# PHANGS-JWST First Results: Mid-infrared Emission Traces Both Gas Column Density and Heating at 100 pc Scales

Adam K. Leroy, Karin Sandstrom, Erik Rosolowsky, Francesco Belfiore, Alberto D. Bolatto, Yixian Cao, Eric W. Koch, Eva Schinnerer, Ashley. T. Barnes, Ivana Bešlić, et al.

► To cite this version:

Adam K. Leroy, Karin Sandstrom, Erik Rosolowsky, Francesco Belfiore, Alberto D. Bolatto, et al. PHANGS-JWST First Results: Mid-infrared Emission Traces Both Gas Column Density and Heating at 100 pc Scales. The Astrophysical journal letters, 2023, 944, 10.3847/2041-8213/acaf85. insu-04473227

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# PHANGS–JWST First Results: Mid-infrared Emission Traces Both Gas Column Density and Heating at 100 pc Scales

Adam K. Leroy<sup>1,2</sup>, Karin Sandstrom<sup>3</sup>, Erik Rosolowsky<sup>4</sup>, Francesco Belfiore<sup>5</sup>, Alberto D. Bolatto<sup>6</sup>, Yixian Cao<sup>7</sup>, Eric W. Koch<sup>8</sup>, Eva Schinnerer<sup>9</sup>, Ashley. T. Barnes<sup>10,11</sup>, Ivana Bešlić<sup>12</sup>, F. Bigiel<sup>12</sup>, Guillermo A. Blanc<sup>13,14</sup>, Jérémy Chastenet<sup>15</sup>, Ness Mayker Chen<sup>1,2</sup>, Mélanie Chevance<sup>16,17</sup>, Ryan Chown<sup>18</sup>, Enrico Congiu<sup>14</sup>, Daniel A. Dale<sup>19</sup>, Oleg V. Egorov<sup>20</sup>, Eric Emsellem<sup>10,21</sup>, Cosima Eibensteiner<sup>22</sup>, Christopher M. Faesi<sup>23</sup>, Simon C. O. Glover<sup>24</sup>, Kathryn Grasha<sup>25,26</sup>, Brent Groves<sup>27</sup>, Hamid Hassani<sup>4</sup>, Jonathan D. Henshaw<sup>9,28</sup>, Annie Hughes<sup>29</sup>, María J. Jiménez-Donaire<sup>30,31</sup>, Jaeyeon Kim<sup>16</sup>, Ralf S. Klessen<sup>24,32</sup>, Kathryn Kreckel<sup>20</sup>, J. M. Diederik Kruijssen<sup>17</sup>, Kirsten L. Larson<sup>33</sup>, Janice C. Lee<sup>34,35</sup>, Rebecca C. Levy<sup>35,47</sup>, Daizhong Liu<sup>7</sup>, Laura A. Lopez<sup>1,2,36</sup>, Sharon E. Meidt<sup>15</sup>, Eric J. Murphy<sup>37</sup>, Justus Neumann<sup>9</sup>, Ismael Pessa<sup>9,38</sup>, Jérôme Pety<sup>39,40</sup>, Toshiki Saito<sup>41</sup>, Amy Sardone<sup>1,2</sup>, Jiayi Sun<sup>42,43</sup>, David A. Thilker<sup>44</sup>, Antonio Usero<sup>30</sup>, Elizabeth J. Watkins<sup>20</sup>, Cory M. Whitcomb<sup>45</sup>, and Thomas G. Williams<sup>9,46</sup>

<figure><img src="image_2.png" /></figure>

<footnote n="1"><sup>1</sup>Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, Ohio 43210, USA; leroy.42@osu.edu</footnote>

<footnote n="2"><sup>2</sup>Center for Cosmology and Astroparticle Physics, 191 West Woodruff Avenue, Columbus, OH 43210, USA</footnote>

<footnote n="3"><sup>3</sup>Center for Astrophysics and Space Sciences, Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA</footnote>

<footnote n="4"><sup>4</sup>Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada</footnote>

<footnote n="5"><sup>5</sup>INAF—Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50157, Firenze, Italy</footnote>

<footnote n="6"><sup>6</sup>Department of Astronomy and Joint Space-Science Institute, University of Maryland, College Park, MD 20742, USA</footnote>

<footnote n="7"><sup>7</sup>Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße 1, D-85748 Garching, Germany</footnote>

<footnote n="8"><sup>8</sup>Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="9"><sup>9</sup>Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany</footnote>

<footnote n="10"><sup>10</sup>European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching, Germany</footnote>

<footnote n="11"><sup>11</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121, Bonn, Germany</footnote>

<footnote n="12"><sup>12</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany</footnote>

<footnote n="13"><sup>13</sup>The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA, USA</footnote>

<footnote n="14"><sup>14</sup>Departamento de Astronomía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile</footnote>

<footnote n="15"><sup>15</sup>Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium</footnote>

<footnote n="16"><sup>16</sup>Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany</footnote>

<footnote n="17"><sup>17</sup>Cosmic Origins Of Life (COOL) Research DAO<sup>48</sup></footnote>

<footnote n="18"><sup>18</sup>Department of Physics & Astronomy, University of Western Ontario, London, ON N6A 3K7, Canada</footnote>

<footnote n="19"><sup>19</sup>Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA</footnote>

<footnote n="20"><sup>20</sup>Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14, D-69120 Heidelberg, Germany</footnote>

<footnote n="21"><sup>21</sup>Univ Lyon, Univ Lyon1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230 Saint-Genis-Laval France</footnote>

<footnote n="22"><sup>22</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany</footnote>

<footnote n="23"><sup>23</sup>University of Connecticut, Department of Physics, 196A Auditorium Road, Unit 3046, Storrs, CT 06269, USA</footnote>

<footnote n="24"><sup>24</sup>Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, D-69120 Heidelberg, Germany</footnote>

<footnote n="25"><sup>25</sup>Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia</footnote>

<footnote n="26"><sup>26</sup>ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia</footnote>

<footnote n="27"><sup>27</sup>International Centre for Radio Astronomy Research, University of Western Australia, 7 Fairway, Crawley, 6009 WA, Australia</footnote>

<footnote n="28"><sup>28</sup>Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK</footnote>

<footnote n="29"><sup>29</sup>CNRS, IRAP, 9 Av. du Colonel Roche, BP 44346, F-31028 Toulouse cedex 4, France</footnote>

<footnote n="30"><sup>30</sup>Observatorio Astronómico Nacional (IGN), C/ Alfonso XII, 3, E-28014 Madrid, Spain</footnote>

<footnote n="31"><sup>31</sup>Centro de Desarrollos Tecnológicos, Observatorio de Yebes (IGN), E-19141 Yebes, Guadalajara, Spain</footnote>

<footnote n="32"><sup>32</sup>Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany</footnote>

<footnote n="33"><sup>33</sup>AURA for the European Space Agency (ESA), Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</footnote>

<footnote n="34"><sup>34</sup>Gemini Observatory/NSF's NOIRLab, 950 N. Cherry Avenue, Tucson, AZ, 85719, USA</footnote>

<footnote n="35"><sup>35</sup>Steward Observatory, University of Arizona, Tucson, AZ 85721, USA</footnote>

<footnote n="36"><sup>36</sup>Flatiron Institute, Center for Computational Astrophysics, NY 10010, USA</footnote>

<footnote n="37"><sup>37</sup>National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, USA</footnote>

<footnote n="38"><sup>38</sup>Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany</footnote>

<footnote n="39"><sup>39</sup>IRAM, 300 rue de la Piscine, F-38400 Saint Martin d'Hères, France</footnote>

<footnote n="40"><sup>40</sup>LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, F-75014 Paris, France</footnote>

<footnote n="41"><sup>41</sup>National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan</footnote>

<footnote n="42"><sup>42</sup>Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada</footnote>

<footnote n="43"><sup>43</sup>Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto, 60 St George Street, Toronto, ON M5S 3H8, Canada</footnote>

<footnote n="44"><sup>44</sup>Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA</footnote>

<footnote n="45"><sup>45</sup>Ritter Astrophysical Center, University of Toledo, 2801 W. Bancroft Street, Toledo, OH 43606, USA</footnote>

<footnote n="46"><sup>46</sup>Sub-department of Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
Received 2022 October 22; revised 2022 December 19; accepted 2023 January 2; published 2023 February 16</footnote>

<footnote n="47"><sup>47</sup>NSF Astronomy and Astrophysics Postdoctoral Fellow.</footnote>

<footnote n="48"><sup>48</sup> coolresearch.io</footnote>
<figure><img src="image_2.png" /></figure>

# PHANGS–JWST First Results: Mid-infrared Emission Traces Both Gas Column Density and Heating at 100 pc Scales

Adam K. Leroy<sup>1,2</sup>, Karin Sandstrom<sup>3</sup>, Erik Rosolowsky<sup>4</sup>, Francesco Belfiore<sup>5</sup>, Alberto D. Bolatto<sup>6</sup>, Yixian Cao<sup>7</sup>, Eric W. Koch<sup>8</sup>, Eva Schinnerer<sup>9</sup>, Ashley. T. Barnes<sup>10,11</sup>, Ivana Bešlić<sup>12</sup>, F. Bigiel<sup>12</sup>, Guillermo A. Blanc<sup>13,14</sup>, Jérémy Chastenet<sup>15</sup>, Ness Mayker Chen<sup>1,2</sup>, Mélanie Chevance<sup>16,17</sup>, Ryan Chown<sup>18</sup>, Enrico Congiu<sup>14</sup>, Daniel A. Dale<sup>19</sup>, Oleg V. Egorov<sup>20</sup>, Eric Emsellem<sup>10,21</sup>, Cosima Eibensteiner<sup>22</sup>, Christopher M. Faesi<sup>23</sup>, Simon C. O. Glover<sup>24</sup>, Kathryn Grasha<sup>25,26</sup>, Brent Groves<sup>27</sup>, Hamid Hassani<sup>4</sup>, Jonathan D. Henshaw<sup>9,28</sup>, Annie Hughes<sup>29</sup>, María J. Jiménez-Donaire<sup>30,31</sup>, Jaeyeon Kim<sup>16</sup>, Ralf S. Klessen<sup>24,32</sup>, Kathryn Kreckel<sup>20</sup>, J. M. Diederik Kruijssen<sup>17</sup>, Kirsten L. Larson<sup>33</sup>, Janice C. Lee<sup>34,35</sup>, Rebecca C. Levy<sup>35,47</sup>, Daizhong Liu<sup>7</sup>, Laura A. Lopez<sup>1,2,36</sup>, Sharon E. Meidt<sup>15</sup>, Eric J. Murphy<sup>37</sup>, Justus Neumann<sup>9</sup>, Ismael Pessa<sup>9,38</sup>, Jérôme Pety<sup>39,40</sup>, Toshiki Saito<sup>41</sup>, Amy Sardone<sup>1,2</sup>, Jiayi Sun<sup>42,43</sup>, David A. Thilker<sup>44</sup>, Antonio Usero<sup>30</sup>, Elizabeth J. Watkins<sup>20</sup>, Cory M. Whitcomb<sup>45</sup>, and Thomas G. Williams<sup>9,46</sup>

<figure><img src="image_3.png" /></figure>

<footnote n="1"><sup>1</sup>Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, Ohio 43210, USA; leroy.42@osu.edu</footnote>

<footnote n="2"><sup>2</sup>Center for Cosmology and Astroparticle Physics, 191 West Woodruff Avenue, Columbus, OH 43210, USA</footnote>

<footnote n="3"><sup>3</sup>Center for Astrophysics and Space Sciences, Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA</footnote>

<footnote n="4"><sup>4</sup>Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada</footnote>

<footnote n="5"><sup>5</sup>INAF—Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50157, Firenze, Italy</footnote>

<footnote n="6"><sup>6</sup>Department of Astronomy and Joint Space-Science Institute, University of Maryland, College Park, MD 20742, USA</footnote>

<footnote n="7"><sup>7</sup>Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße 1, D-85748 Garching, Germany</footnote>

<footnote n="8"><sup>8</sup>Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="9"><sup>9</sup>Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany</footnote>

<footnote n="10"><sup>10</sup>European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching, Germany</footnote>

<footnote n="11"><sup>11</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121, Bonn, Germany</footnote>

<footnote n="12"><sup>12</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany</footnote>

<footnote n="13"><sup>13</sup>The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St., Pasadena, CA, USA</footnote>

<footnote n="14"><sup>14</sup>Departamento de Astronomía, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile</footnote>

<footnote n="15"><sup>15</sup>Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium</footnote>

<footnote n="16"><sup>16</sup>Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany</footnote>

<footnote n="17"><sup>17</sup>Cosmic Origins Of Life (COOL) Research DAO<sup>48</sup></footnote>

<footnote n="18"><sup>18</sup>Department of Physics & Astronomy, University of Western Ontario, London, ON N6A 3K7, Canada</footnote>

<footnote n="19"><sup>19</sup>Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA</footnote>

<footnote n="20"><sup>20</sup>Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstraße 12-14, D-69120 Heidelberg, Germany</footnote>

<footnote n="21"><sup>21</sup>Univ Lyon, Univ Lyon1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230 Saint-Genis-Laval France</footnote>

<footnote n="22"><sup>22</sup>Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany</footnote>

<footnote n="23"><sup>23</sup>University of Connecticut, Department of Physics, 196A Auditorium Road, Unit 3046, Storrs, CT 06269, USA</footnote>

<footnote n="24"><sup>24</sup>Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Straße 2, D-69120 Heidelberg, Germany</footnote>

<footnote n="25"><sup>25</sup>Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia</footnote>

<footnote n="26"><sup>26</sup>ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia</footnote>

<footnote n="27"><sup>27</sup>International Centre for Radio Astronomy Research, University of Western Australia, 7 Fairway, Crawley, 6009 WA, Australia</footnote>

<footnote n="28"><sup>28</sup>Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK</footnote>

<footnote n="29"><sup>29</sup>CNRS, IRAP, 9 Av. du Colonel Roche, BP 44346, F-31028 Toulouse cedex 4, France</footnote>

<footnote n="30"><sup>30</sup>Observatorio Astronómico Nacional (IGN), C/ Alfonso XII, 3, E-28014 Madrid, Spain</footnote>

<footnote n="31"><sup>31</sup>Centro de Desarrollos Tecnológicos, Observatorio de Yebes (IGN), E-19141 Yebes, Guadalajara, Spain</footnote>

<footnote n="32"><sup>32</sup>Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany</footnote>

<footnote n="33"><sup>33</sup>AURA for the European Space Agency (ESA), Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA</footnote>

<footnote n="34"><sup>34</sup>Gemini Observatory/NSF's NOIRLab, 950 N. Cherry Avenue, Tucson, AZ, 85719, USA</footnote>

<footnote n="35"><sup>35</sup>Steward Observatory, University of Arizona, Tucson, AZ 85721, USA</footnote>

<footnote n="36"><sup>36</sup>Flatiron Institute, Center for Computational Astrophysics, NY 10010, USA</footnote>

<footnote n="37"><sup>37</sup>National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, USA</footnote>

<footnote n="38"><sup>38</sup>Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany</footnote>

<footnote n="39"><sup>39</sup>IRAM, 300 rue de la Piscine, F-38400 Saint Martin d'Hères, France</footnote>

<footnote n="40"><sup>40</sup>LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, F-75014 Paris, France</footnote>

<footnote n="41"><sup>41</sup>National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan</footnote>

<footnote n="42"><sup>42</sup>Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada</footnote>

<footnote n="43"><sup>43</sup>Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto, 60 St George Street, Toronto, ON M5S 3H8, Canada</footnote>

<footnote n="44"><sup>44</sup>Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA</footnote>

<footnote n="45"><sup>45</sup>Ritter Astrophysical Center, University of Toledo, 2801 W. Bancroft Street, Toledo, OH 43606, USA</footnote>

<footnote n="46"><sup>46</sup>Sub-department of Astrophysics, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
Received 2022 October 22; revised 2022 December 19; accepted 2023 January 2; published 2023 February 16</footnote>

<footnote n="47"><sup>47</sup>NSF Astronomy and Astrophysics Postdoctoral Fellow.</footnote>

<footnote n="48"><sup>48</sup> coolresearch.io</footnote>
Abstract

We compare mid-infrared (mid-IR), extinction-corrected Hα, and CO (2–1) emission at 70–160 pc resolution in the first four PHANGS–JWST targets. We report correlation strengths, intensity ratios, and power-law fits relating emission in JWST’s F770W, F1000W, F1130W, and F2100W bands to CO and Hα. At these scales, CO and Hα each correlate strongly with mid-IR emission, and these correlations are each stronger than the one relating CO to Hα emission. This reflects that mid-IR emission simultaneously acts as a dust column density tracer, leading to a good match with the molecular-gas-tracing CO, and as a heating tracer, leading to a good match with the Hα. By combining mid-IR, CO, and Hα at scales where the overall correlation between cold gas and star formation begins to break down, we are able to separate these two effects. We model the mid-IR above $I_{\nu} = 0.5$ MJy sr$^{-1}$ at F770W, a cut designed to select regions where the molecular gas dominates the interstellar medium (ISM) mass. This bright emission can be described to first order by a model that combines a CO-tracing component and an Hα-tracing component. The best-fitting models imply that ~50% of the mid-IR flux arises from molecular gas heated by the diffuse interstellar radiation field, with the remaining ~50% associated with bright, dusty star-forming regions. We discuss differences between the F770W, F1000W, and F1130W bands and the continuum-dominated F2100W band and suggest next steps for using the mid-IR as an ISM tracer.

*Unified Astronomy Thesaurus concepts: Disk galaxies (391); Galaxy physics (612); Dust continuum emission (412); Molecular gas (1073); Infrared astronomy (786); Millimeter astronomy (1061); Interstellar emissions (840); Star formation (1569)*

1. Introduction

In our standard picture of dust in galaxies (e.g., Draine & Li 2007; Draine 2011; Galliano et al. 2018; Hensley & Draine 2022), mid-IR dust emission arises mostly from small dust grains that are well mixed with the gaseous phase of the interstellar medium (ISM). The small grains have high opacity to UV radiation and are too small to be in equilibrium with the radiation field. Absorption of individual UV or optical photons can bring these small grains to high-enough temperatures that they emit efficiently in the $\lambda = 7-21$ µm range of interest to this paper, a phenomenon known as stochastic heating. The resulting mid-IR radiation includes strong emission bands related to stretching and bending modes of molecular bonds that are generally attributed to polycyclic aromatic hydrocarbons (PAHs) (e.g., Draine & Li 2007; Smith et al. 2007; Li 2020). These PAH molecules/grains affect the observed spectral energy distribution (SED) throughout the mid-IR, and their abundance (relative to the overall abundance of dust grains) also depends on the environment (e.g., Lebouteiller et al. 2007; Thilker et al. 2007; Sandstrom et al. 2010; Chastenet et al. 2019).

In this picture, we expect that to first order, mid-IR emission simultaneously reflects the following:

1. The distribution of ISM material, dominated by a combination of atomic and molecular hydrogen with which the dust is mixed.

2. The heating of the dust, which in star-forming galaxies is often dominated locally by UV radiation from the youngest, most massive stars but also includes a contribution from the ambient interstellar radiation field (ISRF).

We also expect important second-order dependencies on the abundance of dust relative to gas, i.e., the dust-to-gas ratio (D/G), and on the properties of the dust grains, including the abundance and physical state of the PAHs. Both D/G and the PAH abundance relate closely to metallicity (e.g., Galliano et al. 2018; Li 2020).

The basic dependence of dust emission on ISM column density and UV heating should produce strong correlations between mid-IR emission and CO rotational line emission and

between mid-IR emission and recombination line emission, including Hα. In the inner parts of massive star-forming galaxies, the bulk of ISM material is often molecular gas. Emission from low-J CO rotational transitions is our standard tracer for this molecular material (e.g., Bolatto et al. 2013). This molecular material is mixed with dust, which will emit in the mid-IR when exposed to UV radiation. Meanwhile, hydrogen recombination line emission, including Hα, reflects where the ionizing photons generated by young stars strike gas (e.g., Osterbrock & Miller 1989). Therefore, the H II regions traced out by Hα emission reflect key sources of UV radiation and ISM heating.

In addition to H II regions with typical sizes of ~10–100 pc (e.g., Oey et al. 2003; Barnes et al. 2022a, and references therein), star-forming galaxies also show extended Hα emission, tracing the diffuse ionized gas (DIG; e.g., Thilker et al. 2002; Hoopes & Walterbos 2003; Haffner et al. 2009; Belfiore et al. 2022a). In normal star-forming galaxies, the DIG appears to be produced mostly by ionizing photons leaking from H II regions (e.g., see Belfiore et al. 2022a). Because the DIG reflects the impact of ionizing UV photons on neutral gas, its structure may also provide some template for where dust is heated. However, this is less certain because Hα follows from ionizing photons impacting neutral gas while mid-IR emission primarily reflects the heating of dust by softer, non-ionizing UV photons that can travel through neutral gas.

Likely because of its sensitivity to both dust heating and ISM column density, mid-IR emission correlates very well with both recombination line emission (e.g., Calzetti et al. 2007; Kennicutt et al. 2007) and CO emission (e.g., Regan et al. 2006; Leroy et al. 2013; Chown et al. 2021; Gao et al. 2022; Leroy 2023) in observations that integrate over large regions or whole galaxies. Indeed, Whitcomb et al. (2022) combined CO emission and Spitzer mid-IR spectroscopy to show that different mid-IR bands exhibit different correlation strengths with tracers of star formation and CO emission, providing strong evidence that both heating and column density together generate the observed mid-IR emission. However, the modest angular resolution of mid-IR telescopes prior to JWST limited the physical resolution of such comparisons except in the nearest galaxies (e.g., Helou et al. 2004; Boquien et al. 2015; Kim et al. 2021).
Abstract

We compare mid-infrared (mid-IR), extinction-corrected Hα, and CO (2–1) emission at 70–160 pc resolution in the first four PHANGS–JWST targets. We report correlation strengths, intensity ratios, and power-law fits relating emission in JWST’s F770W, F1000W, F1130W, and F2100W bands to CO and Hα. At these scales, CO and Hα each correlate strongly with mid-IR emission, and these correlations are each stronger than the one relating CO to Hα emission. This reflects that mid-IR emission simultaneously acts as a dust column density tracer, leading to a good match with the molecular-gas-tracing CO, and as a heating tracer, leading to a good match with the Hα. By combining mid-IR, CO, and Hα at scales where the overall correlation between cold gas and star formation begins to break down, we are able to separate these two effects. We model the mid-IR above $I_ν = 0.5$ MJy sr$^{-1}$ at F770W, a cut designed to select regions where the molecular gas dominates the interstellar medium (ISM) mass. This bright emission can be described to first order by a model that combines a CO-tracing component and an Hα-tracing component. The best-fitting models imply that ~50% of the mid-IR flux arises from molecular gas heated by the diffuse interstellar radiation field, with the remaining ~50% associated with bright, dusty star-forming regions. We discuss differences between the F770W, F1000W, and F1130W bands and the continuum-dominated F2100W band and suggest next steps for using the mid-IR as an ISM tracer.

