The Gas–Star Formation Cycle in Nearby Star-forming Galaxies II. Resolved Distributions of CO and H$\alpha$ Emission for 49 PHANGS Galaxies

The 90 PHANGS-ALMA galaxies were observed in CO(2–1) using the ALMA 12-m and 7-m arrays, and total-power antennas. The data were imaged in CASA (McMullin et al., 2007) version 5.4.0. We use the spectral line cubes delivered in the internal data release version 3.4. The data have native spatial resolutions of $\sim$ 25–180 pc, depending on the source distance. The typical 1$\sigma$ noise level is $\sim$ 0.3 K per 2.5 km s^-1 channel, but varies slightly between galaxies. We use the “broad mask” integrated intensity maps. These maps include most CO emission (98% with a 5 – 95th percentile range of 73 – 100%) in the cube, meaning that they have high completeness. For full details of the sample, observing and reduction processes, and final data products see Leroy et al. (2021a).

We create maps of molecular gas surface density ($\Sigma_{\mathrm{H_{2}}}$) by applying a radially-varying CO-to-H₂ conversion factor ($\alpha_{\mathrm{CO}}$) to the CO integrated intensity map, following the method described in Sun et al. (2020a). We briefly summarize the steps here.

Many studies have shown that $\alpha_{\mathrm{CO}}$ increases with decreasing metallicity ($Z$) (e.g., Wilson, 1995; Arimoto et al., 1996; Leroy et al., 2011; Schruba et al., 2012). Our adopted radially-varying $\alpha_{\mathrm{CO}}$ takes into account the radial metallicity gradient of galaxies. The metallicity at one effective radius ($R_{\mathrm{e}}$) in each galaxy is predicted according to the global $M_{\ast}$ and the global $M_{\ast}$–$Z$ relation reported by Sánchez et al. (2019) based on the Pettini & Pagel (2004) metallicity calibration. Then the $Z$ at 1$R_{\mathrm{e}}$ is extended to cover the entire galaxy assuming a universal radial metallicity gradient of $-0.1$ dex $R_{\mathrm{e}}^{-1}$ (Sánchez et al., 2014). Finally, $\alpha_{\mathrm{CO}}$ at each galactocentric radius is calculated via the relation determined by Accurso et al. (2017):

where $Z{}^{\prime}$ is the local gas-phase abundance normalized to the solar value ($12+\log[{\rm O}/{\rm H}])=8.69$; Asplund et al. 2009). Since $\alpha_{\mathrm{CO}}$ is defined for the ${}^{12}\mathrm{CO}(J=1\rightarrow 0)$ transition, we apply a constant ${}^{12}\mathrm{CO}(J=2\rightarrow 1)$ to ${}^{12}\mathrm{CO}(J=1\rightarrow 0)$ brightness temperature ratio of $R_{21}=0.65$. We do not account for galaxy to galaxy (and also inside a galaxy) variations in this ratio, which are typically $\sim$ 0.1 dex (Leroy et al., 2013; Yajima et al., 2021; den Brok et al., 2021; Leroy et al., 2021c). We test our results against using a constant Galactic $\alpha_{\mathrm{CO}}$ and discuss the choice of $R_{21}$ in Appendix A.1 and A.2, respectively.

To create maps of recent star formation in our PHANGS galaxies, we obtained $R$-band and H$\alpha$-centered narrowband imaging for our sample. The 65 PHANGS-H$\alpha$ galaxies were observed by the Wide Field Imager (WFI) instrument at the MPG-ESO 2.2-m telescope at the La Silla Observatory or by the Direct CCD at the Irénée du Pont 2.5-m telescope at the Las Campanas Observatory. Among the 65 galaxies, 32 were observed by the 2.2-m telescope and 36 by du Pont telescope, including three galaxies that were observed by both instruments. For galaxies with repeated observations, we use the observation that has the best spatial resolution. The field of view (FoV) of WFI and du Pont observations are $34\arcmin\times 33\arcmin$ and $8.85\arcmin\times 8.85\arcmin$, respectively. Full details of the observations, data reduction, and map construction can be found in A. Razza et al. (in prep.). The images used in this work correspond to the internal release version 1.0 of the PHANGS-H$\alpha$ survey. The main steps are summarized here (see also Paper I).

The data frames were astrometrically and photometrically calibrated using Gaia DR2 catalogs (Gaia Collaboration et al., 2018) cross-matched to all stars in the full FoV of the images. Typical seeing for the data is $\sim$ 1$\arcsec$ and the final astrometric accuracy is $\lesssim$ 0.1″. The sky background is computed in each exposure by masking all the sources $>$ 2$\sigma$ above the sigma-clipped mean, including an elliptical area around the galaxies based on the galaxy geometric parameters. A 2D plane is then fit to this background and subtracted, with this process occurring for each exposure frame. Each background-subtracted frame is then combined using inverse-variance weighting.

Then the stellar continuum is subtracted from the combined images. The flux scale is determined using the median of the flux ratios for a selection of non-saturated stars that are matched between the H$\alpha$ and the $R$-band images. Using this flux ratio as a basis, we obtain a first estimate of the H$\alpha{+}$[N ii] flux by subtracting the $R$-band image from the H$\alpha{+}$[N ii]+continuum image.

However, the blended H$\alpha{+}$[N ii] line also contributes to the $R$-band data. Using the estimated H$\alpha{+}$[N ii] image we determine the H$\alpha{+}$[N ii] contribution to the $R$-band image. We subtract this estimated H$\alpha{+}$[N ii] contamination from the $R$-band image and iterate this process until successive continuum estimates differ by less than 1%. Then we subtract this continuum estimate to obtain a flux-calibrated line (H$\alpha{+}$[N ii]) image.

We correct the measured H$\alpha$ flux for the loss due to the filter transmission, using the spectral shape of the narrowband filter and the position of the H$\alpha$ line within the filter. We also correct for the contribution of the [N ii] lines at $654.8$ and $658.3$ nm to the narrowband filter flux, assuming a uniform [N ii]/H$\alpha$ ratio of 0.3. This value is derived from high-spectral resolution observations of H ii regions in NGC 0628 with the VLT/MUSE instrument,with a typical scatter of $\pm$ 0.1 (Kreckel et al., 2016; Santoro et al., accepted). We treat this as a characteristic spectrum for all of our targets, but note possible variation in [N ii]/H$\alpha$ as a source of uncertainty. Finally, we correct all images for foreground Galactic extinction using Schlafly & Finkbeiner (2011), who assumes a Fitzpatrick (1999) reddening law with $R_{V}$ = 3.1.

The sample of galaxies used in this work is a subset of the full PHANGS-ALMA and PHANGS H$\alpha$ observations. Since our main analysis is performed at a fiducial resolution of 150 pc, the selected galaxies are required to be detected in both CO and H$\alpha$, and that a physical resolution better than 150 pc is achieved for both observations. Moreover, we only include galaxies that had been observed by all ALMA arrays (i.e., 12-m+7-m+total power) by the time of the internal data release v3.4. No additional cut (e.g. on $M_{\ast}$) is applied to the sample, besides the selection criteria that are inherited from the parent sample (see above). This results in a sample of 51 galaxies. Among these, NGC 2566 has many foreground stars that impact the reliability of the H$\alpha$ data and NGC 6744 has incomplete ALMA coverage. These two galaxies are therefore also excluded from our analysis, resulting in a final sample of 49 galaxies. Global properties of the sample are presented in Table LABEL:tab_galaxy_sampe_props.

