i.e., $\sum |\log_{10} I_{\nu}^{\text{obs}}/I_{\nu}^{\text{model}}|$, over a plausible range of $c$ and $h$ shown by the grid in Figure 11. For first results, this simple approach does a reasonable job of maximizing the match between all bright pixels and the model.

## 5.1. Results of Model Fitting

Table 5 reports the best-fit $c$ and $h$ and the fractional contribution of each component to the best-fitting model for each target, $f_c$ and $f_h$. Figure 11 shows the mean absolute residual in $\log_{10} h$ versus $\log_{10} c$ space (i.e., the grid of plausible coefficients) for the full data set. Then, Figures 12 and 13 show the resulting model mid-IR intensities as a function of the observed mid-IR intensities using the best-fitting $c$ and $h$ for each galaxy.

Table 5 and Figures 11 through 13 show that this simple procedure does a fairly good job of fitting the data. We find coefficients that clearly minimize the residuals at $\approx \pm 0.2$ dex. Figures 12 and 13 show that the resulting models do a good job of matching the observations over a wide range of intensities. The color in Figure 12 indicates the relative contribution of the $H\alpha$-tracing component and CO-tracing component in that bin. As expected, the $H\alpha$-tracing component contributes more emission at the higher mid-IR intensities, while the CO-tracing component makes up most of the model at lower mid-IR intensities.

Figure 11 and Table 5 show that the best-fitting coefficients $c$ and $h$ vary from galaxy to galaxy. Following Section 2, we expect such variations if the ISRF, $U$; $D/G$; and mean extinction vary across galaxies. All of these quantities do vary from galaxy to galaxy (e.g., Draine et al. 2007; Aniano et al. 2020), so we suggest to interpret these variations as indicative of real changes in the emissivity and amount of dust in these galaxies. Supporting this view, in Figure 11 and Table 5 all galaxies show similar relative $c$ and $h$ in all four bands. This would be expected if the drivers of the variations are local conditions in the galaxy. For instance, variations in $U$ or $D/G$ should affect $c$ similarly for all four bands.

The main defect in the model, visible in Figures 12 and 13, is that it overpredicts F770W, F1000W, and F1130W emission at high intensity. Figure 13 shows that the overprediction appears present for all galaxies, and Figure 12 shows that it coincides with regions where the $H\alpha$-tracing component makes up most of the model. This feature reflects the same relative PAH emission drop in bright H II regions seen by Chastenet (2023a) and Egorov (2023) and discussed in Section 4.2 and Section 4.4. The F2100W model, on the other hand, appears quite linear across the full intensity range.

Table 5 also reports the flux associated with each component in the model fit. In almost all cases, $f_c \approx f_h$, meaning that the model fit assigns about equal flux to the CO component and the $H\alpha$ component. Taken at face value, this implies that about half of the mid-IR flux from our targets arises directly from star-forming regions traced by $H\alpha$, while about half of the flux can be attributed to emission from dust that is mixed with molecular gas and heated by the ISRF.

Extended “diffuse” or “cirrus” mid-IR emission not directly associated with local, recent star formation has been a longstanding topic of interest. Various studies have attempted to remove or model the effects of such emission using local background subtractions (e.g., Calzetti et al. 2005), physical dust models (e.g., Leroy et al. 2012), Fourier filtering (e.g., Kim et al. 2021; Kim 2023), multiwavelength comparisons

(Crocker et al. 2013; Calapa et al. 2014; Whitcomb et al. 2022), or scale- (Li et al. 2013; Calzetti 2013; Boquien et al. 2015) or environment-dependent SFR calibrations (Boquien et al. 2016; Belfiore et al. 2022b).

Our experiment uses a physically motivated, template-based approach that leverages JWST's high resolution to estimate that in our target regions, ~40%-60% of the mid-IR flux at 7.7-21 µm lies in a component that resembles the CO emission. This broadly agrees with the magnitude of previous estimates of the fraction of “diffuse” mid-IR emission<sup>54</sup> (e.g., Leroy et al. 2012; Crocker et al. 2013; Kim et al. 2021; Kim 2023) and of the scale- or environment-dependent changes in the prefactor $C$ (Equation (5)) to estimate the SFR (e.g., Boquien et al. 2015; Belfiore et al. 2022b). In addition to prototyping a new approach that yields an independent estimate, our data provide evidence that the “diffuse” mid-IR emission in the star-forming parts of galaxies has a distribution like that of the molecular gas. This could be expected theoretically, because dust mixed with molecular gas will dominate the overall dust budget in these molecule-rich inner parts of galaxies (see Leroy et al. 2012). Here we demonstrate using observations that a large fraction of the dust emission, including 40%-60% of the 21 µm emission often used to trace star formation, appears to resemble the CO.

Conversely, the strong, nearly linear correlation between mid-IR and CO emission at a coarser resolution has led to suggestions that mid-IR can trace molecular gas (e.g., Gao et al. 2019; Chown et al. 2021; Leroy et al. 2021; Leroy 2023; Zhang & Ho 2022). Our analysis supports such a potential use even at a quite high physical resolution. However, the modeling exercise here suggests that at high resolution, emission more directly associated with recent star formation will contribute ≈50% of the mid-IR flux. Because the distributions of recent star formation and neutral gas at these scales no longer perfectly match, this emission will represent an important contaminant that may need to be accounted for or masked out in quantitative gas estimates.

## 5.2. Logical Next Steps to Model the Mid-IR

Our fits offer a good first-order description of the bright mid-IR, but several directions for refinement are also immediately obvious. First, to model the bright F770W, F1000W, and F1130W emission, the $H\alpha$ component should include some nonlinearity to reflect decreased PAH or small-grain emission in the bright H II regions (see references and discussion in Section 4.4).

At the faint-intensity end, a general form of the model must account for mid-IR emission associated with phases of the ISM other than molecular gas, including diffuse atomic gas or CO-dark molecular gas (see Sandstrom 2023b). Though only IC 5332 has significant flux associated with such regions in our current sample, atomic-gas-dominated regions cover most of the area in most galaxy disks. A fixed offset in the model may be a reasonable first approximation given the rough constancy of the atomic gas layer in inner galaxy disks. Alternatively, this

<footnote n="54">54 Note when comparing to previous diffuse fraction estimates that CO and $H\alpha$ do still overlap to some degree in our data (Section 4.3) and that our approach will “split” the emission from such a region, assigning some to the CO and some to the $H\alpha$ component. Many previous morphological approaches will assign all emission near a star-forming region to the “compact” or star formation-tracing component. Our approach might therefore be expected to yield moderately higher cirrus estimates.</footnote>
i.e., $\sum |\log_{10} I_{\nu}^{\text{obs}}/I_{\nu}^{\text{model}}|$, over a plausible range of $c$ and $h$ shown by the grid in Figure 11. For first results, this simple approach does a reasonable job of maximizing the match between all bright pixels and the model.

## 5.1. Results of Model Fitting

Table 5 reports the best-fit $c$ and $h$ and the fractional contribution of each component to the best-fitting model for each target, $f_c$ and $f_h$. Figure 11 shows the mean absolute residual in $\log_{10} h$ versus $\log_{10} c$ space (i.e., the grid of plausible coefficients) for the full data set. Then, Figures 12 and 13 show the resulting model mid-IR intensities as a function of the observed mid-IR intensities using the best-fitting $c$ and $h$ for each galaxy.

Table 5 and Figures 11 through 13 show that this simple procedure does a fairly good job of fitting the data. We find coefficients that clearly minimize the residuals at $\approx \pm 0.2$ dex. Figures 12 and 13 show that the resulting models do a good job of matching the observations over a wide range of intensities. The color in Figure 12 indicates the relative contribution of the $H\alpha$-tracing component and CO-tracing component in that bin. As expected, the $H\alpha$-tracing component contributes more emission at the higher mid-IR intensities, while the CO-tracing component makes up most of the model at lower mid-IR intensities.

Figure 11 and Table 5 show that the best-fitting coefficients $c$ and $h$ vary from galaxy to galaxy. Following Section 2, we expect such variations if the ISRF, $U$; $D/G$; and mean extinction vary across galaxies. All of these quantities do vary from galaxy to galaxy (e.g., Draine et al. 2007; Aniano et al. 2020), so we suggest to interpret these variations as indicative of real changes in the emissivity and amount of dust in these galaxies. Supporting this view, in Figure 11 and Table 5 all galaxies show similar relative $c$ and $h$ in all four bands. This would be expected if the drivers of the variations are local conditions in the galaxy. For instance, variations in $U$ or $D/G$ should affect $c$ similarly for all four bands.

The main defect in the model, visible in Figures 12 and 13, is that it overpredicts F770W, F1000W, and F1130W emission at high intensity. Figure 13 shows that the overprediction appears present for all galaxies, and Figure 12 shows that it coincides with regions where the $H\alpha$-tracing component makes up most of the model. This feature reflects the same relative PAH emission drop in bright H II regions seen by Chastenet (2023a) and Egorov (2023) and discussed in Section 4.2 and Section 4.4. The F2100W model, on the other hand, appears quite linear across the full intensity range.

Table 5 also reports the flux associated with each component in the model fit. In almost all cases, $f_c \approx f_h$, meaning that the model fit assigns about equal flux to the CO component and the $H\alpha$ component. Taken at face value, this implies that about half of the mid-IR flux from our targets arises directly from star-forming regions traced by $H\alpha$, while about half of the flux can be attributed to emission from dust that is mixed with molecular gas and heated by the ISRF.

Extended “diffuse” or “cirrus” mid-IR emission not directly associated with local, recent star formation has been a longstanding topic of interest. Various studies have attempted to remove or model the effects of such emission using local background subtractions (e.g., Calzetti et al. 2005), physical dust models (e.g., Leroy et al. 2012), Fourier filtering (e.g., Kim et al. 2021; Kim 2023), multiwavelength comparisons

(Crocker et al. 2013; Calapa et al. 2014; Whitcomb et al. 2022), or scale- (Li et al. 2013; Calzetti 2013; Boquien et al. 2015) or environment-dependent SFR calibrations (Boquien et al. 2016; Belfiore et al. 2022b).

Our experiment uses a physically motivated, template-based approach that leverages JWST’s high resolution to estimate that in our target regions, ~40%-60% of the mid-IR flux at 7.7–21 µm lies in a component that resembles the CO emission. This broadly agrees with the magnitude of previous estimates of the fraction of “diffuse” mid-IR emission<sup>54</sup> (e.g., Leroy et al. 2012; Crocker et al. 2013; Kim et al. 2021; Kim 2023) and of the scale- or environment-dependent changes in the prefactor $C$ (Equation (5)) to estimate the SFR (e.g., Boquien et al. 2015; Belfiore et al. 2022b). In addition to prototyping a new approach that yields an independent estimate, our data provide evidence that the “diffuse” mid-IR emission in the star-forming parts of galaxies has a distribution like that of the molecular gas. This could be expected theoretically, because dust mixed with molecular gas will dominate the overall dust budget in these molecule-rich inner parts of galaxies (see Leroy et al. 2012). Here we demonstrate using observations that a large fraction of the dust emission, including 40%-60% of the 21 µm emission often used to trace star formation, appears to resemble the CO.

Conversely, the strong, nearly linear correlation between mid-IR and CO emission at a coarser resolution has led to suggestions that mid-IR can trace molecular gas (e.g., Gao et al. 2019; Chown et al. 2021; Leroy et al. 2021; Leroy 2023; Zhang & Ho 2022). Our analysis supports such a potential use even at a quite high physical resolution. However, the modeling exercise here suggests that at high resolution, emission more directly associated with recent star formation will contribute ≈50% of the mid-IR flux. Because the distributions of recent star formation and neutral gas at these scales no longer perfectly match, this emission will represent an important contaminant that may need to be accounted for or masked out in quantitative gas estimates.

## 5.2. Logical Next Steps to Model the Mid-IR

Our fits offer a good first-order description of the bright mid-IR, but several directions for refinement are also immediately obvious. First, to model the bright F770W, F1000W, and F1130W emission, the $H\alpha$ component should include some nonlinearity to reflect decreased PAH or small-grain emission in the bright H II regions (see references and discussion in Section 4.4).

At the faint-intensity end, a general form of the model must account for mid-IR emission associated with phases of the ISM other than molecular gas, including diffuse atomic gas or CO-dark molecular gas (see Sandstrom 2023b). Though only IC 5332 has significant flux associated with such regions in our current sample, atomic-gas-dominated regions cover most of the area in most galaxy disks. A fixed offset in the model may be a reasonable first approximation given the rough constancy of the atomic gas layer in inner galaxy disks. Alternatively, this

<footnote n="54">54 Note when comparing to previous diffuse fraction estimates that CO and $H\alpha$ do still overlap to some degree in our data (Section 4.3) and that our approach will “split” the emission from such a region, assigning some to the CO and some to the $H\alpha$ component. Many previous morphological approaches will assign all emission near a star-forming region to the “compact” or star formation-tracing component. Our approach might therefore be expected to yield moderately higher cirrus estimates.</footnote>
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Template-matching model goodness of fit vs. CO and Hα scaling coefficients, *c* and *h*. Mean absolute log residual for models that attempt to match observed bright mid-IR emission with a linear combination of scaled CO and scaled Hα emission (Equation (12); Section 5). The contours and color image show goodness of fit using all data as a function of possible log₁₀ *c* and log₁₀ *h*. All four bands yield a clear minimum, shown by the circle, at physically plausible values (Section 6), which imply roughly equal flux associated with the CO-tracking and Hα-tracking components. We run a similar minimization for each target galaxy independently, and the figure shows the resulting best-fitting coefficients for each galaxy. The variations from galaxy to galaxy appear similar from band to band, and we expect these reflect real physical variations, e.g., in the ISRF, dust-to-gas ratio, and level of extinction, among our targets. Table 5 gives fits for all bands and targets. Figures 12 and 13 show the model vs. observation for these fits.</figcaption></figure>

approach could be used to isolate non-CO-emitting gas if all the other components were well understood.

We also note that our analysis treats the DIG and H II regions together, positing that both types of emission may track dust reprocessing UV light from recent star formation. This may be reasonable to first order given that the DIG in our targets shows a morphology consistent with being created by light leaking from star-forming regions (Belfiore et al. 2022a). In the future,

distinguishing the two components when comparing to the mid-IR should yield more insight into how UV light from young stars is reprocessed into dust emission.

Finally, we expect that working at even higher resolution will improve the physical insight gained from the modeling. For these first results, we used a fixed 1.7"7, and our physical resolution for NGC 1365 and NGC 7496 remains fairly coarse at ~150 pc. At this resolution, there remains significant overlap
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Template-matching model goodness of fit vs. CO and Hα scaling coefficients, *c* and *h*. Mean absolute log residual for models that attempt to match observed bright mid-IR emission with a linear combination of scaled CO and scaled Hα emission (Equation (12); Section 5). The contours and color image show goodness of fit using all data as a function of possible log₁₀ *c* and log₁₀ *h*. All four bands yield a clear minimum, shown by the circle, at physically plausible values (Section 6), which imply roughly equal flux associated with the CO-tracking and Hα-tracking components. We run a similar minimization for each target galaxy independently, and the figure shows the resulting best-fitting coefficients for each galaxy. The variations from galaxy to galaxy appear similar from band to band, and we expect these reflect real physical variations, e.g., in the ISRF, dust-to-gas ratio, and level of extinction, among our targets. Table 5 gives fits for all bands and targets. Figures 12 and 13 show the model vs. observation for these fits.</figcaption></figure>

approach could be used to isolate non-CO-emitting gas if all the other components were well understood.

We also note that our analysis treats the DIG and H II regions together, positing that both types of emission may track dust reprocessing UV light from recent star formation. This may be reasonable to first order given that the DIG in our targets shows a morphology consistent with being created by light leaking from star-forming regions (Belfiore et al. 2022a). In the future,

distinguishing the two components when comparing to the mid-IR should yield more insight into how UV light from young stars is reprocessed into dust emission.