*Unified Astronomy Thesaurus concepts: Disk galaxies (391); Galaxy physics (612); Dust continuum emission (412); Molecular gas (1073); Infrared astronomy (786); Millimeter astronomy (1061); Interstellar emissions (840); Star formation (1569)*

1. Introduction

In our standard picture of dust in galaxies (e.g., Draine & Li 2007; Draine 2011; Galliano et al. 2018; Hensley & Draine 2022), mid-IR dust emission arises mostly from small dust grains that are well mixed with the gaseous phase of the interstellar medium (ISM). The small grains have high opacity to UV radiation and are too small to be in equilibrium with the radiation field. Absorption of individual UV or optical photons can bring these small grains to high-enough temperatures that they emit efficiently in the $\lambda = 7-21$ µm range of interest to this paper, a phenomenon known as stochastic heating. The resulting mid-IR radiation includes strong emission bands related to stretching and bending modes of molecular bonds that are generally attributed to polycyclic aromatic hydrocarbons (PAHs) (e.g., Draine & Li 2007; Smith et al. 2007; Li 2020). These PAH molecules/grains affect the observed spectral energy distribution (SED) throughout the mid-IR, and their abundance (relative to the overall abundance of dust grains) also depends on the environment (e.g., Lebouteiller et al. 2007; Thilker et al. 2007; Sandstrom et al. 2010; Chastenet et al. 2019).

In this picture, we expect that to first order, mid-IR emission simultaneously reflects the following:

1. The distribution of ISM material, dominated by a combination of atomic and molecular hydrogen with which the dust is mixed.

2. The heating of the dust, which in star-forming galaxies is often dominated locally by UV radiation from the youngest, most massive stars but also includes a contribution from the ambient interstellar radiation field (ISRF).

We also expect important second-order dependencies on the abundance of dust relative to gas, i.e., the dust-to-gas ratio (D/G), and on the properties of the dust grains, including the abundance and physical state of the PAHs. Both D/G and the PAH abundance relate closely to metallicity (e.g., Galliano et al. 2018; Li 2020).

The basic dependence of dust emission on ISM column density and UV heating should produce strong correlations between mid-IR emission and CO rotational line emission and

between mid-IR emission and recombination line emission, including Hα. In the inner parts of massive star-forming galaxies, the bulk of ISM material is often molecular gas. Emission from low-J CO rotational transitions is our standard tracer for this molecular material (e.g., Bolatto et al. 2013). This molecular material is mixed with dust, which will emit in the mid-IR when exposed to UV radiation. Meanwhile, hydrogen recombination line emission, including Hα, reflects where the ionizing photons generated by young stars strike gas (e.g., Osterbrock & Miller 1989). Therefore, the H II regions traced out by Hα emission reflect key sources of UV radiation and ISM heating.

In addition to H II regions with typical sizes of ~10–100 pc (e.g., Oey et al. 2003; Barnes et al. 2022a, and references therein), star-forming galaxies also show extended Hα emission, tracing the diffuse ionized gas (DIG; e.g., Thilker et al. 2002; Hoopes & Walterbos 2003; Haffner et al. 2009; Belfiore et al. 2022a). In normal star-forming galaxies, the DIG appears to be produced mostly by ionizing photons leaking from H II regions (e.g., see Belfiore et al. 2022a). Because the DIG reflects the impact of ionizing UV photons on neutral gas, its structure may also provide some template for where dust is heated. However, this is less certain because Hα follows from ionizing photons impacting neutral gas while mid-IR emission primarily reflects the heating of dust by softer, non-ionizing UV photons that can travel through neutral gas.

Likely because of its sensitivity to both dust heating and ISM column density, mid-IR emission correlates very well with both recombination line emission (e.g., Calzetti et al. 2007; Kennicutt et al. 2007) and CO emission (e.g., Regan et al. 2006; Leroy et al. 2013; Chown et al. 2021; Gao et al. 2022; Leroy 2023) in observations that integrate over large regions or whole galaxies. Indeed, Whitcomb et al. (2022) combined CO emission and Spitzer mid-IR spectroscopy to show that different mid-IR bands exhibit different correlation strengths with tracers of star formation and CO emission, providing strong evidence that both heating and column density together generate the observed mid-IR emission. However, the modest angular resolution of mid-IR telescopes prior to JWST limited the physical resolution of such comparisons except in the nearest galaxies (e.g., Helou et al. 2004; Boquien et al. 2015; Kim et al. 2021).
JWST changes this, enabling observations of mid-IR dust emission from galaxies at 0.′′2–2.′′0 resolution, among the highest obtained for any ISM tracer. During Cycle 1 of JWST, the PHANGS–JWST Treasury program (Lee et al. 2023) is using this capability to produce high $\theta = 0.′′1–0.′′7$ resolution near- and mid-IR images of 19 nearby ($d \le 22$ Mpc), relatively massive star-forming galaxies. The PHANGS–JWST target galaxies are also covered by other major observatories, and as a result, each one has a high-quality ALMA CO (2–1) map from PHANGS–ALMA (Leroy et al. 2021) and resolved sensitive VLT/MUSE mapping of the $H\alpha$ and $H\beta$ recombination lines from PHANGS–MUSE (Emsellem et al. 2022).

This combination of data, angular resolution, and proximity allows us to push the comparison between CO, $H\alpha$, and mid-IR emission to scales of ~70–160 pc so that one resolution element has about the size of a giant molecular cloud complex or a giant H II region. Over the last ~15 yr a wide variety of observations have shown that at these scales, galaxies resolve into distinct regions with different evolutionary states (e.g., Kawamura et al. 2009; Schruba et al. 2010; 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). As a result, comparisons of mid-IR, CO, and $H\alpha$ emission at such high resolution may reveal the separate influence of column density and heating, allowing us to distinguish the two main drivers of mid-IR emission variations. The initial PHANGS–JWST images as well as the Early Release Observations (Pontoppidan et al. 2022) lend themselves to such an interpretation. In these observations, mid-IR emission resolves into a filamentary network that mirrors other maps of the ISM (Barnes et al. 2022b; Meidt et al. 2023; Sandstrom et al. 2023a; Thilker et al. 2023; Watkins et al. 2023), as well as bright knots of emission from dust in the immediate vicinity of massive young stars (Dale et al. 2023; Egorov 2023; Hassani et al. 2023; Kim et al. 2023).

A basic statistical comparison between mid-IR, $H\alpha$, and CO emission will highlight the physics behind the mid-IR emission and will help inform its use as a tool to trace the star formation rate (SFR; e.g., Jarrett et al. 2013; Catalán-Torrecilla et al. 2015; Janowiecki et al. 2017; Belfiore et al. 2022b) or the ISM (e.g., Gao et al. 2019, 2022; Chown et al. 2021; Leroy et al. 2021; Whitcomb et al. 2022). Here we take this initial step for the first four PHANGS–JWST targets. First, in Section 2 we lay out expectations for how mid-IR, CO, and $H\alpha$ emission should relate to one another. Then, in Section 3, we match the angular resolution and astrometry of mid-IR, CO (2–1), and extinction-corrected $H\alpha$ data to produce a combined database at matched 1.′′7 ≈ 70–160 pc resolution. In Section 4, we measure the correlations and fit approximate power laws relating mid-IR, CO (2–1), and extinction-corrected $H\alpha$ emission. Based on these results, in Section 5 we fit the bright emission in our targets using a simple two-component model, with one component following the measured CO distribution and the other following the extinction-corrected $H\alpha$ distribution. Then, in Section 6, we examine the ratios of CO-to-mid-IR and of extinction-corrected $H\alpha$-to-mid-IR found by our statistical analysis and template fitting, and in Section 7, we briefly discuss how to apply our results to use mid-IR to trace gas and recent star formation. While the main text focuses on the relationships among mid-IR, CO, and $H\alpha$ emission, we discuss the correlations among the mid-IR bands themselves in

Appendix B, where we also describe how these correlations can be used to set or verify the background level of JWST maps that do not include a large area of empty sky.

In Section 8, we present a detailed summary and discussion of our results. Readers primarily interested in an overview may wish to start with that section.

## 2. Expectations

To frame our analysis, we first report theoretical and empirically motivated conversions, both among our observables and between our observables and physical quantities. First, we discuss the expected contents of our observed mid-IR bands and note standard ratios among these bands in our targets (Section 2.1 and see Appendix A). Then we discuss common conversions between CO, $H\alpha$, mid-IR intensity, and the mass of molecular gas or SFR (Sections 2.2–2.4). We use these conversions to provide expected relationships between mid-IR, CO, and $H\alpha$ emission in Section 2.5, which compare to our measurements. We also use them to predict the mid-IR characteristic intensity levels that we expect to be associated with emission from a molecular ISM heated by a diffuse radiation field or from dust heated by an H II region (Section 2.6).

### 2.1. Mid-infrared Bands and Band Ratios

We consider mid-IR emission from the four MIRI bands imaged by PHANGS–JWST, F770W (7.7 µm), F1000W (10 µm), F1130W (11.3 µm), and F2100W (21 µm). To first order, the F770W and F1130W bands are expected to be dominated by emission from strong PAH bands while the F2100W filter covers mainly continuum emission from dust (e.g., see spectra in Draine & Li 2007; Smith et al. 2007; Galliano et al. 2018; Hensley & Draine 2022; Lai & Armus 2022). As discussed in Section 4.4, the situation with F1000W appears more ambiguous. Though expected to reflect primarily continuum, its behavior mirrors the PAH-tracing bands, suggesting that either (1) weaker PAH features or the wings of the nearby strong PAH features contribute to the band or (2) that the small grains contributing the emission mimic PAHs in many respects. Silicate absorption near 10 µm may also be important at high column densities, but should make only a minimal contribution for the column densities that cover most of the area in our targets.

Our expectations and calculation of the background levels (Appendices A and B) also make frequent reference to Spitzer's 8 µm and 24 µm bands and WISE's 12 µm band (Werner et al. 2004; Wright et al. 2010). The 8 µm band is dominated by the same PAH band as F770W, while the 24 µm band should reflect mainly continuum emission. The very broad WISE 12 µm filter integrates over both PAH features and the continuum. In SINGS H II regions with mid-IR spectroscopy, Whitcomb et al. (2022) find that ≲50% of the overall emission in the WISE 12 µm band arises from PAH features, but this value might be somewhat higher in more diffuse regions.

Table 1 reports a series of typical band ratios for the first four PHANGS–JWST target galaxies, which can be used to translate between bands. Appendix A describes how we estimate these ratios from comparing our images to one another and to previous mid-IR imaging of our targets at 1.′′7
JWST changes this, enabling observations of mid-IR dust emission from galaxies at 0.′′2–2.′′0 resolution, among the highest obtained for any ISM tracer. During Cycle 1 of JWST, the PHANGS–JWST Treasury program (Lee et al. 2023) is using this capability to produce high $\theta = 0.′′1–0.′′7$ resolution near- and mid-IR images of 19 nearby ($d \le 22$ Mpc), relatively massive star-forming galaxies. The PHANGS–JWST target galaxies are also covered by other major observatories, and as a result, each one has a high-quality ALMA CO (2–1) map from PHANGS–ALMA (Leroy et al. 2021) and resolved sensitive VLT/MUSE mapping of the $H\alpha$ and $H\beta$ recombination lines from PHANGS–MUSE (Emsellem et al. 2022).

This combination of data, angular resolution, and proximity allows us to push the comparison between CO, $H\alpha$, and mid-IR emission to scales of ~70–160 pc so that one resolution element has about the size of a giant molecular cloud complex or a giant H II region. Over the last ~15 yr a wide variety of observations have shown that at these scales, galaxies resolve into distinct regions with different evolutionary states (e.g., Kawamura et al. 2009; Schruba et al. 2010; 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). As a result, comparisons of mid-IR, CO, and $H\alpha$ emission at such high resolution may reveal the separate influence of column density and heating, allowing us to distinguish the two main drivers of mid-IR emission variations. The initial PHANGS–JWST images as well as the Early Release Observations (Pontoppidan et al. 2022) lend themselves to such an interpretation. In these observations, mid-IR emission resolves into a filamentary network that mirrors other maps of the ISM (Barnes et al. 2022b; Meidt et al. 2023; Sandstrom et al. 2023a; Thilker et al. 2023; Watkins et al. 2023), as well as bright knots of emission from dust in the immediate vicinity of massive young stars (Dale et al. 2023; Egorov 2023; Hassani et al. 2023; Kim et al. 2023).

A basic statistical comparison between mid-IR, $H\alpha$, and CO emission will highlight the physics behind the mid-IR emission and will help inform its use as a tool to trace the star formation rate (SFR; e.g., Jarrett et al. 2013; Catalán-Torrecilla et al. 2015; Janowiecki et al. 2017; Belfiore et al. 2022b) or the ISM (e.g., Gao et al. 2019, 2022; Chown et al. 2021; Leroy et al. 2021; Whitcomb et al. 2022). Here we take this initial step for the first four PHANGS–JWST targets. First, in Section 2 we lay out expectations for how mid-IR, CO, and $H\alpha$ emission should relate to one another. Then, in Section 3, we match the angular resolution and astrometry of mid-IR, CO (2–1), and extinction-corrected $H\alpha$ data to produce a combined database at matched 1.′′7 ≈ 70–160 pc resolution. In Section 4, we measure the correlations and fit approximate power laws relating mid-IR, CO (2–1), and extinction-corrected $H\alpha$ emission. Based on these results, in Section 5 we fit the bright emission in our targets using a simple two-component model, with one component following the measured CO distribution and the other following the extinction-corrected $H\alpha$ distribution. Then, in Section 6, we examine the ratios of CO-to-mid-IR and of extinction-corrected $H\alpha$-to-mid-IR found by our statistical analysis and template fitting, and in Section 7, we briefly discuss how to apply our results to use mid-IR to trace gas and recent star formation. While the main text focuses on the relationships among mid-IR, CO, and $H\alpha$ emission, we discuss the correlations among the mid-IR bands themselves in

Appendix B, where we also describe how these correlations can be used to set or verify the background level of JWST maps that do not include a large area of empty sky.

In Section 8, we present a detailed summary and discussion of our results. Readers primarily interested in an overview may wish to start with that section.

## 2. Expectations

To frame our analysis, we first report theoretical and empirically motivated conversions, both among our observables and between our observables and physical quantities. First, we discuss the expected contents of our observed mid-IR bands and note standard ratios among these bands in our targets (Section 2.1 and see Appendix A). Then we discuss common conversions between CO, $H\alpha$, mid-IR intensity, and the mass of molecular gas or SFR (Sections 2.2–2.4). We use these conversions to provide expected relationships between mid-IR, CO, and $H\alpha$ emission in Section 2.5, which compare to our measurements. We also use them to predict the mid-IR characteristic intensity levels that we expect to be associated with emission from a molecular ISM heated by a diffuse radiation field or from dust heated by an H II region (Section 2.6).

### 2.1. Mid-infrared Bands and Band Ratios

We consider mid-IR emission from the four MIRI bands imaged by PHANGS–JWST, F770W (7.7 µm), F1000W (10 µm), F1130W (11.3 µm), and F2100W (21 µm). To first order, the F770W and F1130W bands are expected to be dominated by emission from strong PAH bands while the F2100W filter covers mainly continuum emission from dust (e.g., see spectra in Draine & Li 2007; Smith et al. 2007; Galliano et al. 2018; Hensley & Draine 2022; Lai & Armus 2022). As discussed in Section 4.4, the situation with F1000W appears more ambiguous. Though expected to reflect primarily continuum, its behavior mirrors the PAH-tracing bands, suggesting that either (1) weaker PAH features or the wings of the nearby strong PAH features contribute to the band or (2) that the small grains contributing the emission mimic PAHs in many respects. Silicate absorption near 10 µm may also be important at high column densities, but should make only a minimal contribution for the column densities that cover most of the area in our targets.

Our expectations and calculation of the background levels (Appendices A and B) also make frequent reference to Spitzer's 8 µm and 24 µm bands and WISE's 12 µm band (Werner et al. 2004; Wright et al. 2010). The 8 µm band is dominated by the same PAH band as F770W, while the 24 µm band should reflect mainly continuum emission. The very broad WISE 12 µm filter integrates over both PAH features and the continuum. In SINGS H II regions with mid-IR spectroscopy, Whitcomb et al. (2022) find that ≲50% of the overall emission in the WISE 12 µm band arises from PAH features, but this value might be somewhat higher in more diffuse regions.

Table 1 reports a series of typical band ratios for the first four PHANGS–JWST target galaxies, which can be used to translate between bands. Appendix A describes how we estimate these ratios from comparing our images to one another and to previous mid-IR imaging of our targets at 1.′′7
<table><caption>**Table 1**
Typical Observed Band Ratios in the First Four PHANGS–JWST Targets</caption><thead><tr><th>Band</th><th>R<sup>X</sup><sub>7.7</sub></th><th>R<sup>X</sup><sub>24</sub></th><th>σ<sup>a</sup><br>(dex)</th></tr></thead><tbody><tr><td>F770W</td><td>1.0</td><td>1.31</td><td>...</td></tr><tr><td>F1000W</td><td>0.38</td><td>0.49</td><td>0.06</td></tr><tr><td>F1130W</td><td>1.35</td><td>1.76</td><td>0.05</td></tr><tr><td>F2100W</td><td>0.61</td><td>0.80</td><td>0.11</td></tr><tr><td>WISE3 12 µm</td><td>1.57</td><td>2.06</td><td>0.06</td></tr><tr><td>WISE4 22 µm</td><td>0.80</td><td>1.06</td><td>0.20</td></tr><tr><td>IRAC4 8 µm</td><td>1.0</td><td>1.31</td><td>0.04</td></tr><tr><td>MIPS24 24 µm</td><td>0.77</td><td>1.0</td><td>0.14</td></tr></tbody></table>

**Notes.** Observed ratios estimated from band–band comparisons in our first four targets as described in Appendix A and Figure 15. See definitions of $R$ in Equation (1). Note that $R_{24}^X$ are scaled versions of $R_{7.7}^X$ normalized to Spitzer at 24 µm.

<sup>a</sup> Robustly estimated scatter in the log of the measured ratio between the listed band and F770W, measured at 15" resolution (i.e., scatter in the blue points in Figure 15).

<sup>b</sup> In Appendix A we use F770W as the reference band so no scatter is defined.

and 15" resolution. We quote the ratios in three ways:

$$ 
\begin{aligned}
\mathcal{R}_{7.7}^{X} &\equiv \left( \frac{I_{\nu}^{X}}{I_{\nu}^{\text{F770W}}} \right), \\
\mathcal{R}_{24}^{X} &\equiv \left( \frac{I_{\nu}^{X}}{I_{\nu}^{\text{MIPS24}}} \right), \\
\mathcal{R}_{X}^{Y} &\equiv \frac{\mathcal{R}_{7.7}^{Y}}{\mathcal{R}_{7.7}^{X}},
\end{aligned} 
\qquad (1) $$

where X and Y denote some mid-IR bands, and we work with $I_ν$ in units of MJy sr$^{-1}$. The two sets of ratios in Table 1, $R_{7.7}^X$ and $R_{24}^X$, are self-consistent results of a single calculation, not independent. We quote both because F770W is our highest-resolution image and because a large amount of pre-JWST work has centered on Spitzer’s MIPS 24 µm band. The final line of Equation (1) simply notes that Table 1 can be used to express any pair of bands that we consider.

In framing our expectations, we will assume that all bands can be simply linearly converted to one another, which appears reasonable to first order based on Appendix A. To second order, the ratios among these bands do vary, especially in bright, high-intensity regions like massive H II regions or the starburst ring at the center of our target NGC 1365. These ratio variations offer clues to how the physical properties and abundance of the dust grains producing mid-IR emission change as a function of environment. Measuring and interpreting these variations represent a key topic of other papers in this series (Chastenet 2023a, 2023b; Dale et al. 2023; Egorov 2023; Sandstrom 2023a). For our work, the most relevant effect will be that PAHs appear to be selectively destroyed in regions of intense star formation. This should suppress the PAH-dominated F770W and F1130W relative to the other bands in regions of intense extinction-corrected $H_\alpha$ emission. This effect is indeed present in our data and seen as a secondary correlation in Sections 4.2, 4.4, and 5.2. Perhaps surprisingly, F1000W shows almost identical behavior to F770W and F1130W in this regard, so that to some extent, those three bands contrast with F2100W in overall behavior (Section 4.4).

## 2.2. CO and Molecular Gas

We work with CO (2–1) intensities in units of K km s$^{-1}$, $I_{CO\ 2-1} \equiv I_{CO\ 2-1}/I_{CO\ 1-0} = 0.65$ (den Brok et al. 2021; Yajima et al. 2021; Leroy et al. 2022) and a Galactic CO (1–0)-to-H$_2$ conversion factor $\alpha_{CO\ 1-0}^{\text{MW}} = 4.35 M_\odot \text{ pc}^{-2} (\text{K km s}^{-1})^{-1}$ (e.g., Bolatto et al. 2013),

$$ 
\begin{aligned}
\frac{\Sigma_{\text{mol}}}{M_{\odot} \text{ pc}^{-2}} &\approx 6.7 \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{0.65}{R_{21}} \right) \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right) \\
\frac{N(\text{H})}{10^{20} \text{ cm}^{-2}} &\approx 6.2 \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{0.65}{R_{21}} \right) \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right),
\end{aligned} 
\qquad (2) $$

where $\Sigma_{\text{mol}}$ is the molecular gas mass surface density including a factor of 1.4 to account for helium and heavy elements and N (H) is the total hydrogen column density, with no helium included. We phrase Equation (2) in terms of N(H) not N(H$_2$) = 0.5N(H) because dust emission is frequently normalized to N(H).

## 2.3. Extinction-corrected $H_\alpha$, Ionizing Photons, and SFR

We also work with extinction-corrected $H_\alpha$ intensity in units$^{49}$ of erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$. We provide reference conversions adopting the Murphy et al. (2011) conversion from $H_\alpha$ luminosity to SFR, which is almost identical to the value advocated by Calzetti et al. (2007). In intensity units,

$$ 
\begin{aligned}
\frac{\Sigma_{\text{SFR}}}{M_{\odot} \text{ yr}^{-1} \text{ kpc}^{-2}} &\approx 642 \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right) \\
\frac{\Sigma(Q_0)}{\text{s}^{-1} \text{ pc}^{-2}} &\approx 8.8 \times 10^{49} \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right) \\
\frac{\Sigma(M_{\text{ZAMS}})}{M_{\odot} \text{ pc}^{-2}} &\approx 2200 \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right),
\end{aligned} 
\qquad (3) $$

where $\Sigma_{\text{SFR}}$ is the SFR per unit area for a Kroupa IMF truncated at 100 $M_\odot$. In the second version, $Q_0$ refers to the production rate of hydrogen-ionizing photons with $h\nu > 13.6$ eV and $I_{H\alpha}$.

The ionizing photon production rate may be more concretely related to the recombination line emission than the somewhat abstract SFR, but we also note that at our resolution and since we are studying whole galaxies, $H_\alpha$ can more accurately be thought of as being driven by the number of local ionizations or recombinations than the production rate. The final expression provides a reference conversion to the mass surface density of zero-age main-sequence stars needed to produce that density of ionizing photons for a fiducial Starburst99 run (Leitherer et al. 1999). See Belfiore et al. (2022a) for more discussion on the diffuse ionized medium and Belfiore et al. (2022b) and Murphy et al. (2011) for translations among different SFR tracers.