The left panel of Figure 1 shows the SFR–$M_{\ast}$ relation for our sample overlaid on a sample of local galaxies from the xCOLD GASS survey (grey circles; Saintonge et al. 2017). The integrated SFR and $M_{\ast}$  are derived based on GALEX and WISE (Leroy et al., 2019, 2021b). The line in the figure represents the local star-forming main sequence derived by Leroy et al. (2019). There are roughly equal numbers of galaxies above and below the main sequence. The offset from the main sequence ($\Delta$MS) spans $\pm$ 0.8 dex ($\sim$ a factor of 6). Galaxies already included in the sample of Paper I are highlighted by a green circle (NGC 0628, NGC 3351, NGC 3627, NGC 4254, NGC 4321, NGC 4535, and NGC 5068).

We further classify our galaxies based on the presence of bar and grand-design spiral arms. In Figure 1, blue and red circles denote non-barred and barred galaxies, respectively, while the galaxies with grand-design spiral arms are marked by open squares. Information on the galactic structures is provided in Table LABEL:tab_galaxy_sampe_props. We define a galaxy as barred if a bar component was implemented in the PHANGS environmental masks (Querejeta et al., 2021) (morph$\_$bar$\_$flag in the PHANGS sample table version 1.5). These bar identifications mostly follow Herrera-Endoqui et al. (2015) and Menéndez-Delmestre et al. (2007), with some modifications based on the multi-wavelength and kinematic information available in PHANGS. For spiral arms, we adopt the flags morph$\_$spiral$\_$arms (i.e., grand-design spiral arms) from the PHANGS sample table, which comes from visual inspection of multi-wavelength data by four PHANGS collaboration members. Strictly speaking, the morph$\_$spiral$\_$arms flag in the sample table indicates whether the environmental masks include spiral masks or not. It is generally true that we implemented spiral arms mostly for grand-design spirals (and did not attempt to do so for flocculent arms). However, in some cases, e.g. due to inclination, we found that the spiral mask was not reliable even though the galaxy shows clear spiral arms and was classified as grand-design by Buta et al. (2015). Therefore, our classification does not always agree with arm classifications from the literature (e.g., Buta et al. 2015 for S4G²²2S4G: Spitzer Survey of Stellar Structure in Galaxies).

Morphology classification is presented by Hubble morphological T-type in this work. The T-type values for S0, and Sa – Sd galaxies are approximately -2, 1, 3, 5, and 7, respectively. Note that T-type considers ellipticity and strength of spiral arms, but does not reflect the presence or absence of the bar. The right panel of Figure 1 displays the Hubble type of our target galaxies as a function of $M_{\ast}$. The Hubble type of the galaxies in our sample ranges from $-1.8$ to 7.7 (approximately equivalent to S0–Sd). Our sample shows the expected trend: earlier types (i.e., smaller Hubble type values) are generally more massive (e.g., Kelvin et al., 2014; González Delgado et al., 2015; Laine et al., 2016), but the correlation is rather poor at the high-mass end of our sample of $\log(M_{\ast}/\mathrm{M}_{\sun})>10$. In this work, we use the term “earlier” to denote galaxies with lower values of Hubble type, but note that our working sample does not contain elliptical galaxies; the earliest-type galaxy in our sample is NGC 4694 with Hubble type of $-$1.8 ($\sim$ S0).

Our analysis uses H$\alpha$ as a tracer for the location of recent high-mass star formation. However, H$\alpha$ not only arises from H ii regions surrounding the massive stars that ionize them, but also the larger scale diffuse ionized gas (DIG). To correctly correlate the sites of star formation with molecular gas, our analysis must remove this diffuse component. DIG is warm (⁠$\sim$ 10⁴ K) and low density ($<$ 0.1 cm^-3) gas found in the ISM of galaxies which seems similar to the warm ionized medium observed in the Milky Way (see the review by Haffner et al., 2009). The energy sources of DIG are still not well understood. Spectral features, such as the emission-line ratios and ionizing spectrum, of DIG are different from those of H ii regions powered by massive young stars (e.g., Hoopes & Walterbos, 2003; Blanc et al., 2009; Zhang et al., 2017; Tomičić et al., 2017, 2019), indicating the presence of additional sources of ionization. Since DIG constitutes a substantial fraction of the H$\alpha$ flux in star-forming galaxies (e.g., Oey et al., 2007; Tomičić et al., 2021), one must remove the DIG contribution from the H$\alpha$ fluxes when using H$\alpha$ as a star-formation tracer.

Following the approach utilized in Paper I, a two-step unsharp masking technique is used to remove the DIG from the H$\alpha$ images, We first identify diffuse emission on scales larger than H ii regions, and then we take into account higher levels of DIG contribution and clustering of H ii regions that are often found in galactic structures (e.g., spiral arms, Kreckel et al., 2016). More specifically, the following steps are undertaken to remove DIG in the original H$\alpha$ images.

1. 1.

   Unsharp mask with a kernel of 200 pc. We smooth our original image with a Gaussian kernel with FWHM size of 200 pc, slightly larger than the largest H ii regions (Oey et al., 2003; Azimlu et al., 2011; Whitmore et al., 2011). Then we subtract this smoothed image from the original image. We identify initial H ii regions as the parts of the map still detected at high signal-to-noise in this filtered map. Specifically, first of all, peaks above 5$\sigma$ are identified, and then the mask is expanded to contain all connected regions that are above 3$\sigma$. H ii regions are identified as pixels enclosed within the masks.

2. 2.

   Subtract a scaled version of the initial H ii regions from the DIG map. We subtract a scaled version of the H ii regions identified in the previous step from the original map. The scaling factor is an arbitrary choice, but we do not want to over-subtract at this stage. A scaling factor of 0.1 is adopted in this work.

3. 3.

   Unsharp mask with a kernel of 400 pc. We smooth our H ii region-subtracted image with a Gaussian kernel that has FWHM of 400 pc, larger than that in Step 1. This scale is set such to detect higher levels of DIG contribution and clustering of H ii regions. Then, we subtract this smooth version of the image from the original image. We identify our final set of H ii regions in this filtered map using the same S/N criteria in Step 1.

On average, the DIG removal process removes $\sim$65% of the H$\alpha$ emission across the sample, consistent with the DIG fractions of PHANGS galaxies measured by different approaches (Chevance et al., 2020; Belfiore et al., submitted). Moreover, our mean DIG fraction is in good agreement with the mean DIG fraction ($\sim$ 60%) derived from H$\alpha$-surface brightness-based method for the 109 nearby star-forming galaxies in Oey et al. (2007). A similar mean DIG fraction is also suggested for CALIFA (The Calar Alto Legacy Integral Field Area Survey) galaxies based on integral-field-spectroscopy (IFS)-based H ii/DIG separator (Lacerda et al., 2018). The DIG fractions of our sample galaxies are provided in Table 2. We note that the tuning parameters adopted in this work are different from what was used in Paper I. The choice of parameters in this work is optimized to reproduce H ii regions identified with our PHANGS-MUSE IFS H$\alpha$-line images which have similar spatial resolution (Santoro et al., accepted). Changing the adopted kernel sizes has only a minor impact on the number of H ii regions but does affect their sizes. Therefore, a key assessment of the performance of the DIG removal strategy is to avoid H ii region overgrowth. This can be evaluated using emission-line ratios accessible via spectroscopic observations: for example, the [N ii]/H$\alpha$ and [S ii]/H$\alpha$ ratios are higher in the DIG relative to H ii regions (e.g., Hoopes et al., 1999; Blanc et al., 2009; Kreckel et al., 2016; Tomičić et al., 2017, 2021). The full catalog of H ii regions identified in our narrowband H$\alpha$ maps, including a detailed description of how we verified the narrowband H ii regions using PHANGS-MUSE spectroscopic information and the dependence of DIG fraction on galaxy properties will be presented in a forthcoming paper (H.-A. Pan et al. in prep.). Our results remain qualitatively unchanged when using the tuning parameters in Paper I, as discussed in Appendix A.3. In this work, we assume all the H$\alpha$ emission surviving from the DIG removal process is from H ii regions, and the contribution from other powering sources, such as AGN, post-AGB stars, and shocks, are statistically minor in the analysis. Separating these sources from H ii regions rely on emission-line diagnostics and therefore spectroscopic observations.