Finally, we expect that working at even higher resolution will improve the physical insight gained from the modeling. For these first results, we used a fixed 1.7, and our physical resolution for NGC 1365 and NGC 7496 remains fairly coarse at ~150 pc. At this resolution, there remains significant overlap
<table><caption>**Table 5**
Template-fitting Results</caption><thead><tr><th>Predicted Band</th><th>Quantity</th><th>All Data</th><th>IC 5332</th><th>NGC 0628</th><th>NGC 1365</th><th>NGC 7496</th></tr></thead><tbody><tr><td>F770W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.204</td><td>0.224</td><td>0.180</td><td>0.221</td><td>0.196</td></tr><tr><td>F770W</td><td>c</td><td>0.468</td><td>0.417</td><td>0.525</td><td>0.288</td><td>0.776</td></tr><tr><td>F770W</td><td>h/10<sup>5</sup></td><td>1.318</td><td>0.741</td><td>1.202</td><td>1.862</td><td>0.871</td></tr><tr><td>F770W</td><td>f<sub>c</sub></td><td>0.50</td><td>0.46</td><td>0.51</td><td>0.40</td><td>0.62</td></tr><tr><td>F770W</td><td>f<sub>h</sub></td><td>0.50</td><td>0.54</td><td>0.49</td><td>0.60</td><td>0.38</td></tr><tr><td>F1000W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.223</td><td>0.245</td><td>0.199</td><td>0.239</td><td>0.213</td></tr><tr><td>F1000W</td><td>c</td><td>0.214</td><td>0.162</td><td>0.234</td><td>0.141</td><td>0.339</td></tr><tr><td>F1000W</td><td>h/10<sup>5</sup></td><td>0.447</td><td>0.316</td><td>0.389</td><td>0.692</td><td>0.316</td></tr><tr><td>F1000W</td><td>f<sub>c</sub></td><td>0.58</td><td>0.45</td><td>0.59</td><td>0.47</td><td>0.67</td></tr><tr><td>F1000W</td><td>f<sub>h</sub></td><td>0.42</td><td>0.55</td><td>0.41</td><td>0.53</td><td>0.33</td></tr><tr><td>F1130W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.218</td><td>0.230</td><td>0.190</td><td>0.240</td><td>0.213</td></tr><tr><td>F1130W</td><td>c</td><td>0.724</td><td>0.589</td><td>0.794</td><td>0.490</td><td>1.202</td></tr><tr><td>F1130W</td><td>h/10<sup>5</sup></td><td>1.660</td><td>0.912</td><td>1.445</td><td>2.570</td><td>0.977</td></tr><tr><td>F1130W</td><td>f<sub>c</sub></td><td>0.56</td><td>0.50</td><td>0.56</td><td>0.46</td><td>0.70</td></tr><tr><td>F1130W</td><td>f<sub>h</sub></td><td>0.44</td><td>0.50</td><td>0.44</td><td>0.54</td><td>0.30</td></tr><tr><td>F2100W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.203</td><td>0.230</td><td>0.166</td><td>0.239</td><td>0.211</td></tr><tr><td>F2100W</td><td>c</td><td>0.269</td><td>0.263</td><td>0.282</td><td>0.178</td><td>0.479</td></tr><tr><td>F2100W</td><td>h/10<sup>5</sup></td><td>0.676</td><td>0.479</td><td>0.603</td><td>0.977</td><td>0.550</td></tr><tr><td>F2100W</td><td>f<sub>c</sub></td><td>0.55</td><td>0.43</td><td>0.55</td><td>0.49</td><td>0.61</td></tr><tr><td>F2100W</td><td>f<sub>h</sub></td><td>0.45</td><td>0.57</td><td>0.45</td><td>0.51</td><td>0.39</td></tr></tbody></table>

**Notes.** Best-fit model coefficients, *c* and *h*, to match the observed mid-IR intensity using a linear combination of scaled CO and Hα (Section 5, Equations (12)). *c* is the coefficient to scale CO and has units of MJy sr⁻¹ (K km s⁻¹)⁻¹. *h* is the coefficient to scale extinction-corrected Hα and has units of MJy sr⁻¹ (erg s⁻¹ cm⁻² sr⁻¹)⁻¹. Following Equation (13), *f*<sub>c</sub> and *f*<sub>h</sub> report the fraction of the total model flux associated with the CO-tracing component and Hα-tracing component.

between CO and Hα emission (e.g., see Schinnerer et al. 2019; Kim et al. 2022; Pan et al. 2022), while at higher resolution we expect to be able to distinguish the two components even more sharply. With the full combined PHANGS–JWST, MUSE, and ALMA sample, we will include a larger sample of nearby galaxies and include galaxies with higher-resolution ALMA maps. As a result, we expect to conduct a more extensive analysis at even higher physical resolutions, 50–100 pc, as the survey proceeds.

## 6. CO-to-Mid-IR and Hα to Mid-IR Ratios

We have so far focused on correlations and power-law slopes, but the CO-to-mid-IR and Hα-to-mid-IR ratios also carry physical meaning. Figure 14 visualizes the median ratios that we measure from our data, with associated scatter (Table 4). We also plot our template-fit coefficients (Table 5), which have separately assigned flux to the CO-tracing or Hα-tracing component.

### 6.1. CO-to-Mid-IR Ratios

We measure typical CO-to-mid-IR ratios (blue points, Figure 14) of $I_{CO}/I_{MIR} \approx 0.8–2.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹. This agrees broadly with the “rule of thumb” observed for large parts of galaxies that a CO intensity of 1 K km s⁻¹ corresponds to about 1 MJy sr⁻¹ in the mid-IR (see also Leroy 2023). After accounting for the mean band ratios in Table 1, the typical values expressed in units of 7.7 µm intensity, $I_{CO}/I_{MIR} R_{7.7}^{X} \approx 0.8–1.3$ K km s⁻¹ (MJy sr⁻¹)⁻¹.

The template-fit coefficients (green points) imply higher CO-to-mid-IR when we isolate the CO-tracing component. Here the ratios span $c^{-1} \approx 1.4–4.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹, i.e., about

twice the overall ratio, reflecting that only half the mid-IR flux in the model fit has been assigned to the CO-tracing component. When placed on a common 7.7 µm intensity scale yield, the template fits yield $c^{-1} R_{7.7}^{X} \approx 1.3–2.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹.

For comparison, Equation (6) suggests that for molecular gas heated by a solar neighborhood radiation field ($U=1$) and a typical dust-to-gas ratio:

$$ \frac{I_{CO}}{I_{MIR}} \sim 5.7 \text{ K km s}^{-1} (\text{MJy sr}^{-1})^{-1} \times \left( R_{7.7}^{X} \left( \frac{\alpha_{CO} 1-0}{\alpha_{CO}^{MW} 1-0} \right) \left( \frac{R_{21}}{0.65} \right) \left( \frac{D/G}{0.01} \right) \left( \frac{q_{PAH}}{0.046} \right) \left( \frac{U}{U_0} \right) \right)^{-1} \quad (14) $$

with a prefactor about five times higher than our measured ratio and ≈2.5 times higher than our typical template-fit coefficient.

For the template-fit coefficients, the ISRF factor, *U*, almost certainly explains most of the difference from the fiducial expectation. Studying the whole disk of a local sample of star-forming galaxies, Aniano et al. (2020) find a typical mean ISRF in the range $U/U_0 \sim 2–3$. For the one target where we overlap their study, NGC 0628, they find both the diffuse and mean ISRF to be $U/U_0 \sim 2$. Given that PHANGS–JWST targets the inner part of star-forming galaxies and the ISRF tracks star formation activity and stellar density, it seems very likely that in more diffuse regions $U/U_0 \gtrsim 2$ and plausibly higher. Given this, our reference comparison line in Figure 14 shows $U/U_0 = 2.5$ and this appears to be both physically reasonable and represent a good description of the best-fitting coefficients.
<table><caption>**Table 5**
Template-fitting Results</caption><thead><tr><th>Predicted Band</th><th>Quantity</th><th>All Data</th><th>IC 5332</th><th>NGC 0628</th><th>NGC 1365</th><th>NGC 7496</th></tr></thead><tbody><tr><td>F770W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.204</td><td>0.224</td><td>0.180</td><td>0.221</td><td>0.196</td></tr><tr><td>F770W</td><td>c</td><td>0.468</td><td>0.417</td><td>0.525</td><td>0.288</td><td>0.776</td></tr><tr><td>F770W</td><td>h/10<sup>5</sup></td><td>1.318</td><td>0.741</td><td>1.202</td><td>1.862</td><td>0.871</td></tr><tr><td>F770W</td><td>f<sub>c</sub></td><td>0.50</td><td>0.46</td><td>0.51</td><td>0.40</td><td>0.62</td></tr><tr><td>F770W</td><td>f<sub>h</sub></td><td>0.50</td><td>0.54</td><td>0.49</td><td>0.60</td><td>0.38</td></tr><tr><td>F1000W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.223</td><td>0.245</td><td>0.199</td><td>0.239</td><td>0.213</td></tr><tr><td>F1000W</td><td>c</td><td>0.214</td><td>0.162</td><td>0.234</td><td>0.141</td><td>0.339</td></tr><tr><td>F1000W</td><td>h/10<sup>5</sup></td><td>0.447</td><td>0.316</td><td>0.389</td><td>0.692</td><td>0.316</td></tr><tr><td>F1000W</td><td>f<sub>c</sub></td><td>0.58</td><td>0.45</td><td>0.59</td><td>0.47</td><td>0.67</td></tr><tr><td>F1000W</td><td>f<sub>h</sub></td><td>0.42</td><td>0.55</td><td>0.41</td><td>0.53</td><td>0.33</td></tr><tr><td>F1130W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.218</td><td>0.230</td><td>0.190</td><td>0.240</td><td>0.213</td></tr><tr><td>F1130W</td><td>c</td><td>0.724</td><td>0.589</td><td>0.794</td><td>0.490</td><td>1.202</td></tr><tr><td>F1130W</td><td>h/10<sup>5</sup></td><td>1.660</td><td>0.912</td><td>1.445</td><td>2.570</td><td>0.977</td></tr><tr><td>F1130W</td><td>f<sub>c</sub></td><td>0.56</td><td>0.50</td><td>0.56</td><td>0.46</td><td>0.70</td></tr><tr><td>F1130W</td><td>f<sub>h</sub></td><td>0.44</td><td>0.50</td><td>0.44</td><td>0.54</td><td>0.30</td></tr><tr><td>F2100W</td><td>Mean |log<sub>10</sub> model data<sup>-1</sup>|</td><td>0.203</td><td>0.230</td><td>0.166</td><td>0.239</td><td>0.211</td></tr><tr><td>F2100W</td><td>c</td><td>0.269</td><td>0.263</td><td>0.282</td><td>0.178</td><td>0.479</td></tr><tr><td>F2100W</td><td>h/10<sup>5</sup></td><td>0.676</td><td>0.479</td><td>0.603</td><td>0.977</td><td>0.550</td></tr><tr><td>F2100W</td><td>f<sub>c</sub></td><td>0.55</td><td>0.43</td><td>0.55</td><td>0.49</td><td>0.61</td></tr><tr><td>F2100W</td><td>f<sub>h</sub></td><td>0.45</td><td>0.57</td><td>0.45</td><td>0.51</td><td>0.39</td></tr></tbody></table>

**Notes.** Best-fit model coefficients, *c* and *h*, to match the observed mid-IR intensity using a linear combination of scaled CO and Hα (Section 5, Equations (12)). *c* is the coefficient to scale CO and has units of MJy sr⁻¹ (K km s⁻¹)⁻¹. *h* is the coefficient to scale extinction-corrected Hα and has units of MJy sr⁻¹ (erg s⁻¹ cm⁻² sr⁻¹)⁻¹. Following Equation (13), *f*<sub>c</sub> and *f*<sub>h</sub> report the fraction of the total model flux associated with the CO-tracing component and Hα-tracing component.

between CO and Hα emission (e.g., see Schinnerer et al. 2019; Kim et al. 2022; Pan et al. 2022), while at higher resolution we expect to be able to distinguish the two components even more sharply. With the full combined PHANGS–JWST, MUSE, and ALMA sample, we will include a larger sample of nearby galaxies and include galaxies with higher-resolution ALMA maps. As a result, we expect to conduct a more extensive analysis at even higher physical resolutions, 50–100 pc, as the survey proceeds.

## 6. CO-to-Mid-IR and Hα to Mid-IR Ratios

We have so far focused on correlations and power-law slopes, but the CO-to-mid-IR and Hα-to-mid-IR ratios also carry physical meaning. Figure 14 visualizes the median ratios that we measure from our data, with associated scatter (Table 4). We also plot our template-fit coefficients (Table 5), which have separately assigned flux to the CO-tracing or Hα-tracing component.

### 6.1. CO-to-Mid-IR Ratios

We measure typical CO-to-mid-IR ratios (blue points, Figure 14) of $I_{CO}/I_{MIR} \approx 0.8–2.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹. This agrees broadly with the “rule of thumb” observed for large parts of galaxies that a CO intensity of 1 K km s⁻¹ corresponds to about 1 MJy sr⁻¹ in the mid-IR (see also Leroy 2023). After accounting for the mean band ratios in Table 1, the typical values expressed in units of 7.7 µm intensity, $I_{CO}/I_{MIR} R_{7.7}^X \approx 0.8–1.3$ K km s⁻¹ (MJy sr⁻¹)⁻¹.

The template-fit coefficients (green points) imply higher CO-to-mid-IR when we isolate the CO-tracing component. Here the ratios span $c^{-1} \approx 1.4–4.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹, i.e., about

twice the overall ratio, reflecting that only half the mid-IR flux in the model fit has been assigned to the CO-tracing component. When placed on a common 7.7 µm intensity scale yield, the template fits yield $c^{-1} R_{7.7}^X \approx 1.3–2.7$ K km s⁻¹ (MJy sr⁻¹)⁻¹.

For comparison, Equation (6) suggests that for molecular gas heated by a solar neighborhood radiation field ($U=1$) and a typical dust-to-gas ratio:

$$ \frac{I_{CO}}{I_{MIR}} \sim 5.7 \text{ K km s}^{-1} (\text{MJy sr}^{-1})^{-1} \times \left( R_{7.7}^{X} \left( \frac{\alpha_{CO} 1-0}{\alpha_{CO}^{MW} 1-0} \right) \left( \frac{R_{21}}{0.65} \right) \left( \frac{D/G}{0.01} \right) \left( \frac{q_{PAH}}{0.046} \right) \left( \frac{U}{U_0} \right) \right)^{-1} \quad (14) $$

with a prefactor about five times higher than our measured ratio and ≈2.5 times higher than our typical template-fit coefficient.

For the template-fit coefficients, the ISRF factor, *U*, almost certainly explains most of the difference from the fiducial expectation. Studying the whole disk of a local sample of star-forming galaxies, Aniano et al. (2020) find a typical mean ISRF in the range $U/U_0 \sim 2–3$. For the one target where we overlap their study, NGC 0628, they find both the diffuse and mean ISRF to be $U/U_0 \sim 2$. Given that PHANGS–JWST targets the inner part of star-forming galaxies and the ISRF tracks star formation activity and stellar density, it seems very likely that in more diffuse regions $U/U_0 \gtrsim 2$ and plausibly higher. Given this, our reference comparison line in Figure 14 shows $U/U_0 = 2.5$ and this appears to be both physically reasonable and represent a good description of the best-fitting coefficients.
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Mid-IR intensity predicted from a linear combination of CO and extinction-corrected Hα as a function of observed mid-IR intensity. As Figures 5 and 7 but now showing our model constructed from a linear combination of scaled I<sub>CO</sub> and I<sub>Hα</sub> (Equation (12), Section 5) as a function of the observed mid-IR intensity. We use the best-fitting coefficients for each individual galaxy (Table 5 and the points in Figure 11) and color the data by the mean fractional contribution of the Hα component in that bin. That is, in yellow bins, the model assigns more flux to the Hα-tracing component while in dark green regions, the CO-tracing component contributes most of the flux. The red lines show equality. The shaded regions show the limits of our definition of “bright” emission, which represents the extent of the data fit. See Figure 13 for individual galaxy fits.</figcaption></figure>

Logically, the difference between our higher $c^{-1}$ and the lower measured median ratios should stem from the inclusion of regions of recent star formation and intense heating in the median ratio. The template fit will assign much of the flux associated with these regions to the Hα-tracing component, but they are included in the overall ratio.

## 6.2. Hα-to-Mid-IR Ratios

We measure extinction-corrected Hα-to-mid-IR ratios of $log_{10} H\alpha/I_{MIR} \sim -5.7$ to $-5.2$ (red points, Figure 14) in units of erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (MJy sr$^{-1}$)$^{-1}$. If we adjust these for the band ratios in Table 1 all bands yield a fairly consistent median

$log_{10} H\alpha/I_{MIR} R_{7.7}^{X} \sim -5.6$ to $-5.4$. As with the CO case, the template-fit coefficients yield higher values, $log_{10} h^{-1} R_{7.7}^{X} \sim -5.2$ to $-4.9$, with $log_{10} h^{-1} R_{7.7}^{X} \approx -5.0$ on average. This reflects that these template-fitting values do not include emission associated with the CO-tracing component.