Throughout this paper, we work with $H_\alpha$ emission corrected for the effects of extinction using the Balmer decrement. This approach combines observations of $H_\alpha$ and $H\beta$ with an assumed wavelength-dependent extinction (e.g., see Osterbrock & Miller 1989). It has a long history (e.g., Miller & Mathews 1972), and Balmer decrement-corrected $H_\alpha$ measurements, including

<footnote>$^{49}$ Note that it is common to use erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$ as well. Simply multiply our values by $2.35 \times 10^{-11}$ or subtract 10.63 from the log to make the conversion.</footnote>
<table><caption>**Table 1**
Typical Observed Band Ratios in the First Four PHANGS–JWST Targets</caption><thead><tr><th>Band</th><th>R<sup>X</sup><sub>7.7</sub></th><th>R<sup>X</sup><sub>24</sub></th><th>σ<sup>a</sup><br>(dex)</th></tr></thead><tbody><tr><td>F770W</td><td>1.0</td><td>1.31</td><td>...</td></tr><tr><td>F1000W</td><td>0.38</td><td>0.49</td><td>0.06</td></tr><tr><td>F1130W</td><td>1.35</td><td>1.76</td><td>0.05</td></tr><tr><td>F2100W</td><td>0.61</td><td>0.80</td><td>0.11</td></tr><tr><td>WISE3 12 µm</td><td>1.57</td><td>2.06</td><td>0.06</td></tr><tr><td>WISE4 22 µm</td><td>0.80</td><td>1.06</td><td>0.20</td></tr><tr><td>IRAC4 8 µm</td><td>1.0</td><td>1.31</td><td>0.04</td></tr><tr><td>MIPS24 24 µm</td><td>0.77</td><td>1.0</td><td>0.14</td></tr></tbody></table>

**Notes.** Observed ratios estimated from band–band comparisons in our first four targets as described in Appendix A and Figure 15. See definitions of $R$ in Equation (1). Note that $R_{24}^X$ are scaled versions of $R_{7.7}^X$ normalized to Spitzer at 24 µm.

<sup>a</sup> Robustly estimated scatter in the log of the measured ratio between the listed band and F770W, measured at 15" resolution (i.e., scatter in the blue points in Figure 15).

<sup>b</sup> In Appendix A we use F770W as the reference band so no scatter is defined.

and 15" resolution. We quote the ratios in three ways:

$$ 
\begin{aligned}
\mathcal{R}_{7.7}^{X} &\equiv \left( \frac{I_{\nu}^{X}}{I_{\nu}^{\text{F770W}}} \right), \\
\mathcal{R}_{24}^{X} &\equiv \left( \frac{I_{\nu}^{X}}{I_{\nu}^{\text{MIPS24}}} \right), \\
\mathcal{R}_{X}^{Y} &\equiv \frac{\mathcal{R}_{7.7}^{Y}}{\mathcal{R}_{7.7}^{X}},
\end{aligned} 
\qquad (1) $$

where X and Y denote some mid-IR bands, and we work with $I_ν$ in units of MJy sr$^{-1}$. The two sets of ratios in Table 1, $R_{7.7}^X$ and $R_{24}^X$, are self-consistent results of a single calculation, not independent. We quote both because F770W is our highest-resolution image and because a large amount of pre-JWST work has centered on Spitzer’s MIPS 24 µm band. The final line of Equation (1) simply notes that Table 1 can be used to express any pair of bands that we consider.

In framing our expectations, we will assume that all bands can be simply linearly converted to one another, which appears reasonable to first order based on Appendix A. To second order, the ratios among these bands do vary, especially in bright, high-intensity regions like massive H II regions or the starburst ring at the center of our target NGC 1365. These ratio variations offer clues to how the physical properties and abundance of the dust grains producing mid-IR emission change as a function of environment. Measuring and interpreting these variations represent a key topic of other papers in this series (Chastenet 2023a, 2023b; Dale et al. 2023; Egorov 2023; Sandstrom 2023a). For our work, the most relevant effect will be that PAHs appear to be selectively destroyed in regions of intense star formation. This should suppress the PAH-dominated F770W and F1130W relative to the other bands in regions of intense extinction-corrected $H_\alpha$ emission. This effect is indeed present in our data and seen as a secondary correlation in Sections 4.2, 4.4, and 5.2. Perhaps surprisingly, F1000W shows almost identical behavior to F770W and F1130W in this regard, so that to some extent, those three bands contrast with F2100W in overall behavior (Section 4.4).

## 2.2. CO and Molecular Gas

We work with CO (2–1) intensities in units of K km s$^{-1}$, $I_{CO\ 2-1}$. For a typical $R_{21} \equiv I_{CO\ 2-1}/I_{CO\ 1-0} = 0.65$ (den Brok et al. 2021; Yajima et al. 2021; Leroy et al. 2022) and a Galactic CO (1–0)-to-H$_2$ conversion factor $\alpha_{CO\ 1-0}^{MW} = 4.35 M_\odot$ pc$^{-2}$ (K km s$^{-1}$)$^{-1}$ (e.g., Bolatto et al. 2013),

$$ 
\begin{aligned}
\frac{\Sigma_{\text{mol}}}{M_{\odot} \text{ pc}^{-2}} &\approx 6.7 \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{0.65}{R_{21}} \right) \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right) \\
\frac{N(\text{H})}{10^{20} \text{ cm}^{-2}} &\approx 6.2 \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{0.65}{R_{21}} \right) \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right),
\end{aligned} 
\qquad (2) $$

where $\Sigma_{mol}$ is the molecular gas mass surface density including a factor of 1.4 to account for helium and heavy elements and N (H) is the total hydrogen column density, with no helium included. We phrase Equation (2) in terms of N(H) not N(H$_2$) = 0.5N(H) because dust emission is frequently normalized to N(H).

## 2.3. Extinction-corrected $H_\alpha$, Ionizing Photons, and SFR

We also work with extinction-corrected $H_\alpha$ intensity in units$^{49}$ of erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$. We provide reference conversions adopting the Murphy et al. (2011) conversion from $H_\alpha$ luminosity to SFR, which is almost identical to the value advocated by Calzetti et al. (2007). In intensity units,

$$ 
\begin{aligned}
\frac{\Sigma_{\text{SFR}}}{M_{\odot} \text{ yr}^{-1} \text{ kpc}^{-2}} &\approx 642 \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right) \\
\frac{\Sigma(Q_0)}{\text{s}^{-1} \text{ pc}^{-2}} &\approx 8.8 \times 10^{49} \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right) \\
\frac{\Sigma(M_{\text{ZAMS}})}{M_{\odot} \text{ pc}^{-2}} &\approx 2200 \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}} \right),
\end{aligned} 
\qquad (3) $$

where $\Sigma_{SFR}$ is the SFR per unit area for a Kroupa IMF truncated at 100 $M_\odot$. In the second version, $Q_0$ refers to the production rate of hydrogen-ionizing photons with $h\nu > 13.6$ eV and $I_{H\alpha}$.

The ionizing photon production rate may be more concretely related to the recombination line emission than the somewhat abstract SFR, but we also note that at our resolution and since we are studying whole galaxies, $H_\alpha$ can more accurately be thought of as being driven by the number of local ionizations or recombinations than the production rate. The final expression provides a reference conversion to the mass surface density of zero-age main-sequence stars needed to produce that density of ionizing photons for a fiducial Starburst99 run (Leitherer et al. 1999). See Belfiore et al. (2022a) for more discussion on the diffuse ionized medium and Belfiore et al. (2022b) and Murphy et al. (2011) for translations among different SFR tracers.

Throughout this paper, we work with $H_\alpha$ emission corrected for the effects of extinction using the Balmer decrement. This approach combines observations of $H_\alpha$ and $H\beta$ with an assumed wavelength-dependent extinction (e.g., see Osterbrock & Miller 1989). It has a long history (e.g., Miller & Mathews 1972), and Balmer decrement-corrected $H_\alpha$ measurements, including

<footnote>$^{49}$ Note that it is common to use erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$ as well. Simply multiply our values by $2.35 \times 10^{-11}$ or subtract 10.63 from the log to make the conversion.</footnote>
from SDSS, SINGS, CALIFA, and MaNGA, underpin much of our knowledge of extragalactic SFRs, including the calibration of IR-based SFR tracers (e.g., Brinchmann et al. 2004; Moustakas et al. 2006, 2010; Kennicutt & Hao 2009; Hao et al. 2011; Catalán-Torrecilla et al. 2015; Belfiore et al. 2022b). Although the Balmer decrement has limitations, particularly in dense, high-extinction, mixed media (e.g., Melnick 1979; Lequeux et al. 1981; Wong & Blitz 2002), at the moderate ΣSFR and moderate extinction that we study here, we have every expectation that the Balmer decrement works well. This expectation appears to be borne out by numerical simulations (Tacchella et al. 2022), and studying SINGS Prescott et al. (2007) found no evidence for a substantial highly obscured population pervading normal star-forming disk galaxies. Indeed, in the brightest regions of PHANGS–MUSE (Belfiore et al. 2022b; F. Belfiore et al., in preparation) find good agreement between the estimates of Hα extinction based on the Balmer decrement and those obtained from “hybrid” Hα+IR prescriptions calibrated by Calzetti et al. (2007) to match extinction-corrected Paschen α. Our results in Section 4.2 comparing the extinction-corrected Hα with JWST mid-IR emission also find no evidence that the Balmer decrement significantly underestimates the extinction (see also Hassani et al. 2023, in this Issue).

## 2.4. Mid-infrared Emission, Column Density, and Star Formation Rate

Even in the presence of a relatively weak radiation field, dust in the ISM should produce mid-IR emission, primarily through stochastic, single-photon heating. The intensity of emission depends on the column density of dust and the intensity of the illuminating radiation field. For relatively weak radiation fields, a reasonable fiducial expectation based on the Draine & Li (2007) dust models and also following Compiegne et al. (2010) is

$$ \frac{I_{\nu}^{X}}{\mathrm{MJy sr}^{-1}} \approx 0.022 \mathcal{R}_{24}^{X} \left( \frac{N(\mathrm{H})}{10^{20} \mathrm{cm}^{-2}} \right) \\ \times \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right) \\ \approx 0.020 \mathcal{R}_{24}^{X} \left( \frac{\Sigma_{\mathrm{gas}}}{1 M_{\odot} \mathrm{pc}^{-2}} \right) \\ \times \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right), \qquad (4) $$

where $I_{\nu}^{X}$ is the mid-IR intensity at band X, N(H) is the line-of-sight column density of hydrogen, and Σ$_{gas}$ is the gas mass surface density. The U/U$_{0}$ term expresses the mean local ISRF illuminating the dust in units of the solar neighborhood Mathis et al. (1983) field adopted by Draine & Li (2007). The formulae apply at 24 µm but the factor $\mathcal{R}_{24}^{X}$ can be drawn from Table 1 to express a prediction for any of the mid-IR bands of interest, X.

In Equation (4), the factor D/G is the dust-to-gas mass ratio, where a value of 0.01 represents a typical result applying the Draine & Li (2007) model to star-forming massive galaxies (e.g., Draine et al. 2007; Sandstrom et al. 2013; Aniano et al. 2020). When considering a PAH-dominated band, one should expand this part of the equation with an additional term proportional to $q_{PAH}$, the fraction of the dust mass in PAHs. This allows one to account for variations in the dust composition that may make PAHs either more or less abundant.

Draine et al. (2007) and Draine & Li (2007) note $q_{PAH} \approx 0.046$ as appropriate for Milky Way–like galaxies, and adding a factor

$$ \times \left( \frac{q_{\mathrm{PAH}}}{0.046} \right) $$

to Equation (4) offers a reasonable first-order approach at, e.g., F770W, F1130W, or 8 µm.

For $U \sim U_0$, dust emissivity in the mid-IR depends approximately linearly on U in the Draine & Li (2007) model (see their Figure 13), reflecting the fact that U sets the rate of stochastic, single-photon heating.<fnref n="50" /> Because the mass surface density of the dust is given by the product $\Sigma_{dust} = D/G \times \Sigma_{gas}$, Equation (4) simply predicts that for low-intensity, mid-IR emission tracks the dust column times the illuminating radiation field.

The Σ$_{gas}$ in the second line of Equation (4) includes helium, but N(H) does not. In general, Σ$_{gas}$ includes both atomic and molecular phases of the ISM, but for much of this paper, we will focus on molecular-gas-rich regions and will approximate Σ$_{gas} \approx \Sigma_{mol}$. The ability to generalize a relationship calibrated in the molecular-gas-dominated ISM to the atomic-gas-dominated regime will depend on how D/G, $q_{PAH}$, and U vary as a function of ISM phase or density. This is discussed in Sandstrom (2023b) and in Section 7.1 of this paper.

The mid-IR is also often used to trace star formation. In massive star-forming galaxies, dust absorbs and then re-emits much of the radiation from massive young stars. Some of this emission emerges in the mid-IR, which indicates the UV heating of dust grains. Based on observed excellent correlations between recombination line and mid-IR emission, the mid-IR has become a widely used SFR indicator. A variety of calibrations exist in the literature. Almost all of them have a fundamentally empirical calibration (e.g., see Murphy et al. 2011; Leroy et al. 2012; Kennicutt & Evans 2012; Calzetti 2013). We note here a common formulation for this relation for emission at $\lambda = 24$ µm:

$$ \frac{\Sigma_{\mathrm{SFR}}}{M_{\odot} \mathrm{yr}^{-1} \mathrm{kpc}^{-2}} \approx 2.97 \times 10^{-3} (\mathcal{R}_{24}^{X})^{-1} \\ \times \left( \frac{C_{24}}{10^{-42.7}} \right) \left( \frac{I_{\nu}^{X}}{\mathrm{MJy sr}^{-1}} \right), \qquad (5) $$

where $C_{24}$ is an empirically anchored conversion factor that has units of $M_{\odot} \mathrm{yr}^{-1} (\mathrm{erg s}^{-1})^{-1}$ (e.g., following Kennicutt & Evans 2012). The fiducial conversion in Equation (5) is the one suggested for $\lambda = 24$ µm by Kennicutt & Evans (2012) and Jarrett et al. (2013) and shown by Leroy et al. (2019) to match the integrated-galaxy population synthesis modeling results of Salim et al. (2016, 2018) well.

In a detailed analysis combining PHANGS–MUSE and WISE data, Belfiore et al. (2022b) show that $C_{WISE4} \sim C_{24}$ varies as a function of the local conditions in a galaxy disk, likely reflecting heating due to sources other than star formation contributing to the mid-IR. They consider mid-IR in combination with Hα and UV emission, and we note that

<footnote n="50">⁵⁰ At low U, this is true for both the PAH-dominated bands like F770W, F1130W, or 8 µm and the slightly longer-wavelength continuum-dominated bands like F2100W and 24 µm, but as U increases in the Draine & Li (2007) models, the longer-wavelength continuum bands begin to respond nonlinearly to U at lower U than the shorter-wavelength PAH bands.</footnote>
from SDSS, SINGS, CALIFA, and MaNGA, underpin much of our knowledge of extragalactic SFRs, including the calibration of IR-based SFR tracers (e.g., Brinchmann et al. 2004; Moustakas et al. 2006, 2010; Kennicutt & Hao 2009; Hao et al. 2011; Catalán-Torrecilla et al. 2015; Belfiore et al. 2022b). Although the Balmer decrement has limitations, particularly in dense, high-extinction, mixed media (e.g., Melnick 1979; Lequeux et al. 1981; Wong & Blitz 2002), at the moderate ΣSFR and moderate extinction that we study here, we have every expectation that the Balmer decrement works well. This expectation appears to be borne out by numerical simulations (Tacchella et al. 2022), and studying SINGS Prescott et al. (2007) found no evidence for a substantial highly obscured population pervading normal star-forming disk galaxies. Indeed, in the brightest regions of PHANGS–MUSE (Belfiore et al. 2022b; F. Belfiore et al., in preparation) find good agreement between the estimates of Hα extinction based on the Balmer decrement and those obtained from “hybrid” Hα+IR prescriptions calibrated by Calzetti et al. (2007) to match extinction-corrected Paschen α. Our results in Section 4.2 comparing the extinction-corrected Hα with JWST mid-IR emission also find no evidence that the Balmer decrement significantly underestimates the extinction (see also Hassani et al. 2023, in this Issue).

## 2.4. Mid-infrared Emission, Column Density, and Star Formation Rate

Even in the presence of a relatively weak radiation field, dust in the ISM should produce mid-IR emission, primarily through stochastic, single-photon heating. The intensity of emission depends on the column density of dust and the intensity of the illuminating radiation field. For relatively weak radiation fields, a reasonable fiducial expectation based on the Draine & Li (2007) dust models and also following Compiegne et al. (2010) is

$$ \frac{I_{\nu}^{X}}{\mathrm{MJy sr}^{-1}} \approx 0.022 \mathcal{R}_{24}^{X} \left( \frac{N(\mathrm{H})}{10^{20} \mathrm{cm}^{-2}} \right) \\ \times \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right) \\ \approx 0.020 \mathcal{R}_{24}^{X} \left( \frac{\Sigma_{\mathrm{gas}}}{1 M_{\odot} \mathrm{pc}^{-2}} \right) \\ \times \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right), \qquad (4) $$

where $I_{\nu}^{X}$ is the mid-IR intensity at band X, N(H) is the line-of-sight column density of hydrogen, and Σ$_{gas}$ is the gas mass surface density. The U/U$_{0}$ term expresses the mean local ISRF illuminating the dust in units of the solar neighborhood Mathis et al. (1983) field adopted by Draine & Li (2007). The formulae apply at 24 µm but the factor $R_{24}^{X}$ can be drawn from Table 1 to express a prediction for any of the mid-IR bands of interest, X.

In Equation (4), the factor D/G is the dust-to-gas mass ratio, where a value of 0.01 represents a typical result applying the Draine & Li (2007) model to star-forming massive galaxies (e.g., Draine et al. 2007; Sandstrom et al. 2013; Aniano et al. 2020). When considering a PAH-dominated band, one should expand this part of the equation with an additional term proportional to $q_{PAH}$, the fraction of the dust mass in PAHs. This allows one to account for variations in the dust composition that may make PAHs either more or less abundant.

Draine et al. (2007) and Draine & Li (2007) note $q_{PAH} \approx 0.046$ as appropriate for Milky Way–like galaxies, and adding a factor

$$ \times \left( \frac{q_{\mathrm{PAH}}}{0.046} \right) $$

to Equation (4) offers a reasonable first-order approach at, e.g., F770W, F1130W, or 8 µm.

For $U \sim U_0$, dust emissivity in the mid-IR depends approximately linearly on U in the Draine & Li (2007) model (see their Figure 13), reflecting the fact that U sets the rate of stochastic, single-photon heating.<fnref n="50" /> Because the mass surface density of the dust is given by the product $\Sigma_{dust} = D/G \times \Sigma_{gas}$, Equation (4) simply predicts that for low-intensity, mid-IR emission tracks the dust column times the illuminating radiation field.

The Σ$_{gas}$ in the second line of Equation (4) includes helium, but N(H) does not. In general, Σ$_{gas}$ includes both atomic and molecular phases of the ISM, but for much of this paper, we will focus on molecular-gas-rich regions and will approximate Σ$_{gas} \approx \Sigma_{mol}$. The ability to generalize a relationship calibrated in the molecular-gas-dominated ISM to the atomic-gas-dominated regime will depend on how D/G, $q_{PAH}$, and U vary as a function of ISM phase or density. This is discussed in Sandstrom (2023b) and in Section 7.1 of this paper.

The mid-IR is also often used to trace star formation. In massive star-forming galaxies, dust absorbs and then re-emits much of the radiation from massive young stars. Some of this emission emerges in the mid-IR, which indicates the UV heating of dust grains. Based on observed excellent correlations between recombination line and mid-IR emission, the mid-IR has become a widely used SFR indicator. A variety of calibrations exist in the literature. Almost all of them have a fundamentally empirical calibration (e.g., see Murphy et al. 2011; Leroy et al. 2012; Kennicutt & Evans 2012; Calzetti 2013). We note here a common formulation for this relation for emission at $\lambda = 24$ µm:

$$ \frac{\Sigma_{\mathrm{SFR}}}{M_{\odot} \mathrm{yr}^{-1} \mathrm{kpc}^{-2}} \approx 2.97 \times 10^{-3} (R_{24}^{X})^{-1} \\ \times \left( \frac{C_{24}}{10^{-42.7}} \right) \left( \frac{I_{\nu}^{X}}{\mathrm{MJy sr}^{-1}} \right), \qquad (5) $$

where $C_{24}$ is an empirically anchored conversion factor that has units of $M_{\odot} \mathrm{yr}^{-1} (\mathrm{erg s}^{-1})^{-1}$ (e.g., following Kennicutt & Evans 2012). The fiducial conversion in Equation (5) is the one suggested for $\lambda = 24$ µm by Kennicutt & Evans (2012) and Jarrett et al. (2013) and shown by Leroy et al. (2019) to match the integrated-galaxy population synthesis modeling results of Salim et al. (2016, 2018) well.

In a detailed analysis combining PHANGS–MUSE and WISE data, Belfiore et al. (2022b) show that $C_{WISE4} \sim C_{24}$ varies as a function of the local conditions in a galaxy disk, likely reflecting heating due to sources other than star formation contributing to the mid-IR. They consider mid-IR in combination with Hα and UV emission, and we note that

<footnote n="50">⁵⁰ At low U, this is true for both the PAH-dominated bands like F770W, F1130W, or 8 µm and the slightly longer-wavelength continuum-dominated bands like F2100W and 24 µm, but as U increases in the Draine & Li (2007) models, the longer-wavelength continuum bands begin to respond nonlinearly to U at lower U than the shorter-wavelength PAH bands.</footnote>
their maximum C for UV emission is $log_{10} C_{WISE4} \sim -42.7$, similar to Equation (5), but that for regions with significant heating by old stellar populations or when combining mid-IR and Hα, they find even lower $log_{10} C_{WISE4} \sim -42.9$. We will return to compare to their findings in Section 6.

As above, the factor $R_{24}^X$ in Equation (5) translates from the fiducial 24 µm to other bands assuming the fixed band ratios in Table 1. However, one should bear in mind that these ratios have been calculated for extended regions of moderate intensity emission (Appendix A) and that the strongest band ratio variations observed in other papers in this series are found at high intensity in star-forming regions (see Section 2.1).

## 2.5. Implied Predictions for CO and Hα versus Mid-IR

The conversions in above can be equated to express predictions for the relationships between CO and mid-IR emission and Hα and mid-IR emission. First, when gas is mostly molecular and the dust is illuminated by a relatively weak radiation field, Equations (2) and (4) together yield

$$ \frac{I_{\nu}^{X}}{\text{MJy sr}^{-1}} \approx 0.134 R_{24}^{X} \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right) \times \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{R_{21}}{0.65} \right) \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right), \quad (6) $$

so that for this case, which might be thought of as “molecular IR cirrus,” the mid-IR tracks CO emission with additional dependence on the CO-to-H₂ conversion factor, CO 2–1 to 1–0 line ratio, dust to gas mass ratio, and ISRF. For a PAH-dominated band, the equation should include an additional factor ×($q_{\text{PAH}}$/0.046).