Here we note two important caveats of our DIG removal process. We use a signal-to-noise threshold when identifying H ii regions during the unsharp masking step. Since the noise and native resolution of the input H$\alpha$ images vary, the effective H$\alpha$ surface brightness threshold applied to our fiducial maps therefore also varies, corresponding to SFR surface densities of $\sim$ 10^-3 – 10^-2 M_☉ yr^-1 kpc^-2 depending on the galaxy target³³3We adopt Equation (6) in Calzetti et al. (2007) for the relation between SFR and H$\alpha$ emission, which assumes a Kroupa initial mass function.. For a point source at the native resolution of our H$\alpha$ data, the effective sensitivity limits in terms of H$\alpha$ surface brightness threshold applied to the fiducial maps corresponds to H ii region luminosities ($\log(L_{\mathrm{\textsc{H\,ii}\,region}}^{\mathrm{sensitivity}}/{\rm erg\,s^{-1}}$)) between $36.7$ and $38.4$, with most ($\sim$80%) being between 37 and 38. The $L_{\mathrm{\textsc{H\,ii}\,region}}^{\mathrm{sensitivity}}$ for our galaxies are listed in Table 3. The H ii region sensitivity limits are comparable to the turn-over point of the H ii region luminosity function measured by narrowband H$\alpha$ imaging in the literature (e.g., Bradley et al., 2006; Oey et al., 2007), but we may miss the low-luminosity H ii regions detected by optical integral field units (Kreckel et al., 2016; Rousseau-Nepton et al., 2018; Santoro et al., accepted), which are unavailable at the necessary resolution for the bulk of the galaxies in our sample. Therefore, we may underestimate the number of sight lines with H$\alpha$ emission (see Appendix A.4 for a detailed discussion on the impact of H$\alpha$ sensitivity). Moreover, our H$\alpha$-line images are not corrected for dust attenuation, thus the maps may miss the most heavily embedded regions. Since our main analysis focuses mostly on the location (rather than the amount) of massive star formation, we consider internal extinction as a secondary issue. However, for some analysis based on flux, we may underestimate H$\alpha$ flux for the regions where CO (and therefore dust) is present.

The CO images are treated using a similar scheme. We clip the CO images at our best-matching resolution of 150 pc using a $\Sigma_{\mathrm{H_{2}}}$ threshold of 10 M_☉ pc^-2 accounting for galaxy inclination. This corresponds to a 3$\sigma$ $\Sigma_{\mathrm{H_{2}}}$ sensitivity of our CO map with the lowest sensitivity at this spatial scale (Table 3). The applied threshold value is lower than the threshold used in Paper I (i.e., 12.6 M_☉ pc^-2) due to the lower sensitivity of the PAWS M51 observations. To have a data sample with homogeneous observational properties, M51 is not included in this work. Our results remain qualitatively unchanged if different $\Sigma_{\mathrm{H_{2}}}$ clipping values are adopted (see Appendix A.5).

First of all, the thresholded H$\alpha$ maps are regridded to match the pixel grid of the CO maps since the FoV of our ALMA observations is considerably smaller than that of narrowband observations. We convolve each thresholded CO and H$\alpha$ image by a Gaussian to a succession of resolutions, ranging from our highest common resolution of 150 pc to 1500 pc, in steps of 100 pc. Then we clip the low-intensity emission in the convolved images. For each convolved image, we blank the faintest sight lines that collectively contribute 2% of the total flux in the image to suppress convolution artifacts. The results remain robust to small variations (1 – 4%) of this threshold.

Finally, we measure the presence or absence of the two tracers at each resolution in a FoV extending to 0.6 $R_{25}$, which is the largest radial extent probed by our data in all galaxies, corresponding to $\sim$ 6.4 kpc on average (5 – 22 kpc, mostly $<$ 15 kpc). We divide each sight line (pixel) within 0.6 $R_{25}$ in the thresholded and artifact-clipped CO and H$\alpha$ images into one of four categories:

• •

  CO-only: only CO emission is present

• •

  H$\alpha$-only: only H$\alpha$ emission is present

• •

  overlap: both CO and H$\alpha$ emission are present

• •

  empty: neither CO nor H$\alpha$ emission is present⁴⁴4We note that the empty pixels in the filtered maps may contain DIG and/or CO emission with surface density below the applied threshold in the original maps..

The fraction of sight lines with (i.e., CO-only$+$H$\alpha$-only$+$overlap) and without (i.e., empty) any emission are given in Table 4. At the highest common resolution of 150 pc, the median fraction of sight lines without any emission within 0.6 $R_{25}$ of our galaxies is as high as 70%, ranging from 13 – 97%. Moreover, the fractions of empty sight lines decrease with increasing spatial scales (Figure B.20, see also Pessa et al. 2021). The distributions of empty pixels among galaxies is a potentially interesting diagnostic of ISM evolution and host-galaxy properties. We defer a detailed analysis of the statistics relating to empty pixels to a future investigation, since the main focus of this paper is the impact of host galaxy properties and observing scale on the relative distribution of molecular and ionized gas.

We measure the fraction of sight lines and the fraction of flux in each region type, i.e., CO-only, H$\alpha$-only, and overlap, at each resolution. All galaxies in our sample have non-zero fractions for the three region types at the highest common resolution of 150 pc (Appendix B). Since we do not consider the sight lines where neither CO nor H$\alpha$ emission is present, the sum of CO-only, H$\alpha$-only, and overlap sight lines is 100%. We also define CO sight lines as regions that are classified as either CO-only or overlap (i.e., sight lines with CO emission, regardless of whether they are associated with H$\alpha$ emission or not), while H$\alpha$ sight lines are defined as regions of H$\alpha$-only or overlap (i.e., sight lines with H$\alpha$ emission, regardless of whether they are associated with CO emission).

There are significant galaxy-to-galaxy variations in the CO and H$\alpha$ distributions. Figure 2 presents some examples of the distribution of different sight line categories at 150 pc resolution (maps for the full sample are provided in Appendix B). The blue, red, and yellow regions denote CO-only, H$\alpha$-only, and overlap sight lines, respectively. We define the galactic center as the region within 1 kpc (i.e., 2 kpc in diameter) of the galaxy nucleus. The region that we define as the center is indicated in each panel as a magenta ellipse in Figure 2, while the region that we use to measure the global sight fraction is indicate as a white ellipse (i.e., 0.6 $R_{25}$).

The histograms of Figure 3, from left to right, show the distribution of CO-only, H$\alpha$-only, and overlap fractions within the fiducial FoV at 150 pc scale, respectively. The boxplots shown at the top of each panel summarize the statistics for the sight line fractions. The sight line fractions for each individual galaxy are provided in Table LABEL:tab_fractions of Appendix B). The median and mean sight line fractions are given in the upper-right corner of the panels. In the rest of the paper, we will use the median as the measure of central tendency because the mean is more sensitive to extreme values. The mean values are given in the relevant figures and tables for reference.

We find a wide range of CO-only fraction in our sample from 3 to 78%, with a median of 36%. While the H$\alpha$-only fraction peaks at the lower end ($<$ 20%), H$\alpha$-only sight lines show a wider range of spatial coverage than the CO-only sight lines, from nearly 0 to almost 95%. The median H$\alpha$-only fraction is 20%. The overlap region exhibits a narrower range than the CO-only or H$\alpha$-only regions, and shows a preference for intermediate values from 20 to 50%, with a median of 30%.

In terms of the relative frequency of the three types of sight lines, our results are qualitatively consistent with the conclusions of Paper I based on a smaller sample of only eight galaxies. However, Paper I reports considerably higher median values for CO-only and overlap sight lines (42% for CO-only and 37% for overlap) and slightly higher median for H$\alpha$-only (23%). We ascribe this difference to the combined effect of different thresholds for CO and H$\alpha$ images and sample composition (e.g., $M_{\ast}$ distribution; see Figure 1 and next subsection).