Following Equations (5) and (7) the normalization of the Hα-to-mid-IR ratio can be expressed in terms of the coefficient $C_{24}$ to translate mid-IR to SFR, with $log_{10} H\alpha/I_{MIR} \sim -5.2$ expected at 7.7 µm for a standard $log_{10} C_{24} \sim -42.7$ often used for whole galaxies or large parts of galaxies (e.g., see Kennicutt & Evans 2012; Belfiore et al. 2022b). The line that goes through the purple points in Figure 14 shows a value two
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Mid-IR intensity predicted from a linear combination of CO and extinction-corrected Hα as a function of observed mid-IR intensity. As Figures 5 and 7 but now showing our model constructed from a linear combination of scaled I<sub>CO</sub> and I<sub>Hα</sub> (Equation (12), Section 5) as a function of the observed mid-IR intensity. We use the best-fitting coefficients for each individual galaxy (Table 5 and the points in Figure 11) and color the data by the mean fractional contribution of the Hα component in that bin. That is, in yellow bins, the model assigns more flux to the Hα-tracing component while in dark green regions, the CO-tracing component contributes most of the flux. The red lines show equality. The shaded regions show the limits of our definition of “bright” emission, which represents the extent of the data fit. See Figure 13 for individual galaxy fits.</figcaption></figure>

Logically, the difference between our higher $c^{-1}$ and the lower measured median ratios should stem from the inclusion of regions of recent star formation and intense heating in the median ratio. The template fit will assign much of the flux associated with these regions to the Hα-tracing component, but they are included in the overall ratio.

## 6.2. Hα-to-Mid-IR Ratios

We measure extinction-corrected Hα-to-mid-IR ratios of $log_{10} H\alpha/I_{MIR} \sim -5.7$ to $-5.2$ (red points, Figure 14) in units of erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (MJy sr$^{-1}$)$^{-1}$. If we adjust these for the band ratios in Table 1 all bands yield a fairly consistent median

$log_{10} H\alpha/I_{MIR} R_{7,7}^{X} \sim -5.6$ to $-5.4$. As with the CO case, the template-fit coefficients yield higher values, $log_{10} h^{-1} R_{7,7}^{X} \sim -5.2$ to $-4.9$, with $log_{10} h^{-1} R_{7,7}^{X} \approx -5.0$ on average. This reflects that these template-fitting values do not include emission associated with the CO-tracing component.

Following Equations (5) and (7) the normalization of the Hα-to-mid-IR ratio can be expressed in terms of the coefficient $C_{24}$ to translate mid-IR to SFR, with $log_{10} H\alpha/I_{MIR} \sim -5.2$ expected at 7.7 µm for a standard $log_{10} C_{24} \sim -42.7$ often used for whole galaxies or large parts of galaxies (e.g., see Kennicutt & Evans 2012; Belfiore et al. 2022b). The line that goes through the purple points in Figure 14 shows a value two
<figure><img src="image_15.png" /><figcaption>**Figure 13.** Mid-IR intensity predicted from a linear combination of CO and extinction-corrected Hα as a function of observed mid-IR intensity, separated by galaxy. As Figures 6, 8, and 9 but now showing the mid-IR intensity predicted by our model (Equation (12), Section 5) as a function of observed mid-IR intensity for individual galaxies. As in those figures, the dark gray region shows results for all galaxies combined with the extent showing the 16th to 84th range. The individual symbols show median results for individual galaxies and the line indicates one-to-one agreement. Overall, the agreement between prediction and observation appears excellent for all four galaxies, with the models failure to account for suppression of PAH emission in H II regions leading to mild overpredictions at high F770W, F1000W, and F1130W intensities.</figcaption></figure>

times lower than this, $\log_{10} C_{24} \sim -43.0$, implying that two times higher SFR-to-mid-IR ratio describes the template-fit values of *h* compared to whole galaxies or large regions. This result agrees qualitatively with the results of Belfiore et al. (2022b) for the brightest regions and for the overall literature, which finds lower $C_{24}$ when focusing on the most intense star-forming regions rather than whole galaxies (e.g., Kennicutt & Evans 2012; Calzetti 2013).

Our median ratios correspond to somewhat lower SFR-to-mid-IR ratios, or higher $C_{24}$, than this typical value. This partially reflects our methodology. We plot median ratios, but the Hα-to-mid-IR relation (Section 4.2) is superlinear with much of the flux in a set of bright regions. Our approach downweights these bright regions and emphasizes the lower intensity regions, which tend to be dominated by emission associated with molecular gas (see Figure 12). More generally the lower overall ratio reflects the fact that averaging over whole

galaxies, emission from dust associated with molecular gas and other “diffuse” emission will be averaged in with emission directly from star-forming regions. This tends to be calibrated out by SFR conversion recipes at low resolution yielding the sort of higher $C_{24}$ and lower SFR-to-mid-IR ratios that we observe here.

## 6.3. The Impact of Metallicity Based on Differences between IC 5332 and the Other Targets

IC 5332 has lower stellar mass and only 0.6 times the metallicity of our other three targets (Table 2). Consistent with the general trends for lower stellar mass galaxies to have lower star formation activity and a lower molecular to atomic gas fraction (e.g., Saintonge & Catinella 2022), the galaxy shows overall lower surface brightness in the mid-IR and in CO than the other three targets. We expect the dust-to-gas ratio, *D*/*G*, to
<figure><img src="image_16.png" /><figcaption>**Figure 13.** Mid-IR intensity predicted from a linear combination of CO and extinction-corrected Hα as a function of observed mid-IR intensity, separated by galaxy. As Figures 6, 8, and 9 but now showing the mid-IR intensity predicted by our model (Equation (12), Section 5) as a function of observed mid-IR intensity for individual galaxies. As in those figures, the dark gray region shows results for all galaxies combined with the extent showing the 16th to 84th range. The individual symbols show median results for individual galaxies and the line indicates one-to-one agreement. Overall, the agreement between prediction and observation appears excellent for all four galaxies, with the models failure to account for suppression of PAH emission in H II regions leading to mild overpredictions at high F770W, F1000W, and F1130W intensities.</figcaption></figure>

times lower than this, $\log_{10} C_{24} \sim -43.0$, implying that two times higher SFR-to-mid-IR ratio describes the template-fit values of *h* compared to whole galaxies or large regions. This result agrees qualitatively with the results of Belfiore et al. (2022b) for the brightest regions and for the overall literature, which finds lower $C_{24}$ when focusing on the most intense star-forming regions rather than whole galaxies (e.g., Kennicutt & Evans 2012; Calzetti 2013).

Our median ratios correspond to somewhat lower SFR-to-mid-IR ratios, or higher $C_{24}$, than this typical value. This partially reflects our methodology. We plot median ratios, but the Hα-to-mid-IR relation (Section 4.2) is superlinear with much of the flux in a set of bright regions. Our approach downweights these bright regions and emphasizes the lower intensity regions, which tend to be dominated by emission associated with molecular gas (see Figure 12). More generally the lower overall ratio reflects the fact that averaging over whole

galaxies, emission from dust associated with molecular gas and other “diffuse” emission will be averaged in with emission directly from star-forming regions. This tends to be calibrated out by SFR conversion recipes at low resolution yielding the sort of higher $C_{24}$ and lower SFR-to-mid-IR ratios that we observe here.

## 6.3. The Impact of Metallicity Based on Differences between IC 5332 and the Other Targets

IC 5332 has lower stellar mass and only 0.6 times the metallicity of our other three targets (Table 2). Consistent with the general trends for lower stellar mass galaxies to have lower star formation activity and a lower molecular to atomic gas fraction (e.g., Saintonge & Catinella 2022), the galaxy shows overall lower surface brightness in the mid-IR and in CO than the other three targets. We expect the dust-to-gas ratio, *D*/*G*, to
<figure><img src="image_16.png" /><figcaption>**Figure 14.** Summary CO-to-mid-IR and extinction-corrected Hα-to-mid-IR median ratios and template-matching coefficients. Each point in the left panel shows a CO (2-1) to mid-IR ratio, and each point in the right panel shows an extinction-corrected Hα-to-mid-IR ratio. To allow easy comparisons between bands, all ratios have been scaled to an F770W intensity scale using the coefficients in Table 1. The blue and red points with error bars show the median ratios and scatter from Table 4. The green and purple points show results from the model-fitting analysis in Table 5. Gray points show results for individual galaxies. The solid black lines show conversions based on the equations in Section 2 that describe the template-fitting coefficients reasonably well. For the CO, this is emission from a Draine & Li (2007) model with *D/G* = 0.01 and an ISRF *U/U*₀ = 2.5. For the Hα, this is an SFR conversion with normalization *C*₂₄ = 10⁻⁴².⁹. The ratios show consistently lower ratios than the templates, reflecting that both heating and column density terms contribute to the overall distribution.</figcaption></figure>

correlate linearly with metallicity to first order (e.g., see Galliano et al. 2018). Therefore we expect *D/G* to also be ≈0.6 times lower in IC 5332 than the other three targets.

Likely reflecting this lower dust abundance, Table 4 and Figure 8 do show that IC 5332 exhibits a moderately higher Hα-to-mid-IR ratio than the other galaxies, as one would expect if the lower dust content leads to lower overall UV extinction and less IR emission. On the other hand, the CO-to-mid-IR ratio in IC 5332 closely resembles that in the other three galaxies, especially for F770W, F1000W, and F1130W. We note that this is effectively a stacking result because IC 5332 is only weakly detected in PHANGS–ALMA. Figure 6 shows that if we stack our “flat” CO cubes (Section 3.1) as a function of mid-IR intensity, we observe a linear relationship with a similar normalization to the other three galaxies. This result

qualitatively resembles the observation of a good correlation between PAH and CO emission in the Magellanic Clouds (e.g., Sandstrom et al. 2010; Chastenet et al. 2019).

This might appear surprising given IC 5332’s expected lower *D/G* compared to the other targets. In theory, a lower *D/G* should yield a lower IR emission per gas column (Equation (4)). The quantitative agreement between IC 5332 and the other galaxies may emerge because the CO-to-H₂ conversion factor αCO (Equation (2)) also depends on metallicity (e.g., Glover & Low 2011; Leroy et al. 2011a; Bolatto et al. 2013; Hu et al. 2021). The sense of that relationship is that the CO emission per unit H₂ drops at low metallicity. Our results suggest that the drop in *D/G* may cancel with a rise in αCO in IC 5332 to produce a CO versus mid-IR correlation similar to that found in higher-metallicity
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Summary CO-to-mid-IR and extinction-corrected Hα-to-mid-IR median ratios and template-matching coefficients. Each point in the left panel shows a CO (2-1) to mid-IR ratio, and each point in the right panel shows an extinction-corrected Hα-to-mid-IR ratio. To allow easy comparisons between bands, all ratios have been scaled to an F770W intensity scale using the coefficients in Table 1. The blue and red points with error bars show the median ratios and scatter from Table 4. The green and purple points show results from the model-fitting analysis in Table 5. Gray points show results for individual galaxies. The solid black lines show conversions based on the equations in Section 2 that describe the template-fitting coefficients reasonably well. For the CO, this is emission from a Draine & Li (2007) model with $D/G = 0.01$ and an ISRF $U/U_0 = 2.5$. For the Hα, this is an SFR conversion with normalization $C_{24} = 10^{-42.9}$. The ratios show consistently lower ratios than the templates, reflecting that both heating and column density terms contribute to the overall distribution.</figcaption></figure>

correlate linearly with metallicity to first order (e.g., see Galliano et al. 2018). Therefore we expect $D/G$ to also be ≈0.6 times lower in IC 5332 than the other three targets.

Likely reflecting this lower dust abundance, Table 4 and Figure 8 do show that IC 5332 exhibits a moderately higher Hα-to-mid-IR ratio than the other galaxies, as one would expect if the lower dust content leads to lower overall UV extinction and less IR emission. On the other hand, the CO-to-mid-IR ratio in IC 5332 closely resembles that in the other three galaxies, especially for F770W, F1000W, and F1130W. We note that this is effectively a stacking result because IC 5332 is only weakly detected in PHANGS–ALMA. Figure 6 shows that if we stack our “flat” CO cubes (Section 3.1) as a function of mid-IR intensity, we observe a linear relationship with a similar normalization to the other three galaxies. This result

qualitatively resembles the observation of a good correlation between PAH and CO emission in the Magellanic Clouds (e.g., Sandstrom et al. 2010; Chastenet et al. 2019).

This might appear surprising given IC 5332’s expected lower $D/G$ compared to the other targets. In theory, a lower $D/G$ should yield a lower IR emission per gas column (Equation (4)). The quantitative agreement between IC 5332 and the other galaxies may emerge because the CO-to-H$_2$ conversion factor $\alpha_{CO}$ (Equation (2)) also depends on metallicity (e.g., Glover & Low 2011; Leroy et al. 2011a; Bolatto et al. 2013; Hu et al. 2021). The sense of that relationship is that the CO emission per unit H$_2$ drops at low metallicity. Our results suggest that the drop in $D/G$ may cancel with a rise in $\alpha_{CO}$ in IC 5332 to produce a CO versus mid-IR correlation similar to that found in higher-metallicity
galaxies. With proper calibration this might offer a mid-IR-
based approach to explore αCO variations, something explored
by Gratier et al. (2010) using Local Group Spitzer data.
However, we note that such low surface densities, dust mixed
with H I, or an extended CO-dark phase may also play a role
(see Sandstrom 2023b for more discussion and quantitative
exploration).

7. Applying Our Results

Finally, we briefly discuss how our results can be applied to
use high-resolution mid-IR data to trace the gas distribution or
recent massive star formation. Here, especially, we caution that
these are first results from PHANGS–JWST and that we expect
to substantially refine and improve this work over the course of
the full survey.

## 7.1. Predicting CO Intensity or Gas Column Density from the Mid-IR

One main result from our analysis is that the mid-IR traces
the molecular gas surprisingly well. This implies that one can
use the mid-IR to trace gas column density, analogous to the
way that longer-wavelength dust emission has long been used
to trace the ISM in galaxies at low and high redshift
(Israel 1997; Leroy et al. 2011a; Eales et al. 2012; Sandstrom
et al. 2013; Scoville et al. 2014; Shi et al. 2014; Groves et al.
2015; Tacconi et al. 2020).

Using JWST mid-IR observations to trace the ISM
represents an exciting prospect because these observations are
sensitive, high resolution, and relatively phase-agnostic. As
pointed out in Section 3.3 and Table 3, if we simply adopt our
median CO-to-mid-IR ratio, then at matched resolution, our
relatively short integration time JWST observations have
significantly better mass sensitivity, σgas ~ 0.2 M⊙ pc⁻² at
F770W, F1130W, or F2100W, than our (also relatively short
integration time) ALMA observations, σgas ~ 6.7 M⊙ pc⁻².
Second, JWST naturally achieves very high angular resolution.
As an interferometer, ALMA often requires large time
investments to achieve surface brightness sensitivity at high
angular resolution. Mapping a single galaxy in the relatively
bright CO lines at resolution matched to JWST at 11.3 µm,
7.7 µm, or even the 3.3 µm PAH feature (see Sandstrom 2023a)
comes with prohibitive cost. Third, none of our expectations
(Section 2) specifically require that mid-IR emission arise from
dust mixed with molecular gas. We have simply focused our
own comparison on CO because we have an independent tracer
of that phase of the ISM. As pointed out and explored by
Sandstrom (2023b) in this Issue, the dust traced by the mid-IR
should have a broader phase sensitivity than just CO-emitting
molecular gas, including both CO-dark gas and atomic gas.

Practically, what should one do to predict the gas distribution
from the mid-IR? Before giving recommendations, we first
emphasize again that these are early days for these kinds of
observations, and we expect our approach to evolve. That said,
to first order, one can adopt a purely empirical approach to
estimate the gas column density. One can use either our
measured median ratios or our power-law fits (both in Table 4)
to predict I<sub>CO</sub> from mid-IR emission (the median ratios may be
slightly less accurate, but are also less scale dependent). Then
one can convert to Σ<sub>gas</sub> = Σ<sub>mol</sub> from Equation (2), leveraging
the fact that our data selection was designed to pick regions
where most of the gas is likely to be molecular so that we can

treat the result as a general relation between the total gas
column density and the mid-IR.