Meanwhile, if we consider mid-IR driven only by heating due to star formation and require consistency between extinction-corrected Hα and mid-IR results, then Equations (3) and (5) together imply

$$ \frac{I_{\nu}^{X}}{\text{MJy sr}^{-1}} \approx 2.16 \times 10^{5} R_{24}^{X} \times \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{cm}^{-2} \text{sr}^{-1}} \right) \left( \frac{10^{-42.7}}{C_{24}} \right) \quad (7) $$

for the case of “mid-IR produced directly by reprocessed light from young stars.” We caution that while Equation (7) appears simple, depending only on $C_{24}$ and $R_{24}^X$, this largely reflects that Equation (5) combines all of the physics behind the empirically calibrated mid-IR to SFR conversion into a single number. Moreover, because $C_{24}$ for the mid-IR is empirical and often calibrated against Balmer decrement-corrected Hα or other recombination line emission, Equation (7) is somewhat circular. We still find this a useful way to frame the current field. For a C calibrated based on star-forming regions or overwhelmingly star-forming galaxies, we might expect Equation (7) to hold for bright star-forming regions within our target galaxies.

## 2.6. Two Physical Definitions of “Bright” Emission

In our analysis we will be interested in “bright” mid-IR emission, by which we mean emission that we might plausibly expect to emerge from regions dominated by molecular gas or

recent star formation. The equations in Section 2.5 allow us to roughly define two plausible thresholds.

**Intensity for molecular-gas-dominated lines of sight:** For metal-rich star-forming galaxies, molecular gas typically makes up most of the ISM in regions with $\Sigma_{\text{gas}} \gtrsim 15 M_{\odot} \text{ pc}^{-2}$ (e.g., Bigiel et al. 2008; Leroy et al. 2008; Schruba et al. 2011). Assuming $U \sim (1-2)U_0$ and $D/G \sim 0.01$ then this implies

$$ I_{\nu}^{X} \gtrsim 0.3 - 0.6 R_{24}^{X} \text{MJy sr}^{-1} \quad (8) $$

for “molecular cirrus” with the range affecting a plausible range of U and D/G, each of which affects the estimate linearly (Equation (4)).

**Intensity for H II regions:** Meanwhile, though there is no single cutoff between H II region emission and DIG, the 16th percentile for H II region surface brightness in Belfiore et al. (2022a) is $log_{10} I_{H\alpha} \sim 38.9$ for $I_{H\alpha}$ in units of erg s⁻¹ kpc⁻², which translates to $log_{10} I_{H\alpha} \sim -5.2$ in our units of erg s⁻¹ cm⁻² sr⁻¹. Following Equation (7), this implies

$$ I_{\nu}^{X} \gtrsim 1.4 R_{24}^{X} \text{MJy sr}^{-1} \quad (9) $$

for H II regions.

We will return to an empirical version of the two thresholds below.

# 3. Data

We study the first four PHANGS–JWST targets: NGC 628, NGC 1365, NGC 7496, and IC 5332 and compare mid-IR emission at 7.7 µm, 10 µm, 11.3 µm, and 21 µm obtained as part of the PHANGS–JWST survey (Lee et al. 2023) to CO (2–1) observed by ALMA as part of the PHANGS–ALMA survey (Leroy et al. 2021) and extinction-corrected Hα obtained as part of the PHANGS–MUSE survey (Emsellem et al. 2022). For this comparison, we work with all data sets at a common angular resolution of $\theta = 1''$. This is set by the resolution of our ALMA CO data for NGC 7496, which is the coarsest resolution for any data in our sample. Figures 1 through 4 illustrate our data sets at our working resolution, and Table 2 summarizes the physical properties, distance, and orientation for each target.

## 3.1. Data Sets

The mid-IR data were obtained using the MIRI instrument with the F770W, F1000W, F1130W, and F2100W filters. Details of the observations and data reduction appear in Lee et al. (2023). We used the PHANGS–JWST internal release “version 0.5,” which uses pipeline version 1.7.0 and CRDS context 0968 and follows the procedure described in Appendix B to set the background level in the maps to be self-consistent among the four MIRI bands and to match previous wide-field observations at 8 µm by Spitzer or 12 µm by WISE.

We compare the mid-IR images to ALMA CO (2–1) maps obtained as part of the PHANGS–ALMA survey (Leroy et al. 2021). We use the combined 12-m+7-m+total power data cubes from the public data release (“v4”). Taking into account typical CO/Hα and CO-to-MIR ratios, the CO (2–1) data are significantly less sensitive than the other data in this work (Section 3.3 and Table 3). Therefore, we construct a special set of “flat” CO-integrated intensity maps, designed to allow simple, robust statistical averaging. To do this, after convolving the CO cube to our working resolution of 1''7, we shift each
their maximum C for UV emission is $log_{10} C_{\text{WISE4}} \sim -42.7$, similar to Equation (5), but that for regions with significant heating by old stellar populations or when combining mid-IR and H$\alpha$, they find even lower $log_{10} C_{\text{WISE4}} \sim -42.9$. We will return to compare to their findings in Section 6.

As above, the factor $R_{24}^X$ in Equation (5) translates from the fiducial 24 µm to other bands assuming the fixed band ratios in Table 1. However, one should bear in mind that these ratios have been calculated for extended regions of moderate intensity emission (Appendix A) and that the strongest band ratio variations observed in other papers in this series are found at high intensity in star-forming regions (see Section 2.1).

## 2.5. Implied Predictions for CO and H$\alpha$ versus Mid-IR

The conversions in above can be equated to express predictions for the relationships between CO and mid-IR emission and H$\alpha$ and mid-IR emission. First, when gas is mostly molecular and the dust is illuminated by a relatively weak radiation field, Equations (2) and (4) together yield

$$ \frac{I_{\nu}^{X}}{\text{MJy sr}^{-1}} \approx 0.134 R_{24}^{X} \left( \frac{I_{\text{CO 2-1}}}{\text{K km s}^{-1}} \right) \times \left( \frac{\alpha_{\text{CO 1-0}}}{\alpha_{\text{CO 1-0}}^{\text{MW}}} \right) \left( \frac{R_{21}}{0.65} \right) \left( \frac{D/G}{0.01} \right) \left( \frac{U}{U_0} \right), \quad (6) $$

so that for this case, which might be thought of as “molecular IR cirrus,” the mid-IR tracks CO emission with additional dependence on the CO-to-H$_2$ conversion factor, CO 2–1 to 1–0 line ratio, dust to gas mass ratio, and ISRF. For a PAH-dominated band, the equation should include an additional factor $\times (q_{\text{PAH}}/0.046)$.

Meanwhile, if we consider mid-IR driven only by heating due to star formation and require consistency between extinction-corrected H$\alpha$ and mid-IR results, then Equations (3) and (5) together imply

$$ \frac{I_{\nu}^{X}}{\text{MJy sr}^{-1}} \approx 2.16 \times 10^{5} R_{24}^{X} \times \left( \frac{I_{H\alpha}}{\text{erg s}^{-1} \text{cm}^{-2} \text{sr}^{-1}} \right) \left( \frac{10^{-42.7}}{C_{24}} \right) \quad (7) $$

for the case of “mid-IR produced directly by reprocessed light from young stars.” We caution that while Equation (7) appears simple, depending only on $C_{24}$ and $R_{24}^X$, this largely reflects that Equation (5) combines all of the physics behind the empirically calibrated mid-IR to SFR conversion into a single number. Moreover, because $C_{24}$ for the mid-IR is empirical and often calibrated against Balmer decrement-corrected H$\alpha$ or other recombination line emission, Equation (7) is somewhat circular. We still find this a useful way to frame the current field. For a C calibrated based on star-forming regions or overwhelmingly star-forming galaxies, we might expect Equation (7) to hold for bright star-forming regions within our target galaxies.

## 2.6. Two Physical Definitions of “Bright” Emission

In our analysis we will be interested in “bright” mid-IR emission, by which we mean emission that we might plausibly expect to emerge from regions dominated by molecular gas or

recent star formation. The equations in Section 2.5 allow us to roughly define two plausible thresholds.

**Intensity for molecular-gas-dominated lines of sight:** For metal-rich star-forming galaxies, molecular gas typically makes up most of the ISM in regions with $\Sigma_{\text{gas}} \gtrsim 15 M_{\odot} \text{ pc}^{-2}$ (e.g., Bigiel et al. 2008; Leroy et al. 2008; Schruba et al. 2011). Assuming $U \sim (1-2)U_0$ and $D/G \sim 0.01$ then this implies

$$ I_{\nu}^{X} \gtrsim 0.3 - 0.6 R_{24}^{X} \text{MJy sr}^{-1} \quad (8) $$

for “molecular cirrus” with the range affecting a plausible range of U and D/G, each of which affects the estimate linearly (Equation (4)).

**Intensity for H II regions:** Meanwhile, though there is no single cutoff between H II region emission and DIG, the 16th percentile for H II region surface brightness in Belfiore et al. (2022a) is $log_{10} I_{H\alpha} \sim 38.9$ for $I_{H\alpha}$ in units of erg s$^{-1}$ kpc$^{-2}$, which translates to $log_{10} I_{H\alpha} \sim -5.2$ in our units of erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$. Following Equation (7), this implies

$$ I_{\nu}^{X} \gtrsim 1.4 R_{24}^{X} \text{MJy sr}^{-1} \quad (9) $$

for H II regions.

We will return to an empirical version of the two thresholds below.

# 3. Data

We study the first four PHANGS–JWST targets: NGC 628, NGC 1365, NGC 7496, and IC 5332 and compare mid-IR emission at 7.7 µm, 10 µm, 11.3 µm, and 21 µm obtained as part of the PHANGS–JWST survey (Lee et al. 2023) to CO (2–1) observed by ALMA as part of the PHANGS–ALMA survey (Leroy et al. 2021) and extinction-corrected H$\alpha$ obtained as part of the PHANGS–MUSE survey (Emsellem et al. 2022). For this comparison, we work with all data sets at a common angular resolution of $\theta = 1''$. This is set by the resolution of our ALMA CO data for NGC 7496, which is the coarsest resolution for any data in our sample. Figures 1 through 4 illustrate our data sets at our working resolution, and Table 2 summarizes the physical properties, distance, and orientation for each target.

## 3.1. Data Sets

The mid-IR data were obtained using the MIRI instrument with the F770W, F1000W, F1130W, and F2100W filters. Details of the observations and data reduction appear in Lee et al. (2023). We used the PHANGS–JWST internal release “version 0.5,” which uses pipeline version 1.7.0 and CRDS context 0968 and follows the procedure described in Appendix B to set the background level in the maps to be self-consistent among the four MIRI bands and to match previous wide-field observations at 8 µm by Spitzer or 12 µm by WISE.

We compare the mid-IR images to ALMA CO (2–1) maps obtained as part of the PHANGS–ALMA survey (Leroy et al. 2021). We use the combined 12-m+7-m+total power data cubes from the public data release (“v4”). Taking into account typical CO/H$\alpha$ and CO-to-MIR ratios, the CO (2–1) data are significantly less sensitive than the other data in this work (Section 3.3 and Table 3). Therefore, we construct a special set of “flat” CO-integrated intensity maps, designed to allow simple, robust statistical averaging. To do this, after convolving the CO cube to our working resolution of $1''$, we shift each
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Mid-IR, CO, and extinction-corrected Hα maps for NGC 0628. These images show our matched 80 pc resolution, matched astrometry data for NGC 628. The top row shows two of the four analyzed JWST mid-IR images, F770W and F2100W. The bottom row shows the ALMA CO (2–1) image and the VLT/MUSE extinction-corrected Hα. All images are displayed using an identical arcsinh stretch from 0.5 to 30 MJy sr⁻¹ after converting all bands to equivalent F770W using the band ratios in Table 1 for the mid-IR and the median ratios in Table 4 for CO (2–1) and Hαcorr. We have blanked data outside the common JWST MIRI/MUSE/ALMA footprint. A scale bar shows 1 kpc at the distance of the galaxy and the 1.7 (FWHM) beam appears in the top-right corner of the image. The blue contour in all panels shows an F770W contour at 1.5 MJy sr⁻¹, and the red contour shows an Hα contour at an equivalent of F770W intensity 10 MJy sr⁻¹.</figcaption></figure>

spectrum of the cube along its velocity axis, recentering the spectrum for each line of sight so that $v = 0$ km s⁻¹ now corresponds to the expected mean local rotation velocity. For

NGC 0628, 1365, and 7496 we use the low-resolution velocity field derived from the CO as a reference, filling in with a predicted local velocity from the rotation curve in the few
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Mid-IR, CO, and extinction-corrected Hα maps for NGC 0628. These images show our matched 80 pc resolution, matched astrometry data for NGC 628. The top row shows two of the four analyzed JWST mid-IR images, F770W and F2100W. The bottom row shows the ALMA CO (2–1) image and the VLT/MUSE extinction-corrected Hα. All images are displayed using an identical arcsinh stretch from 0.5 to 30 MJy sr⁻¹ after converting all bands to equivalent F770W using the band ratios in Table 1 for the mid-IR and the median ratios in Table 4 for CO (2–1) and Hαcorr. We have blanked data outside the common JWST MIRI/MUSE/ALMA footprint. A scale bar shows 1 kpc at the distance of the galaxy and the 1.′′7 (FWHM) beam appears in the top-right corner of the image. The blue contour in all panels shows an F770W contour at 1.5 MJy sr⁻¹, and the red contour shows an Hα contour at an equivalent of F770W intensity 10 MJy sr⁻¹.</figcaption></figure>

spectrum of the cube along its velocity axis, recentering the
spectrum for each line of sight so that v = 0 km s⁻¹ now
corresponds to the expected mean local rotation velocity. For

NGC 0628, 1365, and 7496 we use the low-resolution velocity
field derived from the CO as a reference, filling in with a
predicted local velocity from the rotation curve in the few
<table><caption>**Table 2**
Targets</caption><thead><tr><th>Galaxy</th><th>log<sub>10</sub> M<sub>*</sub><br>(log<sub>10</sub> M<sub>*</sub>)</th><th>log<sub>10</sub> SFR<br>(log<sub>10</sub> M<sub>☉</sub>/yr)</th><th>Z at r<sub>eff</sub><br>(12 + log<sub>10</sub> R<sub>H</sub><sup>O</sup>)</th><th>i<br>(°)</th><th>PA<br>(°)</th><th>days<br>(Mpc)</th><th>θ<sub>bm</sub><br>(pc)</th><th>A<sub>bm</sub><br>(pc<sup>2</sup>)</th><th>Notes</th></tr></thead><tbody><tr><td>NGC 0628</td><td>10.3</td><td>0.2</td><td>8.5</td><td>9</td><td>21</td><td>9.8</td><td>80</td><td>7300</td><td>grand-design spiral</td></tr><tr><td>NGC 1365</td><td>11.0</td><td>1.2</td><td>8.5</td><td>55</td><td>201</td><td>19.6</td><td>160</td><td>50,000</td><td>strong bar, AGN (Sy1.8), starburst ring</td></tr><tr><td>NGC 7496</td><td>10.0</td><td>0.4</td><td>8.5</td><td>36</td><td>194</td><td>18.7</td><td>150</td><td>32,000</td><td>strong bar, AGN (Sy2)</td></tr><tr><td>IC 5332</td><td>9.7</td><td>-0.4</td><td>8.3</td><td>27</td><td>74</td><td>9.0</td><td>70</td><td>6700</td><td>dwarf spiral</td></tr></tbody></table>

Note. Properties adopted from Leroy et al. (2021), which draw orientations from Lang et al. (2020) and distances from Anand et al. (2021a) based on Shaya et al. (2017), Kourkchi et al. (2020), Anand et al. (2021b). “S-cal” metallicities quoted at $r_{eff}$ drawn from Groves et al. (2023) and see also Kreckel et al. (2019). $\theta_{bm}$ gives the approximate linear beam size for $\theta = 1''7$ with no inclination correction. $A_{bm}$ gives the physical beam area with inclination correction.

regions without detection. For IC 5332, which has lower signal to noise than the other galaxies in CO, we use an estimated rotation curve for the reference at all locations. After adjusting the cube so that all emission is centered in roughly the same channel, we integrate over a fixed velocity window picked to encompass all readily detected emission in the disk ($\delta v = 25, 35, 80$, and $55$ km s$^{-1}$ for IC 5332, NGC 0628, 1365, and 7496). The integration also includes all bright (signal-to-noise ratio, S/N > 3 in 2 channels) emission in extended line wings, which effectively captures the broad wings in the centers of NGC 1365 and NGC 7496.

The resulting “flat” moment maps appear in the bottom-left corners of Figures 1, 2, 3, and 4. These maps include almost all of the CO flux in each data cube, similar to the standard PHANGS–ALMA high-completeness “broad” moment maps. However, those broad maps use a local velocity window based on multiresolution signal detection algorithms and do include empty lines of sight where no signal is detected. The “flat” maps that we use here have a more even noise distribution because they use a single fixed velocity window and have no blank pixels within the region of interest. As a result, they are moderately noisier in any given pixel than the fiducial PHANGS–ALMA products but can be averaged spatially in a simple way to produce results equivalent to spectral stacking (e.g., Schruba et al. 2011; Ianjamasimanana et al. 2012). Aside from the higher but more even noise, which can be seen particularly clearly in the images of NGC 1365 (Figure 2) and IC 5332 (Figure 4), these maps capture essentially the same features as the standard PHANGS broad maps (compare to the atlas images for the same galaxies in Leroy et al. 2021).

We compare both mid-IR and CO emission to extinction-corrected $H\alpha$ emission from the PHANGS–MUSE survey (Emsellem et al. 2022). In this work, we primarily use maps of $H\alpha$ emission corrected for internal extinction using the Balmer decrement method contrasting $H\beta$ and $H\alpha$. These maps were produced from the “convolved and optimized” maps PHANGS–MUSE internal data release 2.2 (see Emsellem et al. 2022) and have been described in Belfiore et al. (2022a, 2022b) and Pessa et al. (2021, 2022).

## 3.2. Matched-resolution Database

We use kernels produced following the method of Aniano et al. (2011) and the preflight estimates of the JWST PSFs to convolve all of our data to share a common Gaussian PSF with FWHM $\theta = 1''7$. Table 2 gives the corresponding physical beam size for each target, which ranges from 70 to 160 pc. After convolution, we reproject all data onto a common

astrometric grid centered at the galaxy center with 0''83-wide pixels, i.e., 4 pixels per PSF area.

Both NGC 1365 and NGC 7496 have a bright active galactic nucleus (AGN) in the inner galaxy, which leads to diffraction spikes that extend well into the surrounding galaxy disks. Following Hassani et al. (2023) we use an image of the PSF centered at the bright peak to identify the diffraction spikes. We convolve this mask to the working resolution of our data and drop pixels where diffraction spikes are expected to cover >1% of the area from our analysis.

After this processing, we build a database consisting of pixel-by-pixel measurements of the intensities of CO (2–1), extinction-corrected $H\alpha$, mid-IR emission at 7.7 µm (F770W), 10 µm (F1000W), 11.3 µm (F1130W), and 21 µm (F2100W). We correct all intensities by a factor of $\cos i$ to the values expected had we observed the galaxies face on. We draw inclinations from Lang et al. (2020) and Leroy et al. (2021).

We mostly utilize intensities in our expectations and analysis, it can also be of interest to compute the flux, luminosity, mass, or SFR of an individual resolution element. For our common angular resolution of $\theta = 1''7$, to convert from intensity to flux per beam, the beam area is $\approx 7.4 \times 10^{-11}$ sr. To allow easy conversion from inclination-corrected surface density to mass or SFR within a resolution element, Table 2 also quotes the physical beam size $A_{beam} = \pi(\theta d)^2 (4 \ln 2)^{-1} (\cos i)^{-1}$ for each target.

## 3.3. Typical Uncertainties

Table 3 provides characteristic noise levels for our $\theta = 1''7$ images. We quote a single value for each band estimated before any inclination correction is applied. We give single, approximate values per band because we work with early versions of the data and our images lack significant “empty sky.” Given that we have convolved the data to significantly coarser-than-native resolution, we view an empirical estimate as more appropriate than an aggressive extrapolation of the native resolution pipeline noise estimate.

To derive these estimates, we use a version of the procedure described in Appendix B. We consider the low-intensity region of each galaxy. As shown in Sandstrom (2023b), even these faint regions still often have significant real emission from the galaxy, which could masquerade as noise. To account for this, we scale another band by the typical band ratio and subtract that scaled image from the original then measure the noise in the difference, e.g., considering $I_{\nu}^{F770W} - R_{11.3}^{7.7}I_{\nu}^{F1130W}$. After running a broad median filter across the difference image, we solve for the implied rms noise, taking into account both the measured band ratio and the noise ratio expected based on the pipeline noise estimates. That is, we measure the noise in the
<table><caption>**Table 2**
Targets</caption><thead><tr><th>Galaxy</th><th>log<sub>10</sub> M<sub>*</sub><br>(log<sub>10</sub> M<sub>☉</sub>)</th><th>log<sub>10</sub> SFR<br>(log<sub>10</sub> M<sub>☉</sub>/yr)</th><th>Z at r<sub>eff</sub><br>(12 + log<sub>10</sub> R/H)</th><th>i<br>(°)</th><th>PA<br>(°)</th><th>days<br>(Mpc)</th><th>θ<sub>bm</sub><br>(pc)</th><th>A<sub>bm</sub><br>(pc<sup>2</sup>)</th><th>Notes</th></tr></thead><tbody><tr><td>NGC 0628</td><td>10.3</td><td>0.2</td><td>8.5</td><td>9</td><td>21</td><td>9.8</td><td>80</td><td>7300</td><td>grand-design spiral</td></tr><tr><td>NGC 1365</td><td>11.0</td><td>1.2</td><td>8.5</td><td>55</td><td>201</td><td>19.6</td><td>160</td><td>50,000</td><td>strong bar, AGN (Sy1.8), starburst ring</td></tr><tr><td>NGC 7496</td><td>10.0</td><td>0.4</td><td>8.5</td><td>36</td><td>194</td><td>18.7</td><td>150</td><td>32,000</td><td>strong bar, AGN (Sy2)</td></tr><tr><td>IC 5332</td><td>9.7</td><td>-0.4</td><td>8.3</td><td>27</td><td>74</td><td>9.0</td><td>70</td><td>6700</td><td>dwarf spiral</td></tr></tbody></table>

Note. Properties adopted from Leroy et al. (2021), which draw orientations from Lang et al. (2020) and distances from Anand et al. (2021a) based on Shaya et al. (2017), Kourkchi et al. (2020), Anand et al. (2021b). “S-cal” metallicities quoted at $r_{eff}$ drawn from Groves et al. (2023) and see also Kreckel et al. (2019). $\theta_{bm}$ gives the approximate linear beam size for $\theta = 1''7$ with no inclination correction. $A_{bm}$ gives the physical beam area with inclination correction.

regions without detection. For IC 5332, which has lower signal to noise than the other galaxies in CO, we use an estimated rotation curve for the reference at all locations. After adjusting the cube so that all emission is centered in roughly the same channel, we integrate over a fixed velocity window picked to encompass all readily detected emission in the disk ($\delta v = 25, 35, 80$, and $55$ km s$^{-1}$ for IC 5332, NGC 0628, 1365, and 7496). The integration also includes all bright (signal-to-noise ratio, S/N > 3 in 2 channels) emission in extended line wings, which effectively captures the broad wings in the centers of NGC 1365 and NGC 7496.