Molecular gas is preferentially formed or collected efficiently in galactic structures such as bars and spiral arms. Since the distribution of molecular gas subsequently determines the potential sites of star formation, it is natural to expect that the distributions of CO and H$\alpha$ emission are also regulated by galactic structures.

We classify our target galaxies into four groups according to the presence and absence of bar and grand-design (GD) spiral arms:

1. 1.

   no structures (NS): galaxies without bar and GD spiral arms (e.g., galaxies with flocculent/multiple arms are in this category)

2. 2.

   Bar: galaxies with a bar but no GD spiral arms

3. 3.

   Bar+GD: galaxies with a bar and grand-design spiral arms

4. 4.

   GD: galaxies with grand-design spiral arms but without a bar.

The number of galaxy in groups (1) to (4) are 12, 19, 11, and 7, respectively. The statistics of sight line fractions for each category at 150 pc resolution are provided in Table 7; the corresponding boxplots are shown in Figure 6. While the sight line fractions for NS, Bar, and Bar+GD span over a similar range, GD galaxies exhibits a distinct sign of higher CO-only and overlap fractions and lower H$\alpha$-only fractions than the other populations. Since GD galaxies have a lower median $M_{\ast}$ (log($M_{\ast}$/M_☉) $=$ 10.3) than the Bar+GD galaxies (10.7) (Table 7), the differences in CO-only and H$\alpha$-only fractions between GD and Bar+GD are opposite to what one would expect if $M_{\ast}$ is the dominant driver of the sight line fractions, and points to the potential importance of galactic structure on regulating the star formation process.

Figure 7 presents the radial sight line fractions for each structure type at 150 pc resolution. The bar length in our galaxy sample ranges from $\sim$ $0.1{-}0.9$ $R_{25}$, with most bar lengths around $0.1{-}0.5$ $R_{25}$. The median bar length of Bar+GD galaxies (0.3 $R_{25}$) is slightly longer than that of Bar galaxies (0.2 $R_{25}$). Galaxies with a bar (Bar and Bar+GD) visually show stronger radial dependence of CO-only sight lines than galaxies without a bar (NS and GD), in the sense that their median CO-only fraction gradually decreases with increasing radius. The opposite trend is observed for overlap regions. Moreover, Figure 7 suggests that the high total CO-only fraction in GD galaxies (Figure 6) is due to the increased fraction at $\sim$ $0.4{-}0.6$ $R_{25}$. On the other hand, the low total H$\alpha$-only fraction can be attributed to a lack of H$\alpha$-only  regions at $<0.4~{}R_{25}$.

In summary, the results in this section show that, in addition to global galaxy properties, galactic dynamics add a further layer of complexity to the distribution of CO and H$\alpha$ emission. We note that the FoV covering fraction of galactic structures could affect the sight line fractions. For example, while bars are fully covered by our FoV, we may miss the outer part of some GD spiral arms. This analysis could be taken further by counting the sight lines within individual fully-sampled structures, but that is beyond the scope of this paper. We refer the reader to Querejeta et al. (2021) for a comprehensive empirical characterisation of the molecular gas and star formation properties in different galactic environments of PHANGS galaxies.

In this section, we explore whether there is any difference between regions where both tracers are observed (overlap) and regions where only one tracer is observed (CO-only and H$\alpha$-only). We estimate the fractional contribution of CO-only (i.e., only one tracer is observed) and overlap (two tracers are observed; CO-overlap) to the total CO sight lines, and the fractional contribution of H$\alpha$-only and overlap (H$\alpha$-overlap) to the total H$\alpha$ sight lines. In other words, the sum of CO-only and CO-overlap is normalized to 100%, and so is the sum of H$\alpha$-only and H$\alpha$-overlap. To compare with the results based on the number of sight lines (our default fraction), the corresponding fractions for flux are also estimated.

Figure 8 shows the comparison of sight line fractions with flux fractions. Specifically, for each data point, the values on the $x$- and $y$-axis are calculated based on exactly the same pixels (sight lines), but the $x$-axis shows their fractional contribution to the total sight line of the tracer and the $y$-axis shows their fractional contribution to the total flux of the tracer. The black line indicates a one-to-one correlation.

The median sight line fractions of CO-only and CO-overlap are approximately equal ($x$-axes in the upper panels of Figure 8), but the latter contributes a larger portion to the overall flux (66%; $y$-axis of upper-right panel). Nonetheless, CO-only regions still contribute one third of the CO flux (33%; $y$-axis of upper-left panel). The difference between the fractions by number of sight lines and by flux is larger for H$\alpha$, as shown in Figure 8 (lower panels). Taking all the pixels in our galaxies, the H$\alpha$-only accounts for 36% of the area of H$\alpha$-emitting regions, but contributes only $\sim$ 14% of the H$\alpha$ flux. On the other hand, H$\alpha$-overlap contributes 85% to the total H$\alpha$ flux, and it is higher than the 64% sight line fraction. Since the H$\alpha$-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 H$\alpha$ maps due to the lack of extinction tracers (Section 2.2). Therefore, the true flux contribution of H$\alpha$-overlap is probably higher.

While covering only a small area, galaxy centers often substantially contribute to the total flux (Querejeta et al., 2021). Since the flux in the central region of galaxies is not necessarily associated with star formation, we therefore repeat the analysis while excluding the central 2 kpc in deprojected diameter (Figure 8). For CO, the agreement between area and flux is much tighter; the deviation from the one-to-one line for high CO fractions almost vanishes, implying that galactic centers drive the difference. On the other hand, H$\alpha$ fractions appear less dominated by the centers. This is at least partially due to higher extinction present in the centers. The trend of higher flux in H$\alpha$-overlap regions than in H$\alpha$-only regions persists even when excluding the centers.

Figure 9 compares the fractions by number of sight lines (upper panel) and flux (lower panel) for galaxies in different $M_{\ast}$ and Hubble type bins. The distributions of CO-only and CO-overlap are shown by blue and green boxes, respectively, while H$\alpha$-only and H$\alpha$-overlap are shown by red and orange boxes. For each $M_{\ast}$ or Hubble type bin (indicated by the darkness of the boxes), the sum of a data point in the blue (red) box and the corresponding data point in the green (orange) box is normalized to 100. The median and mean for each $M_{\ast}$ and Hubble type bin are summarized in Table 8. The trends with $M_{\ast}$ and Hubble type are the same for sight lines and flux, but the difference among the $M_{\ast}$ and Hubble type bins are sightly larger when considering flux instead of number of sight lines. For all $M_{\ast}$ and Hubble type bins, the overlap regions contribute to a larger proportion of CO and H$\alpha$ flux than regions with only one type of emission.

Interestingly, CO-only becomes dominant in the highest $M_{\ast}$ galaxies, occupying $\sim$ 60% of the CO-emitting regions. However, they are almost as equivalently low in flux contribution as other populations, implying a generally (i.e., more extended distributed) low H₂ surface density in the highest $M_{\ast}$ galaxies in our sample. The same feature is seen for the earliest type galaxies, hinting that star-formation ceases to prevail over a significant area of a galaxy while gas remains there. However, we cannot rule out that this result arises from our methodology. Some CO-onlygas in the low-mass galaxies may not pass our threshold due to its intrinsically low $\Sigma_{\mathrm{H_{2}}}$, while in higher mass galaxies, their CO-onlygas is slightly brighter than our threshold. This would potentially add many CO-emitting sight lines, but very little flux. Such a possibility again highlights the differences in molecular gas properties among galaxies with different $M_{\ast}$ and Hubble type.