We state the result in this way because we expect that the
mid-IR traces the total neutral gas column. Dust is mixed with
all gas, not only with molecular gas (e.g., see Bohlin et al.
1978; Sandstrom et al. 2013; Galliano et al. 2018), and we
assume that to first order that the combination of the dust-to-gas
ratio, PAH abundance, and ISRF strength remains about fixed
for the gas outside star-forming regions. The ambient ISRF is
indeed observed to vary smoothly based on resolved SED
modeling of nearby galaxies (Aniano et al. 2012, 2020; Draine
et al. 2014), though note that it does vary, showing, e.g., radial
variations that track the overall stellar density. The PAH
abundance outside star-forming regions also appears to vary
relatively smoothly (e.g., Chastenet et al. 2019;
Chastenet 2023a, the latter in this Issue), though again showing
large scale variations. And the dust-to-gas ratio also shows
coherent, slowly varying behavior across galaxies, tracking the
metallicity well (e.g., Sandstrom et al. 2013; Draine et al. 2014;
Chiang et al. 2018; Galliano et al. 2018). We note an important
caveat here, that there is good evidence for a density or phase
dependence of the dust-to-gas ratio (e.g., Jenkins 2009;
Roman-Duval et al. 2014; Chiang et al. 2018). This has the
sense that gas with very low densities could have lower dust-to-
gas ratios, but the variations are relatively modest in magnitude
and the dust-to-gas ratio in the dense, cold atomic phase is
likely to more closely resemble that in molecular gas (see
Jenkins 2009; Draine 2011). We leave a detailed treatment of
this effect, along with a deeper investigation of the phase
dependence of the ISRF or q<sub>PAH</sub>, for future work, noting that
even with an associated uncertainty of ~50%, the mid-IR still
represents a powerful new ISM tracer.

In this approach, bright star-forming regions will represent
an important contaminant. One can mask them imprecisely by
clipping on mid-IR brightness, e.g., using the approximate mid-
IR cuts noted in Section 2.6 based on Belfiore et al. (2022a).
Better, one can use a Hα map and the results of this paper to
estimate where local star-forming regions make an important
contribution to the mid-IR (i.e., scale the Hα, perhaps after
decomposition into H II regions, using our results and compare
to the local mid-IR to gauge where local contamination rises
above some user-specified tolerance). The downside of
masking the star-forming regions is that one will then miss
molecular gas associated directly with these regions. To
address this, one could conduct a version of our template-
fitting exercise and attempt to subtract the Hα-tracing
component. With a broader set of JWST targets, it should also
be possible to identify general prescriptions to subtract the Hα.
Though subtracting bright emission or otherwise modeling the
local radiation field to infer the local column density is the most
appealing route forward, it remains to be seen if this approach
can deliver accurate estimates of gas even in the presence of
bright star-forming regions.

Physically, as outlined in Section 2.5 and Equations (4), the
mapping between mid-IR emission and gas surface density
depends on the dust-to-gas ratio and the ISRF, as well as the
PAH abundance, and in the short term, we can hope to take a
more physical and less empirical approach to this topic by
directly estimating all of these quantities. The PHANGS data
sets contain information on the resolved recent star formation,
older stellar content, star formation history, and metallicity of
our targets. The JWST data themselves constrain variations in
galaxies. With proper calibration this might offer a mid-IR-
based approach to explore αCO variations, something explored
by Gratier et al. (2010) using Local Group Spitzer data.
However, we note that such low surface densities, dust mixed
with H I, or an extended CO-dark phase may also play a role
(see Sandstrom 2023b for more discussion and quantitative
exploration).

7. Applying Our Results

Finally, we briefly discuss how our results can be applied to
use high-resolution mid-IR data to trace the gas distribution or
recent massive star formation. Here, especially, we caution that
these are first results from PHANGS–JWST and that we expect
to substantially refine and improve this work over the course of
the full survey.

7.1. Predicting CO Intensity or Gas Column Density from the Mid-IR

One main result from our analysis is that the mid-IR traces
the molecular gas surprisingly well. This implies that one can
use the mid-IR to trace gas column density, analogous to the
way that longer-wavelength dust emission has long been used
to trace the ISM in galaxies at low and high redshift
(Israel 1997; Leroy et al. 2011a; Eales et al. 2012; Sandstrom
et al. 2013; Scoville et al. 2014; Shi et al. 2014; Groves et al.
2015; Tacconi et al. 2020).

Using JWST mid-IR observations to trace the ISM
represents an exciting prospect because these observations are
sensitive, high resolution, and relatively phase-agnostic. As
pointed out in Section 3.3 and Table 3, if we simply adopt our
median CO-to-mid-IR ratio, then at matched resolution, our
relatively short integration time JWST observations have
significantly better mass sensitivity, σ<sub>gas</sub> ~ 0.2 M<sub>☉</sub> pc<sup>-2</sup> at
F770W, F1130W, or F2100W, than our (also relatively short
integration time) ALMA observations, σ<sub>gas</sub> ~ 6.7 M<sub>☉</sub> pc<sup>-2</sup>.
Second, JWST naturally achieves very high angular resolution.
As an interferometer, ALMA often requires large time
investments to achieve surface brightness sensitivity at high
angular resolution. Mapping a single galaxy in the relatively
bright CO lines at resolution matched to JWST at 11.3 µm,
7.7 µm, or even the 3.3 µm PAH feature (see Sandstrom 2023a)
comes with prohibitive cost. Third, none of our expectations
(Section 2) specifically require that mid-IR emission arise from
dust mixed with molecular gas. We have simply focused our
own comparison on CO because we have an independent tracer
of that phase of the ISM. As pointed out and explored by
Sandstrom (2023b) in this Issue, the dust traced by the mid-IR
should have a broader phase sensitivity than just CO-emitting
molecular gas, including both CO-dark gas and atomic gas.

Practically, what should one do to predict the gas distribution
from the mid-IR? Before giving recommendations, we first
emphasize again that these are early days for these kinds of
observations, and we expect our approach to evolve. That said,
to first order, one can adopt a purely empirical approach to
estimate the gas column density. One can use either our
measured median ratios or our power-law fits (both in Table 4)
to predict I<sub>CO</sub> from mid-IR emission (the median ratios may be
slightly less accurate, but are also less scale dependent). Then
one can convert to Σ<sub>gas</sub> = Σ<sub>mol</sub> from Equation (2), leveraging
the fact that our data selection was designed to pick regions
where most of the gas is likely to be molecular so that we can

treat the result as a general relation between the total gas
column density and the mid-IR.

We state the result in this way because we expect that the
mid-IR traces the total neutral gas column. Dust is mixed with
all gas, not only with molecular gas (e.g., see Bohlin et al.
1978; Sandstrom et al. 2013; Galliano et al. 2018), and we
assume that to first order that the combination of the dust-to-gas
ratio, PAH abundance, and ISRF strength remains about fixed
for the gas outside star-forming regions. The ambient ISRF is
indeed observed to vary smoothly based on resolved SED
modeling of nearby galaxies (Aniano et al. 2012, 2020; Draine
et al. 2014), though note that it does vary, showing, e.g., radial
variations that track the overall stellar density. The PAH
abundance outside star-forming regions also appears to vary
relatively smoothly (e.g., Chastenet et al. 2019;
Chastenet 2023a, the latter in this Issue), though again showing
large scale variations. And the dust-to-gas ratio also shows
coherent, slowly varying behavior across galaxies, tracking the
metallicity well (e.g., Sandstrom et al. 2013; Draine et al. 2014;
Chiang et al. 2018; Galliano et al. 2018). We note an important
caveat here, that there is good evidence for a density or phase
dependence of the dust-to-gas ratio (e.g., Jenkins 2009;
Roman-Duval et al. 2014; Chiang et al. 2018). This has the
sense that gas with very low densities could have lower dust-to-
gas ratios, but the variations are relatively modest in magnitude
and the dust-to-gas ratio in the dense, cold atomic phase is
likely to more closely resemble that in molecular gas (see
Jenkins 2009; Draine 2011). We leave a detailed treatment of
this effect, along with a deeper investigation of the phase
dependence of the ISRF or $q_{\text{PAH}}$, for future work, noting that
even with an associated uncertainty of ~50%, the mid-IR still
represents a powerful new ISM tracer.

In this approach, bright star-forming regions will represent
an important contaminant. One can mask them imprecisely by
clipping on mid-IR brightness, e.g., using the approximate mid-
IR cuts noted in Section 2.6 based on Belfiore et al. (2022a).
Better, one can use a Hα map and the results of this paper to
estimate where local star-forming regions make an important
contribution to the mid-IR (i.e., scale the Hα, perhaps after
decomposition into H II regions, using our results and compare
to the local mid-IR to gauge where local contamination rises
above some user-specified tolerance). The downside of
masking the star-forming regions is that one will then miss
molecular gas associated directly with these regions. To
address this, one could conduct a version of our template-
fitting exercise and attempt to subtract the Hα-tracing
component. With a broader set of JWST targets, it should also
be possible to identify general prescriptions to subtract the Hα.
Though subtracting bright emission or otherwise modeling the
local radiation field to infer the local column density is the most
appealing route forward, it remains to be seen if this approach
can deliver accurate estimates of gas even in the presence of
bright star-forming regions.

Physically, as outlined in Section 2.5 and Equations (4), the
mapping between mid-IR emission and gas surface density
depends on the dust-to-gas ratio and the ISRF, as well as the
PAH abundance, and in the short term, we can hope to take a
more physical and less empirical approach to this topic by
directly estimating all of these quantities. The PHANGS data
sets contain information on the resolved recent star formation,
older stellar content, star formation history, and metallicity of
our targets. The JWST data themselves constrain variations in
the PAH abundance via the band ratios. In the near future, the combined PHANGS data sets should allow us to make predictions for how the ISRF, $D/G$, and $q_{PAH}$ vary across each of our targets, and use these to calibrate local conversions from mid-IR to column density. In parallel, we expect our ability to identify and subtract emission from bright star-forming regions to improve, and both of these avenues should lead to higher-quality estimates of the gas column density.

## 7.2. Predicting Extinction-corrected $H\alpha$ from the Mid-IR

The classical application of mid-IR emission is to trace star formation. Extinction-corrected $H\alpha$ does correlate very well with mid-IR emission in our data. There remains a great deal of work to do on this topic with these data. Here we note that from this work, the power-law fits relating extinction-corrected $H\alpha$-to-mid-IR emission (Table 4) represent our most straightforwardly useful result. They capture the nonlinearity in the overall $H\alpha$ versus mid-IR relations well, and the results for the three massive disk galaxies agree very well (though we clearly also expect metallicity effects; see Section 6.3). The fits have been derived for mid-IR intensities of ~0.5–30 MJy sr⁻¹ and physical scales of 50–150 pc, and we expect them to perform best in this range. After estimating the extinction-corrected $H\alpha$, one can apply Equation (3) to estimate the SFR but should recall that our analysis used the entire $H\alpha$ map and not explicitly separated the DIG and H II regions (see Belfiore et al. 2022a; Groves et al. 2023).

## 8. Summary and Discussion

With the goal of diagnosing the physical origins of mid-IR emission and exploring its use as a tracer of both the ISM and recent star formation, we present first results from a direct comparison of mid-IR emission from PHANGS–JWST (Lee et al. 2023), extinction-corrected $H\alpha$ emission from PHANGS–MUSE (Emsellem et al. 2022), and CO (2–1) emission from PHANGS–ALMA (Leroy et al. 2021). The extinction-corrected $H\alpha$ traces recombinations that follow from ionizations by photons produced overwhelmingly by young, massive stars. The CO (2–1) emission traces molecular gas, which makes up most of the ISM by mass in most of the regions targeted by PHANGS–JWST. Mid-IR emission from small grains stochastically heated by single photons should relate closely to both $H\alpha$ and CO emission because it is expected to depend on both the distribution of dust, which tends to be well mixed with gas, and on the heating of the grains by UV light from stars (Section 2).

To test these expectations, we construct a matched-resolution database that spans the overlap of the PHANGS–JWST, VLT/MUSE, and ALMA data sets in the first four PHANGS–JWST target galaxies (Table 2). We record the 7.7 µm (F770W), 10 µm (F1000W), 11.3 µm (F1130W), 21 µm (F2100W), CO (2–1), and extinction-corrected $H\alpha$ intensity at each point at 1"7 = 70–160 pc resolution (Section 3.2). Using this database, we conduct a statistical analysis of the relationship between mid-IR, CO, and $H\alpha$. We focus this analysis on regions of “bright” mid-IR emission, which we define via an F770W intensity cut at 0.5 MJy sr⁻¹, a level chosen to select regions where we expect the mid-IR to reflect either mostly emission from dust mixed with molecular gas or H II regions (Sections 2.6, 3.4). Such regions account for >95% of the flux and ≈60% of the area across our whole data set (Table 4). For

most analyses, we also exclude the starburst ring in NGC 1365 because it appears to represent a physically distinct regime. Our results can thus be thought of as primarily describing the molecular gas-dominated, actively star-forming parts of normal galaxy disks.

We measure correlation strengths, calculate ratios, and fit power-law relationships among mid-IR, CO, and $H\alpha$ emission. Table 4 reports these results in detail. Our findings include the following:

1. CO (2–1) emission observed by ALMA and mid-IR emission observed by JWST show a strong correlation for all mid-IR bands (Section 4.1, Table 4, and Figures 5 and 6). Despite the relatively high noise in the CO data, we find high rank correlation coefficients and a clear correlation that spans more than an order of magnitude in mid-IR intensity (Figures 5, 9; Table 4). This quantitative result matches the visual impression that the extended emission in the mid-IR maps looks like the ALMA CO maps (Figures 1 through 4). The best-fit power-law relationships have slopes, $m_{CO-MIR}$ in the range of ≈0.7–1.3 (Table 4, Figures 6, 10). The shallower slopes are associated with the continuum-dominated F2100W band and the steeper slopes associated with the PAH-tracing bands, which may be suppressed within active star-forming regions (see Section 4.4). For a given band, the average relationship between CO and mid-IR appears quite similar among all four targets (Figure 9).

Strong correlations between mid-IR emission and CO have been observed at coarser resolution, often in the context of analyses focused on studying star formation scaling relations (e.g., Regan et al. 2006; Kennicutt et al. 2007; Bigiel et al. 2008; Schruba et al. 2011; Leroy et al. 2013; Leroy 2023), and the coincidence of the brightest CO and mid-IR peaks is a key result of Kim et al. (2021), Kim (2023) and Hassani et al. (2023). Whitcomb et al. (2022) also recently demonstrated that in mid-IR spectroscopy of SINGS H II regions, a broad set of continuum and mid-IR spectral features related to dust correlate well with CO. The strength of these observed low-resolution scaling relations has even led to proposals that galaxy-integrated or low-resolution mid-IR emission can be used as an empirically calibrated molecular gas tracer (Gao et al. 2019, 2022; Chown et al. 2021; Leroy et al. 2021; Leroy 2023). Almost all of these studies have either worked at relatively coarse scales or focused selectively on bright emission peaks or star-forming regions. Here we demonstrate that a strong relationship between CO and mid-IR emission holds across the full area of the first four PHANGS–JWST targets even at relatively high 70–160 pc resolution.

Mid-IR emission is often utilized as a tracer of recent star formation (e.g., Calzetti et al. 2005, 2007; Kennicutt & Evans 2012), not molecular gas. We also compare the PHANGS–JWST mid-IR maps to VLT/MUSE maps of $H\alpha$ emission corrected for extinction via the Balmer decrement and find that:

2. Extinction-corrected $H\alpha$ emission observed by VLT/MUSE also shows a very strong but steeper-than-linear correlation with all mid-IR bands observed by PHANGS–JWST (Section 4.2, Table 4, Figures 7 and 8). At our 70–160 pc resolution the rank correlation coefficient relating $H\alpha$-to-mid-IR emission is >0.75 for all four PHANGS–JWST mid-IR bands (Table 4). The slope of
the PAH abundance via the band ratios. In the near future, the combined PHANGS data sets should allow us to make predictions for how the ISRF, $D/G$, and $q_{PAH}$ vary across each of our targets, and use these to calibrate local conversions from mid-IR to column density. In parallel, we expect our ability to identify and subtract emission from bright star-forming regions to improve, and both of these avenues should lead to higher-quality estimates of the gas column density.

## 7.2. Predicting Extinction-corrected $H\alpha$ from the Mid-IR

The classical application of mid-IR emission is to trace star formation. Extinction-corrected $H\alpha$ does correlate very well with mid-IR emission in our data. There remains a great deal of work to do on this topic with these data. Here we note that from this work, the power-law fits relating extinction-corrected $H\alpha$-to-mid-IR emission (Table 4) represent our most straightforwardly useful result. They capture the nonlinearity in the overall $H\alpha$ versus mid-IR relations well, and the results for the three massive disk galaxies agree very well (though we clearly also expect metallicity effects; see Section 6.3). The fits have been derived for mid-IR intensities of ~0.5–30 MJy sr$^{-1}$ and physical scales of 50–150 pc, and we expect them to perform best in this range. After estimating the extinction-corrected $H\alpha$, one can apply Equation (3) to estimate the SFR but should recall that our analysis used the entire $H\alpha$ map and not explicitly separated the DIG and H II regions (see Belfiore et al. 2022a; Groves et al. 2023).

