouds (e.g., see Heyer et al. 2009; Fukui & Kawamura 2010 for typical cloud properties), including those in our sample (e.g., see Utomo et al. 2018 for direct estimates). Many models have taken either the crossing time (e.g., Elmegreen 2000) or the freefall time (e.g., Krumholz & McKee 2005) as the relevant timescale for star formation. Numerical models find similar results; e.g., based on recent highly resolved simulations of galaxy disks, Semenov et al. (2018) quote star formation timescales of ∼5–15 Myr. Our measurements support the idea that the onset of star formation and dispersal of clouds occur over roughly this timescale.

5.2.2. A More Dynamic View

Our maps show clear signatures of galactic dynamics. In addition to the high overlap fraction in most galaxy nuclei, we observe signatures of the suppression of star formation in bars and offsets between Hα and molecular gas emission along spiral arms.

Central regions. All our eight galaxies show prominent overlap regions in the central 1 kpc (see Figure 5). Close inspection of the CO intensity maps and Hα images presented in Figure 1 suggests that the overlap is arising mainly due to Hα emission related to (a) central star formation mostly distributed in so-called nuclear star-forming rings (e.g., NGC 3351 and NGC 4321 are listed in the AINUR catalog of Comerón et al. 2010) or along the stellar bar (in NGC 5068) or (b) the presence of AGNs (e.g., as good examples see NGC 3627, NGC 5194) where the Hα emission is coming from the ionized gas in the narrow-line region (e.g., in NGC 5194; Blanc et al. 2009). Thus, unlike the Central Molecular Zone in our own Galaxy, other nearby galaxies can show significant star formation, especially in the nuclear star-forming rings that are typically found in barred galaxies (see also the review by Kennicutt 1998). Our inability to discriminate between Hα emission arising from truly star-forming structures or from a central AGN is a caveat for the interpretation of our results in galaxy centers (see Section 5.4 for further discussion).

Stellar bars. Observational and theoretical work on the role of stellar bars in star formation still draws somewhat conflicting conclusions about the roles for these structures. It is clear that bars help drive material to the central regions of galaxies, but whether they enhance or suppress star formation along the way remains debated (e.g., see Meidt et al. 2013; Renaud et al. 2016; James & Percival 2018). Two of our targets, NGC 3351 and NGC 4535, show strong signatures of suppressed star formation along a strong stellar bar. Two more, NGC 3627 and NGC 4321, show some evidence of this phenomenon.

The signatures are a clear gap between the spiral arms, where overlapping CO and Hα emission appears common, and the center. CO emission remains visible in this gap, while Hα emission appears to be largely absent. In NGC 3627 in particular, the phenomenon is harder to identify because of the brightness of star-forming complexes at the bar ends (e.g., see Beuther et al. 2017). A similar depression in star formation has been identified along the spiral arms in NGC 5194 and attributed to streaming motions along the spiral arms (not a stellar bar) by Meidt et al. (2013).

In theoretical calculations, the high shear and/or diverging streamlines (caused by changing orbits) present at the location of the gas lanes along the stellar bar either prevent clouds from forming or tear them apart before star formation can occur (e.g., Athanassoula 1992; Regan et al. 1997). Observationally, this "star formation desert" (along the stellar bar) is not evident in all barred galaxies (see, e.g., Sheth et al. 2000; James & Percival 2018). This suggests that the exact bar properties and/or the time evolution of bars may also be important to the suppression of star formation.

Overall, our data provide support for the idea that star formation in molecular gas is inhibited along many stellar bars. Despite the presence of bright CO emission, H ii regions appear less common in these regions.

Spiral arms. For several galaxies we find a pronounced spatial offset between CO and Hα emission along spiral arms. In these cases, we observe a general pattern where CO only sightlines are more prominent on the concave side, while overlap sightlines are found along the convex side of a spiral arm, with Hα only sightlines sitting outside the overlap regions away from the CO only regions.