In summary, at 150 pc spatial scale, the fluxes of CO and H$\alpha$ emission are higher in overlap regions where emission from both tracers is observed compared to regions where only one tracer is observed, consistent with the finding of Paper I. This trend holds for galaxies with different $M_{\ast}$ and Hubble type. Nonetheless, the contribution from regions with only one tracer (CO-only and H$\alpha$-only) to the total flux remain substantial for most systems.

We investigate the impact of spatial scale on the distributions of CO and H$\alpha$ emission. Figure 10 shows the sight line fractions for individual galaxies as a function of spatial scale from 150 pc to 1.5 kpc. For most of the galaxies, their CO-only sight lines decrease to $\lesssim$ 20% at spatial scale $\gtrsim$ 800 pc, regardless of their CO-only fractions at spatial scale of 150 pc. The overlap regions substantially increase and become the dominant sight lines when resolution is degraded. This is the case for all galaxies in our sample, and the vertical ordering of overlap fractions among the galaxies is almost maintained until 1.5 kpc resolution. At the lowest resolution we consider, more than half of the regions are populated by both CO and H$\alpha$ emission in most galaxies. While the variations of CO-only and overlap sight line fractions with spatial scale are rather uniform across the sample, the relation between H$\alpha$-only fractions and spatial scale is more diverse. Specifically, galaxies with low H$\alpha$-only fractions at 150 pc scale exhibit a low, roughly constant fraction toward large spatial scale (lower resolution); galaxies with the highest H$\alpha$-only fractional percentages at the best 150 pc scale decrease rapidly toward low resolutions; and some galaxies show increasing H$\alpha$-only fractions with decreasing resolutions. For all sight line categories, the variations with spatial scale become less evident at $>$500 pc resolution. The flattening point determines the critical resolution at which we stop resolving the CO and H$\alpha$ distributions.

Figures 11 sheds light on the nature of the different H$\alpha$-only versus spatial scale relation. These figures are analogous to Figure 10, except that now galaxies are binned by their $M_{\ast}$ and Hubble type. The high global H$\alpha$-only  fractions at 150 pc scale, which tend to be relatively isolated toward the outer parts of low-$M_{\ast}$ and/or later-type galaxies, become quickly contaminated by other types of sight lines in the inner regions when the resolution is lowered. In other words, we see that the CO-only and overlap regions increase in size and expand toward outer disks when the resolution decreases, e.g., NGC 2090, NGC 2835, and NGC 4951 in Figure B.20), leading to a rapid decrease of the H$\alpha$-only fraction as a function of increasing spatial scale. On the other hand, the H$\alpha$-only fraction of galaxies with low-H$\alpha$-only  are less sensitive to resolution. They tend to be higher-$M_{\ast}$ galaxies. Their H$\alpha$-only sight lines populate both outer and/or inner disks (e.g., inter-arm regions, NGC 1300 and NGC 4321 in Figure 2 and NGC 2997 and NGC 3627 in Figure B.20). Whether a galaxy’s H$\alpha$-only fractions increases or decreases with resolution depends on the relative distribution of gas traced by CO and H$\alpha$.

By contrast, CO-only sight lines vary relatively uniformly as a function of spatial scale among different galaxy populations. The profiles show a clear ranking with $M_{\ast}$ and Hubble type at spatial scale $<$ 500 pc. At spatial scale $\gtrsim$ 500 pc, the dependence of CO-only fraction on $M_{\ast}$ and Hubble type becomes less pronounced. While we find no strong dependence of overlap regions with $M_{\ast}$ at resolution of 150 pc (Figure 4), Figure 11 shows that galaxies in the highest $M_{\ast}$ bin tend to have lower overlap fractions when the spatial scales are larger than $\sim$ 300 pc. On the other hand, the trend with Hubble type at 150 pc resolution only holds when the spatial scale is smaller than $\sim$ 500 pc.

In summary, the results of this section demonstrate the important role that spatial scale can play when characterizing the distribution of CO and H$\alpha$ emission and their dependence on host galaxy properties. The trend between sight line fractions and spatial scale was also observed in Paper I for individual galaxies, here we further show that the resolution dependence depends on galaxy type and the underlying high resolution CO and H$\alpha$ emission structure, indicating that there may be no simple (universal) prescription to infer the physical connection between gas and star formation from kpc-scale measurements.

We find that galaxies in our sample contain a substantial reservoir of CO-only molecular gas not associated with optical tracers of high-mass star formation (or above SFR surface densities of $\sim$ 10^-3 – 10^-2 M_☉ yr^-1 kpc^-2 depending on the galaxy target). Our result is qualitatively consistent with studies of Local Group galaxies. In these galaxies (the Small and Large Magellanic Clouds (SMC and LMC) and M33), about 20–50% of GMCs are not associated with H ii regions or young clusters⁵⁵5Note that one should not compare the fraction of non-star-forming “GMCs” in the Local Group galaxies with our “sight line” fractions directly due to the different counting methods, i.e., object-based or pixel-based approaches. Direct comparison is only possible if we assume that GMCs have a fixed size, which is unlikely to be true (e.g., Hughes et al., 2013; Colombo et al., 2014; Rosolowsky et al., 2021). (e.g., Mizuno et al., 2001; Engargiola et al., 2003; Kawamura et al., 2009; Gratier et al., 2012; Corbelli et al., 2017). Our results further reveal that these starless clouds are not restricted to lower mass spiral and irregular galaxies, as in the Local Group, but are observed across the whole range of the galaxy population.

Non-star-forming gas: The sensitivity of PHANGS-ALMA is able to detect GMCs with mass of $\gtrsim$ 10⁵ M_⊙; moreover, the CO-only sight lines are found at all surface densities from the adopted threshold to a few thousands of M_⊙ pc^-2. Massive star formation is certainly expected to proceed in these relatively high-mass and high density regions. This implies that part of the CO-only gas consists of non-star-forming clouds; the gas is unable to form stars because of its intrinsic properties. For example, molecular gas in some CO-only regions might be a diffuse, dynamically hot component (Pety et al., 2013) that is not prone to star formation, or may be analogous to the gas in the centers of early-type (elliptical) galaxies that seems not to be forming stars (Crocker et al., 2011; Davis et al., 2014). Nonetheless, we note that although the non-star-forming gas does not currently participate in the local on-going star-formation cycle, it may participate in star formation at some point in the future, i.e. made possible by relocating to a different, favorable site in the galactic potential that prompts a change in its dynamical state and/or organization, for example.

Low-mass star formation: It is possible that high-mass star formation is suppressed in the CO-only regions, forming stars that are not massive enough to produce detectable H$\alpha$ emission. Such molecular clouds have been found in the Large Magellanic Cloud (Indebetouw et al., 2008).

Embedded star formation: Massive stars may be formed in part of the CO-only gas, but their H$\alpha$ emission is obscured by dust. However, the embedded phase is relatively short, lasting only for a few to several Myr (Kim et al., 2021), and therefore may not account for all CO-only regions.

Pre- and/or post-star formation: The CO-only gas might be in the process of collapsing or may be remnant molecular gas dispersed from previous star-forming sites by stellar feedback (e.g., photoionization, stellar winds, and supernova explosions).

Distinguishing these scenarios requires the analysis of multi-wavelength data, such as line widths and surface densities of molecular clouds, dense gas tracers, better tracers of obscured star formation (e.g. infrared emission), and extinction tracers, but such an analysis is beyond the scope of this paper. Future James Webb Space Telescope (JWST) observations will also provide crucial insight into the complex processes of star formation and the nature of our CO-only sight lines.