## 8. Summary and Discussion

With the goal of diagnosing the physical origins of mid-IR emission and exploring its use as a tracer of both the ISM and recent star formation, we present first results from a direct comparison of mid-IR emission from PHANGS–JWST (Lee et al. 2023), extinction-corrected $H\alpha$ emission from PHANGS–MUSE (Emsellem et al. 2022), and CO (2–1) emission from PHANGS–ALMA (Leroy et al. 2021). The extinction-corrected $H\alpha$ traces recombinations that follow from ionizations by photons produced overwhelmingly by young, massive stars. The CO (2–1) emission traces molecular gas, which makes up most of the ISM by mass in most of the regions targeted by PHANGS–JWST. Mid-IR emission from small grains stochastically heated by single photons should relate closely to both $H\alpha$ and CO emission because it is expected to depend on both the distribution of dust, which tends to be well mixed with gas, and on the heating of the grains by UV light from stars (Section 2).

To test these expectations, we construct a matched-resolution database that spans the overlap of the PHANGS–JWST, VLT/MUSE, and ALMA data sets in the first four PHANGS–JWST target galaxies (Table 2). We record the 7.7 µm (F770W), 10 µm (F1000W), 11.3 µm (F1130W), 21 µm (F2100W), CO (2–1), and extinction-corrected $H\alpha$ intensity at each point at 1"7 = 70–160 pc resolution (Section 3.2). Using this database, we conduct a statistical analysis of the relationship between mid-IR, CO, and $H\alpha$. We focus this analysis on regions of “bright” mid-IR emission, which we define via an F770W intensity cut at 0.5 MJy sr$^{-1}$, a level chosen to select regions where we expect the mid-IR to reflect either mostly emission from dust mixed with molecular gas or H II regions (Sections 2.6, 3.4). Such regions account for >95% of the flux and ≈60% of the area across our whole data set (Table 4). For

most analyses, we also exclude the starburst ring in NGC 1365 because it appears to represent a physically distinct regime. Our results can thus be thought of as primarily describing the molecular gas-dominated, actively star-forming parts of normal galaxy disks.

We measure correlation strengths, calculate ratios, and fit power-law relationships among mid-IR, CO, and $H\alpha$ emission. Table 4 reports these results in detail. Our findings include the following:

1. CO (2–1) emission observed by ALMA and mid-IR emission observed by JWST show a strong correlation for all mid-IR bands (Section 4.1, Table 4, and Figures 5 and 6). Despite the relatively high noise in the CO data, we find high rank correlation coefficients and a clear correlation that spans more than an order of magnitude in mid-IR intensity (Figures 5, 9; Table 4). This quantitative result matches the visual impression that the extended emission in the mid-IR maps looks like the ALMA CO maps (Figures 1 through 4). The best-fit power-law relationships have slopes, $m_{CO-MIR}$ in the range of ≈0.7–1.3 (Table 4, Figures 6, 10). The shallower slopes are associated with the continuum-dominated F2100W band and the steeper slopes associated with the PAH-tracing bands, which may be suppressed within active star-forming regions (see Section 4.4). For a given band, the average relationship between CO and mid-IR appears quite similar among all four targets (Figure 9).

Strong correlations between mid-IR emission and CO have been observed at coarser resolution, often in the context of analyses focused on studying star formation scaling relations (e.g., Regan et al. 2006; Kennicutt et al. 2007; Bigiel et al. 2008; Schruba et al. 2011; Leroy et al. 2013; Leroy 2023), and the coincidence of the brightest CO and mid-IR peaks is a key result of Kim et al. (2021), Kim (2023) and Hassani et al. (2023). Whitcomb et al. (2022) also recently demonstrated that in mid-IR spectroscopy of SINGS H II regions, a broad set of continuum and mid-IR spectral features related to dust correlate well with CO. The strength of these observed low-resolution scaling relations has even led to proposals that galaxy-integrated or low-resolution mid-IR emission can be used as an empirically calibrated molecular gas tracer (Gao et al. 2019, 2022; Chown et al. 2021; Leroy et al. 2021; Leroy 2023). Almost all of these studies have either worked at relatively coarse scales or focused selectively on bright emission peaks or star-forming regions. Here we demonstrate that a strong relationship between CO and mid-IR emission holds across the full area of the first four PHANGS–JWST targets even at relatively high 70–160 pc resolution.

Mid-IR emission is often utilized as a tracer of recent star formation (e.g., Calzetti et al. 2005, 2007; Kennicutt & Evans 2012), not molecular gas. We also compare the PHANGS–JWST mid-IR maps to VLT/MUSE maps of $H\alpha$ emission corrected for extinction via the Balmer decrement and find that:

2. Extinction-corrected $H\alpha$ emission observed by VLT/MUSE also shows a very strong but steeper-than-linear correlation with all mid-IR bands observed by PHANGS–JWST (Section 4.2, Table 4, Figures 7 and 8). At our 70–160 pc resolution the rank correlation coefficient relating $H\alpha$-to-mid-IR emission is >0.75 for all four PHANGS–JWST mid-IR bands (Table 4). The slope of
the power-law fits relating extinction-corrected Hα-to-mid-IR tend to be steeper and further from linear compared to those that we found for CO, $m_{Hα-MIR} \approx 1.5$ on average (Table 4, Figures 7, 8, and 10). Put another way, the ratio of extinction-corrected Hα-to-mid-IR emission becomes higher in regions with more recent massive star formation. Other work on PHANGS-MUSE has shown that the extinction affecting Hα, $A_{Hα}$, correlates with the Hα intensity (Emsellem et al. 2022; Belfiore et al. 2022a, 2022b; Groves et al. 2023). Taking these results together, the brightest regions have both high extinction and relatively fainter mid-IR emission compared to extinction-corrected Hα.

Over the last few decades, the mid-IR has become a standard SFR tracer (e.g., Kennicutt & Evans 2012; Calzetti 2013). Our observations of a very strong correlation between mid-IR and extinction-corrected Hα supports this, echoing results obtained by Belfiore et al. (2022b) at coarser resolution using the whole PHANGS-MUSE survey and in good agreement with the good, quantitative correspondence between the Hα and F2100W peaks seen in this Issue by Hassani et al. (2023). However, while the Hα and mid-IR correlate well, the mid-IR also shows a much more significant “diffuse” or extended component, which drives the steep Hα versus IR slope. The existence of such a component has been noted many times (see Walterbos & Schwering 1987; Calzetti et al. 2005; Leroy et al. 2012; Li et al. 2013; Groves et al. 2012; Crocker et al. 2013; Calapa et al. 2014; Boquien et al. 2015, 2016; Kim et al. 2021; Kim 2023; Belfiore et al. 2022b) and is clearly visible in Figures 1 through 4. Because the bright Hα emission tends to be concentrated in the H II regions, this extended IR emission is associated with low Hα-to-mid-IR ratios while the most luminous regions show the highest Hα-to-mid-IR ratios.

Partially as a result of this extended component, establishing a general quantitative conversion of mid-IR emission into an SFR estimate as a function of scale and environment remains an important and complex topic (e.g., Murphy et al. 2011; Leroy et al. 2012; Crocker et al. 2013; Calapa et al. 2014; Boquien et al. 2014, 2015, 2016; Catalán-Torrecilla et al. 2015; Belfiore et al. 2022b), one that appears likely to see even more attention with JWST operational. Qualitatively, our results suggest that the finding by Belfiore et al. (2022b) that the calibration of mid-IR-based SFR tracers depends on the local specific star formation and star formation surface density holds down to the scale of individual regions, reflecting a spatially varying contribution of extended “cirrus” emission. Quantitatively, the fits that we provide in Table 4 offer a way to predict the extinction-corrected Hα from the mid-IR at our $1''7 = 60-170$ pc resolution, though we expect these results to be superseded by work with the full PHANGS-JWST survey.

Of course, due to the basic link between molecular gas, dust, and star formation, all of these quantities will scale together at coarse resolution. JWST’s critical new capability is its resolution. When applied to nearby galaxies, this resolution allows us to break targets apart into individual regions. A series of observational studies over the last 15 years have shown that at sufficient resolution, the distributions of clusters, clouds, and H II regions spatially separate, and the ratios of gas and star formation tracers show wide variations, consistent with finding regions in distinct evolutionary states (Kawamura et al. 2009; Schruba et al. 2010; Leroy et al. 2013; Corbelli et al. 2017;

Grasha et al. 2018; Kreckel et al. 2018; Schinnerer et al. 2019; Kruijssen et al. 2019; Chevance et al. 2020; Kim et al. 2021; Pan et al. 2022; Turner et al. 2022). PHANGS-ALMA and PHANGS-MUSE reach this resolution in our data and:

3. We observe a weaker, shallower correlation between CO and extinction-corrected Hα than we find relating either CO versus mid-IR emission or Hα versus mid-IR emission (Section 4.3, Table 4, Figures 9, 10). Rather than a single relationship reflecting an underlying star formation scaling relation, at these scales the data suggest that separate relationships link CO-to-mid-IR and Hα-to-mid-IR. The large scatter, shallow slope in CO versus Hα when binning by Hα, and comparatively weak correlation coefficient relating the two bands all indicate that our observations have reached the scale where the global scaling between molecular gas and recent star formation begins to break down. Despite this, the correlations between mid-IR and CO and mid-IR and extinction-corrected Hα both remain strong. Moreover, the residuals about the CO versus mid-IR relation correlate with Hα, while the residuals about the Hα versus mid-IR emission correlate with CO. Together, these results point to the existence of separate correlations linking mid-IR to CO and mid-IR to Hα.

Because the mid-IR emission depends on both UV heating and dust column density (Section 2), these separate relationships could be expected when we reach scales where we can resolve galaxies into distinct regions, some with intense heating and some with high column density. To test this idea, we implement a simple model and find:

4. The observed bright mid-IR data can be described well by a two-component model in which the mid-IR reflects a scaled version of the CO (2–1) map added to a scaled version of the extinction-corrected Hα map (Section 5, Table 5, Figures 11, 12, and 13). On average, this simple model can describe the bright emission from our targets within ±0.2 dex, and the model appears to work well for all four target galaxies (Figures 12 and 13, Table 5). We solve for the coefficients c and h used to scale the CO (2–1) and Hα maps and find a clear set of best-fitting parameters (Figure 11) that have physically plausible values (Section 6). The best-fitting coefficients vary from galaxy to galaxy in a consistent way across the different mid-IR bands, suggesting that c and h reflect local physical conditions in the galaxy.

This simple model views the mid-IR as the combination of (1) a component driven mostly by stochastic, single-photon heating of dust mixed with molecular gas and bathed in the ISRF and (2) a component driven by dust immediately associated with intense radiation fields in H II regions. In some sense, this resembles a resolved version to the dust population synthesis model by Draine et al. (2007), which models integrated dust SEDs as a combination of intensely heated emission from photodissociation regions and dust bathed in a uniform ISRF. The combined sensitivity to heating and many phases of the ISM also suggests that the mid-IR may qualitatively resemble C II fine-structure line emission in tracing both heating by star formation and multiple ISM phases. Fortunately, the resolution of the combined PHANGS data sets appears able to break this degeneracy, a conclusion
the power-law fits relating extinction-corrected Hα-to-mid-IR tend to be steeper and further from linear compared to those that we found for CO, $m_{Hα-MIR} \approx 1.5$ on average (Table 4, Figures 7, 8, and 10). Put another way, the ratio of extinction-corrected Hα-to-mid-IR emission becomes higher in regions with more recent massive star formation. Other work on PHANGS-MUSE has shown that the extinction affecting Hα, $A_{Hα}$, correlates with the Hα intensity (Emsellem et al. 2022; Belfiore et al. 2022a, 2022b; Groves et al. 2023). Taking these results together, the brightest regions have both high extinction and relatively fainter mid-IR emission compared to extinction-corrected Hα.

Over the last few decades, the mid-IR has become a standard SFR tracer (e.g., Kennicutt & Evans 2012; Calzetti 2013). Our observations of a very strong correlation between mid-IR and extinction-corrected Hα supports this, echoing results obtained by Belfiore et al. (2022b) at coarser resolution using the whole PHANGS-MUSE survey and in good agreement with the good, quantitative correspondence between the Hα and F2100W peaks seen in this Issue by Hassani et al. (2023). However, while the Hα and mid-IR correlate well, the mid-IR also shows a much more significant “diffuse” or extended component, which drives the steep Hα versus IR slope. The existence of such a component has been noted many times (see Walterbos & Schwering 1987; Calzetti et al. 2005; Leroy et al. 2012; Li et al. 2013; Groves et al. 2012; Crocker et al. 2013; Calapa et al. 2014; Boquien et al. 2015, 2016; Kim et al. 2021; Kim 2023; Belfiore et al. 2022b) and is clearly visible in Figures 1 through 4. Because the bright Hα emission tends to be concentrated in the H II regions, this extended IR emission is associated with low Hα-to-mid-IR ratios while the most luminous regions show the highest Hα-to-mid-IR ratios.

Partially as a result of this extended component, establishing a general quantitative conversion of mid-IR emission into an SFR estimate as a function of scale and environment remains an important and complex topic (e.g., Murphy et al. 2011; Leroy et al. 2012; Crocker et al. 2013; Calapa et al. 2014; Boquien et al. 2014, 2015, 2016; Catalán-Torrecilla et al. 2015; Belfiore et al. 2022b), one that appears likely to see even more attention with JWST operational. Qualitatively, our results suggest that the finding by Belfiore et al. (2022b) that the calibration of mid-IR-based SFR tracers depends on the local specific star formation and star formation surface density holds down to the scale of individual regions, reflecting a spatially varying contribution of extended “cirrus” emission. Quantitatively, the fits that we provide in Table 4 offer a way to predict the extinction-corrected Hα from the mid-IR at our $1''7 = 60-170$ pc resolution, though we expect these results to be superseded by work with the full PHANGS-JWST survey.

Of course, due to the basic link between molecular gas, dust, and star formation, all of these quantities will scale together at coarse resolution. JWST’s critical new capability is its resolution. When applied to nearby galaxies, this resolution allows us to break targets apart into individual regions. A series of observational studies over the last 15 years have shown that at sufficient resolution, the distributions of clusters, clouds, and H II regions spatially separate, and the ratios of gas and star formation tracers show wide variations, consistent with finding regions in distinct evolutionary states (Kawamura et al. 2009; Schruba et al. 2010; Leroy et al. 2013; Corbelli et al. 2017;

Grasha et al. 2018; Kreckel et al. 2018; Schinnerer et al. 2019; Kruijssen et al. 2019; Chevance et al. 2020; Kim et al. 2021; Pan et al. 2022; Turner et al. 2022). PHANGS-ALMA and PHANGS-MUSE reach this resolution in our data and:

3. We observe a weaker, shallower correlation between CO and extinction-corrected Hα than we find relating either CO versus mid-IR emission or Hα versus mid-IR emission (Section 4.3, Table 4, Figures 9, 10). Rather than a single relationship reflecting an underlying star formation scaling relation, at these scales the data suggest that separate relationships link CO-to-mid-IR and Hα-to-mid-IR. The large scatter, shallow slope in CO versus Hα when binning by Hα, and comparatively weak correlation coefficient relating the two bands all indicate that our observations have reached the scale where the global scaling between molecular gas and recent star formation begins to break down. Despite this, the correlations between mid-IR and CO and mid-IR and extinction-corrected Hα both remain strong. Moreover, the residuals about the CO versus mid-IR relation correlate with Hα, while the residuals about the Hα versus mid-IR emission correlate with CO. Together, these results point to the existence of separate correlations linking mid-IR to CO and mid-IR to Hα.

Because the mid-IR emission depends on both UV heating and dust column density (Section 2), these separate relationships could be expected when we reach scales where we can resolve galaxies into distinct regions, some with intense heating and some with high column density. To test this idea, we implement a simple model and find:

4. The observed bright mid-IR data can be described well by a two-component model in which the mid-IR reflects a scaled version of the CO (2–1) map added to a scaled version of the extinction-corrected Hα map (Section 5, Table 5, Figures 11, 12, and 13). On average, this simple model can describe the bright emission from our targets within ±0.2 dex, and the model appears to work well for all four target galaxies (Figures 12 and 13, Table 5). We solve for the coefficients c and h used to scale the CO (2–1) and Hα maps and find a clear set of best-fitting parameters (Figure 11) that have physically plausible values (Section 6). The best-fitting coefficients vary from galaxy to galaxy in a consistent way across the different mid-IR bands, suggesting that c and h reflect local physical conditions in the galaxy.