Figure 2 shows impressive examples of this phenomenon in the grand-design spiral galaxies NGC 0628 (particularly at smaller galactocentric radii; see also Figure 1 in Kreckel et al. 2018) and NGC 5194 (e.g., Schinnerer et al. 2013, 2017). The spiral arms emanating from the stellar bars in NGC 4321 and NGC 4535 also exhibit offsets along significant arm segments. This suggests that a similar mechanism causes this offset in grand-design spirals and spiral arms dynamically linked to stellar bars. Assuming the spiral arms are trailing, the Hα offsets occur on the downstream side consistent with expectations for a rotating spiral density wave (inside co-rotation) (for a sketch see, e.g., Figure 1 of Pour-Imani et al. 2016).

Trends with global properties. We compared the overlap fraction and amount of apparently quiescent CO emission to the integrated properties of the host galaxy, including stellar mass (M_star), SFR, and specific SFR (sSFR ≡ SFR/M_star). While our sample of eight galaxies represents a significant improvement compared to previous work, a much larger sample will be required to measure quantitative relationships. Still, some trends are already evident from these first results.

First, targets that have a large fraction of CO only sightlines at 140 pc resolution are all more massive than log(M_⋆[M_⊙]) = 10.2, tend to have higher SFRs (SFR[M_⊙ yr⁻¹] > 2), and also tend to lie above the average stellar mass–SFR relation. Such galaxies tend to be rich in molecular gas compared to lower-mass and more quiescent galaxies. This result suggests that, at least at any given moment, a large fraction of the gas in such galaxies may not be immediately associated with high-mass star formation. We do caution that our present sample is heavily biased toward such objects.

By contrast, Hα only sightlines are most prominent in the two lowest-mass and lowest-SFR galaxies, which also have the latest (NGC 5068) and earliest (NGC 3351) Hubble type of the sample. Though we do not include M33 in the analysis, this would appear to be consistent with the widespread Hα and confined CO emission visible in that galaxy (e.g., see Schruba et al. 2010; Druard et al. 2014; Corbelli et al. 2017). Here, sensitivity, conversion factor effects, and the choice of thresholds will play an important role, because these are also among our most quiescent targets.

The one galaxy where overlap sightlines dominate (NGC 3627) exhibits on average low SFR and sSFR values and is also part of a group currently undergoing a large-scale interaction.

No trend with the presence or absence of a (large-scale) stellar bar is evident. Similarly, we find no clear trend with the presence or absence of an AGN (all galaxies with log(M_star(M_⊙) ≳ 10.4, i.e., five out of eight, show evidence for an AGN). This is not surprising given the small sample size, the relatively low number of sightlines directly associated with the galaxy center or bar, and the temporal evolution expected for both phenomena.

Does feedback or galactic dynamics drive the CO morphology? In a series of recent papers, Semenov et al. (2017, 2018) put forward a star formation model based on high-resolution simulations of gas and star formation in galaxy disks. Semenov et al. (2018) distinguish two distinct regimes, which may relate to the morphology of CO and Hα emission seen in our observations. In the "self-regulation" regime, the lifetime of gas in the star-forming state is limited by consumption via star formation and feedback. A stochastic, patchy appearance might be expected, with the CO emission shaped by stellar feedback. By contrast, in the "dynamics-regulation" regime, the lifetime of the star-forming gas is limited by dynamical processes. In this case, they expect the star formation to reflect the underlying distribution of the cold gas rather than being shaped by star formation and/or associated feedback.

In our observations, both the star-forming and quiescent molecular gas trace distinct bars, rings, and arms in most galaxies. In other words, it appears that the star formation traces the underlying molecular gas distribution, which in turn traces the underlying potential (see Figure 4). The patchy stochastic appearance that we might expect for morphology dominated by self-regulation is most prominent in the outer disk of NGC 3351 and the low-mass galaxy NGC 5068. This qualitative comparison, as well as the discussion above, demonstrates that the different dynamical environments and host galaxy properties do lead to varying conditions for star formation and that a simple assumption of self-regulation by stellar feedback that results in stochastic, isolated regions is probably too simplistic for many galaxies.

For three of our targets, bright CO emission from the center (see Figure 1; NGC 3351, NGC 4321, and NGC 4535) makes a large fractional contribution to the total CO luminosity (e.g., see the flux-weighted histograms in Figure 1 of Sun et al. 2018). When we consider the distribution of flux, these bright centers exert a large influence on the fractions of emission associated with CO only, Hα only, and overlap regions (see Figure 9 and Table 6). Because they cover relatively little area, the centers have a weaker effect on the distributions of covering fraction.