The resulting “flat” moment maps appear in the bottom-left corners of Figures 1, 2, 3, and 4. These maps include almost all of the CO flux in each data cube, similar to the standard PHANGS–ALMA high-completeness “broad” moment maps. However, those broad maps use a local velocity window based on multiresolution signal detection algorithms and do include empty lines of sight where no signal is detected. The “flat” maps that we use here have a more even noise distribution because they use a single fixed velocity window and have no blank pixels within the region of interest. As a result, they are moderately noisier in any given pixel than the fiducial PHANGS–ALMA products but can be averaged spatially in a simple way to produce results equivalent to spectral stacking (e.g., Schruba et al. 2011; Ianjamasimanana et al. 2012). Aside from the higher but more even noise, which can be seen particularly clearly in the images of NGC 1365 (Figure 2) and IC 5332 (Figure 4), these maps capture essentially the same features as the standard PHANGS broad maps (compare to the atlas images for the same galaxies in Leroy et al. 2021).

We compare both mid-IR and CO emission to extinction-corrected $H\alpha$ emission from the PHANGS–MUSE survey (Emsellem et al. 2022). In this work, we primarily use maps of $H\alpha$ emission corrected for internal extinction using the Balmer decrement method contrasting $H\beta$ and $H\alpha$. These maps were produced from the “convolved and optimized” maps PHANGS–MUSE internal data release 2.2 (see Emsellem et al. 2022) and have been described in Belfiore et al. (2022a, 2022b) and Pessa et al. (2021, 2022).

## 3.2. Matched-resolution Database

We use kernels produced following the method of Aniano et al. (2011) and the preflight estimates of the JWST PSFs to convolve all of our data to share a common Gaussian PSF with FWHM $\theta = 1''7$. Table 2 gives the corresponding physical beam size for each target, which ranges from 70 to 160 pc. After convolution, we reproject all data onto a common

astrometric grid centered at the galaxy center with 0''83-wide pixels, i.e., 4 pixels per PSF area.

Both NGC 1365 and NGC 7496 have a bright active galactic nucleus (AGN) in the inner galaxy, which leads to diffraction spikes that extend well into the surrounding galaxy disks. Following Hassani et al. (2023) we use an image of the PSF centered at the bright peak to identify the diffraction spikes. We convolve this mask to the working resolution of our data and drop pixels where diffraction spikes are expected to cover >1% of the area from our analysis.

After this processing, we build a database consisting of pixel-by-pixel measurements of the intensities of CO (2–1), extinction-corrected $H\alpha$, mid-IR emission at 7.7 µm (F770W), 10 µm (F1000W), 11.3 µm (F1130W), and 21 µm (F2100W). We correct all intensities by a factor of $\cos i$ to the values expected had we observed the galaxies face on. We draw inclinations from Lang et al. (2020) and Leroy et al. (2021).

We mostly utilize intensities in our expectations and analysis, it can also be of interest to compute the flux, luminosity, mass, or SFR of an individual resolution element. For our common angular resolution of $\theta = 1''7$, to convert from intensity to flux per beam, the beam area is $\approx 7.4 \times 10^{-11}$ sr. To allow easy conversion from inclination-corrected surface density to mass or SFR within a resolution element, Table 2 also quotes the physical beam size $A_{beam} = \pi(\theta d)^2 (4 \ln 2)^{-1} (\cos i)^{-1}$ for each target.

## 3.3. Typical Uncertainties

Table 3 provides characteristic noise levels for our $\theta = 1''7$ images. We quote a single value for each band estimated before any inclination correction is applied. We give single, approximate values per band because we work with early versions of the data and our images lack significant “empty sky.” Given that we have convolved the data to significantly coarser-than-native resolution, we view an empirical estimate as more appropriate than an aggressive extrapolation of the native resolution pipeline noise estimate.

To derive these estimates, we use a version of the procedure described in Appendix B. We consider the low-intensity region of each galaxy. As shown in Sandstrom (2023b), even these faint regions still often have significant real emission from the galaxy, which could masquerade as noise. To account for this, we scale another band by the typical band ratio and subtract that scaled image from the original then measure the noise in the difference, e.g., considering $I_{\nu}^{F770W} - R_{11.3}^{7.7}I_{\nu}^{F1130W}$. After running a broad median filter across the difference image, we solve for the implied rms noise, taking into account both the measured band ratio and the noise ratio expected based on the pipeline noise estimates. That is, we measure the noise in the
<table><caption>**Table 3**
Characteristic Noise at 1.7 Expressed in Different Units</caption><thead><tr><th>Band</th><th>Expected σ/σ<sup>7.7</sup></th><th>σ<sub>1.7</sub><br>(MJy sr<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>7.7</sup><br>(MJy sr<sup>-1</sup> at F770W)</th><th>σ<sub>1.7</sub><sup>Hα</sup><br>(erg s<sup>-1</sup> cm<sup>-2</sup> sr<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>CO 2-1</sup><br>(K km s<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>gas</sup><br>(M<sub>☉</sub> pc<sup>-2</sup>)</th></tr></thead><tbody><tr><td>F770W</td><td>1.0</td><td>0.025</td><td>0.025</td><td>0.63 × 10<sup>-7</sup></td><td>0.027</td><td>0.18</td></tr><tr><td>F1000W</td><td>1.1 ± 0.1</td><td>0.028</td><td>0.072</td><td>1.7 × 10<sup>-7</sup></td><td>0.076</td><td>0.51</td></tr><tr><td>F1130W</td><td>1.35 ± 0.1</td><td>0.033</td><td>0.025</td><td>0.59 × 10<sup>-7</sup></td><td>0.027</td><td>0.18</td></tr><tr><td>F2100W</td><td>2.5 ± 0.2</td><td>0.063</td><td>0.10</td><td>2.9 × 10<sup>-7</sup></td><td>0.031</td><td>0.21</td></tr><tr><td>CO (2–1)<sup>a</sup></td><td>...</td><td>...</td><td>...</td><td>...</td><td>1.0</td><td>6.7</td></tr><tr><td>Hα<sup>b</sup></td><td>...</td><td>...</td><td>...</td><td>0.035 × 10<sup>-7</sup></td><td>...</td><td>...</td></tr></tbody></table>

**Notes.** Approximate characteristic noises for our data before any inclination correction for our sample at our working resolution of $\theta = 1.7''$. Columns: Expected $\sigma/\sigma^{7.7}$—approximate ratio of pipeline noise estimate at this band to that at F770W at their native resolutions; $\sigma_{1.7}$—noise on the scale of intensity in that band; $\sigma_{1.7}^{7.7}$—noise scaled to units of 7.7 $\mu$m via $R^X$ for comparison; $\sigma_{1.7}^{Hα}$—noise in equivalent extinction-corrected Hα units assuming the data set wide median ratio; $\sigma_{1.7}^{CO 2-1}$—noise in CO (2–1) units assuming the data set wide median ratio; and $\sigma_{1.7}^{gas}$—noise in gas surface density units assuming data-set-wide median CO-to-mid-IR ratio and a typical CO-to-H$_2$ conversion factor (Equation (2)).

<sup>a</sup> Median noise across all four “flat” integrated intensity (i.e., moment 0) maps (Section 3.1) used for this analysis. Varies moderately from target to target.

<sup>b</sup> Typical noise in the MUSE NGC 1365 and NGC 7496 Hα maps at $\theta \sim 150$ pc. The extinction correction introduces additional uncertainty but does not affect detection.

difference image and use this, with an appropriate scaling, to estimate the noise in the original images.

In order to compare the sensitivity of different bands to gas column or recent star formation, Table 3 also re-expresses the noise in the bands scaled in several different ways. We first express the relative sensitivity of all bands to “typical” dust emission by scaling by the band ratios in Table 1 onto a common F770W intensity scale, $\sigma_{1.7}^{7.7}$. Then we adopt the median CO-to-mid-IR and Hα-to-mid-IR ratios found in Section 4 to express the mid-IR noises in equivalent $I_{Hα}$, $I_{CO}$, and $\Sigma_{gas}$ units. In Section 6, we will use these to comment on the sensitivity of the JWST images to recent star formation and gas column density.

In addition to the noise levels quoted in Table 3, there is an overall $\lesssim 0.1$ MJy sr$^{-1}$ uncertainty in the level of the background in the MIRI images. Realistically, based on a visual inspection of the images at high stretch, this background level clearly varies across the images at a fraction of this level. To assess this quantitatively, we note that the medium-scale median filter level in the difference images mentioned above imply an rms variation $\sim \pm 0.04-0.07$ MJy sr$^{-1}$ in the background level. Comparing to Table 3 highlights that at our working resolution the uncertainty in the background is often as important as the statistical noise.

### 3.4. Data Selection

We focus our analysis on regions with an inclination-corrected F770W intensity above 0.5 MJy sr$^{-1}$. We target this level because based on the calculations in Section 2.6, we expect that where molecular gas makes up most of the ISM along a line of sight it will likely produce at least this level of emission, even if it is only weakly illuminated. The threshold for emission associated with H II regions is even higher, so we expect this selection to capture most of the area in our targets where either dust mixed with molecular gas or dust heated by H II regions contributes. This level is also high enough that uncertainty in the background level and the statistical noise, which both have a maximum magnitude $\sim \pm 0.1$ MJy sr$^{-1}$, are only secondary concerns for the mid-IR.

Table 4 reports the fractions of flux in each band and area within the PHANGS–JWST footprint associated with this

“bright” emission. In our three more massive targets, this selection captures $\gtrsim 90\%$ of mid-IR band, CO (2–1), and Hα flux, though only a much lower $\sim 50\%$ fraction of the area. This partially reflects that PHANGS–JWST specifically targets the regions of active star formation in our target galaxies. In less molecular-gas-dominated, less actively star-forming regions, lower intensity emission from dust mixed with atomic or CO-dark gas will contribute larger fractions of the flux (Section 2 and see Sandstrom 2023a). In our sample, the lower surface density IC 5332 exemplifies this case, and our selection captures only about half of the total flux and about 20% of the area (see Figure 4).

We also exclude the bright center of NGC 1365, defined by a cut of $I_{\nu}^{F770W} > 30$ MJy sr$^{-1}$ from most of our statistical analysis. This region hosts an AGN, forms stars at a rate of order $\sim 10 M_{\odot} yr^{-1}$, and represents a distinct regime from our other targets in terms of gas surface density, star formation intensity, and dust properties. We focus this paper on normal galaxy disks and leave the contrast between disk and starburst environments for future work, but note that several other papers in this Issue focus specifically on this rich region in NGC 1365 (Liu et al. 2023; Schinnerer et al. 2023; Whitmore et al. 2023). For the correlations, we do plot the data from this higher intensity region but indicate the region excluded from statistical analysis by shading.

When analyzing CO (2–1) as a function of extinction-corrected Hα, we focus on an intensity range defined by scaling our bright emission definitions by the typical $Hα^{corr}$ to mid-IR ratio (Table 4) and then adopting the same limits used for the mid-IR.

### 4. Correlations and Power-law Fits

In Table 4 and Figures 5–10, we report the results of using our database to analyze the relationships between CO (2–1) and mid-IR emission, extinction-corrected Hα and mid-IR emission, and CO (2–1) and extinction-corrected Hα emission. We assess each relationship in the following ways:

1. We measure the Spearman rank correlation between each variable pair.
<table><caption>**Table 3**
Characteristic Noise at 1.7 Expressed in Different Units</caption><thead><tr><th>Band</th><th>Expected σ/σ<sup>7.7</sup></th><th>σ<sub>1.7</sub><br>(MJy sr<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>7.7</sup><br>(MJy sr<sup>-1</sup> at F770W)</th><th>σ<sub>1.7</sub><sup>Hα</sup><br>(erg s<sup>-1</sup> cm<sup>-2</sup> sr<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>CO 2-1</sup><br>(K km s<sup>-1</sup>)</th><th>σ<sub>1.7</sub><sup>gas</sup><br>(M<sub>☉</sub> pc<sup>-2</sup>)</th></tr></thead><tbody><tr><td>F770W</td><td>1.0</td><td>0.025</td><td>0.025</td><td>0.63 × 10<sup>-7</sup></td><td>0.027</td><td>0.18</td></tr><tr><td>F1000W</td><td>1.1 ± 0.1</td><td>0.028</td><td>0.072</td><td>1.7 × 10<sup>-7</sup></td><td>0.076</td><td>0.51</td></tr><tr><td>F1130W</td><td>1.35 ± 0.1</td><td>0.033</td><td>0.025</td><td>0.59 × 10<sup>-7</sup></td><td>0.027</td><td>0.18</td></tr><tr><td>F2100W</td><td>2.5 ± 0.2</td><td>0.063</td><td>0.10</td><td>2.9 × 10<sup>-7</sup></td><td>0.031</td><td>0.21</td></tr><tr><td>CO (2–1)<sup>a</sup></td><td>...</td><td>...</td><td>...</td><td>...</td><td>1.0</td><td>6.7</td></tr><tr><td>Hα<sup>b</sup></td><td>...</td><td>...</td><td>...</td><td>0.035 × 10<sup>-7</sup></td><td>...</td><td>...</td></tr></tbody></table>

**Notes.** Approximate characteristic noises for our data before any inclination correction for our sample at our working resolution of $\theta = 1.7''$. Columns: Expected $\sigma/\sigma^{7.7}$—approximate ratio of pipeline noise estimate at this band to that at F770W at their native resolutions; $\sigma_{1.7}$—noise on the scale of intensity in that band; $\sigma_{1.7}^{7.7}$—noise scaled to units of 7.7 µm via $R^X$ for comparison; $\sigma_{1.7}^{Hα}$—noise in equivalent extinction-corrected Hα units assuming the data set wide median ratio; $\sigma_{1.7}^{CO 2-1}$—noise in CO (2–1) units assuming the data set wide median ratio; and $\sigma_{1.7}^{gas}$—noise in gas surface density units assuming data-set-wide median CO-to-mid-IR ratio and a typical CO-to-H$_2$ conversion factor (Equation (2)).

<sup>a</sup> Median noise across all four “flat” integrated intensity (i.e., moment 0) maps (Section 3.1) used for this analysis. Varies moderately from target to target.

<sup>b</sup> Typical noise in the MUSE NGC 1365 and NGC 7496 Hα maps at $\theta \sim 150$ pc. The extinction correction introduces additional uncertainty but does not affect detection.

difference image and use this, with an appropriate scaling, to estimate the noise in the original images.

In order to compare the sensitivity of different bands to gas column or recent star formation, Table 3 also re-expresses the noise in the bands scaled in several different ways. We first express the relative sensitivity of all bands to “typical” dust emission by scaling by the band ratios in Table 1 onto a common F770W intensity scale, $\sigma_{1.7}^{7.7}$. Then we adopt the median CO-to-mid-IR and Hα-to-mid-IR ratios found in Section 4 to express the mid-IR noises in equivalent $I_{Hα}$, $I_{CO}$, and $\Sigma_{gas}$ units. In Section 6, we will use these to comment on the sensitivity of the JWST images to recent star formation and gas column density.

In addition to the noise levels quoted in Table 3, there is an overall $\lesssim 0.1$ MJy sr$^{-1}$ uncertainty in the level of the background in the MIRI images. Realistically, based on a visual inspection of the images at high stretch, this background level clearly varies across the images at a fraction of this level. To assess this quantitatively, we note that the medium-scale median filter level in the difference images mentioned above imply an rms variation $\sim \pm 0.04-0.07$ MJy sr$^{-1}$ in the background level. Comparing to Table 3 highlights that at our working resolution the uncertainty in the background is often as important as the statistical noise.

### 3.4. Data Selection

We focus our analysis on regions with an inclination-corrected F770W intensity above 0.5 MJy sr$^{-1}$. We target this level because based on the calculations in Section 2.6, we expect that where molecular gas makes up most of the ISM along a line of sight it will likely produce at least this level of emission, even if it is only weakly illuminated. The threshold for emission associated with H II regions is even higher, so we expect this selection to capture most of the area in our targets where either dust mixed with molecular gas or dust heated by H II regions contributes. This level is also high enough that uncertainty in the background level and the statistical noise, which both have a maximum magnitude $\sim \pm 0.1$ MJy sr$^{-1}$, are only secondary concerns for the mid-IR.

Table 4 reports the fractions of flux in each band and area within the PHANGS–JWST footprint associated with this

“bright” emission. In our three more massive targets, this selection captures $\gtrsim 90\%$ of mid-IR band, CO (2–1), and Hα flux, though only a much lower $\sim 50\%$ fraction of the area. This partially reflects that PHANGS–JWST specifically targets the regions of active star formation in our target galaxies. In less molecular-gas-dominated, less actively star-forming regions, lower intensity emission from dust mixed with atomic or CO-dark gas will contribute larger fractions of the flux (Section 2 and see Sandstrom 2023a). In our sample, the lower surface density IC 5332 exemplifies this case, and our selection captures only about half of the total flux and about 20% of the area (see Figure 4).

We also exclude the bright center of NGC 1365, defined by a cut of $I_{\nu}^{F770W} > 30$ MJy sr$^{-1}$ from most of our statistical analysis. This region hosts an AGN, forms stars at a rate of order $\sim 10 M_{\odot} yr^{-1}$, and represents a distinct regime from our other targets in terms of gas surface density, star formation intensity, and dust properties. We focus this paper on normal galaxy disks and leave the contrast between disk and starburst environments for future work, but note that several other papers in this Issue focus specifically on this rich region in NGC 1365 (Liu et al. 2023; Schinnerer et al. 2023; Whitmore et al. 2023). For the correlations, we do plot the data from this higher intensity region but indicate the region excluded from statistical analysis by shading.

When analyzing CO (2–1) as a function of extinction-corrected Hα, we focus on an intensity range defined by scaling our bright emission definitions by the typical $Hα^{corr}$ to mid-IR ratio (Table 4) and then adopting the same limits used for the mid-IR.

### 4. Correlations and Power-law Fits

In Table 4 and Figures 5–10, we report the results of using our database to analyze the relationships between CO (2–1) and mid-IR emission, extinction-corrected Hα and mid-IR emission, and CO (2–1) and extinction-corrected Hα emission. We assess each relationship in the following ways:

1. We measure the Spearman rank correlation between each variable pair.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Mid-IR, CO, and extinction-corrected Hα maps for NGC 1365. As Figure 1 but for NGC 1365 at 160 pc resolution. As in that figure, the arcsinh stretch runs from 0.5 to 30 MJy sr⁻¹, and all bands are expressed in equivalent F770W intensity. As there, the blue shows an F770W contour at 1.5 MJy sr⁻¹, and the red shows an Hα contour at equivalent to 10 MJy sr⁻¹. Note the region blanked due to PSF effects at the galaxy center and also note that the bright region with I<sub>nu</sub> > 30 MJy sr⁻¹ is excluded from most of our statistical analysis.</figcaption></figure>

2. For each variable pair, we calculate the median log<sub>10</sub>y/x and use the median absolute deviation to robustly estimate the scatter in this quantity.

3. We bin the dependent variable y as a function of the independent variable x and fit a power law to the data for each variable pair. Within each bin, we calculate the median and 16%-84% range for the dependent variable.

4. We estimate a power law intended to describe the underlying trend in the data by fitting a line in log-log space (Equation (10)) to the binned data.

When comparing to CO (2–1) or Hα, we treat mid-IR intensity as our independent variable (i.e., the x-axis), and when comparing CO (2–1) to Hα, we treat Hα as the independent variable. We do so because, partially by construction, mid-IR emission is detected at good S/N throughout our region of interest. By contrast, the CO (2–1) emission is both noisier and not detected everywhere. As discussed in Section 3.1, we have constructed CO (2–1) data products that allow us to stack low signal-to-noise data to access the underlying relationship. To leverage this, when binning or conducting our statistical analysis, we make no distinction between detections and nondetections. By stacking in this way, we expect our binned median values, typical ratios, and power-law fits to access the underlying relationship well, but this does mean that the measured scatter and correlation strengths in the CO (2–1) results reflect significant contributions from statistical noise. A full modeling of the noise budget and scatter lies beyond the scope of this first results paper but will be a goal of analyzing the full PHANGS–JWST data set. Hα emission is detected

everywhere in our maps, and we therefore treat Hα as the independent variable when comparing to CO (2–1). When comparing Hα to mid-IR emission we treat Hα as the dependent (y-axis) variable for symmetry with the CO versus mid-IR comparison.

With the mid-IR as the independent variable, the power laws that we fit have the form

$$ \log_{10} I_{\text{CO}} = m_{\text{CO-MIR}} \log_{10} I_{\nu}^{X} + b_{\text{CO-MIR}} \\ \log_{10} I_{\text{H}\alpha} = m_{\text{H}\alpha-\text{MIR}} \log_{10} I_{\nu}^{X} + b_{\text{H}\alpha-\text{MIR}}, \quad (10) $$

where I<sub>CO</sub> is CO (2–1) intensity in units of K km s⁻¹, I<sub>Hα</sub> is extinction-corrected Hα in units of erg s⁻¹ cm⁻² sr⁻¹ and I<sub>ν</sub> is mid-IR intensity at band X, e.g., F770W or F2100W. We use an analogous form to relate CO (2–1) to extinction-corrected Hα:

$$ \log_{10} I_{\text{CO}} = m_{\text{CO-H}\alpha} \log_{10}(I_{\text{H}\alpha}) + 5.0 + b_{\text{CO-H}\alpha}, \quad (11) $$

where the main difference is the offset of 5.0, which recenters the fit near the middle of the distribution. This minimizes covariance in the quoted slope and intercept but will not otherwise affect the fit (e.g., see Barlow 1989; Press et al. 2002). In units of MJy sr⁻¹, the mid-IR distribution is already naturally centered close to unity so we do not carry out any similar shift for Equation (10). We summarize the full set of fit slopes in Figure 10.

For the figures, we do construct and plot bins across the full intensity range and show all data points. However, we restrict our calculation of correlation coefficients, ratios, and power-
<figure><img src="image_5.png" /><figcaption>Figure 2. Mid-IR, CO, and extinction-corrected Hα maps for NGC 1365. As Figure 1 but for NGC 1365 at 160 pc resolution. As in that figure, the arcsinh stretch runs from 0.5 to 30 MJy sr⁻¹, and all bands are expressed in equivalent F770W intensity. As there, the blue shows an F770W contour at 1.5 MJy sr⁻¹, and the red shows an Hα contour at equivalent to 10 MJy sr⁻¹. Note the region blanked due to PSF effects at the galaxy center and also note that the bright region with I<sub>nu</sub> > 30 MJy sr⁻¹ is excluded from most of our statistical analysis.</figcaption></figure>

2. For each variable pair, we calculate the median log<sub>10</sub>y/x and use the median absolute deviation to robustly estimate the scatter in this quantity.

3. We bin the dependent variable y as a function of the independent variable x and fit a power law to the data for each variable pair. Within each bin, we calculate the median and 16%-84% range for the dependent variable.

4. We estimate a power law intended to describe the underlying trend in the data by fitting a line in log-log space (Equation (10)) to the binned data.

When comparing to CO (2–1) or Hα, we treat mid-IR intensity as our independent variable (i.e., the x-axis), and when comparing CO (2–1) to Hα, we treat Hα as the independent variable. We do so because, partially by construction, mid-IR emission is detected at good S/N throughout our region of interest. By contrast, the CO (2–1) emission is both noisier and not detected everywhere. As discussed in Section 3.1, we have constructed CO (2–1) data products that allow us to stack low signal-to-noise data to access the underlying relationship. To leverage this, when binning or conducting our statistical analysis, we make no distinction between detections and nondetections. By stacking in this way, we expect our binned median values, typical ratios, and power-law fits to access the underlying relationship well, but this does mean that the measured scatter and correlation strengths in the CO (2–1) results reflect significant contributions from statistical noise. A full modeling of the noise budget and scatter lies beyond the scope of this first results paper but will be a goal of analyzing the full PHANGS–JWST data set. Hα emission is detected

everywhere in our maps, and we therefore treat Hα as the independent variable when comparing to CO (2–1). When comparing Hα to mid-IR emission we treat Hα as the dependent (y-axis) variable for symmetry with the CO versus mid-IR comparison.