This simple model views the mid-IR as the combination of (1) a component driven mostly by stochastic, single-photon heating of dust mixed with molecular gas and bathed in the ISRF and (2) a component driven by dust immediately associated with intense radiation fields in H II regions. In some sense, this resembles a resolved version to the dust population synthesis model by Draine et al. (2007), which models integrated dust SEDs as a combination of intensely heated emission from photodissociation regions and dust bathed in a uniform ISRF. The combined sensitivity to heating and many phases of the ISM also suggests that the mid-IR may qualitatively resemble C II fine-structure line emission in tracing both heating by star formation and multiple ISM phases. Fortunately, the resolution of the combined PHANGS data sets appears able to break this degeneracy, a conclusion
also reached by Whitcomb et al. (2022), who found SINGS mid-IR spectroscopy of H II regions to break apart into distinct gas- or star-formation-tracing behavior even at slightly coarser scales than we observe.

Taking our fitting results at face value, we calculate the fraction of flux associated with each model component and find that:

5. *On average, the model implies that about half of the mid-IR emission in each band comes from the CO-tracing component, while about half comes from the Hα-tracing component* (Section 5 and Table 5). This appears to hold for all four bands and all four targets. Typically, the high-intensity mid-IR emission comes mostly from the Hα-tracing component, while the lower intensity emission stems more from the CO-tracing component (Figure 12).

If we associate the CO-tracing component with “cirrus” or “background” emission, these results sit in broad agreement with previous estimates of the magnitude of mid-IR cirrus based on physical dust modeling, Fourier filtering, or inferring scale- or environment-dependent changes to SFR calibrations (e.g., Leroy et al. 2012; Li et al. 2013; Calzetti 2013; Boquien et al. 2015; Kim et al. 2021; Kim 2023; Belfiore et al. 2022b). Here we provide evidence that the “cirrus” in fact traces the neutral gas distribution.

6. *The CO-to-IR and extinction-corrected Hα-to-IR ratios that we measure agree with physical expectations and previous work* (Section 6, Figure 14, Section 2). Specifically, the CO-scaling coefficient *c* in our model agrees well with predictions from the Draine & Li (2007) model for a reasonable dust-to-gas ratio *D*/*G* ~ 0.01 and ISRF, *U* ~ 2*U*₀. Meanwhile, the coefficient *h* to scale Hα agrees well with SFR calibrations derived for bright H II regions. The CO-to-mid-IR and Hα-to-mid-IR ratios measured when using all data, i.e., not separating the emission using a model fit, are lower (i.e., they have more mid-IR), in line with previous work, and imply that a mixture of heating and column density contributes to the overall ratios.

7. *Putting our results together, we discuss how mid-IR emission can be used to estimate gas column density or trace recent star formation in our data* (Section 7). We also note current shortcomings and next steps that leverage the combined PHANGS–JWST, VLT/MUSE, and ALMA data.

In discussing these results, we have referred to “mid-IR” emission in general, no distinguishing our four bands. To first order, all four bands do show similar behavior and correlate with one another (see Section 2.1 and Appendix A). In more detail, the 21 µm (F2100W) emission shows distinct behavior from the other three bands. Its relationship with extinction-corrected Hα is more nearly linear and its relation with CO emission is shallower (Section 4.4). Overall, the sense of this relationship is that the 21 µm emission appears more directly related to Hα than the other mid-IR bands. It still mirrors the structure of the CO at low intensity and shows evidence for a substantial component tracing dust mixed with molecular gas, but it appears less suppressed in the brightest Hα-emitting regions than the other three bands. This agrees well with previous results and other papers in this Issue showing the suppression of PAH emission in bright H II regions (e.g., Helou

et al. 2004; Povich et al. 2007; Bendo et al. 2008; Gordon et al. 2008; Relaño & Kennicutt 2009; Calapa et al. 2014; Anderson et al. 2014; Chastenet et al. 2019; Chastenet 2023a; Dale et al. 2023; Egorov 2023). The degree to which the 10 µm band tracks the two PAH-dominated bands is a somewhat unexpected outcome in the first results from PHANGS–JWST.

Overall, our first analysis demonstrates the power of the combined JWST–MUSE–ALMA data set, shows the strength of mid-IR emission as both an ISM tracer and a star formation tracer, takes first steps toward realizing this potential, and suggests a path forward. As a closing note, we particularly highlight the power of the mid-IR maps to trace ISM structure in a quantitative way at a resolution and sensitivity that compares very favorably even to ALMA. In this Issue, the potential of this approach is already illustrated by studies identifying filamentary structure (Meidt et al. 2023; Thilker et al. 2023), feedback and dynamically driven shells (Barnes et al. 2022b; Watkins et al. 2023), and even digging in to faint structures associated with atomic gas (Sandstrom 2023b). Here we have provided first steps to make the mid-IR-based ISM maps quantitative. We have also discussed that to make more progress in this direction, we will need to both (1) deal with contamination by emission associated directly with recent star formation and (2) calibrate normalization terms that vary with the local ISRF and dust-to-gas ratio. This is eminently possible given the information in the combined PHANGS surveys. Then, as seen in Sandstrom (2023a, 2023b), the potential for such maps to reach very high physical resolution and mass sensitivity is outstanding.

We thank the anonymous referee for a careful read of a long paper during a busy time.

This work was carried out as part of the PHANGS collaboration.

A.K.L. thanks Prof. Todd Thompson for input on the draft. A.K.L. gratefully acknowledges support by grants 1653300 and 2205628 from the National Science Foundation, by award JWST-GO-02107.009-A, and by a Humboldt Research Award from the Alexander von Humboldt Foundation. A.D.B. acknowledges support by NSF-AST2108140 and award JWST-GO-02107.008-A.

J. P.ety acknowledges support by the DAOISM grant ANR-21-CE31-0010 and by the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with INC/INP, co-funded by CEA and CNES.

E.J.W., R.S.K., and S.C.O.G. acknowledge the funding provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project ID 138713538—SFB 881 (“The Milky Way System,” subprojects A1, B1, B2, B8, and P1).

T.G.W. and J.N. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 694343).

J.M.D.K. gratefully acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program via the ERC Starting Grant MUSTANG (grant agreement No. 714907). COOL Research DAO is a Decentralized Autonomous Organization supporting research in astrophysics aimed at uncovering our cosmic origins.
also reached by Whitcomb et al. (2022), who found SINGS mid-IR spectroscopy of H II regions to break apart into distinct gas- or star-formation-tracing behavior even at slightly coarser scales than we observe.

Taking our fitting results at face value, we calculate the fraction of flux associated with each model component and find that:

5. *On average, the model implies that about half of the mid-IR emission in each band comes from the CO-tracing component, while about half comes from the Hα-tracing component* (Section 5 and Table 5). This appears to hold for all four bands and all four targets. Typically, the high-intensity mid-IR emission comes mostly from the Hα-tracing component, while the lower intensity emission stems more from the CO-tracing component (Figure 12).

If we associate the CO-tracing component with “cirrus” or “background” emission, these results sit in broad agreement with previous estimates of the magnitude of mid-IR cirrus based on physical dust modeling, Fourier filtering, or inferring scale- or environment-dependent changes to SFR calibrations (e.g., Leroy et al. 2012; Li et al. 2013; Calzetti 2013; Boquien et al. 2015; Kim et al. 2021; Kim 2023; Belfiore et al. 2022b). Here we provide evidence that the “cirrus” in fact traces the neutral gas distribution.

6. *The CO-to-IR and extinction-corrected Hα-to-IR ratios that we measure agree with physical expectations and previous work* (Section 6, Figure 14, Section 2). Specifically, the CO-scaling coefficient *c* in our model agrees well with predictions from the Draine & Li (2007) model for a reasonable dust-to-gas ratio *D*/*G* ~ 0.01 and ISRF, *U* ~ 2*U*₀. Meanwhile, the coefficient *h* to scale Hα agrees well with SFR calibrations derived for bright H II regions. The CO-to-mid-IR and Hα-to-mid-IR ratios measured when using all data, i.e., not separating the emission using a model fit, are lower (i.e., they have more mid-IR), in line with previous work, and imply that a mixture of heating and column density contributes to the overall ratios.

7. *Putting our results together, we discuss how mid-IR emission can be used to estimate gas column density or trace recent star formation in our data* (Section 7). We also note current shortcomings and next steps that leverage the combined PHANGS–JWST, VLT/MUSE, and ALMA data.

In discussing these results, we have referred to “mid-IR” emission in general, no distinguishing our four bands. To first order, all four bands do show similar behavior and correlate with one another (see Section 2.1 and Appendix A). In more detail, the 21 µm (F2100W) emission shows distinct behavior from the other three bands. Its relationship with extinction-corrected Hα is more nearly linear and its relation with CO emission is shallower (Section 4.4). Overall, the sense of this relationship is that the 21 µm emission appears more directly related to Hα than the other mid-IR bands. It still mirrors the structure of the CO at low intensity and shows evidence for a substantial component tracing dust mixed with molecular gas, but it appears less suppressed in the brightest Hα-emitting regions than the other three bands. This agrees well with previous results and other papers in this Issue showing the suppression of PAH emission in bright H II regions (e.g., Helou

et al. 2004; Povich et al. 2007; Bendo et al. 2008; Gordon et al. 2008; Relaño & Kennicutt 2009; Calapa et al. 2014; Anderson et al. 2014; Chastenet et al. 2019; Chastenet 2023a; Dale et al. 2023; Egorov 2023). The degree to which the 10 µm band tracks the two PAH-dominated bands is a somewhat unexpected outcome in the first results from PHANGS–JWST.

Overall, our first analysis demonstrates the power of the combined JWST–MUSE–ALMA data set, shows the strength of mid-IR emission as both an ISM tracer and a star formation tracer, takes first steps toward realizing this potential, and suggests a path forward. As a closing note, we particularly highlight the power of the mid-IR maps to trace ISM structure in a quantitative way at a resolution and sensitivity that compares very favorably even to ALMA. In this Issue, the potential of this approach is already illustrated by studies identifying filamentary structure (Meidt et al. 2023; Thilker et al. 2023), feedback and dynamically driven shells (Barnes et al. 2022b; Watkins et al. 2023), and even digging in to faint structures associated with atomic gas (Sandstrom 2023b). Here we have provided first steps to make the mid-IR-based ISM maps quantitative. We have also discussed that to make more progress in this direction, we will need to both (1) deal with contamination by emission associated directly with recent star formation and (2) calibrate normalization terms that vary with the local ISRF and dust-to-gas ratio. This is eminently possible given the information in the combined PHANGS surveys. Then, as seen in Sandstrom (2023a, 2023b), the potential for such maps to reach very high physical resolution and mass sensitivity is outstanding.

We thank the anonymous referee for a careful read of a long paper during a busy time.

This work was carried out as part of the PHANGS collaboration.

A.K.L. thanks Prof. Todd Thompson for input on the draft. A.K.L. gratefully acknowledges support by grants 1653300 and 2205628 from the National Science Foundation, by award JWST-GO-02107.009-A, and by a Humboldt Research Award from the Alexander von Humboldt Foundation. A.D.B. acknowledges support by NSF-AST2108140 and award JWST-GO-02107.008-A.

J. P.ety acknowledges support by the DAOISM grant ANR-21-CE31-0010 and by the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with INC/INP, co-funded by CEA and CNES.

E.J.W., R.S.K., and S.C.O.G. acknowledge the funding provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project ID 138713538—SFB 881 (“The Milky Way System,” subprojects A1, B1, B2, B8, and P1).

T.G.W. and J.N. acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 694343).

J.M.D.K. gratefully acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program via the ERC Starting Grant MUSTANG (grant agreement No. 714907). COOL Research DAO is a Decentralized Autonomous Organization supporting research in astrophysics aimed at uncovering our cosmic origins.
J.K. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the DFG Sachbeihilfe (grant No. KR4801/2-1).

M.C. gratefully acknowledges funding from the DFG through an Emmy Noether Research Group (grant No. CH2137/1-1).

F.B. would like to acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No.726384/Empire).

R.S.K. and S.C.O.G. acknowledge support from the European Research Council via the ERC Synergy Grant "ECOGAL" (project ID 855130), from the Heidelberg Cluster of Excellence (EXC 2181-390900948) "STRUCTURES," funded by the German Excellence Strategy, and from the German Ministry for Economic Affairs and Climate Action in project "MAINN" (funding ID 50002206).

K.K. and O.E. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the form of an Emmy Noether Research Group (grant No. KR4598/2-1, PI Kreckel). G.A.B. acknowledges the support from ANID Basal project FB210003.

R.C.L. acknowledges support for this work provided by a National Science Foundation (NSF) Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2102625.

K.G. is supported by the Australian Research Council through the Discovery Early Career Researcher Award (DECRA) Fellowship DE220100766 funded by the Australian Government. K.G. is supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project No. CE170100013.

C.E. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) Sachbeihilfe, grant No. BI1546/3-1

A.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1903834.

E.W.K. acknowledges support from the Smithsonian Institution as a Submillimeter Array (SMA) Fellow and the Natural Sciences and Engineering Research Council of Canada (NSERC).

E.R. and H.H. acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2022-03499.

J.S. acknowledges support from NSERC through a Canadian Institute for Theoretical Astrophysics (CITA) National Fellowship.

E.C. acknowledges support from ANID Basal projects ACE210002 and FB210003.

This work is based in part on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with program 2017. The specific observations analyzed can be accessed via 10.17909/9bdf-jn24.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00650.S, ADS/JAO.ALMA#2013.1.01161.S, ADS/JAO.ALMA#2015.1.00925.S, ADS/JAO.ALM A#2017.1.00392.S, ADS/JAO.ALMA#2017.1.00886.L. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada),

NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Based on observations collected at the European Southern Observatory under ESO programmes 094.C-0623 (PI: Kreckel), 095.C-0473, 098.C-0484 (PI: Blanc), 1100.B-0651 (PHANGS-MUSE; PI: Schinnerer), as well as 094.B-0321 (MAGNUM; PI: Marconi), 099.B-0242, 0100.B-0116, 098.B-0551 (MAD; PI: Carollo) and 097.B-0640 (TIMER; PI: Gadotti).

Facility: ALMA.

Software: astropy (Astropy Collaboration et al. 2013, 2018).

## Appendix A

### Typical Mid-infrared Band Ratios in the First Four PHANGS-JWST Targets

The main text focuses on the correlations between mid-IR emission and other tracers of gas and recent star formation. This appendix reports the basic scaling of mid-IR bands with one another in the first four PHANGS-JWST galaxies. Section 2.1 for a short description of the bands considered and Table 1 for some key numerical results.

Figure 15 plots intensity versus intensity for a series of mid-IR band pairs, and Figure 16 shows the corresponding histograms of band ratios. The comparison includes Spitzer 8 µm and 24 µm data, which are available for IC 5332, NGC 0628, and NGC 1365 but not for NGC 7496, and WISE 12 µm data, which are available for all targets.

At 1"7 we conduct this comparison using the database constructed in Section 3. We also build two new databases, one at 15" resolution and one at 4" resolution, following the same method adopted in the main paper: We convolve all data to the same resolution, place them on the same astrometric grid, and then sample the data with two pixels per FWHM of the PSF. At 15" we are able to include Spitzer data at 8 µm and 24 µm, at 1"7 we only consider the JWST data, and we use the 4" data set to compare IRAC 8 µm and JWST F770W emission at the highest "safe" resolution allowed by the Aniano et al. (2011) convolution kernels.

We compare each pair of mid-IR bands. Figure 15 shows a subset of these comparisons that demonstrate our key results:

1. To first order, all of the mid-IR bands dominated by dust emission track one another in our images. That is, in Figure 15 all band pairs show correlations. The full spread of the points somewhat masks how tight the correlations actually are, which is more visible from the 16%-84% range shown as error bars on the bins. Quantitatively, the median Spearman rank correlation considering all mid-IR band pairs and galaxies is 0.95, indicating a nearly monotonic relationship between all mid-IR band pairs across our sample. The ~10% of cases with rank correlation <0.8 can be attributed to low signal to noise or artifacts in either the JWST or comparison data.

2. Also to first order, the bands in Figure 15 all show approximately linear relations at the moderate intensities plotted here. This implies that these are characteristic band ratios that can be used to translate results between
J.K. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the DFG Sachbeihilfe (grant No. KR4801/2-1).

M.C. gratefully acknowledges funding from the DFG through an Emmy Noether Research Group (grant No. CH2137/1-1).

F.B. would like to acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No.726384/Empire).