In Section 4.4, we saw that the observed sight line fractions depend on spatial scale. We repeated our analysis for a subsample of 17 galaxies for which our observations achieve a common 90 pc resolution to test whether the fraction of CO-only sight lines in galaxies is larger at even higher physical resolution. A CO threshold of 13 M_☉ pc^-2 is adopted, corresponding to the 3$\sigma$ of the lowest sensitivity of these galaxies at 90 pc resolution. The CO-only fractions in all galaxies show an increase by $\sim$14% (median) as the resolution improves from 150 to 90 pc, while the fraction of H$\alpha$-only and overlap regions for the 90 pc maps decreases by $\sim$ 4% and 8%. This suggests that there remains a non-negligible fraction of CO-only gas that is not well resolved at our fiducial scale of 150 pc. If we increased the resolution even more, e.g., to 10 pc, we might expect to find even more CO-only sight lines, but testing this will require higher resolution ALMA observations. At some point, such observations will highly resolve individual clouds or other star-forming structures, and we might even detect that individual regions within a molecular cloud remain quiescent (e.g., genuinely non-star-forming or pre-star-forming) while stars already form elsewhere. This is not yet the case for our data, however.

Both bar and grand-design spiral arms are known to stabilize the gas against collapse and thus star formation under certain circumstances (Reynaud & Downes, 1998; Zurita et al., 2004; Verley et al., 2007; Meidt et al., 2013). However, while we indeed observe a higher fraction of CO-only sight lines in grand-design spiral galaxies (Figure 6), the CO-only fractions of Bar and Bar+GD are comparable to NS galaxies. It is probably because we do not consider bar strength in this work which is known to be correlated with SFR and star formation history of galaxies (Martinet & Friedli, 1997; Carles et al., 2016; Kim et al., 2017). An alternative explanation could be that the gas distribution in barred galaxies is evolving heavily over time (e.g., Donohoe-Keyes et al., 2019), leading to a wide variety in the gas distribution in the barred galaxies seen in PHANGS (Leroy et al., 2021b).

Nonetheless, our results show a possible trend for galaxies with bars (Bar and Bar+GD) to exhibit a stronger radial dependence in the fraction of CO-only sight lines (Figure 7). This may be attributed to bar-driven gas inflows which increase the gas concentrations in the central regions (Sakamoto et al., 1999; Sheth et al., 2005; Sun et al., 2020b). Moreover, the Bar and Bar+GD galaxies show a weaker radial dependence of overlap fraction than the NS and GD galaxies in terms of median values. Star-forming complexes are often observed at bar ends. Although bar footprints are not necessarily forming stars, the star-forming bar ends may smooth the profiles of the overlap sight lines (James et al., 2009; Beuther et al., 2017; Díaz-García et al., 2020). Finally, we note that we did not control for other trends (e.g., $M_{\ast}$) when comparing sight line fractions between galaxies with different structures. A very large sample is required in order to distinguish the effects of global galaxy properties and galactic dynamics.

Some galaxies show a pronounced offset between the different sigh line types with a sequence of CO-only to overlap and to H$\alpha$-only when going from up- to downstream (assuming the spiral arms are trailing, e.g., NGC 4321 in Figure 2 and NGC 0628, NGC 1566, NGC 2997 in Figure B.20), consistent with expectations for a spiral density wave (see Figure 1 of Pour-Imani et al., 2016). These offsets are almost exclusively found in well-defined grand-design spiral arms and presumably lead in turn to the high (or even highest) CO-only fraction in the disk (0.4 and 0.6 $R_{25}$) of GD in Figure 7, suggesting that most of GD structures may indeed be density waves. This demonstrates the potential of the sight line method as a diagnostic of the relationship between ISM condition and galactic dynamics. Detailed analysis of individual galaxies would be necessary to confirm the (dynamical) nature of our grand-design spiral arms.

Besides, the offsets between molecular gas and star formation tracers also allow measurement of the angular rotation velocity of a spiral pattern and the timescale for star formation (e.g., Egusa et al., 2004, 2009; Louie et al., 2013). While such analyses have been restricted to small-sample studies in the past, PHANGS allows for a systematic exploration of the spatial offset between the gas spiral arms and star-forming regions. Some barred galaxies also exhibit such CO-only and overlap offsets along their spiral arms, e.g. NGC 4321 and NGC 3627 in Figure 2 and NGC 1365 in Figure B.20, suggesting a dynamical link between spiral arms and stellar bar (Meidt et al., 2009; Hilmi et al., 2020).

We find no correlation between sight line fractions and star formation properties (Section 4.1.1) and no correlation with the fractions of flux contributed by CO-only, H$\alpha$-only, CO-overlap, and H$\alpha$-overlap regions (correlation coefficients $\lesssim$ 0.2). Figure 12 shows the sight line fractions against $\Delta$MS, color-coded by Hubble type. Although there is no statistical relationship between the sight line fractions and $\Delta$MS, galaxies with low $\Delta$MS in our sample, $\lesssim$ $-0.58$ dex or $\sim$ 4 times below the main sequence (NGC 1317, NGC 3626, NGC 4457, and NGC 4694), tend to have high CO-only sight line fractions ($\sim$ 50–80%). These low-$\Delta$MS galaxies are all earlier types with Hubble type $\mathrm{T}\leq 1$ (S0–Sa). The spatial distribution of their CO-only regions are relatively compact inner disks, analogues to the molecular gas in elliptical galaxies (e.g., Crocker et al., 2011; Davis et al., 2014). By contrast, among the six highest-$\Delta$MS galaxies ($>$ 0.4 dex or 2.5 times above the main sequence) in our sample, four show relatively high CO-only sight line fractions ($\gtrsim$ 50%; NGC 1365, NGC 1559, NGC 4254, and NGC 5643). All these high-CO-only and high-$\Delta$MS galaxies have grand-design spiral arms and/or a bar; moreover, their CO-only sight lines follow well these galactic structures, implying a dynamic origin of the high CO-only fractions. Although both galaxies with the highest- and lowest-$\Delta$MS in our sample show substantial CO-emitting regions not associated with star formation, the spatial distribution of their CO-only regions is markedly different, potentially pointing to different underlying causes for the suppressed star formation in these regions.

The other two highest-$\Delta$MS galaxies (NGC 1385 and NGC 1511) have lower, but not necessarily low, CO-only fractions (28 and 48%). Both of them happen to be peculiar systems. In fact, four out of the six highest-$\Delta$MS galaxies (NGC 1365, NGC 1385, NGC 1511, and NGC 4254) show signs of interactions with other galaxies.

In our working sample, 33 galaxies show signs of interactions in terms of their morphology. The median overlap sight line fraction of the merger candidates (28%) is slightly lower than that of isolated galaxies (36%). However, the overlap sight lines in the merger candidates contribute a higher fraction flux (90%) to the total H$\alpha$ flux than for the apparently undisturbed galaxies (73%). Taking these numbers at face value, a given unit of star-forming region (overlap) in merger candidates contribute more significantly to the total SFR of a galaxy than a given unit of star-forming region in undisturbed galaxies, assuming that all the H$\alpha$ emission is powered by star formation. We should note that galaxy interactions may trigger central AGN (e.g., Ellison et al., 2019) and shocks prevailing over the disks, which could contribute to H$\alpha$ emission. However, we are not able to cleanly separate H ii regions from other H$\alpha$-emitting sources when using only narrowband data. Spectroscopic observations are necessary to confirm the differences between merger candidates and undisturbed galaxies.

The H$\alpha$-only  sight lines are preferentially found at large galactocentric radii and even become dominant at $R$ $>$ 0.4 $R_{25}$ ($\geq$ 60%) in low-$M_{\ast}$ galaxies. Moreover, the fraction of H$\alpha$-only sight lines is always higher for low-$M_{\ast}$ galaxies than higher-$M_{\ast}$ galaxies at all radii (Figure 5). The lack of CO sight lines at large radii may be due to (1) the lack of gas and/or (2) the existence of low-$\Sigma_{\mathrm{H_{2}}}$ gas that drops below our applied $\Sigma_{\mathrm{H_{2}}}$ threshold (Section 3.2).