With the mid-IR as the independent variable, the power laws that we fit have the form

$$ \begin{aligned} \log_{10} I_{\text{CO}} &= m_{\text{CO-MIR}} \log_{10} I_{\nu}^{X} + b_{\text{CO-MIR}} \\ \log_{10} I_{\text{H}\alpha} &= m_{\text{H}\alpha-\text{MIR}} \log_{10} I_{\nu}^{X} + b_{\text{H}\alpha-\text{MIR}}, \end{aligned} \quad (10) $$

where I<sub>CO</sub> is CO (2–1) intensity in units of K km s⁻¹, I<sub>Hα</sub> is extinction-corrected Hα in units of erg s⁻¹ cm⁻² sr⁻¹ and I<sub>ν</sub> is mid-IR intensity at band X, e.g., F770W or F2100W. We use an analogous form to relate CO (2–1) to extinction-corrected Hα:

$$ \log_{10} I_{\text{CO}} = m_{\text{CO-H}\alpha} \log_{10}(I_{\text{H}\alpha}) + 5.0 + b_{\text{CO-H}\alpha}, \quad (11) $$

where the main difference is the offset of 5.0, which recenters the fit near the middle of the distribution. This minimizes covariance in the quoted slope and intercept but will not otherwise affect the fit (e.g., see Barlow 1989; Press et al. 2002). In units of MJy sr⁻¹, the mid-IR distribution is already naturally centered close to unity so we do not carry out any similar shift for Equation (10). We summarize the full set of fit slopes in Figure 10.

For the figures, we do construct and plot bins across the full intensity range and show all data points. However, we restrict our calculation of correlation coefficients, ratios, and power-
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Mid-IR, CO, and extinction-corrected Hα maps for NGC 7496. As Figure 1 but for NGC 7496 at 150 pc resolution. As in that figure, the arcsinh stretch runs from 0.5 to 30 MJy sr⁻¹, and all bands are expressed in equivalent F770W intensity. As there, the blue shows an F770W contour at 1.5 MJy sr⁻¹, and the red shows an Hα contour at equivalent to 10 MJy sr⁻¹. Note the region blanked due to PSF effects at the galaxy center.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Mid-IR, CO, and extinction-corrected Hα maps for NGC 7496. As Figure 1 but for NGC 7496 at 150 pc resolution. As in that figure, the arcsinh stretch runs from 0.5 to 30 MJy sr⁻¹, and all bands are expressed in equivalent F770W intensity. As there, the blue shows an F770W contour at 1.5 MJy sr⁻¹, and the red shows an Hα contour at equivalent to 10 MJy sr⁻¹. Note the region blanked due to PSF effects at the galaxy center.</figcaption></figure>
<table><caption>**Table 4**
Correlation, Ratio, and Fitting Results</caption><thead><tr><th>Quantity</th><th>Variable(s)</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 colspan="7" style="text-align: center; font-weight: bold;">Fraction Associated with “Bright” Emission<br>(Entries Report Fraction of Flux at the Indicated Band or Area Selected for Our Analysis)</td></tr><tr><td>Flux</td><td>F770W</td><td>0.94</td><td>0.44</td><td>0.97</td><td>0.95<sup>a</sup></td><td>0.90</td></tr><tr><td>Flux</td><td>F1000W</td><td>0.93</td><td>0.46</td><td>0.97</td><td>0.94<sup>a</sup></td><td>0.90</td></tr><tr><td>Flux</td><td>F1130W</td><td>0.93</td><td>0.46</td><td>0.97</td><td>0.94<sup>a</sup></td><td>0.91</td></tr><tr><td>Flux</td><td>F2100W</td><td>0.96</td><td>0.49</td><td>0.98</td><td>0.98<sup>a</sup></td><td>0.95</td></tr><tr><td>Flux</td><td>CO (2–1)</td><td>0.97</td><td>0.68</td><td>0.97</td><td>0.98<sup>a</sup></td><td>0.96</td></tr><tr><td>Flux</td><td>Hα</td><td>0.96</td><td>0.55</td><td>0.98</td><td>0.99<sup>a</sup></td><td>0.96</td></tr><tr><td>Area</td><td>...</td><td>0.60</td><td>0.17</td><td>0.87</td><td>0.60<sup>a</sup></td><td>0.54</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Rank Correlations<br>(Entries Report Rank Correlation Coefficient Relating Indicated Variable Pair)</td></tr><tr><td>Rank correlation</td><td>CO (2–1) versus Hα</td><td>0.47</td><td>0.12</td><td>0.47</td><td>0.41</td><td>0.57</td></tr><tr><td>Rank correlation</td><td>CO (2–1) versus F770W</td><td>0.63</td><td>0.20</td><td>0.70</td><td>0.52</td><td>0.72</td></tr><tr><td>Rank correlation</td><td>CO (2–1) versus F1000W</td><td>0.62</td><td>0.19</td><td>0.70</td><td>0.52</td><td>0.71</td></tr><tr><td>Rank correlation</td><td>CO (2–1) versus F1130W</td><td>0.63</td><td>0.21</td><td>0.71</td><td>0.53</td><td>0.72</td></tr><tr><td>Rank correlation</td><td>CO (2–1) versus F2100W</td><td>0.61</td><td>0.17</td><td>0.71</td><td>0.50</td><td>0.66</td></tr><tr><td>Rank correlation</td><td>Hα versus F770W</td><td>0.78</td><td>0.63</td><td>0.74</td><td>0.80</td><td>0.85</td></tr><tr><td>Rank correlation</td><td>Hα versus F1000W</td><td>0.74</td><td>0.65</td><td>0.67</td><td>0.75</td><td>0.83</td></tr><tr><td>Rank correlation</td><td>Hα versus F1130W</td><td>0.74</td><td>0.54</td><td>0.71</td><td>0.76</td><td>0.81</td></tr><tr><td>Rank correlation</td><td>Hα versus F2100W</td><td>0.75</td><td>0.63</td><td>0.72</td><td>0.73</td><td>0.78</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Median Ratios for Bright Emission<br>(Entries Report Median log<sub>10</sub>y/x and Scatter for Indicated Ratio)</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2–1)/Hα</td><td>5.63 ± 0.59</td><td>5.42 ± 0.66</td><td>5.63 ± 0.55</td><td>5.76 ± 0.64</td><td>5.46 ± 0.60</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2–1)/F770W</td><td>0.04 ± 0.33</td><td>0.10 ± 0.36</td><td>0.03 ± 0.29</td><td>0.14 ± 0.40</td><td>-0.11 ± 0.30</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2–1)/F1000W</td><td>0.44 ± 0.32</td><td>0.51 ± 0.37</td><td>0.44 ± 0.28</td><td>0.53 ± 0.38</td><td>0.28 ± 0.29</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2–1)/F1130W</td><td>-0.10 ± 0.32</td><td>-0.03 ± 0.36</td><td>-0.11 ± 0.28</td><td>-0.03 ± 0.39</td><td>-0.25 ± 0.29</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2–1)/F2100W</td><td>0.30 ± 0.34</td><td>0.31 ± 0.41</td><td>0.32 ± 0.29</td><td>0.37 ± 0.43</td><td>0.09 ± 0.33</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F770W</td><td>-5.60 ± 0.43</td><td>-5.39 ± 0.48</td><td>-5.62 ± 0.42</td><td>-5.62 ± 0.41</td><td>-5.57 ± 0.47</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F1000W</td><td>-5.21 ± 0.47</td><td>-4.97 ± 0.52</td><td>-5.22 ± 0.47</td><td>-5.23 ± 0.45</td><td>-5.20 ± 0.51</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F1130W</td><td>-5.76 ± 0.45</td><td>-5.51 ± 0.50</td><td>-5.77 ± 0.44</td><td>-5.79 ± 0.44</td><td>-5.73 ± 0.51</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F2100W</td><td>-5.34 ± 0.44</td><td>-5.13 ± 0.46</td><td>-5.33 ± 0.42</td><td>-5.38 ± 0.44</td><td>-5.36 ± 0.50</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Power-law Fits to Binned Data<br>(Entries Report Slope *m* and Intercept *b* in Equations (10) and (11))</td></tr><tr><td>m, b</td><td>CO (2–1) versus Hα<sup>b</sup></td><td>0.47, 0.30</td><td>0.56, -0.29</td><td>0.39, 0.40</td><td>0.50, 0.29</td><td>0.51, 0.12</td></tr><tr><td>m, b</td><td>CO (2–1) versus F770W</td><td>1.10, -0.07</td><td>0.80, -0.08</td><td>0.84, 0.05</td><td>1.25, -0.10</td><td>1.08, -0.17</td></tr><tr><td>m, b</td><td>CO (2–1) versus F1000W</td><td>1.22, 0.37</td><td>0.71, 0.19</td><td>0.92, 0.39</td><td>1.33, 0.39</td><td>1.16, 0.27</td></tr><tr><td>m, b</td><td>CO (2–1) versus F1130W</td><td>1.21, -0.28</td><td>0.97, -0.21</td><td>0.93, -0.11</td><td>1.33, -0.34</td><td>1.16, -0.36</td></tr><tr><td>m, b</td><td>CO (2–1) versus F2100W</td><td>0.74, 0.24</td><td>0.22, -0.08</td><td>0.61, 0.32</td><td>0.95, 0.20</td><td>0.79, 0.05</td></tr><tr><td>m, b</td><td>Hα versus F770W</td><td>1.51, -5.72</td><td>1.98, -5.39</td><td>1.67, -5.80</td><td>1.43, -5.68</td><td>1.53, -5.68</td></tr><tr><td>m, b</td><td>Hα versus F1000W</td><td>1.51, -5.14</td><td>1.96, -4.64</td><td>1.72, -5.13</td><td>1.44, -5.19</td><td>1.66, -5.07</td></tr><tr><td>m, b</td><td>Hα versus F1130W</td><td>1.55, -5.97</td><td>2.20, -5.70</td><td>1.71, -6.03</td><td>1.47, -5.98</td><td>1.71, -6.00</td></tr><tr><td>m, b</td><td>Hα versus F2100W</td><td>1.29, -5.35</td><td>1.66, -5.04</td><td>1.35, -5.34</td><td>1.24, -5.42</td><td>1.29, -5.34</td></tr></tbody></table>

**Notes.** See Section 5. Hα refers to extinction-corrected Hα in units of erg s⁻¹ cm⁻² sr⁻¹. CO (2–1) intensity has units of K km s⁻¹. All mid-IR intensities have units of MJy sr⁻¹.

<sup>a</sup> Fraction of flux and area above the lower threshold. In NGC 1365, we also exclude bright emission from the center of the galaxy from our analysis.

<sup>b</sup> Note the definition for the intercept location for CO (2–1) versus Hα in Equation (11).

law fits to the range of “bright” emission defined in Section 3.4, motivated in Section 2.6, and indicated by the white background in Figures 5–9. Also note that Figures 6, 8, and 9 illustrate the motivation for excluding the highest intensity emission: In our current sample, only the starburst ring in

NGC 1365 contributes emission, and this region often exhibits a distinct behavior from the rest of the data set.

We repeat each analysis for each band and for each galaxy separately as well as all galaxies together. For the most part, individual galaxies and the combined data exhibit consistent
<table><caption>**Table 4**
Correlation, Ratio, and Fitting Results</caption><thead><tr><th>Quantity</th><th>Variable(s)</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 colspan="7" style="text-align: center; font-weight: bold;">Fraction Associated with "Bright" Emission<br>(Entries Report Fraction of Flux at the Indicated Band or Area Selected for Our Analysis)</td></tr><tr><td>Flux</td><td>F770W</td><td>0.94</td><td>0.44</td><td>0.97</td><td>0.95<sup>a</sup></td><td>0.90</td></tr><tr><td>Flux</td><td>F1000W</td><td>0.93</td><td>0.46</td><td>0.97</td><td>0.94<sup>a</sup></td><td>0.90</td></tr><tr><td>Flux</td><td>F1130W</td><td>0.93</td><td>0.46</td><td>0.97</td><td>0.94<sup>a</sup></td><td>0.91</td></tr><tr><td>Flux</td><td>F2100W</td><td>0.96</td><td>0.49</td><td>0.98</td><td>0.98<sup>a</sup></td><td>0.95</td></tr><tr><td>Flux</td><td>CO (2-1)</td><td>0.97</td><td>0.68</td><td>0.97</td><td>0.98<sup>a</sup></td><td>0.96</td></tr><tr><td>Flux</td><td>Hα</td><td>0.96</td><td>0.55</td><td>0.98</td><td>0.99<sup>a</sup></td><td>0.96</td></tr><tr><td>Area</td><td>...</td><td>0.60</td><td>0.17</td><td>0.87</td><td>0.60<sup>a</sup></td><td>0.54</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Rank Correlations<br>(Entries Report Rank Correlation Coefficient Relating Indicated Variable Pair)</td></tr><tr><td>Rank correlation</td><td>CO (2-1) versus Hα</td><td>0.47</td><td>0.12</td><td>0.47</td><td>0.41</td><td>0.57</td></tr><tr><td>Rank correlation</td><td>CO (2-1) versus F770W</td><td>0.63</td><td>0.20</td><td>0.70</td><td>0.52</td><td>0.72</td></tr><tr><td>Rank correlation</td><td>CO (2-1) versus F1000W</td><td>0.62</td><td>0.19</td><td>0.70</td><td>0.52</td><td>0.71</td></tr><tr><td>Rank correlation</td><td>CO (2-1) versus F1130W</td><td>0.63</td><td>0.21</td><td>0.71</td><td>0.53</td><td>0.72</td></tr><tr><td>Rank correlation</td><td>CO (2-1) versus F2100W</td><td>0.61</td><td>0.17</td><td>0.71</td><td>0.50</td><td>0.66</td></tr><tr><td>Rank correlation</td><td>Hα versus F770W</td><td>0.78</td><td>0.63</td><td>0.74</td><td>0.80</td><td>0.85</td></tr><tr><td>Rank correlation</td><td>Hα versus F1000W</td><td>0.74</td><td>0.65</td><td>0.67</td><td>0.75</td><td>0.83</td></tr><tr><td>Rank correlation</td><td>Hα versus F1130W</td><td>0.74</td><td>0.54</td><td>0.71</td><td>0.76</td><td>0.81</td></tr><tr><td>Rank correlation</td><td>Hα versus F2100W</td><td>0.75</td><td>0.63</td><td>0.72</td><td>0.73</td><td>0.78</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Median Ratios for Bright Emission<br>(Entries Report Median log<sub>10</sub>y/x and Scatter for Indicated Ratio)</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2-1)/Hα</td><td>5.63 ± 0.59</td><td>5.42 ± 0.66</td><td>5.63 ± 0.55</td><td>5.76 ± 0.64</td><td>5.46 ± 0.60</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2-1)/F770W</td><td>0.04 ± 0.33</td><td>0.10 ± 0.36</td><td>0.03 ± 0.29</td><td>0.14 ± 0.40</td><td>-0.11 ± 0.30</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2-1)/F1000W</td><td>0.44 ± 0.32</td><td>0.51 ± 0.37</td><td>0.44 ± 0.28</td><td>0.53 ± 0.38</td><td>0.28 ± 0.29</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2-1)/F1130W</td><td>-0.10 ± 0.32</td><td>-0.03 ± 0.36</td><td>-0.11 ± 0.28</td><td>-0.03 ± 0.39</td><td>-0.25 ± 0.29</td></tr><tr><td>log<sub>10</sub>y/x</td><td>CO (2-1)/F2100W</td><td>0.30 ± 0.34</td><td>0.31 ± 0.41</td><td>0.32 ± 0.29</td><td>0.37 ± 0.43</td><td>0.09 ± 0.33</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F770W</td><td>-5.60 ± 0.43</td><td>-5.39 ± 0.48</td><td>-5.62 ± 0.42</td><td>-5.62 ± 0.41</td><td>-5.57 ± 0.47</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F1000W</td><td>-5.21 ± 0.47</td><td>-4.97 ± 0.52</td><td>-5.22 ± 0.47</td><td>-5.23 ± 0.45</td><td>-5.20 ± 0.51</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F1130W</td><td>-5.76 ± 0.45</td><td>-5.51 ± 0.50</td><td>-5.77 ± 0.44</td><td>-5.79 ± 0.44</td><td>-5.73 ± 0.51</td></tr><tr><td>log<sub>10</sub>y/x</td><td>Hα/F2100W</td><td>-5.34 ± 0.44</td><td>-5.13 ± 0.46</td><td>-5.33 ± 0.42</td><td>-5.38 ± 0.44</td><td>-5.36 ± 0.50</td></tr><tr><td colspan="7" style="text-align: center; font-weight: bold;">Power-law Fits to Binned Data<br>(Entries Report Slope *m* and Intercept *b* in Equations (10) and (11))</td></tr><tr><td>m, b</td><td>CO (2-1) versus Hα<sup>b</sup></td><td>0.47, 0.30</td><td>0.56, -0.29</td><td>0.39, 0.40</td><td>0.50, 0.29</td><td>0.51, 0.12</td></tr><tr><td>m, b</td><td>CO (2-1) versus F770W</td><td>1.10, -0.07</td><td>0.80, -0.08</td><td>0.84, 0.05</td><td>1.25, -0.10</td><td>1.08, -0.17</td></tr><tr><td>m, b</td><td>CO (2-1) versus F1000W</td><td>1.22, 0.37</td><td>0.71, 0.19</td><td>0.92, 0.39</td><td>1.33, 0.39</td><td>1.16, 0.27</td></tr><tr><td>m, b</td><td>CO (2-1) versus F1130W</td><td>1.21, -0.28</td><td>0.97, -0.21</td><td>0.93, -0.11</td><td>1.33, -0.34</td><td>1.16, -0.36</td></tr><tr><td>m, b</td><td>CO (2-1) versus F2100W</td><td>0.74, 0.24</td><td>0.22, -0.08</td><td>0.61, 0.32</td><td>0.95, 0.20</td><td>0.79, 0.05</td></tr><tr><td>m, b</td><td>Hα versus F770W</td><td>1.51, -5.72</td><td>1.98, -5.39</td><td>1.67, -5.80</td><td>1.43, -5.68</td><td>1.53, -5.68</td></tr><tr><td>m, b</td><td>Hα versus F1000W</td><td>1.51, -5.14</td><td>1.96, -4.64</td><td>1.72, -5.13</td><td>1.44, -5.19</td><td>1.66, -5.07</td></tr><tr><td>m, b</td><td>Hα versus F1130W</td><td>1.55, -5.97</td><td>2.20, -5.70</td><td>1.71, -6.03</td><td>1.47, -5.98</td><td>1.71, -6.00</td></tr><tr><td>m, b</td><td>Hα versus F2100W</td><td>1.29, -5.35</td><td>1.66, -5.04</td><td>1.35, -5.34</td><td>1.24, -5.42</td><td>1.29, -5.34</td></tr></tbody></table>

Notes. See Section 5. Hα refers to extinction-corrected Hα in units of erg s⁻¹ cm⁻² sr⁻¹. CO (2–1) intensity has units of K km s⁻¹. All mid-IR intensities have units of MJy sr⁻¹.

<sup>a</sup> Fraction of flux and area above the lower threshold. In NGC 1365, we also exclude bright emission from the center of the galaxy from our analysis.

<sup>b</sup> Note the definition for the intercept location for CO (2–1) versus Hα in Equation (11).

law fits to the range of “bright” emission defined in Section 3.4, motivated in Section 2.6, and indicated by the white background in Figures 5–9. Also note that Figures 6, 8, and 9 illustrate the motivation for excluding the highest intensity emission: In our current sample, only the starburst ring in

NGC 1365 contributes emission, and this region often exhibits a distinct behavior from the rest of the data set.

We repeat each analysis for each band and for each galaxy separately as well as all galaxies together. For the most part, individual galaxies and the combined data exhibit consistent
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Mid-IR, CO, and extinction-corrected Hα maps for IC 5332. As Figure 1 but for IC 5332 at 70 pc resolution. Because the galaxy has a lower surface brightness than the other targets, the arcsinh stretch here runs from 0.25 to 5 MJy sr⁻¹. All bands are expressed in equivalent F770W intensity, the blue shows an F770W contour now at a lower 0.5 MJy sr⁻¹ and the red shows an Hα contour still at 10 MJy sr⁻¹.</figcaption></figure>

slopes for a given variable pair, within $\Delta m \pm 0.2$. Among galaxies, IC 5332 shows the most distinct behavior, likely due to its lower brightness, mass, and metallicity. We discuss this more in Section 6.3. Among the mid-IR bands, F770W, F1000W, and F1130W show very similar results. F2100W exhibits somewhat distinct behavior from the other three JWST bands, and we discuss these differences more in Section 4.4. First we focus on the overall results of the correlation analysis.

4.1. CO (2–1) Correlates Well with Mid-IR Emission

In our analysis, all of the mid-IR bands correlate well with CO (2–1) at 70–160 pc resolution. Given the conventional view of the mid-IR as a star formation tracer, we emphasize the impressive agreement between the CO and mid-IR maps at high physical resolution as one of our key results. Despite the comparatively high noise level in the CO, CO and mid-IR typically exhibit correlation coefficients of $\rho \approx 0.62$ and show a clear correlation across a wide range of mid-IR intensities.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Mid-IR, CO, and extinction-corrected Hα maps for IC 5332. As Figure 1 but for IC 5332 at 70 pc resolution. Because the galaxy has a lower surface brightness than the other targets, the arcsinh stretch here runs from 0.25 to 5 MJy sr⁻¹. All bands are expressed in equivalent F770W intensity, the blue shows an F770W contour now at a lower 0.5 MJy sr⁻¹ and the red shows an Hα contour still at 10 MJy sr⁻¹.</figcaption></figure>

slopes for a given variable pair, within $\Delta m \pm 0.2$. Among galaxies, IC 5332 shows the most distinct behavior, likely due to its lower brightness, mass, and metallicity. We discuss this more in Section 6.3. Among the mid-IR bands, F770W, F1000W, and F1130W show very similar results. F2100W exhibits somewhat distinct behavior from the other three JWST bands, and we discuss these differences more in Section 4.4. First we focus on the overall results of the correlation analysis.