R.S.K. and S.C.O.G. acknowledge support from the European Research Council via the ERC Synergy Grant "ECOGAL" (project ID 855130), from the Heidelberg Cluster of Excellence (EXC 2181-390900948) "STRUCTURES," funded by the German Excellence Strategy, and from the German Ministry for Economic Affairs and Climate Action in project "MAINN" (funding ID 50002206).

K.K. and O.E. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the form of an Emmy Noether Research Group (grant No. KR4598/2-1, PI Kreckel). G.A.B. acknowledges the support from ANID Basal project FB210003.

R.C.L. acknowledges support for this work provided by a National Science Foundation (NSF) Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2102625.

K.G. is supported by the Australian Research Council through the Discovery Early Career Researcher Award (DECRA) Fellowship DE220100766 funded by the Australian Government. K.G. is supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project No. CE170100013.

C.E. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) Sachbeihilfe, grant No. BI1546/3-1

A.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1903834.

E.W.K. acknowledges support from the Smithsonian Institution as a Submillimeter Array (SMA) Fellow and the Natural Sciences and Engineering Research Council of Canada (NSERC).

E.R. and H.H. acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2022-03499.

J.S. acknowledges support from NSERC through a Canadian Institute for Theoretical Astrophysics (CITA) National Fellowship.

E.C. acknowledges support from ANID Basal projects ACE210002 and FB210003.

This work is based in part on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with program 2017. The specific observations analyzed can be accessed via 10.17909/9bdf-jn24.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00650.S, ADS/JAO.ALMA#2013.1.01161.S, ADS/JAO.ALMA#2015.1.00925.S, ADS/JAO.ALM A#2017.1.00392.S, ADS/JAO.ALMA#2017.1.00886.L. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada),

NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Based on observations collected at the European Southern Observatory under ESO programmes 094.C-0623 (PI: Kreckel), 095.C-0473, 098.C-0484 (PI: Blanc), 1100.B-0651 (PHANGS-MUSE; PI: Schinnerer), as well as 094.B-0321 (MAGNUM; PI: Marconi), 099.B-0242, 0100.B-0116, 098.B-0551 (MAD; PI: Carollo) and 097.B-0640 (TIMER; PI: Gadotti).

Facility: ALMA.

Software: astropy (Astropy Collaboration et al. 2013, 2018).

## Appendix A

### Typical Mid-infrared Band Ratios in the First Four PHANGS–JWST Targets

The main text focuses on the correlations between mid-IR emission and other tracers of gas and recent star formation. This appendix reports the basic scaling of mid-IR bands with one another in the first four PHANGS–JWST galaxies. Section 2.1 for a short description of the bands considered and Table 1 for some key numerical results.

Figure 15 plots intensity versus intensity for a series of mid-IR band pairs, and Figure 16 shows the corresponding histograms of band ratios. The comparison includes Spitzer 8 µm and 24 µm data, which are available for IC 5332, NGC 0628, and NGC 1365 but not for NGC 7496, and WISE 12 µm data, which are available for all targets.

At 1"7 we conduct this comparison using the database constructed in Section 3. We also build two new databases, one at 15" resolution and one at 4" resolution, following the same method adopted in the main paper: We convolve all data to the same resolution, place them on the same astrometric grid, and then sample the data with two pixels per FWHM of the PSF. At 15" we are able to include Spitzer data at 8 µm and 24 µm, at 1"7 we only consider the JWST data, and we use the 4" data set to compare IRAC 8 µm and JWST F770W emission at the highest "safe" resolution allowed by the Aniano et al. (2011) convolution kernels.

We compare each pair of mid-IR bands. Figure 15 shows a subset of these comparisons that demonstrate our key results:

1. To first order, all of the mid-IR bands dominated by dust emission track one another in our images. That is, in Figure 15 all band pairs show correlations. The full spread of the points somewhat masks how tight the correlations actually are, which is more visible from the 16%–84% range shown as error bars on the bins. Quantitatively, the median Spearman rank correlation considering all mid-IR band pairs and galaxies is 0.95, indicating a nearly monotonic relationship between all mid-IR band pairs across our sample. The ~10% of cases with rank correlation <0.8 can be attributed to low signal to noise or artifacts in either the JWST or comparison data.

2. Also to first order, the bands in Figure 15 all show approximately linear relations at the moderate intensities plotted here. This implies that these are characteristic band ratios that can be used to translate results between
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Comparison among intensities in different mid-IR bands at matched resolution in the first four PHANGS–JWST target galaxies. Each panel compares a different mid-IR band and F770W. For pairs of JWST MIRI bands, the pink points and red bins show the comparison at the $\theta = 1''7$ resolution used in the main text of this paper. For all bands, the blue points and bins show comparisons after convolution of all data to a common Gaussian beam with FWHM $\theta = 15''$. The bins show the median and 16%–84% range for the y-axis band when binned by F770W intensity quantity. The dashed black lines show linear fits to the bins for the 15'' data, which also describe the $1''7$ data well. The fits appear overall consistent with passing through the origin, indicating a self-consistent overall background level among all data and good agreement with previous mapping that covered wider areas at coarser resolution. The slopes of these lines are the fiducial band ratios that we adopt in the main text (Table 1), and the scatter in the blue points sets the reported scatter in that table. The scatter among the best-fitting intercepts informs our estimate that the JWST MIRI background levels are currently uncertain by $\sim\pm0.1$ MJy sr$^{-1}$. The overall consistency and linearity motivate our suggested approach to background level adjustment or validation in Appendix B.</figcaption></figure>

bands. Note that unlike the plots in the main text, these are linear–linear plots, so that the lines fitted to the bins indicate that approximately fixed ratios describe the data fairly well. We use these fitted slopes to calculate the median band ratios in Table 1. That table specifically quotes the slopes derived at 15" resolution when comparing other bands to F770W and using data for all available galaxies. These are the blue data in Figure 15 and the quoted ratios correspond to the slopes of the dashed black lines, which go through the dark blue bins. The quoted error is the log scatter in the ratios at this 15" resolution. We present the ratios on a scale relative to

F770W and one relative to MIPS 24 µm, but in both cases the fits are the ones shown in Figure 15.

3. The fit relationships are all broadly consistent with going through the origin, implying that the backgrounds of the MIRI images are in overall good agreement with one another and with previous mid-IR mapping. More concretely, if we consider all galaxies and all band pairs, then the median intercept for all binned fits is $0.05$ MJy sr$^{-1}$ with a scatter of $\sim\pm0.08$ MJy sr$^{-1}$ from band pair to band pair. Based on this, we suggest that a reasonable estimate of the overall uncertainty in the current background level of the PHANGS–JWST MIRI images is $\sim\pm0.1$ MJy sr$^{-1}$.
<figure><img src="image_18.png" /><figcaption>**Figure 15.** Comparison among intensities in different mid-IR bands at matched resolution in the first four PHANGS–JWST target galaxies. Each panel compares a different mid-IR band and F770W. For pairs of JWST MIRI bands, the pink points and red bins show the comparison at the $\theta = 1''7$ resolution used in the main text of this paper. For all bands, the blue points and bins show comparisons after convolution of all data to a common Gaussian beam with FWHM $\theta = 15''$. The bins show the median and 16%–84% range for the y-axis band when binned by F770W intensity quantity. The dashed black lines show linear fits to the bins for the 15'' data, which also describe the $1''7$ data well. The fits appear overall consistent with passing through the origin, indicating a self-consistent overall background level among all data and good agreement with previous mapping that covered wider areas at coarser resolution. The slopes of these lines are the fiducial band ratios that we adopt in the main text (Table 1), and the scatter in the blue points sets the reported scatter in that table. The scatter among the best-fitting intercepts informs our estimate that the JWST MIRI background levels are currently uncertain by $\sim\pm0.1$ MJy sr$^{-1}$. The overall consistency and linearity motivate our suggested approach to background level adjustment or validation in Appendix B.</figcaption></figure>

bands. Note that unlike the plots in the main text, these are linear–linear plots, so that the lines fitted to the bins indicate that approximately fixed ratios describe the data fairly well. We use these fitted slopes to calculate the median band ratios in Table 1. That table specifically quotes the slopes derived at 15" resolution when comparing other bands to F770W and using data for all available galaxies. These are the blue data in Figure 15 and the quoted ratios correspond to the slopes of the dashed black lines, which go through the dark blue bins. The quoted error is the log scatter in the ratios at this 15" resolution. We present the ratios on a scale relative to

F770W and one relative to MIPS 24 µm, but in both cases the fits are the ones shown in Figure 15.

3. *The fit relationships are all broadly consistent with going through the origin, implying that the backgrounds of the MIRI images are in overall good agreement with one another and with previous mid-IR mapping.* More concretely, if we consider all galaxies and all band pairs, then the median intercept for all binned fits is $0.05$ MJy sr$^{-1}$ with a scatter of $\sim\pm0.08$ MJy sr$^{-1}$ from band pair to band pair. Based on this, we suggest that a reasonable estimate of the overall uncertainty in the current background level of the PHANGS–JWST MIRI images is $\sim\pm0.1$ MJy sr$^{-1}$.
<figure><img src="image_18.png" /><figcaption>**Figure 16.** Histograms of band ratios among different mid-IR bands at matched resolution in the first four PHANGS–JWST target galaxies. As Figure 15 but now showing the histogram of $log_{10}$ of the band ratio indicated in the figure. Light blue histograms show results for individual data at 15" resolution, pink histograms show JWST band ratios at 1"/67 resolution, and the purple histogram (only comparing IRAC 8 µm and F770W) shows results at 4" resolution. The dashed black line shows the adopted typical ratio $R$ for each band ratio (Table 1, Section 2.1), and the square dark points show the bins from Figure 15.</figcaption></figure>

Although these characteristic ratios are useful, we caution that in this Issue Chastenet (2023a, 2023b), Dale et al. (2023), Egorov (2023), and Sandstrom (2023a) demonstrate clear local variations in the observed band ratios, which trace changes in the underlying dust properties (in good agreement with previous work; e.g., Galliano et al. 2018; Chastenet et al. 2019; Li 2020).

The ratios we quote have been calculated at relatively low resolution and focused on relatively low-intensity regions, which averages over some of these variations and contributes to the relatively uniform band ratios in Figures 15 and 16. Even so, ratio variations are clearly evident in our plots, particularly the change in ratios of PAH-tracing bands to the continuum-dominated F2100W or 24 µm between diffuse and star-forming regions, are also evident. We discuss these in the main text, e.g., Section 4.4, and they also appear in Figures 15 and 16 as a modest population of points scattering to high F2100W at fixed

F770W in Figure 15 and the “wing” of the F2100W/F770W or MIPS 24 µm/F770W histogram toward high values in Figure 16. In addition to local variations, the global mid-IR color of galaxies is also known to correlate with global galaxy properties (e.g., Dale et al. 2009), and we would expect these band ratios to show more scatter if we studied a more diverse sample. The ratios we quote here are characteristic ratios for the inner disks of our four targets, all relatively massive main-sequence, star-forming disk galaxies.

# Appendix B

## A Method to Validate or Anchor Mid-IR Backgrounds in the Absence of Empty Sky

PHANGS–JWST targets the area of active star formation in galaxies that often have diffuse, low-activity emission extending well beyond the field of view of the MIRI imager. As a result, in some cases the images contain little or no area that
<figure><img src="image_19.png" /><figcaption>**Figure 16.** Histograms of band ratios among different mid-IR bands at matched resolution in the first four PHANGS–JWST target galaxies. As Figure 15 but now showing the histogram of $log_{10}$ of the band ratio indicated in the figure. Light blue histograms show results for individual data at 15" resolution, pink histograms show JWST band ratios at 1"/67 resolution, and the purple histogram (only comparing IRAC 8 µm and F770W) shows results at 4" resolution. The dashed black line shows the adopted typical ratio $R$ for each band ratio (Table 1, Section 2.1), and the square dark points show the bins from Figure 15.</figcaption></figure>

Although these characteristic ratios are useful, we caution that in this Issue Chastenet (2023a, 2023b), Dale et al. (2023), Egorov (2023), and Sandstrom (2023a) demonstrate clear local variations in the observed band ratios, which trace changes in the underlying dust properties (in good agreement with previous work; e.g., Galliano et al. 2018; Chastenet et al. 2019; Li 2020).

The ratios we quote have been calculated at relatively low resolution and focused on relatively low-intensity regions, which averages over some of these variations and contributes to the relatively uniform band ratios in Figures 15 and 16. Even so, ratio variations are clearly evident in our plots, particularly the change in ratios of PAH-tracing bands to the continuum-dominated F2100W or 24 µm between diffuse and star-forming regions, are also evident. We discuss these in the main text, e.g., Section 4.4, and they also appear in Figures 15 and 16 as a modest population of points scattering to high F2100W at fixed

F770W in Figure 15 and the “wing” of the F2100W/F770W or MIPS 24 µm/F770W histogram toward high values in Figure 16. In addition to local variations, the global mid-IR color of galaxies is also known to correlate with global galaxy properties (e.g., Dale et al. 2009), and we would expect these band ratios to show more scatter if we studied a more diverse sample. The ratios we quote here are characteristic ratios for the inner disks of our four targets, all relatively massive main-sequence, star-forming disk galaxies.

## Appendix B

### A Method to Validate or Anchor Mid-IR Backgrounds in the Absence of Empty Sky

PHANGS–JWST targets the area of active star formation in galaxies that often have diffuse, low-activity emission extending well beyond the field of view of the MIRI imager. As a result, in some cases the images contain little or no area that
can be confidently identified as containing only foreground and background emission. That is, the PHANGS–JWST images often lack “empty sky.” We expect this challenge to be widespread for JWST given that the NIRCam and MIRI imagers have fields of view of $1'^{-2'}$, insufficient to cover the full area of many of the nearest galaxies or Milky Way structures. Even as the pipeline and data-processing strategy mature, validation of the background level in images “crowded” by dust emission will be an important quality assurance step for many studies.

Validating the background level or even defining some empirical background to subtract off any residual foreground, background, or instrumental contribution to the intensity can be important for many science applications. For example, both the absolute mid-IR intensity and band ratios from faint, extended dust structures can be crucial to understand the diffuse ISM (e.g., see Sandstrom 2023b in this Issue). Aperture photometry techniques, which address this problem locally, are inappropriate for this problem, rendering the overall background level of the image important.

Figure 15 and Appendix A suggest one simple, empirical approach to address this problem:

1. The approximately linear correlation among the bands tracing mid-IR dust emission can be used to establish or validate a common background system internal to crowded JWST images. Figure 15 and Appendix A show that at moderate resolution and moderate intensity, mid-IR at one band emission correlates approximately linearly with mid-IR at most other bands. Though not shown, we also found similar correlations when convolving the MIRI data to share the native ~0.7 resolution of JWST at F2100W. When fitting linear relationships to each mid-IR band pair (i.e., $I_{v,A} = m_{AB}I_{v,B} + b_{AB}$), one derives the slope, $m_{AB}$, which reflects the typical band ratio (i.e., $\langle I_{v,A}/I_{v,B} \rangle$, Table 1), and an intercept, $b_{AB}$, which can be most naturally interpreted as the offset in background level between the two bands in units of $I_{v,A}$. In the simplest case, each band should have a single background level offset that brings it into best agreement with the other bands. To solve for this offset, one could conduct a full minimization of this matrix. In practice, for our initial PHANGS–JWST processing, we identified F770W as our reference band because of its high quality and good signal to noise. Then we solved for the offset value needed to bring the other bands into agreement with F770W. In the case where the bands are all self-consistently background-subtracted already, this exercise should yield intercepts near 0 for all band pairs. Otherwise, this can be used to place all bands on a common background scale. Note that this does not independently verify that this shared scale is indeed anchored to the correct value, only that the backgrounds between the bands are self-consistent.

2. Wide-area maps at related but not identical bands, especially the widely available WISE3, can be used to set or check the absolute background level. The first part of this exercise leaves a single degree of freedom, the absolute background level. Figure 15 and Appendix A also show a strong, linear correlation between the JWST dust-tracing mid-IR bands and previous mid-IR mapping. For example, see the strong correlations of F770W with Spitzer 8µm, WISE 12µm, and Spitzer 24 µm emission.