To gain insight into the extent of cold gas reservoirs in our galaxies, we compute the radial profiles of gas fractions ($f_{\mathrm{gas}}$) and molecular-to-atomic gas mass ratio ($R_{\mathrm{mol}}$) for galaxies that have spatially-resolved measurements of atomic gas and stellar mass surface densities ($\Sigma_{\mathrm{HI}}$ and $\Sigma_{\ast}$). $f_{\mathrm{gas}}$ is defined as the ratio of the total gas mass ($\Sigma_{\mathrm{H_{2}}}$ +$\Sigma_{\mathrm{HI}}$) to $\Sigma_{\ast}$, while $R_{\mathrm{mol}}$ is defined as the ratio between $\Sigma_{\mathrm{H_{2}}}$ and $\Sigma_{\mathrm{HI}}$. The spatially-resolved HI data are taken from various sources in the literature, including the PHANGS-VLA (D. Utomo et al. in prep.), VLA THINGS (Walter et al., 2008) and VIVA (Chung et al., 2009) surveys, and VLA archive. The spatially-resolved $\Sigma_{\ast}$ are measured based on Spitzer IRAC 3.6$\mu$m or WISE 3.4$\mu$m (Leroy et al., 2019, 2021b). The typical resolution of $\Sigma_{\mathrm{HI}}$ and $\Sigma_{\ast}$ measurements is 1 – 2 kpc. Since we are interested in the general trend of the $f_{\mathrm{gas}}$ and $R_{\mathrm{mol}}$ distributions, high spatial resolution is not needed for this purpose. In total, for 28 and 32 galaxies we can compute their radial $f_{\mathrm{gas}}$ and $R_{\mathrm{mol}}$, respectively. For this analysis, we rely on radial measurements at matched kpc resolution from the PHANGS multi-wavelength database presented in Sun et al. (2020b) and J. Sun et al. (in prep.).

Figure 13 shows the radial $f_{\mathrm{gas}}$ (upper row) and $R_{\mathrm{mol}}$ (lower row) for galaxies with different $M_{\ast}$ (left) and Hubble type (right). Our sample shows a gradual decrease of $f_{\mathrm{gas}}$ with increasing $M_{\ast}$ at all radii. Moreover, $R_{\mathrm{mol}}$ increases with $M_{\ast}$ (when looking at $R$ $\lesssim$ 0.6 $R_{25}$). The trends with Hubble types are consistent in the sense that later type galaxies are less massive. The results in Figure 13 are in good agreement with Saintonge et al. (2011, 2016) based on integrated measurements for a large sample of galaxies

Furthermore, Figure 13 shows that the high-H$\alpha$-only regime ($R>0.4R_{25}$) of low mass galaxies still harbors a significant reservoir of gas with respect to stellar mass ($f_{\mathrm{gas}}$ $\gtrsim$ 0.2), but the gas is predominantly atomic ($R_{\mathrm{mol}}$ $<$ 1). Therefore, it is likely that there are molecular clouds in the outer atomic-dominated, high-H$\alpha$-only regions, but their $\Sigma_{\mathrm{H_{2}}}$ is low and below our applied threshold.

For galaxies with log($M_{\ast}$/M_⊙) $>$ 10.3, around 70–98% of the total CO emission (both median and mean are $\sim$ 90%) are included in our analysis of sight line fractions (i.e., $\Sigma_{\mathrm{H_{2}}}$ $>$ 10 M_☉ pc^-2), while the fraction of CO emission above our applied threshold decreases to $\sim$ 40–90% (both median and mean are $\sim$ 65%) for log($M_{\ast}$/M_⊙) $<$ 10.3. We also observe a stronger variation in the H$\alpha$-only fractions for low-$M_{\ast}$ galaxies when lowering CO threshold while keeping H$\alpha$ threshold fixed. These imply a prevalence of lower mass molecular clouds ($\sim 10^{4}{-}10^{5}$ M_☉) in lower-mass galaxies and significant galaxy-to-galaxy variations in their molecular cloud properties (e.g., Hughes et al., 2013; Schruba et al., 2019; Sun et al., 2020a, b; Rosolowsky et al., 2021). The galaxy-to-galaxy variations in cloud properties also leads to the correlations, albeit relatively weak, between the sight line fractions and CO effective sensitivity in Table 5. Moreover, the gas depletion time of molecular gas ($\tau_{\mathrm{dep}}$) is found to anti-correlate with galaxy $M_{\ast}$, with lower-$M_{\ast}$ galaxies showing shorter $\tau_{\mathrm{dep}}$ even after accounting for the metallicity dependence of $\alpha_{\mathrm{CO}}$ (Utomo et al., 2018). The $\tau_{\mathrm{dep}}$-$M_{\ast}$ relation also causes substantial H$\alpha$ emission not associated with molecular gas in low-$M_{\ast}$ galaxies.

Finally, dissociation is presumably more efficient in low-$\Sigma_{\mathrm{H_{2}}}$ environments due to less dust shielding (e.g., Wolfire et al., 2010). Therefore, CO emission is preferentially seen in high-extinction regions (e.g., inner galactic disks). The need for high extinction to form CO may lead to the consequence that the radial profiles of CO are steeper than that of H$\alpha$ (e.g., Leroy et al., 2008). Since $\Sigma_{\mathrm{H_{2}}}$ decreases rapidly with increasing galactocentric radii, the choice of $\Sigma_{\mathrm{H_{2}}}$ threshold has a significant impact on the overlap fractions at large galactocentric radii, especially for low-$M_{\ast}$ galaxies, whose $\Sigma_{\mathrm{H_{2}}}$ are systematically lower (e.g., Hughes et al., 2013; Sun et al., 2020b).

If we assume that all the CO-only sight lines are pre-star-forming clouds, the three categories of regions we define roughly sample the evolutionary sequence of star-forming regions, in the sense that a cold molecular gas cloud (CO-only) evolves into a star-forming molecular cloud (overlap), and then to a region of (exposed) massive young stars (H$\alpha$-only) where the molecular gas has been largely dispersed and/or dissociated. In this scenario, the areal fractions that we measure are an approximate reflection of the time spent by a star-forming region in each of these different evolutionary phases. Similar frameworks (i.e., counting the number of GMCs and H ii regions) have been applied previously to estimate the duration for which the molecular cloud traced by CO emission is visible in the LMC (Kawamura et al., 2009), constrain the cloud life-cycle in M33 (Gratier et al., 2012; Corbelli et al., 2017), and determine the timescales for dense molecular clumps to evolve from being starless to star-forming in the Milky Way (Battersby et al., 2017).

The evolution of molecular clouds provides constraints on the mechanisms triggering or halting star formation at a specific location in a galaxy. In Paper I, we apply a simple version of the approach to estimate the duration that molecular gas traced by CO emission is visible ($t_{\mathrm{gas}}$):

where $t_{\mathrm{H\alpha}}$ represents the duration that H$\alpha$ emission from H ii regions is visible. $f_{\textrm{CO-only}}$, $f_{\textrm{H$\alpha$-only}}$, and $f_{\mathrm{overlap}}$ denote the fraction of CO-only, H$\alpha$-only, and overlap sight lines, respectively. Then $f_{\mathrm{scale}}$ represents the scaling factor to translate from the fiducial timescale, here $t_{\mathrm{H\alpha}}$, to $t_{\mathrm{gas}}$⁶⁶6We note that the cloud visibility time $t_{\mathrm{gas}}$ is different from the dynamic timescale or the depletion time. A comparison of various relevant timescales, such as cloud visibility time, free fall time, crossing time, and the characteristic timescale for star formation regulated by galactic dynamical processes has been discussed in Chevance et al. (2020) for a subset of PHANGS galaxies. A further discussion will also be presented in the upcoming paper by J. Sun et al. (in prep.).. We emphasize that, by applying Equation (3), we are implicitly assuming that our individual pixels are discrete star-forming units and all the CO-only sight lines contain pre-star-forming clouds (see Section 5.1).