### 4.1. CO (2–1) Correlates Well with Mid-IR Emission

In our analysis, all of the mid-IR bands correlate well with CO (2–1) at 70–160 pc resolution. Given the conventional view of the mid-IR as a star formation tracer, we emphasize the impressive agreement between the CO and mid-IR maps at high physical resolution as one of our key results. Despite the comparatively high noise level in the CO, CO and mid-IR typically exhibit correlation coefficients of $\rho \approx 0.62$ and show a clear correlation across a wide range of mid-IR intensities.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** CO (2–1) intensity as a function of mid-IR intensity at 1.7"/7 resolution. Individual points show individual lines of sight from our matched-resolution database with all four target galaxies plotted together. The points are colored by the mean extinction-corrected Hα intensity averaging all data within ±0.1 dex along each axis. Black and white points and error bars show the median and 16%–84% range in $I_{CO}$ after binning the data by mid-IR intensity. The red line shows the best-fitting power-law relation fit to the bins (Table 4) over the white region. Additional dotted lines indicate fixed $I_{CO}$ to mid-IR ratios. The white region shows our definition of “bright” emission (Section 3.4) while the gray-shaded regions are excluded from most statistical analyses either because we expect significant contamination by emission associated with non-CO-emitting gas (left region) or because only the starburst ring of NGC 1365 contributes data (right region). Each panel gives the slope (m) and intercept (b), and Table 4 gives the full numerical results. Figure 6 shows individual galaxy results.</figcaption></figure>

CO (2–1) as a function of mid-IR emission shows an approximately linear slope, i.e., near $m \sim 1$, with slope $m_{CO-MIR}$ in the range $m_{CO-MIR} \sim 0.8–1.3$ for most cases, and all four galaxies are in fairly good agreement with one another (Figures 5, 6, and 10). Treating all galaxies together, we find a mildly superlinear slope, $m_{CO-MIR} \sim 1.1–1.2$ for F770W, F1000W, and F1130W and a mildly sublinear slope for F2100W. In the simplest terms, this slope near $m_{CO-MIR} \sim 1$ implies that these bands not only correlate with CO, but that the CO and mid-IR actually track one another with a nearly fixed constant of proportionality.

Visually, this agrees with the impression of excellent agreement when one “blinks” the CO and mid-IR maps (e.g., Figures 1 through 4). The structure of the low-intensity, extended emission in the mid-IR map resembles that seen in the CO map. Observationally, this reflects that the JWST mid-IR observations have reached the resolution and sensitivity where they capture the glow of dust in neutral ISM heated by the ISRF. Physically, the nearly linear slope could reflect that variations in the dust-to-gas ratio, radiation field, and PAH abundance are weak compared to overall column density
<figure><img src="image_8.png" /><figcaption>**Figure 5.** CO (2–1) intensity as a function of mid-IR intensity at 1.7" resolution. Individual points show individual lines of sight from our matched-resolution database with all four target galaxies plotted together. The points are colored by the mean extinction-corrected Hα intensity averaging all data within ±0.1 dex along each axis. Black and white points and error bars show the median and 16%–84% range in $I_{CO}$ after binning the data by mid-IR intensity. The red line shows the best-fitting power-law relation fit to the bins (Table 4) over the white region. Additional dotted lines indicate fixed $I_{CO}$ to mid-IR ratios. The white region shows our definition of “bright” emission (Section 3.4) while the gray-shaded regions are excluded from most statistical analyses either because we expect significant contamination by emission associated with non-CO-emitting gas (left region) or because only the starburst ring of NGC 1365 contributes data (right region). Each panel gives the slope (m) and intercept (b), and Table 4 gives the full numerical results. Figure 6 shows individual galaxy results.</figcaption></figure>

CO (2–1) as a function of mid-IR emission shows an approximately linear slope, i.e., near $m \sim 1$, with slope $m_{CO-MIR}$ in the range $m_{CO-MIR} \sim 0.8–1.3$ for most cases, and all four galaxies are in fairly good agreement with one another (Figures 5, 6, and 10). Treating all galaxies together, we find a mildly superlinear slope, $m_{CO-MIR} \sim 1.1–1.2$ for F770W, F1000W, and F1130W and a mildly sublinear slope for F2100W. In the simplest terms, this slope near $m_{CO-MIR} \sim 1$ implies that these bands not only correlate with CO, but that the CO and mid-IR actually track one another with a nearly fixed constant of proportionality.

Visually, this agrees with the impression of excellent agreement when one “blinks” the CO and mid-IR maps (e.g., Figures 1 through 4). The structure of the low-intensity, extended emission in the mid-IR map resembles that seen in the CO map. Observationally, this reflects that the JWST mid-IR observations have reached the resolution and sensitivity where they capture the glow of dust in neutral ISM heated by the ISRF. Physically, the nearly linear slope could reflect that variations in the dust-to-gas ratio, radiation field, and PAH abundance are weak compared to overall column density
<figure><img src="image_8.png" /><figcaption>**Figure 6.** CO (2–1) intensity as a function of mid-IR intensity at 1.7 resolution, separated by galaxy. As Figure 5 but now showing the binned relation for each individual galaxy (colored points) along with a power-law fit to the binned data for each galaxy (colored lines). The dark gray-shaded curve indicates the 16%–84% range for the full data set, and the gray line indicates the same best-fitting power law for all data as shown in Figure 5. Each panel gives the slope (m) of the relationship, and Table 4 gives the full numerical fit values.</figcaption></figure>

variations, so that over a large part of the region mapped by PHANGS–JWST, the bright mid-IR simply traces the molecular gas. The slightly superlinear slope in the relation for F770W, F1000W, and F1130W might indicate that either the dust-to-gas ratio, the PAH abundance, or the radiation field have a modest correlation with column density (all of these are reasonable to expect; e.g., Jenkins 2009; Sandstrom et al. 2010; Roman-Duval et al. 2017; Chastenet et al. 2019). The slightly sublinear slope for F2100W may reflect that bright star-forming regions influence the observed CO versus mid-IR correlation more heavily for this band. We attempt to disentangle these regions from the cold ISM in Section 5.

Mid-IR emission should depend on the ISRF. We do note that CO (2–1) brightness may also track the ISRF, *U*, because the ISRF should affect molecular gas heating and the CO (2–1) brightness will reflect the underlying excitation and temperature of the molecular gas (e.g., Bolatto et al. 2013; Gong et al. 2020; Liu et al. 2021). This could enhance the

correlation that we observe, and these temperature and excitation effects can render the interpretation of both CO and mid-IR as a simple gas tracer more challenging.

## 4.2. Extinction-corrected $H\alpha$ also Correlates Well, Albeit Nonlinearly, with Mid-IR Emission

In our analysis, extinction-corrected $H\alpha$ and mid-IR show an even stronger correlation than CO and mid-IR emission, with $\rho \approx 0.75$. Though the difference in $\rho$ can probably be ascribed to the much better S/N in the $H\alpha$ compared to the CO (Section 3.3), the fact remains that $H\alpha$ and mid-IR correlate very well in our data. Given that both mid-IR emission and $H\alpha$ are widely viewed as tracers of massive, recent star formation, this correlation is expected, and the power-law fits in Table 4 can be applied to predict the extinction-corrected $H\alpha$ from the mid-IR intensity with reasonable accuracy.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** CO (2–1) intensity as a function of mid-IR intensity at 1.7 resolution, separated by galaxy. As Figure 5 but now showing the binned relation for each individual galaxy (colored points) along with a power-law fit to the binned data for each galaxy (colored lines). The dark gray-shaded curve indicates the 16%–84% range for the full data set, and the gray line indicates the same best-fitting power law for all data as shown in Figure 5. Each panel gives the slope (m) of the relationship, and Table 4 gives the full numerical fit values.</figcaption></figure>

variations, so that over a large part of the region mapped by PHANGS–JWST, the bright mid-IR simply traces the molecular gas. The slightly superlinear slope in the relation for F770W, F1000W, and F1130W might indicate that either the dust-to-gas ratio, the PAH abundance, or the radiation field have a modest correlation with column density (all of these are reasonable to expect; e.g., Jenkins 2009; Sandstrom et al. 2010; Roman-Duval et al. 2017; Chastenet et al. 2019). The slightly sublinear slope for F2100W may reflect that bright star-forming regions influence the observed CO versus mid-IR correlation more heavily for this band. We attempt to disentangle these regions from the cold ISM in Section 5.

Mid-IR emission should depend on the ISRF. We do note that CO (2–1) brightness may also track the ISRF, $U$, because the ISRF should affect molecular gas heating and the CO (2–1) brightness will reflect the underlying excitation and temperature of the molecular gas (e.g., Bolatto et al. 2013; Gong et al. 2020; Liu et al. 2021). This could enhance the

correlation that we observe, and these temperature and excitation effects can render the interpretation of both CO and mid-IR as a simple gas tracer more challenging.

## 4.2. Extinction-corrected $H\alpha$ also Correlates Well, Albeit Nonlinearly, with Mid-IR Emission

In our analysis, extinction-corrected $H\alpha$ and mid-IR show an even stronger correlation than CO and mid-IR emission, with $\rho \approx 0.75$. Though the difference in $\rho$ can probably be ascribed to the much better S/N in the $H\alpha$ compared to the CO (Section 3.3), the fact remains that $H\alpha$ and mid-IR correlate very well in our data. Given that both mid-IR emission and $H\alpha$ are widely viewed as tracers of massive, recent star formation, this correlation is expected, and the power-law fits in Table 4 can be applied to predict the extinction-corrected $H\alpha$ from the mid-IR intensity with reasonable accuracy.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Extinction-corrected Hα intensity as a function of mid-IR intensity at 1.7" resolution. As Figure 5 but now showing the relationship between extinction-corrected Hα intensity and mid-IR intensity with data points colored as in Figure 5 but now based on CO (2–1) intensity. The gray regions show the range of intensities excluded from statistical analysis and the red line shows the best-fitting power law describing the binned data for all galaxies. Each panel gives the slope (m) and intercept (b), and Table 4 gives numerical results. Figure 8 shows results for individual galaxies.</figcaption></figure>

Figure 10 and Table 4 show that Hα as a function of mid-IR emission exhibits a consistently steeper-than-unity slope. For F770W, F1000W, and F1130 we find $m_{Hα-MIR} \sim 1.4-1.7$ with $m_{Hα-MIR} \sim 1.5$ on average. F2100W also shows a superlinear slope, but a shallower one, $m_{Hα-MIR} \sim 1.3$ on average (see Section 4.4 for a discussion of the differences).

These slopes with $m_{Hα-MIR} > 1$ have the sense that extinction-corrected Hα becomes brighter relative to mid-IR at high intensities and such a trend appears consistent between all four systems (Figure 8). Visually, this agrees with the impression from Figures 1–4 that there is more extended and low-intensity mid-IR emission compared to Hα emission. That is, the peaks of the Hα and mid-IR align well, but the mid-IR

shows a much more significant “diffuse” or extended component. The existence of such a component is in good agreement with previous infrared observations of very nearby galaxies (e.g., 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 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.
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Extinction-corrected Hα intensity as a function of mid-IR intensity at 1.7" resolution. As Figure 5 but now showing the relationship between extinction-corrected Hα intensity and mid-IR intensity with data points colored as in Figure 5 but now based on CO (2–1) intensity. The gray regions show the range of intensities excluded from statistical analysis and the red line shows the best-fitting power law describing the binned data for all galaxies. Each panel gives the slope (m) and intercept (b), and Table 4 gives numerical results. Figure 8 shows results for individual galaxies.</figcaption></figure>

Figure 10 and Table 4 show that Hα as a function of mid-IR emission exhibits a consistently steeper-than-unity slope. For F770W, F1000W, and F1130 we find $m_{Hα-MIR} \sim 1.4-1.7$ with $m_{Hα-MIR} \sim 1.5$ on average. F2100W also shows a superlinear slope, but a shallower one, $m_{Hα-MIR} \sim 1.3$ on average (see Section 4.4 for a discussion of the differences).

These slopes with $m_{Hα-MIR} > 1$ have the sense that extinction-corrected Hα becomes brighter relative to mid-IR at high intensities and such a trend appears consistent between all four systems (Figure 8). Visually, this agrees with the impression from Figures 1–4 that there is more extended and low-intensity mid-IR emission compared to Hα emission. That is, the peaks of the Hα and mid-IR align well, but the mid-IR

shows a much more significant “diffuse” or extended component. The existence of such a component is in good agreement with previous infrared observations of very nearby galaxies (e.g., 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 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.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Extinction-corrected Hα intensity as a function of mid-IR intensity at 1.77 resolution, separated by galaxy. As Figure 7 but now showing the binned relation between extinction-corrected Hα and mid-IR intensity for each individual galaxy and band (colored points) along with a power-law fit to the binned data for each galaxy (colored lines). The dark gray-shaded curve represents the 16%–84% range for the full data set and the gray line indicates the best-fitting power law for all data seen as a red line in Figure 7. The figure legends list the slope (m) for each fit. See Table 4 for the full numerical fit values.</figcaption></figure>

A number of recent studies using PHANGS–MUSE have shown that Balmer decrement extinctions show a positive correlation between Hα intensity and Hα extinction, $A_{H\alpha}$ (see Belfiore et al. 2022a; Emsellem et al. 2022; Santoro et al. 2022). The same trend of high extinction associated with high Hα emission or SFR appears to hold for integrated star-forming galaxies (e.g., Garn & Best 2010; Ly et al. 2012; Dominguez et al. 2013). As a result, in this data set, the regions with high $I_{H\alpha}$ that show the lowest mid-IR emission relative to Hα also show the highest Hα extinction, on average.

This result has the same sense as the trend found by Belfiore et al. (2022b) at coarser resolution for the whole PHANGS–MUSE sample, that mid-IR emission becomes brighter relative to other tracers of star formation at low intensities. They expressed this as a dependence of the mid-IR-to-SFR coefficient C (Section 2.4, Equation (5)) on specific SFR or star formation surface density and found that more intensely star-forming parts of galaxies required a smaller C (i.e., a more

negative exponent) than more quiescent regions. Here we see that this result continues to hold line of sight by line of sight on scales of 70–160 pc.

Note that this behavior differs somewhat from results focusing directly on star-forming complexes or actively star-forming galaxy centers by Calzetti et al. (2007). In their work, the ratio of mid-IR-to-extinction-corrected Pα increases or remains approximately constant with increasing star formation activity (they find the equivalent of $m_{P\alpha-\text{MIR}} \approx 1.06$ for 8 µm while $m_{P\alpha-\text{MIR}} \approx 0.81$ for 24 µm). Any of the “hybrid” tracers that linearly use the mid-IR with an obscured term also predict a ratio of mid-IR to extinction-corrected Hα that increases with extinction. The difference seems naturally explained by our inclusion of all mid-IR emission in our analysis, including emission not directly associated with star-forming regions. In Section 5, we return to this question, attempting to describe the full mid-IR emission as a combination of “cirrus” emission associated with gas and emission tracing star-forming regions.
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Extinction-corrected Hα intensity as a function of mid-IR intensity at 1.77 resolution, separated by galaxy. As Figure 7 but now showing the binned relation between extinction-corrected Hα and mid-IR intensity for each individual galaxy and band (colored points) along with a power-law fit to the binned data for each galaxy (colored lines). The dark gray-shaded curve represents the 16%–84% range for the full data set and the gray line indicates the best-fitting power law for all data seen as a red line in Figure 7. The figure legends list the slope (m) for each fit. See Table 4 for the full numerical fit values.</figcaption></figure>

A number of recent studies using PHANGS–MUSE have shown that Balmer decrement extinctions show a positive correlation between Hα intensity and Hα extinction, $A_{H\alpha}$ (see Belfiore et al. 2022a; Emsellem et al. 2022; Santoro et al. 2022). The same trend of high extinction associated with high Hα emission or SFR appears to hold for integrated star-forming galaxies (e.g., Garn & Best 2010; Ly et al. 2012; Dominguez et al. 2013). As a result, in this data set, the regions with high $I_{H\alpha}$ that show the lowest mid-IR emission relative to Hα also show the highest Hα extinction, on average.

This result has the same sense as the trend found by Belfiore et al. (2022b) at coarser resolution for the whole PHANGS–MUSE sample, that mid-IR emission becomes brighter relative to other tracers of star formation at low intensities. They expressed this as a dependence of the mid-IR-to-SFR coefficient C (Section 2.4, Equation (5)) on specific SFR or star formation surface density and found that more intensely star-forming parts of galaxies required a smaller C (i.e., a more

negative exponent) than more quiescent regions. Here we see that this result continues to hold line of sight by line of sight on scales of 70–160 pc.

Note that this behavior differs somewhat from results focusing directly on star-forming complexes or actively star-forming galaxy centers by Calzetti et al. (2007). In their work, the ratio of mid-IR-to-extinction-corrected Pα increases or remains approximately constant with increasing star formation activity (they find the equivalent of $m_{P\alpha-\text{MIR}} \approx 1.06$ for 8 µm while $m_{P\alpha-\text{MIR}} \approx 0.81$ for 24 µm). Any of the “hybrid” tracers that linearly use the mid-IR with an obscured term also predict a ratio of mid-IR to extinction-corrected Hα that increases with extinction. The difference seems naturally explained by our inclusion of all mid-IR emission in our analysis, including emission not directly associated with star-forming regions. In Section 5, we return to this question, attempting to describe the full mid-IR emission as a combination of “cirrus” emission associated with gas and emission tracing star-forming regions.
<figure><img src="image_11.png" /><figcaption>**Figure 9.** CO (2–1) intensity as a function of extinction-corrected Hα intensity. The left panel follows Figures 5 and 7 but now plotting CO (2–1) intensity as a function of extinction-corrected Hα intensity color-coded by 10 µm intensity. The right panel similarly follows Figures 6 and 8, showing results for individual galaxies. Annotations follow the other figures: shading shows regions excluded from statistical analysis, the thick red (left) and black (right) lines show the best-fitting power law to the binned data for all galaxies, and colored lines show power-law fits for individual galaxies, with *m* and *b* giving the slope and intercept of the fits respectively.</figcaption></figure>

Thus the explanation for our steep Hα versus mid-IR slope appears to mix at least two effects: (1) the impact of “cirrus” emission by dust not immediately associated with the star-forming regions, which preferentially contributes mid-IR to low-intensity regions and (2) the destruction of PAHs and small dust grains (for the F770W, F1000W, and F1130W bands), which we discuss more in Section 4.4 and likely explains the difference between the F2100W and the other bands.

The overall nonlinear slope of the relationship between extinction-corrected Hα and the mid-IR intensity also shows that at these resolutions, the mid-IR cannot be translated into a local estimate of star formation activity at high precision by a single factor. Even if one ignores that much of the Hα emission arises from nonlocal ionizations, i.e., the DIG, the slope of ~1.3–1.5 relating Hα-to-mid-IR emission still leads to a scatter of 0.4–0.5 dex, implying an FWHM of a full order of magnitude in the ratio of Hα-to-mid-IR across our data set. Our power-law fits or the two-component model in Section 5 offer a better approach, and we expect to produce even sharper prescriptions using the full PHANGS–JWST survey.

### 4.3. The CO versus Mid-IR and Hα versus Mid-IR Correlations Appear Distinct

To help interpret the CO versus mid-IR and Hα versus mid-IR correlation, we apply an identical analysis of the correlation of CO (2–1) and extinction-corrected Hα and show the results in Figure 9 and Table 4.

The relationship between CO and Hα is weaker, more scattered, and less linear than that between mid-IR and either CO or Hα. Over the whole data set, CO and extinction-corrected Hα show a rank correlation coefficient $ρ \approx 0.47$, weaker than either the correlation between CO and mid-IR emission or Hα and mid-IR emission. The scatter in the CO-to-Hα ratio is larger than that in either the CO-to-mid-IR ratio or Hα-to-mid-IR ratio, and the scatter of CO intensity within individual Hα intensity bins is larger than that of CO in bins of mid-IR emission (compare Figures 5 and 9). Finally, the best-fitting slope of the CO versus Hα relation is very shallow, $m_{CO-H\alpha} \approx 0.5$.

The shallow slope, high scatter, and weaker correlation coefficient all indicate that the global scaling between molecular gas and star formation activity traced by Hα is beginning to break down at the 70–160 pc scales of our data. For reference, at 1.5 kpc resolution and comparing extinction-corrected Hα and molecular gas estimated from CO in the full PHANGS–MUSE sample, Sun et al. (2022a) and Sun et al. (2022b) find a slope of $m \sim 1.1$, scatter about the best-fit power law of $σ \approx 0.3$ dex, and a rank correlation coefficient of $\approx 0.88$ (see also Pessa et al. 2021, 2022). This agrees with previous work showing a separation of CO and Hα emission in this sample at similar scales (Kreckel et al. 2018; Schinnerer et al. 2019; Chevance et al. 2020; Kim et al. 2022; Pan et al. 2022). It also agrees with the wider literature demonstrating a spatial separation between tracers of recent massive star formation and molecular gas at high resolution (including Kawamura et al. 2009;
<figure><img src="image_12.png" /><figcaption>**Figure 9.** CO (2–1) intensity as a function of extinction-corrected Hα intensity. The left panel follows Figures 5 and 7 but now plotting CO (2–1) intensity as a function of extinction-corrected Hα intensity color-coded by 10 µm intensity. The right panel similarly follows Figures 6 and 8, showing results for individual galaxies. Annotations follow the other figures: shading shows regions excluded from statistical analysis, the thick red (left) and black (right) lines show the best-fitting power law to the binned data for all galaxies, and colored lines show power-law fits for individual galaxies, with *m* and *b* giving the slope and intercept of the fits respectively.</figcaption></figure>

Thus the explanation for our steep Hα versus mid-IR slope appears to mix at least two effects: (1) the impact of “cirrus” emission by dust not immediately associated with the star-forming regions, which preferentially contributes mid-IR to low-intensity regions and (2) the destruction of PAHs and small dust grains (for the F770W, F1000W, and F1130W bands), which we discuss more in Section 4.4 and likely explains the difference between the F2100W and the other bands.

The overall nonlinear slope of the relationship between extinction-corrected Hα and the mid-IR intensity also shows that at these resolutions, the mid-IR cannot be translated into a local estimate of star formation activity at high precision by a single factor. Even if one ignores that much of the Hα emission arises from nonlocal ionizations, i.e., the DIG, the slope of ~1.3–1.5 relating Hα-to-mid-IR emission still leads to a scatter of 0.4–0.5 dex, implying an FWHM of a full order of magnitude in the ratio of Hα-to-mid-IR across our data set. Our power-law fits or the two-component model in Section 5 offer a better approach, and we expect to produce even sharper prescriptions using the full PHANGS–JWST survey.

### 4.3. The CO versus Mid-IR and Hα versus Mid-IR Correlations Appear Distinct

To help interpret the CO versus mid-IR and Hα versus mid-IR correlation, we apply an identical analysis of the correlation of CO (2–1) and extinction-corrected Hα and show the results in Figure 9 and Table 4.

The relationship between CO and Hα is weaker, more scattered, and less linear than that between mid-IR and either CO or Hα. Over the whole data set, CO and extinction-corrected Hα show a rank correlation coefficient $ρ \approx 0.47$, weaker than either the correlation between CO and mid-IR emission or Hα and mid-IR emission. The scatter in the CO-to-Hα ratio is larger than that in either the CO-to-mid-IR ratio or Hα-to-mid-IR ratio, and the scatter of CO intensity within individual Hα intensity bins is larger than that of CO in bins of mid-IR emission (compare Figures 5 and 9). Finally, the best-fitting slope of the CO versus Hα relation is very shallow, $m_{CO-H\alpha} \approx 0.5$.