These maps by previous facilities lack the resolution achieved by JWST but they do typically cover a much larger area, with clear regions of empty sky or otherwise well-established background levels. They are also widely available. WISE maps are available for the whole sky, and the sensitive WISE 12 µm (WISE Band 3) has a bandpass that integrates over a large part of the mid-IR spectral range (see Wright et al. 2010). Bespoke data products exist for the Milky Way (e.g., Meisner & Finkbeiner 2014) and many nearby galaxies (e.g., Jarrett et al. 2019; Leroy et al. 2019) but for many purposes, the observatory-provided images or the unWISE reprocessing (Lang 2014) will work just as well. Spitzer was even more sensitive than WISE and because of its fast mapping speed, it covered many galaxies during its cold mission (e.g., Kennicutt et al. 2003; Armus et al. 2009; Dale et al. 2009; Bendo et al. 2012, and many others). Spitzer maps at either 8 µm and 24 µm should represent a sensitive, reliable anchor to validate JWST background levels. Once all of the JWST bands have been placed on a common scale, one can compare either a high-quality JWST reference band or all of the JWST bands together to the wide-area previous maps to establish an absolute background level for the JWST images. For the initial PHANGS–JWST analysis, we made a matched-resolution comparison between our reference band, F770W, and either Spitzer 8 µm (IRAC channel 4) or WISE3 at $\theta = 15''$, preferring Spitzer when available. Similar to the comparisons above, we binned the F770W data as a function of the reference band, Spitzer 8 µm or WISE 12 µm. Then we fit a line to the binned results after identifying a low-intensity regime where the relationship looked linear. The typical range fit was typically $I_{nu} \sim 0.2–1.5$ MJy sr$^{-1}$ at 15'' for the Spitzer or WISE data (see Figure 15).

In addition to validating or setting the background level of the data and establishing characteristic band ratios, we note that this approach can be used to check the noise levels in crowded data against expectations. Once the relative background levels and characteristic band ratios are reasonably established, one can measure the scatter in the difference between scaled versions of the various maps in low-intensity regions. This measured scatter represents an estimate of the noise summed in quadrature between the two bands (i.e., one can measure $\sigma_{AB}$ from the residual image of $I_{v,A} - m_{AB}I_{v,B}$, with $m_{AB}$ the slope from point 1 above, and expect $\sigma_{AB} \approx \sqrt{\sigma_A^2 + \sigma_B^2}$). This formally yields an upper limit because astronomical signal may contribute to the scatter, but it should still be among the most direct ways to empirically estimate the noise from very crowded regions and so validate expectations from the pipeline processing and theoretical expectations.

## Appendix C
### Histograms of Ratios among CO, H$\alpha$, and Mid-IR Emission

For completeness, Figure 17 shows the distribution of ratios among mid-IR, CO, and H$\alpha$ emission for individual lines of sight that meet our selection criteria. The median and 16%–84% range of these ratios are reported in Table 4 and Figure 14. The two-dimensional distribution of the data corresponding to these ratios appears in Figures 5 through 9.
can be confidently identified as containing only foreground and background emission. That is, the PHANGS–JWST images often lack “empty sky.” We expect this challenge to be widespread for JWST given that the NIRCam and MIRI imagers have fields of view of $1^{\prime\prime}-2^{\prime\prime}$, insufficient to cover the full area of many of the nearest galaxies or Milky Way structures. Even as the pipeline and data-processing strategy matures, validation of the background level in images “crowded” by dust emission will be an important quality assurance step for many studies.

Validating the background level or even defining some empirical background to subtract off any residual foreground, background, or instrumental contribution to the intensity can be important for many science applications. For example, both the absolute mid-IR intensity and band ratios from faint, extended dust structures can be crucial to understand the diffuse ISM (e.g., see Sandstrom 2023b in this Issue). Aperture photometry techniques, which address this problem locally, are inappropriate for this problem, rendering the overall background level of the image important.

Figure 15 and Appendix A suggest one simple, empirical approach to address this problem:

1. The approximately linear correlation among the bands tracing mid-IR dust emission can be used to establish or validate a common background system internal to crowded JWST images. Figure 15 and Appendix A show that at moderate resolution and moderate intensity, mid-IR at one band emission correlates approximately linearly with mid-IR at most other bands. Though not shown, we also found similar correlations when convolving the MIRI data to share the native ~0.0"7 resolution of JWST at F2100W. When fitting linear relationships to each mid-IR band pair (i.e., $I_{v,A} = m_{AB}I_{v,B} + b_{AB}$), one derives the slope, $m_{AB}$, which reflects the typical band ratio (i.e., $\langle I_{v,A}/I_{v,B} \rangle$, Table 1), and an intercept, $b_{AB}$, which can be most naturally interpreted as the offset in background level between the two bands in units of $I_{v,A}$. In the simplest case, each band should have a single background level offset that brings it into best agreement with the other bands. To solve for this offset, one could conduct a full minimization of this matrix. In practice, for our initial PHANGS–JWST processing, we identified F770W as our reference band because of its high quality and good signal to noise. Then we solved for the offset value needed to bring the other bands into agreement with F770W. In the case where the bands are all self-consistently background-subtracted already, this exercise should yield intercepts near 0 for all band pairs. Otherwise, this can be used to place all bands on a common background scale. Note that this does not independently verify that this shared scale is indeed anchored to the correct value, only that the backgrounds between the bands are self-consistent.

2. Wide-area maps at related but not identical bands, especially the widely available WISE3, can be used to set or check the absolute background level. The first part of this exercise leaves a single degree of freedom, the absolute background level. Figure 15 and Appendix A also show a strong, linear correlation between the JWST dust-tracing mid-IR bands and previous mid-IR mapping. For example, see the strong correlations of F770W with Spitzer 8µm, WISE 12µm, and Spitzer 24 µm emission.

These maps by previous facilities lack the resolution achieved by JWST but they do typically cover a much larger area, with clear regions of empty sky or otherwise well-established background levels. They are also widely available. WISE maps are available for the whole sky, and the sensitive WISE 12 µm (WISE Band 3) has a bandpass that integrates over a large part of the mid-IR spectral range (see Wright et al. 2010). Bespoke data products exist for the Milky Way (e.g., Meisner & Finkbeiner 2014) and many nearby galaxies (e.g., Jarrett et al. 2019; Leroy et al. 2019) but for many purposes, the observatory-provided images or the unWISE reprocessing (Lang 2014) will work just as well. Spitzer was even more sensitive than WISE and because of its fast mapping speed, it covered many galaxies during its cold mission (e.g., Kennicutt et al. 2003; Armus et al. 2009; Dale et al. 2009; Bendo et al. 2012, and many others). Spitzer maps at either 8 µm and 24 µm should represent a sensitive, reliable anchor to validate JWST background levels. Once all of the JWST bands have been placed on a common scale, one can compare either a high-quality JWST reference band or all of the JWST bands together to the wide-area previous maps to establish an absolute background level for the JWST images. For the initial PHANGS–JWST analysis, we made a matched-resolution comparison between our reference band, F770W, and either Spitzer 8 µm (IRAC channel 4) or WISE3 at $\theta = 15''$, preferring Spitzer when available. Similar to the comparisons above, we binned the F770W data as a function of the reference band, Spitzer 8 µm or WISE 12 µm. Then we fit a line to the binned results after identifying a low-intensity regime where the relationship looked linear. The typical range fit was typically $I_{nu} \sim 0.2–1.5$ MJy sr$^{-1}$ at 15'' for the Spitzer or WISE data (see Figure 15).

In addition to validating or setting the background level of the data and establishing characteristic band ratios, we note that this approach can be used to check the noise levels in crowded data against expectations. Once the relative background levels and characteristic band ratios are reasonably established, one can measure the scatter in the difference between scaled versions of the various maps in low-intensity regions. This measured scatter represents an estimate of the noise summed in quadrature between the two bands (i.e., one can measure $\sigma_{AB}$ from the residual image of $I_{v,A} - m_{AB}I_{v,B}$, with $m_{AB}$ the slope from point 1 above, and expect $\sigma_{AB} \approx \sqrt{\sigma_A^2 + \sigma_B^2}$). This formally yields an upper limit because astronomical signal may contribute to the scatter, but it should still be among the most direct ways to empirically estimate the noise from very crowded regions and so validate expectations from the pipeline processing and theoretical expectations.

## Appendix C
### Histograms of Ratios among CO, H$\alpha$, and Mid-IR Emission

For completeness, Figure 17 shows the distribution of ratios among mid-IR, CO, and H$\alpha$ emission for individual lines of sight that meet our selection criteria. The median and 16%–84% range of these ratios are reported in Table 4 and Figure 14. The two-dimensional distribution of the data corresponding to these ratios appears in Figures 5 through 9.
<figure><img src="image_19.png" /><figcaption>**Figure 17.** Histograms of the ratios among CO, Hα, and mid-IR emission. Histograms showing log₁₀ ratios of (top two rows) CO to mid-IR emission, (middle rows) extinction-corrected Hα to mid-IR emission, and (bottom row) CO to extinction-corrected Hα. The lines and shaded regions show the median and 16%–84% range reported in the main text of the paper (Table 4 and Figure 14). Note that we show only values with a positive ratio, but this caveat affects only a small subset of the CO data (e.g., see that the 16% to 84% range is positive).</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 17.** Histograms of the ratios among CO, Hα, and mid-IR emission. Histograms showing log₁₀ ratios of (top two rows) CO to mid-IR emission, (middle rows) extinction-corrected Hα to mid-IR emission, and (bottom row) CO to extinction-corrected Hα. The lines and shaded regions show the median and 16%–84% range reported in the main text of the paper (Table 4 and Figure 14). Note that we show only values with a positive ratio, but this caveat affects only a small subset of the CO data (e.g., see that the 16% to 84% range is positive).</figcaption></figure>
ORCID iDs

Adam K. Leroy https://orcid.org/0000-0002-2545-1700

Karin Sandstrom https://orcid.org/0000-0002-4378-8534

Erik Rosolowsky https://orcid.org/0000-0002-5204-2259

Francesco Belfiore https://orcid.org/0000-0002-2545-5752

Alberto D. Bolatto https://orcid.org/0000-0002-5480-5686

Yixian Cao https://orcid.org/0000-0001-5301-1326

Eric W. Koch https://orcid.org/0000-0001-9605-780X

Eva Schinnerer https://orcid.org/0000-0002-3933-7677

Ashley. T. Barnes https://orcid.org/0000-0003-0410-4504

Ivana Bešlić https://orcid.org/0000-0003-0783-0157

F. Bigiel https://orcid.org/0000-0003-0166-9745

Guillermo A. Blanc https://orcid.org/0000-0003-4218-3944

Jérémy Chastenet https://orcid.org/0000-0002-5235-5589

Ness Mayker Chen https://orcid.org/0000-0002-5993-6685

Mélanie Chévance https://orcid.org/0000-0002-5635-5180

Ryan Chown https://orcid.org/0000-0001-8241-7704

Enrico Congiu https://orcid.org/0000-0002-8549-4083

Daniel A. Dale https://orcid.org/0000-0002-5782-9093

Oleg V. Egorov https://orcid.org/0000-0002-4755-118X

Eric Emsellem https://orcid.org/0000-0002-6155-7166

Cosima Eibensteiner https://orcid.org/0000-0002-1185-2810

Christopher M. Faesi https://orcid.org/0000-0001-5310-467X

Simon C. O. Glover https://orcid.org/0000-0001-6708-1317

Kathryn Grasha https://orcid.org/0000-0002-3247-5321

Brent Groves https://orcid.org/0000-0002-9768-0246

Hamid Hassani https://orcid.org/0000-0002-8806-6308

Jonathan D. Henshaw https://orcid.org/0000-0001-9656-7682

Annie Hughes https://orcid.org/0000-0002-9181-1161

María J. Jiménez-Donaire https://orcid.org/0000-0002-9165-8080

Jaeyeon Kim https://orcid.org/0000-0002-0432-6847

Ralf S. Klessen https://orcid.org/0000-0002-0560-3172

Kathryn Kreckel https://orcid.org/0000-0001-6551-3091

J. M. Diederik Kruijssen https://orcid.org/0000-0002-8804-0212

Kirsten L. Larson https://orcid.org/0000-0003-3917-6460

Janice C. Lee https://orcid.org/0000-0002-2278-9407

Rebecca C. Levy https://orcid.org/0000-0003-2508-2586

Daizhong Liu https://orcid.org/0000-0001-9773-7479

Laura A. Lopez https://orcid.org/0000-0002-1790-3148

Sharon E. Meidt https://orcid.org/0000-0002-6118-4048

Eric J. Murphy https://orcid.org/0000-0001-7089-7325

Justus Neumann https://orcid.org/0000-0002-3289-8914

Ismael Pessa https://orcid.org/0000-0002-0873-5744

Jérôme Pety https://orcid.org/0000-0003-3061-6546

Toshiki Saito https://orcid.org/0000-0001-9016-2641

Amy Sardone https://orcid.org/0000-0002-5783-145X

Jiayi Sun https://orcid.org/0000-0003-0378-4667

David A. Thilker https://orcid.org/0000-0002-8528-7340

Antonio Usero https://orcid.org/0000-0003-1242-505X

Elizabeth J. Watkins https://orcid.org/0000-0002-7365-5791

Cory M. Whitcomb https://orcid.org/0000-0003-2093-4452

Thomas G. Williams https://orcid.org/0000-0002-0012-2142

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ORCID iDs

Adam K. Leroy https://orcid.org/0000-0002-2545-1700

Karin Sandstrom https://orcid.org/0000-0002-4378-8534

Erik Rosolowsky https://orcid.org/0000-0002-5204-2259

Francesco Belfiore https://orcid.org/0000-0002-2545-5752

Alberto D. Bolatto https://orcid.org/0000-0002-5480-5686

Yixian Cao https://orcid.org/0000-0001-5301-1326

Eric W. Koch https://orcid.org/0000-0001-9605-780X

Eva Schinnerer https://orcid.org/0000-0002-3933-7677

Ashley. T. Barnes https://orcid.org/0000-0003-0410-4504

Ivana Bešlić https://orcid.org/0000-0003-0783-0157

F. Bigiel https://orcid.org/0000-0003-0166-9745

Guillermo A. Blanc https://orcid.org/0000-0003-4218-3944

Jérémy Chastenet https://orcid.org/0000-0002-5235-5589

Ness Mayker Chen https://orcid.org/0000-0002-5993-6685

Mélanie Chévance https://orcid.org/0000-0002-5635-5180

Ryan Chown https://orcid.org/0000-0001-8241-7704

Enrico Congiu https://orcid.org/0000-0002-8549-4083

Daniel A. Dale https://orcid.org/0000-0002-5782-9093

Oleg V. Egorov https://orcid.org/0000-0002-4755-118X

Eric Emsellem https://orcid.org/0000-0002-6155-7166

Cosima Eibensteiner https://orcid.org/0000-0002-1185-2810

Christopher M. Faesi https://orcid.org/0000-0001-5310-467X

Simon C. O. Glover https://orcid.org/0000-0001-6708-1317

Kathryn Grasha https://orcid.org/0000-0002-3247-5321

Brent Groves https://orcid.org/0000-0002-9768-0246

Hamid Hassani https://orcid.org/0000-0002-8806-6308

Jonathan D. Henshaw https://orcid.org/0000-0001-9656-7682

Annie Hughes https://orcid.org/0000-0002-9181-1161

María J. Jiménez-Donaire https://orcid.org/0000-0002-9165-8080

Jaeyeon Kim https://orcid.org/0000-0002-0432-6847

Ralf S. Klessen https://orcid.org/0000-0002-0560-3172

Kathryn Kreckel https://orcid.org/0000-0001-6551-3091

J. M. Diederik Kruijssen https://orcid.org/0000-0002-8804-0212

Kirsten L. Larson https://orcid.org/0000-0003-3917-6460

Janice C. Lee https://orcid.org/0000-0002-2278-9407

Rebecca C. Levy https://orcid.org/0000-0003-2508-2586

Daizhong Liu https://orcid.org/0000-0001-9773-7479

Laura A. Lopez https://orcid.org/0000-0002-1790-3148

Sharon E. Meidt https://orcid.org/0000-0002-6118-4048

Eric J. Murphy https://orcid.org/0000-0001-7089-7325

Justus Neumann https://orcid.org/0000-0002-3289-8914

Ismael Pessa https://orcid.org/0000-0002-0873-5744

Jérôme Pety https://orcid.org/0000-0003-3061-6546

Toshiki Saito https://orcid.org/0000-0001-9016-2641

Amy Sardone https://orcid.org/0000-0002-5783-145X

Jiayi Sun https://orcid.org/0000-0003-0378-4667

David A. Thilker https://orcid.org/0000-0002-8528-7340

Antonio Usero https://orcid.org/0000-0003-1242-505X

Elizabeth J. Watkins https://orcid.org/0000-0002-7365-5791

Cory M. Whitcomb https://orcid.org/0000-0003-2093-4452

Thomas G. Williams https://orcid.org/0000-0002-0012-2142

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