Figure 14 shows the radial trend in $f_{\mathrm{scale}}$ averaged in bins of $M_{\ast}$ (upper panel) and Hubble type (lower panel)⁷⁷7$f_{\mathrm{scale}}$ has to be calculated in radial bins or in any region-by-region manner, otherwise $f_{\mathrm{scale}}$ is heavily determined by the bright CO in the inner part and bright H$\alpha$ in the outer part, but those regions do not form part of the same evolutionary cycle.. There is a ranking of $f_{\mathrm{scale}}$ along $M_{\ast}$ where molecular clouds in high-$M_{\ast}$ galaxies tend to have longer $f_{\mathrm{scale}}$ than clouds in low-$M_{\ast}$ over the radial range probed. Given that typical estimates for $t_{\mathrm{H\alpha}}$ are 5–10 Myr (e.g., Leroy et al., 2012; Kennicutt & Evans, 2012; Haydon et al., 2020), the $t_{\mathrm{gas}}$ of our sample at 150 pc scale, therefore, decreases from $\sim$ 5 –25 Myr for the high-$M_{\ast}$ galaxies, to $\sim$ 5 –15 Myr for the intermediate-$M_{\ast}$ galaxies, and to a few Myr for the low-$M_{\ast}$ galaxies in our sample when applying a CO threshold of 10 M_☉ pc^-2. $f_{\mathrm{scale}}$ also decreases from earlier- to later-type spiral galaxies, but the trend is not as strong as for $M_{\ast}$.

The dependence of $f_{\mathrm{scale}}$ on host galaxy properties suggests the potential importance of environment for regulating star formation (see also Paper I and Chevance et al. 2020). However, the evolution of star-forming regions is only visible when the spatial scale is close enough to the typical region separation length between molecular clouds and H ii regions. Figure 15 shows the dependence of radial $f_{\mathrm{scale}}$ on spatial scale as a function of $M_{\ast}$. Light to dark gray circles denote $f_{\mathrm{scale}}$ at different spatial scales of 300, 500, 1000, and 1500 pc, while $f_{\mathrm{scale}}$ at 150 pc resolution is indicated by red squares. At spatial scales $\leq$ 300 pc, there is a distinct difference in $f_{\mathrm{scale}}$ between galaxy populations, as parameterized by $M_{\ast}$. The differences between galaxies become considerably smaller at spatial scale of $>$ 300 pc due to the significant decrease in CO-only sight lines and increase in overlap sight lines, indicating a critical resolution requirement to resolve the evolution of individual star-forming regions. The critical spatial scale of 300 pc is consistent with the characteristic separation length between independent clouds or star-forming regions reported by Chevance et al. (2020).

While there is a clear dependence on spatial scale, the derived $t_{\mathrm{gas}}$ at 150 pc resolution are in reasonable agreement within a factor of a few (two to three) in most radial bins with the cloud lifetime ($t_{\mathrm{GMC}}$) during which CO emission is visible estimated by Chevance et al. (2020) for seven of our galaxies using the statistical method developed by Kruijssen et al. (2018). We present a direct comparison of the radial variation of our $t_{\mathrm{gas}}$ with $t_{\mathrm{GMC}}$ from Chevance et al. (2020) in Appendix D. The $t_{\mathrm{gas}}$ measured at 150 pc resolution also agrees well with the estimates of cloud (CO) visibility time based on counting the number of GMCs with and without H ii regions (e.g., Kawamura et al., 2009).

Finally, there are several systematic differences in cloud properties and uncertainties to bear in mind when using Equation (3) to estimate the visibility time of molecular clouds traced by CO. First of all, more massive galaxies typically have larger mid-plane ISM pressures, which leads to higher molecular gas surface densities and thus larger GMC sizes traced by CO. On the other hand, in a high-pressure environment, H ii regions might be smaller. Therefore, the number of CO and H$\alpha$ sight lines may reflect not only the variation of cloud visibility time, but also the intrinsic differences in GMC and H ii region properties among galaxies. Moreover, our measurements of H$\alpha$ sight lines  (Section 3.1) is affected by internal extinction and non-H ii powering mechanisms. In principle, the identification of H ii sight lines could be refined by the use of optical IFS observations. Similarly, the fractions of CO sight lines  depend on the applied surface density threshold (Section 3.2). Though our filtering methods are verified by visual inspection of the filtered CO and H$\alpha$ images and comparing with the H ii regions identified in the PHANGS-MUSE images, the impact of methodology remains a potential source of bias (see Appendix A). Finally, molecular clouds and H ii regions may have not yet been fully resolved by our 150 pc resolution as discussed in Section 5.1. A handful of our galaxies have PHANGS-ALMA CO and PHANGS-MUSE H$\alpha$ images with a resolution of $\sim$50 pc, comparable to the size of GMCs and H ii regions (e.g., NGC 0628, NGC 2835, and NGC 5068). At such high resolution, counting number of objects and sight lines should become almost identical, and thus would provide a more robust estimate on cloud (CO) visibility time and even the actual lifetime of molecular clouds. In summary, in addition to cloud visibility time, the region sizes traced by CO and H$\alpha$ emission, the ratio between the resolution and the region separation length, and the data processing strategy may also contribute to the derived $f_{\mathrm{scale}}$.

Many studies have shown that the Kennicutt–Schmidt relation between the surface densities of molecular gas and SFR is tight with an index $\sim$ 0.7–1.4 on kpc scales (e.g., Bigiel et al., 2008; Leroy et al., 2008; Schruba et al., 2011; Leroy et al., 2013; Momose et al., 2013). These findings resonate with our analysis, where overlap sight lines dominate the maps when spatial scale is approximately or greater than 1 kpc; in other words, maps of molecular gas and star formation tracers become very similar.

The picture becomes more complex when the resolution increases. When the resolution is high enough to separate molecular clouds and star-forming regions, molecular gas and star formation surface densities become loosely correlated (e.g., Blanc et al., 2009; Onodera et al., 2010; Kreckel et al., 2018; Pessa et al., 2021) or even anti-correlated (e.g., Schruba et al., 2010) because the two components no longer coincide at all times. This spatial separation between different evolutionary stages of the star formation process is also evident in our sight line maps at the resolution of 150 pc (Figure 2 and Figure B.20). The loosely (anti-)correlated molecular gas and SFR tracers lead to an increasing scatter in the Kennicutt–Schmidt relation at small spatial scales, as a result of incomplete sampling of different evolutionary stages of the gas and star formation cycle (e.g., Schruba et al., 2010; Feldmann et al., 2011; Leroy et al., 2013; Kruijssen & Longmore, 2014).

Our results at 150 pc resolution reveal an important dependence between host galaxy properties and the relative distribution of molecular gas and star formation tracers to each other. Namely, how molecular gas and SFR tracers relate (or do not relate) to one another on the Kennicutt–Schmidt plane depends on the host galaxy properties, such as $M_{\ast}$ and Hubble type. However, any relation between the sight line fractions and host galaxy properties seen at 150 pc resolution is gradually diminished as resolution decreases, and becomes non-identifiable when at resolutions coarser than $\sim$ 500 pc. Galactic structures add a further complexity to the Kennicutt–Schmidt relation as the relation varies among galactic environments (Pan & Kuno, 2017; Pessa et al., 2021; Querejeta et al., 2021). Since the contribution of the different environments varies as a function of galactic radius, the impact of environments could be transferred to the Kennicutt–Schmidt relation when averaging the environments.

Moreover, if the relative distributions of CO-only and H$\alpha$-only  sight lines are complex at high resolution, we might be missing important $\tau_{\mathrm{dep}}$ variations (i.e., slope and intercept of Kennicutt–Schmidt relation) and change in cloud life cycle/time variations (i.e., scatter of the relation) when using Kennicutt–Schmidt relation alone as a diagnostics of star formation process because the relation, by definition, only sees the overlap regions.