Excluding the centers leads to a slightly better agreement between a flux-weighted approach and a sightline-based approach. There are still differences between the two approaches, however. In general, the fraction of luminosity associated with overlapping CO and Hα is larger than the fraction of overlapping sightlines. This implies that the intensity of CO emission is higher in regions that also show Hα emission and, similarly, that the brighter Hα emission is associated with regions of higher CO emission.

Brighter CO emission in regions with Hα emission could be expected if star formation increases the temperature and excitation of the CO gas. This appears to be the case in a subset of our targets (T. Saito 2019, private communication). It may also reflect that the molecular gas structure differs between actively star-forming regions and quiescent regions. This also appears to be the case, with higher surface density gas being associated with active regions.

We adopt relatively simple methods to identify pixels tracing CO emission and likely H ii regions that could bias our results. They also highlight natural next steps as we apply the method to a larger sample of galaxies.

Our fixed CO threshold leads to variable completeness across our sample (see Sun et al. 2018). Specifically, using our fixed threshold, we recover a lower fraction of the total CO emission in low-mass galaxies and outer disks compared to massive spiral galaxies. Hughes et al. (2013) showed that molecular clouds in such systems have lower molecular gas surface densities (see also Sun et al. 2018; Schruba et al. 2019). This appears strongest in NGC 5068 and the outer part of NGC 3351, but may be present at large radii in most of our sample.

A bias against recovering all of the CO emission present affects the inferred f_scale, driving the apparent cycling time to artificially low values. Future work will need to address that the CO emission in some regions of our sample is faint compared to our sensitivity. This can be achieved by using statistical methods that account for the effects of noise and by informing the measurements using the known total CO flux from each region of the galaxy.

Local variations of the CO-to-H₂ conversion factor, α_CO, could also impact our analysis. In this case, our estimates for CO-emitting fractions "by flux" would no longer straightforwardly correspond to a mass fraction of the molecular gas reservoir. Moreover, the meaning of our adopted threshold would change across the galaxy. Previous work does not suggest enormous α_CO variations across this specific sample. Sandstrom et al. (2013) derived α_CO at ∼kpc resolution for five galaxies in our sample (NGC 0628, NGC 3351, NGC 3627, NGC 4254, NGC 4321) and saw no significant variations across the disks or with radius (excluding some central depression which cover only a small area in our analysis). Similarly, Leroy et al. (2017) found a basically constant α_CO across the PAWS area in NGC 5194. Nonetheless, in a preliminary comparison, we do find some modest differences between molecular cloud properties and CO excitation in the CO only regions and overlap regions.

Likewise, our identification method for H ii regions in narrowband Hα maps has an impact on our results. If we insufficiently subtract the DIG, we expect to find an artifical increase of Hα only sightlines at small scales. This, in turn, will drive f_scale to artificially low values. Though we inspected our images and verified our algorithm works to first order, adopting a single simple algorithm to analyze galaxy centers, spiral arms, and low-density flocculent galaxies will likely yield significant biases. Compounding this situation, the Hα line emission is significantly affected by extinction, and both flux-based approaches and the interpretation of thresholds depend on local, robust extinction corrections.

More sophisticated morphological separation methods (e.g., newer versions of HiIPHOT; Thilker et al. 2000) offer some prospect to improve the situation. The main hope for improvement here comes from the use of optical integral field spectroscopy (IFS). IFS allows for simultaneous correction for internal extinction and improved tools for distinguishing the Hα emission from DIG and shocks or X-ray-dominated regions associated with AGNs. Very Large Telescope/MUSE IFS data are currently being obtained for ∼19 PHANGS targets, which have the prospect to then act as a training set for improved morphological and multi-wavelength methods for H ii region identification and extinction corrections. Initial tests on the MUSE data for four galaxies yield H ii region masks that are more restricted than those constructed in Section 2.2.5. This suggests that our H ii region identification scheme may bias us to slightly low f_scale and thus shorter CO-emitting region lifetimes.

Despite these caveats, we emphasize that most of our analysis focuses on the presence or absence of CO or Hα emission, not their exact translation into physical quantities. We made this choice exactly to minimize the bias due to uncertain conversions between CO and H₂ or Hα and a local SFR.