The shallow slope, high scatter, and weaker correlation coefficient all indicate that the global scaling between molecular gas and star formation activity traced by Hα is beginning to break down at the 70–160 pc scales of our data. For reference, at 1.5 kpc resolution and comparing extinction-corrected Hα and molecular gas estimated from CO in the full PHANGS–MUSE sample, Sun et al. (2022a) and Sun et al. (2022b) find a slope of $m \sim 1.1$, scatter about the best-fit power law of $σ \approx 0.3$ dex, and a rank correlation coefficient of $\approx 0.88$ (see also Pessa et al. 2021, 2022). This agrees with previous work showing a separation of CO and Hα emission in this sample at similar scales (Kreckel et al. 2018; Schinnerer et al. 2019; Chevance et al. 2020; Kim et al. 2022; Pan et al. 2022). It also agrees with the wider literature demonstrating a spatial separation between tracers of recent massive star formation and molecular gas at high resolution (including Kawamura et al. 2009;
Schruba et al. 2010; Leroy et al. 2013; Corbelli et al. 2017; Grasha et al. 2018; Kruijssen et al. 2019; Turner et al. 2022).<fnref n="51" />

The results that the CO versus mid-IR and Hα versus mid-IR relationships each appear significantly stronger than the CO versus Hα relationship and that the CO versus Hα relationship has begun to break down in our data both support the idea that our observations can distinguish the impacts of column density and heating on mid-IR emission. Lending further support to this view, the residuals about the CO versus mid-IR and Hα versus mid-IR show clear secondary correlations. In Figures 5 and 7, we color the data points by the mean intensity of the unplotted variable (i.e., Hα in the CO–IR plot, CO in the Hα–IR plot). Both figures reveal a secondary dependence on this unplotted variable. That is, for a given CO intensity, the mid-IR still appears to correlate with Hα and vice versa.

Taken together, the results of our analysis suggest that we are observing distinct relationships between CO versus mid-IR and Hα versus mid-IR. These are probably amplified by the still-present, if weak, correlation between CO and Hα in our data. Beyond these first results, analysis of the partial correlation coefficients or principal component analysis represent logical ways forward. In this paper we adopt a simple two-component modeling approach as the next step (Section 5).

### 4.4. F2100W Shows Moderately Different Behavior and Appears to be a More Direct Star Formation Tracer than the Other Mid-IR Bands

To first order, we find consistent results among all four mid-IR bands and Appendix A shows that a single scaling relating the bands represents a reasonable description at modest intensity and modest resolution. In more detail, Table 4 and Figures 5 through 10 suggest moderately different behavior for the F2100W 21 µm band compared to the other three PHANGS–JWST mid-IR bands. Hα versus F2100W shows a shallower, nearly linear slope of $m_{Hα–MIR} \sim 1.3$ compared to the other bands, which show $m_{Hα–MIR} \sim 1.5$. Meanwhile CO (2–1) versus F2100W also shows a shallower slope, $m_{CO–MIR} \sim 0.7$, compared to $m_{CO–MIR} \sim 1.2$ for the other bands. These differences hold within each galaxy, as well as across the whole data set.

The differences between the Hα versus F2100W and Hα versus F770W that we observe agree well with the results of Calzetti et al. (2007) studying 8 µm and 24 µm in star-forming regions in SINGS galaxies. They used extinction-corrected Paschen α and found that $m_{Pα–MIR} \approx 1.06$ for 8 µm while $m_{Pα–MIR} \approx 0.81$ for 24 µm.<fnref n="52" /> The difference in slopes between the 8 µm and 24 µm is almost identical to what we observe here between the F2100W and F770W. However, the values of the

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Best-fitting power-law slopes comparing mid-IR, CO (2–1), and extinction-corrected Hα. Each point shows the slope, *m*, from Equations (10) and (11), for one variable pair and data set. Colored points show results from fitting our full combined data set. Overall, the figure shows consistent results for individual galaxies and the combined data set, with the lower-mass, lower-metallicity IC 5332 the most consistent outlier. The CO vs. mid-IR relation shows slopes fairly close to unity (the black line), corresponding to a linear relation. Meanwhile, the extinction-corrected Hα shows a consistently steeper slope vs. mid-IR, indicating high Hα-to-mid-IR ratio in bright star-forming regions. CO (2–1) vs. extinction-corrected Hα shows a much shallower slope when treating Hα as the independent variable, consistent with approaching the scale where the CO–Hα correlation breaks down. Throughout, F2100W shows a moderately different behavior from the other three mid-IR bands (Section 4.4). See Table 4 for the corresponding numerical results and Section 4 for discussion.</figcaption></figure>

slopes themselves differ due to differences in experiment design and sample, with our analysis yielding significantly steeper slopes. As discussed above, the difference should be expected, since Calzetti et al. (2007) focuses on star-forming regions and galaxy centers, while we plot all lines of sight for our target galaxies.

The simplest explanation of the differences in slopes between Hα and the mid-IR for different bands is that

<footnote n="51">⁵¹ The physics behind this breakdown are not the focus of this paper. We note that star formation relations for individual clouds have been measured using young stellar objects as near-instantaneous SFR tracers (Gutermuth et al. 2011; Pokhrel et al. 2021) and refer the reader to those papers for information on Galactic scaling relations. In nearby galaxies, the observed relationship between gas structure at the ~50–150 pc scale has been explored by Leroy et al. (2017), Hirota et al. (2018), Utomo et al. (2018), Kreckel et al. (2018), Schruba et al. (2019), and Sun et al. (2022a). The interpretation of the observed breakdown in correspondence between Hα and CO in terms of region evolution has been discussed by Kawamura et al. (2009), Schruba et al. (2010), Corbelli et al. (2017), Kruijssen et al. (2019), Chevance et al. (2020), and Kim et al. (2022). We refer the interested reader to these papers for more extensive discussion of the physics behind the breakdown.</footnote>

<footnote n="52">⁵² They quote the slopes for mid-IR as a function of Pα. We quote the inverse here to be consistent with our axis choice.</footnote>
Schruba et al. 2010; Leroy et al. 2013; Corbelli et al. 2017; Grasha et al. 2018; Kruijssen et al. 2019; Turner et al. 2022).<fnref n="51" />

The results that the CO versus mid-IR and Hα versus mid-IR relationships each appear significantly stronger than the CO versus Hα relationship and that the CO versus Hα relationship has begun to break down in our data both support the idea that our observations can distinguish the impacts of column density and heating on mid-IR emission. Lending further support to this view, the residuals about the CO versus mid-IR and Hα versus mid-IR show clear secondary correlations. In Figures 5 and 7, we color the data points by the mean intensity of the unplotted variable (i.e., Hα in the CO–IR plot, CO in the Hα–IR plot). Both figures reveal a secondary dependence on this unplotted variable. That is, for a given CO intensity, the mid-IR still appears to correlate with Hα and vice versa.

Taken together, the results of our analysis suggest that we are observing distinct relationships between CO versus mid-IR and Hα versus mid-IR. These are probably amplified by the still-present, if weak, correlation between CO and Hα in our data. Beyond these first results, analysis of the partial correlation coefficients or principal component analysis represent logical ways forward. In this paper we adopt a simple two-component modeling approach as the next step (Section 5).

### 4.4. F2100W Shows Moderately Different Behavior and Appears to be a More Direct Star Formation Tracer than the Other Mid-IR Bands

To first order, we find consistent results among all four mid-IR bands and Appendix A shows that a single scaling relating the bands represents a reasonable description at modest intensity and modest resolution. In more detail, Table 4 and Figures 5 through 10 suggest moderately different behavior for the F2100W 21 µm band compared to the other three PHANGS–JWST mid-IR bands. Hα versus F2100W shows a shallower, nearly linear slope of $m_{H\alpha–MIR} \sim 1.3$ compared to the other bands, which show $m_{H\alpha–MIR} \sim 1.5$. Meanwhile CO (2–1) versus F2100W also shows a shallower slope, $m_{CO–MIR} \sim 0.7$, compared to $m_{CO–MIR} \sim 1.2$ for the other bands. These differences hold within each galaxy, as well as across the whole data set.

The differences between the Hα versus F2100W and Hα versus F770W that we observe agree well with the results of Calzetti et al. (2007) studying 8 µm and 24 µm in star-forming regions in SINGS galaxies. They used extinction-corrected Paschen α and found that $m_{Pα–MIR} \approx 1.06$ for 8 µm while $m_{Pα–MIR} \approx 0.81$ for 24 µm.<fnref n="52" /> The difference in slopes between the 8 µm and 24 µm is almost identical to what we observe here between the F2100W and F770W. However, the values of the

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Best-fitting power-law slopes comparing mid-IR, CO (2–1), and extinction-corrected Hα. Each point shows the slope, *m*, from Equations (10) and (11), for one variable pair and data set. Colored points show results from fitting our full combined data set. Overall, the figure shows consistent results for individual galaxies and the combined data set, with the lower-mass, lower-metallicity IC 5332 the most consistent outlier. The CO vs. mid-IR relation shows slopes fairly close to unity (the black line), corresponding to a linear relation. Meanwhile, the extinction-corrected Hα shows a consistently steeper slope vs. mid-IR, indicating high Hα-to-mid-IR ratio in bright star-forming regions. CO (2–1) vs. extinction-corrected Hα shows a much shallower slope when treating Hα as the independent variable, consistent with approaching the scale where the CO–Hα correlation breaks down. Throughout, F2100W shows a moderately different behavior from the other three mid-IR bands (Section 4.4). See Table 4 for the corresponding numerical results and Section 4 for discussion.</figcaption></figure>

slopes themselves differ due to differences in experiment design and sample, with our analysis yielding significantly steeper slopes. As discussed above, the difference should be expected, since Calzetti et al. (2007) focuses on star-forming regions and galaxy centers, while we plot all lines of sight for our target galaxies.

The simplest explanation of the differences in slopes between Hα and the mid-IR for different bands is that

<footnote n="51">⁵¹ The physics behind this breakdown are not the focus of this paper. We note that star formation relations for individual clouds have been measured using young stellar objects as near-instantaneous SFR tracers (Guttermuth et al. 2011; Pokhrel et al. 2021) and refer the reader to those papers for information on Galactic scaling relations. In nearby galaxies, the observed relationship between gas structure at the ~50–150 pc scale has been explored by Leroy et al. (2017), Hirota et al. (2018), Utomo et al. (2018), Kreckel et al. (2018), Schruba et al. (2019), and Sun et al. (2022a). The interpretation of the observed breakdown in correspondence between Hα and CO in terms of region evolution has been discussed by Kawamura et al. (2009), Schruba et al. (2010), Corbelli et al. (2017), Kruijssen et al. (2019), Chevance et al. (2020), and Kim et al. (2022). We refer the interested reader to these papers for more extensive discussion of the physics behind the breakdown.</footnote>

<footnote n="52">⁵² They quote the slopes for mid-IR as a function of Pα. We quote the inverse here to be consistent with our axis choice.</footnote>
F2100W appears to trace the extinction-corrected $H\alpha$, itself a tracer of recent star formation and heating, more directly than the other mid-IR bands trace $H\alpha$. This is consistent with the observation that the emission of the PAH-tracing bands, F770W and F1130W, relative to the dust continuum, diminishes in bright H II regions. This result is the main topic of Chastenet (2023a), Dale et al. (2023), and Egorov (2023) in this Issue. Previously, many Spitzer and WISE studies of the Milky Way and the nearest galaxies observed similar effects, either as a decline in the 8 µm/24 µm (or WISE 12µm/22µm) ratio in H II regions or as a visible ringlike morphology for the PAH-tracing band, suggesting that the brightest emission surrounds the H II region while the 22 µm or 24 µm emission peaks in the star-forming region (e.g., Helou et al. 2004; Povich et al. 2007; Bendo et al. 2008; Gordon et al. 2008; Relaño & Kennicutt 2009; Anderson et al. 2014; Calapa et al. 2014; Chastenet et al. 2019).

The differing slopes of the CO versus mid-IR relation for different bands could arise from the same effect. At high mid-IR intensities, there will be more contribution from bright star-forming regions to F2100W than to the PAH-tracing bands. This might mean relatively lower CO-to-F2100W ratios compared to, e.g., CO-to-F770W ratios in these bright regions, and help explain why the PAH-tracing bands tend to show $m_{CO-MIR} \sim 1.2$ while the F2100W shows $m_{CO-MIR} \sim 0.7$.

This relative suppression of PAH emission compared to ~24 µm emission in star-forming regions is frequently ascribed to PAH destruction in ionized gas. Given this explanation, it may be surprising that F1000W appears better matched to F770W and F1130W than to F2100W. In theory, the F1000W band should be primarily continuum rather than PAH-dominated, with the main feature of note being the silicate absorption band, which we do not expect to be strong at these column densities (e.g., Draine & Li 2007; Smith et al. 2007). The closer coupling of F1000W to the two PAH-dominated bands rather than F2100W is a somewhat surprising result of the first PHANGS–JWST science. Apparently, either the smaller, hotter, more easily destroyed dust grains responsible for 10 µm compared to 21 µm heating mimic PAHs in their behavior, or alternatively weaker PAH features or the line wings of the adjacent strong bands contribute significantly to the band.

This apparent suppression of PAH emission in bright regions, combined with significant metallicity trends observed in the PAH abundance (e.g., Engelbracht et al. 2005; Calzetti et al. 2007; Gordon et al. 2008; Chastenet et al. 2019; Li 2020), led to a preference for the continuum-dominated 24 µm emission over 8 µm as a star formation tracer during the Spitzer era (e.g., Calzetti et al. 2007; Murphy et al. 2011; Kennicutt & Evans 2012; Catalán-Torrecilla et al. 2015). Despite this, PAH-dominated bands, including the 8 µm emission and the 12 µm emission from WISE still often yielded good quantitative correspondence with independent SFR estimates, especially when used as part of “hybrid” tracers with $H\alpha$ or UV (e.g., Calzetti et al. 2007; Kennicutt & Hao 2009; Jarrett et al. 2013, though see also Calzetti et al. 2005).

Finally, we note that we are finding F2100W to be more linearly associated with extinction-corrected $H\alpha$, not only associated with $H\alpha$. The slopes relating $H\alpha$ to F2100W and CO (2–1) to F2100W lie about equidistant from unity, and F2100W still correlates quite well with CO emission, especially

at low intensities. The overall local correlation of F2100W with CO still appears excellent and in Section 5 we will find a substantial CO-associated component to contribute to the emission. Similarly, the PAH-tracing bands still correlate exceptionally well with $H\alpha$ emission; they simply do so nonlinearly. Indeed a main conclusion of this paper is that all four of the bands act simultaneously as tracers of recent star formation and the neutral ISM.

## 5. Describing Mid-IR Emission with a Two-component Model

In Section 4 we observe that both CO and extinction-corrected $H\alpha$ correlate with mid-IR emission, that the correlations appear at least partially independent of one another with distinct slopes, and that the correlation of each band with the mid-IR is tighter than the correlation of CO and $H\alpha$ with one another. This agrees qualitatively with the expectations in Sections 1 and 2. Mid-IR emission traces both column density and heating, and column density, primarily traced by CO in our data, has a different distribution than heating, here traced by $H\alpha$.

To explore this picture more quantitatively, we construct and then fit a simple model where the bright mid-IR emission reflects a linear combination of a scaled CO map and a scaled extinction-corrected $H\alpha$ map. That is,

$$I_{\text{MIR}}^{\text{model}} = c \times I_{\text{CO}} + h \times I_{H\alpha}^{\text{corr}}, \quad (12)$$

with $c$ and $h$ being free parameters to be fit with units$^{53}$ of MJy sr$^{-1}$ (K km s$^{-1}$)$^{-1}$ and MJy sr$^{-1}$ (erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$)$^{-1}$.

Here we obtain a single best-fit $c$ or $h$ to each data set at our common 1.7 resolution, so that this exercise amounts to using the CO and $H\alpha$ as “templates” and solving for the combination that best matches the observed mid-IR. Physically, this approach assumes that mid-IR reflects a linear combination of (1) dust mixed with molecular gas illuminated by some uniform, presumably low, radiation field, traced by CO, as in Equation (6), and (2) dust heated by intense radiation fields, traced by $H\alpha$, as in Equation (7). We focus on this simple linear combination because our selection of bright emission (Section 3.4) already restricts our analysis to the regions where we expect molecular gas to make up most of the ISM. Still, this simple approach remains highly approximate. Among a host of other second-order concerns, the association of $H\alpha$ with dust heating is questionable, and the model ignores any contribution from atomic or molecular gas not traced by CO. We discuss ways to improve the model in Section 5.2.

Given $c$ and $h$, we also record the fraction of the total flux in the model associated with each component,

$$f_c = \frac{\sum c \times I_{\text{CO}}}{\sum I_{\text{MIR}}^{\text{model}}} \\ f_h = \frac{\sum h \times I_{H\alpha}}{\sum I_{\text{MIR}}^{\text{model}}}, \quad (13)$$

where the sum runs over the whole map.

We select the best $c$ and $h$ for each band and galaxy by minimizing the mean absolute residual for bright emission in log space. That is, we find the $c$ and $h$ that minimize the absolute value of the log ratio between the model and the data,

<footnote>$^{53}$ For comparison, one can also re-express $c$ and $h$ in terms of the ratios measured in Section 4, $I_{\text{CO}}/I_{\text{MIR}} = c^{-1}$ and $I_{H\alpha}/I_{\text{MIR}} = h^{-1}$.</footnote>
F2100W appears to trace the extinction-corrected $H\alpha$, itself a tracer of recent star formation and heating, more directly than the other mid-IR bands trace $H\alpha$. This is consistent with the observation that the emission of the PAH-tracing bands, F770W and F1130W, relative to the dust continuum, diminishes in bright H II regions. This result is the main topic of Chastenet (2023a), Dale et al. (2023), and Egorov (2023) in this Issue. Previously, many Spitzer and WISE studies of the Milky Way and the nearest galaxies observed similar effects, either as a decline in the 8 µm/24 µm (or WISE 12µm/22µm) ratio in H II regions or as a visible ringlike morphology for the PAH-tracing band, suggesting that the brightest emission surrounds the H II region while the 22 µm or 24 µm emission peaks in the star-forming region (e.g., Helou et al. 2004; Povich et al. 2007; Bendo et al. 2008; Gordon et al. 2008; Relaño & Kennicutt 2009; Anderson et al. 2014; Calapa et al. 2014; Chastenet et al. 2019).

The differing slopes of the CO versus mid-IR relation for different bands could arise from the same effect. At high mid-IR intensities, there will be more contribution from bright star-forming regions to F2100W than to the PAH-tracing bands. This might mean relatively lower CO-to-F2100W ratios compared to, e.g., CO-to-F770W ratios in these bright regions, and help explain why the PAH-tracing bands tend to show $m_{CO-MIR} \sim 1.2$ while the F2100W shows $m_{CO-MIR} \sim 0.7$.

This relative suppression of PAH emission compared to ~24 µm emission in star-forming regions is frequently ascribed to PAH destruction in ionized gas. Given this explanation, it may be surprising that F1000W appears better matched to F770W and F1130W than to F2100W. In theory, the F1000W band should be primarily continuum rather than PAH-dominated, with the main feature of note being the silicate absorption band, which we do not expect to be strong at these column densities (e.g., Draine & Li 2007; Smith et al. 2007). The closer coupling of F1000W to the two PAH-dominated bands rather than F2100W is a somewhat surprising result of the first PHANGS–JWST science. Apparently, either the smaller, hotter, more easily destroyed dust grains responsible for 10 µm compared to 21 µm heating mimic PAHs in their behavior, or alternatively weaker PAH features or the line wings of the adjacent strong bands contribute significantly to the band.

This apparent suppression of PAH emission in bright regions, combined with significant metallicity trends observed in the PAH abundance (e.g., Engelbracht et al. 2005; Calzetti et al. 2007; Gordon et al. 2008; Chastenet et al. 2019; Li 2020), led to a preference for the continuum-dominated 24 µm emission over 8 µm as a star formation tracer during the Spitzer era (e.g., Calzetti et al. 2007; Murphy et al. 2011; Kennicutt & Evans 2012; Catalán-Torrecilla et al. 2015). Despite this, PAH-dominated bands, including the 8 µm emission and the 12 µm emission from WISE still often yielded good quantitative correspondence with independent SFR estimates, especially when used as part of “hybrid” tracers with $H\alpha$ or UV (e.g., Calzetti et al. 2007; Kennicutt & Hao 2009; Jarrett et al. 2013, though see also Calzetti et al. 2005).

Finally, we note that we are finding F2100W to be more linearly associated with extinction-corrected $H\alpha$, not only associated with $H\alpha$. The slopes relating $H\alpha$ to F2100W and CO (2–1) to F2100W lie about equidistant from unity, and F2100W still correlates quite well with CO emission, especially

at low intensities. The overall local correlation of F2100W with CO still appears excellent and in Section 5 we will find a substantial CO-associated component to contribute to the emission. Similarly, the PAH-tracing bands still correlate exceptionally well with $H\alpha$ emission; they simply do so nonlinearly. Indeed a main conclusion of this paper is that all four of the bands act simultaneously as tracers of recent star formation and the neutral ISM.

## 5. Describing Mid-IR Emission with a Two-component Model

In Section 4 we observe that both CO and extinction-corrected $H\alpha$ correlate with mid-IR emission, that the correlations appear at least partially independent of one another with distinct slopes, and that the correlation of each band with the mid-IR is tighter than the correlation of CO and $H\alpha$ with one another. This agrees qualitatively with the expectations in Sections 1 and 2. Mid-IR emission traces both column density and heating, and column density, primarily traced by CO in our data, has a different distribution than heating, here traced by $H\alpha$.

To explore this picture more quantitatively, we construct and then fit a simple model where the bright mid-IR emission reflects a linear combination of a scaled CO map and a scaled extinction-corrected $H\alpha$ map. That is,

$$I_{\text{MIR}}^{\text{model}} = c \times I_{\text{CO}} + h \times I_{H\alpha}^{\text{corr}}, \quad (12)$$

with $c$ and $h$ being free parameters to be fit with units$^{53}$ of MJy sr$^{-1}$ (K km s$^{-1}$)$^{-1}$ and MJy sr$^{-1}$ (erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$)$^{-1}$.

Here we obtain a single best-fit $c$ or $h$ to each data set at our common 1"/7 resolution, so that this exercise amounts to using the CO and $H\alpha$ as “templates” and solving for the combination that best matches the observed mid-IR. Physically, this approach assumes that mid-IR reflects a linear combination of (1) dust mixed with molecular gas illuminated by some uniform, presumably low, radiation field, traced by CO, as in Equation (6), and (2) dust heated by intense radiation fields, traced by $H\alpha$, as in Equation (7). We focus on this simple linear combination because our selection of bright emission (Section 3.4) already restricts our analysis to the regions where we expect molecular gas to make up most of the ISM. Still, this simple approach remains highly approximate. Among a host of other second-order concerns, the association of $H\alpha$ with dust heating is questionable, and the model ignores any contribution from atomic or molecular gas not traced by CO. We discuss ways to improve the model in Section 5.2.

Given $c$ and $h$, we also record the fraction of the total flux in the model associated with each component,

$$f_c = \frac{\sum c \times I_{\text{CO}}}{\sum I_{\text{MIR}}^{\text{model}}} \\ f_h = \frac{\sum h \times I_{H\alpha}}{\sum I_{\text{MIR}}^{\text{model}}}, \quad (13)$$

where the sum runs over the whole map.

We select the best $c$ and $h$ for each band and galaxy by minimizing the mean absolute residual for bright emission in log space. That is, we find the $c$ and $h$ that minimize the absolute value of the log ratio between the model and the data,

<footnote>$^{53}$ For comparison, one can also re-express $c$ and $h$ in terms of the ratios measured in Section 4, $I_{\text{CO}}/I_{\text{MIR}} = c^{-1}$ and $I_{H\alpha}/I_{\text{MIR}} = h^{-1}$.</footnote>