<figure><img src="image_1.png" /></figure>

# Using [C II] 158 µm Emission from Isolated ISM Phases as a Star Formation Rate Indicator

Jessica Sutter<fnref n="1" />, Daniel A. Dale<fnref n="1" />, Kevin V. Croxall<fnref n="2" />, Eric W. Pelligrini<fnref n="3" />, J. D. T. Smith<fnref n="4" />, Philip N. Appleton<fnref n="5" />,
Pedro Beirão<fnref n="6" />, Alberto D. Bolatto<fnref n="7" />, Daniela Calzetti<fnref n="8" />, Alison Crocker<fnref n="9" />, Ilse De Looze<fnref n="10" />, Bruce Draine<fnref n="11" />,
Maud Galametz<fnref n="12" />, Brent A. Groves<fnref n="13" />, George Helou<fnref n="5" />, Rodrigo Herrera-Camus<fnref n="14" />, Leslie K. Hunt<fnref n="15" />,
Robert C. Kennicutt<fnref n="16" />,<fnref n="17" />, Hélène Roussel<fnref n="18" />, and Mark G. Wolfire<fnref n="4" />

Received 2019 March 15; revised 2019 October 1; accepted 2019 October 10; published 2019 November 20

## Abstract

The brightest observed emission line in many star-forming galaxies is the [C II] 158 µm line, making it detectable up to $z \sim 7$. In order to better understand and quantify the [C II] emission as a tracer of star formation, the theoretical ratio between the [N II] 205 µm emission and the [C II] 158 µm emission has been employed to empirically determine the fraction of [C II] emission that originates from the ionized and neutral phases of the interstellar medium (ISM). Sub-kiloparsec measurements of the [C II] 158 µm and [N II] 205 µm lines in nearby galaxies have recently become available as part of the Key Insights in Nearby Galaxies: a Far Infrared Survey with Herschel (KINGFISH) and Beyond the Peak programs. With the information from these two far-infrared lines along with the multi-wavelength suite of KINGFISH data, a calibration of the [C II] emission line as a star formation rate (SFR) indicator and a better understanding of the [C II] deficit are pursued. [C II] emission is also compared to polycyclic aromatic hydrocarbon (PAH) emission in these regions to compare photoelectric heating from PAH molecules to cooling by [C II] in the neutral and ionized phases of the ISM. We find that the [C II] emission originating in the neutral phase of the ISM does not exhibit a deficit with respect to the infrared luminosity and is therefore preferred over the [C II] emission originating in the ionized phase of the ISM as an SFR indicator for the normal star-forming galaxies included in this sample.

Unified Astronomy Thesaurus concepts: Galactic and extragalactic astronomy (563); Far infrared astronomy (529); Interstellar medium (847); Photodissociation regions (1223); Star forming regions (1565)

## 1. Introduction

The [C II] 158 µm line is frequently the brightest observed emission line in star-forming galaxies (Luhman et al. 2003; Brauher et al. 2008). This prominence is due to the prevalence of carbon, its dominant role in cooling neutral atomic gas (Wolfire et al. 2003), its sub-Rydberg ionization potential, and the minimal dust attenuation it undergoes given its long wavelength (Heiles 1994; Luhman et al. 1998). The brightness of this line makes [C II] 158 µm emission an invaluable tool for probing the interstellar medium (ISM) of remote galaxies and the fainter regions within the disks of nearby galaxies. As [C II] 158 µm is a prominent and typically unattenuated emission line, it has naturally become a target of interest for tracing physical properties such as star formation rate (SFR). [C II] emission is expected to trace star formation because [C II] is a primary coolant of the photodissociation regions (PDRs),

meaning cooling by [C II] emission should balance photoelectric heating from young, hot stars to maintain thermal stability. However, the relatively low ionization potential of neutral carbon (11.3 eV) complicates the potential diagnostic capabilities of this line. Due to its low ionization potential, $C^+$ can exist within both the ionized and neutral ISM, including ISM phases spanning H II regions, warm ionized gas, cold atomic gas, and PDRs, which affects the interpretive power of the 158 µm emission line as a tracer of any specific galactic property (Stacey et al. 1985; Shibai et al. 1991; Bennett et al. 1994; Pineda et al. 2013).

This multiphase origin also affects [C II]'s potential as an SFR indicator through the effect known as the "[C II] deficit" (Malhotra et al. 2001; Herrera-Camus et al. 2015; Croxall et al. 2017). The [C II] deficit is the decreasing trend in the ratio of [C II] 158 µm luminosity to total infrared (TIR) luminosity

<footnote n="1">¹Department of Physics & Astronomy, University of Wyoming, Laramie, WY, USA; jsutter4@uwyo.edu</footnote>

<footnote n="2">²Expeed Software, Columbus, OH, USA</footnote>

<footnote n="3">³Institute for Theoretical Astrophysics Heidelberg, Germany</footnote>

<footnote n="4">⁴Department of Physics & Astronomy, University of Toledo, Toledo, OH, USA</footnote>

<footnote n="5">⁵IPAC, California Institute of Technology, Pasadena, CA, USA</footnote>

<footnote n="6">⁶Machine Learning Company, Oss, The Netherlands</footnote>

<footnote n="7">⁷Department of Astronomy, University of Maryland, College Park, MD, USA</footnote>

<footnote n="8">⁸Department of Astronomy, University of Massachusetts, Amherst, MA, USA</footnote>

<footnote n="9">⁹Physics Department, Reed College, Portland, OR, USA</footnote>

<footnote n="10">¹⁰Department of Physics & Astronomy, University College London, London, UK</footnote>

<footnote n="11">¹¹Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA</footnote>

<footnote n="12">¹²Laboratoire AIM, CEA, Université Paris Diderot, IRFU/Service d'Astrophysique, Gif-sur-Yvette, France</footnote>

<footnote n="13">¹³Research School of Astronomy & Astrophysics, Australian National University, Canberra, Australia</footnote>

<footnote n="14">¹⁴Departamento de Astronomía, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile</footnote>

<footnote n="15">¹⁵INAF—Osservatorio Astrofisico di Arcetri, Firenze, Italy</footnote>

<footnote n="16">¹⁶Steward Observatory, University of Arizona, Tucson, AZ, USA</footnote>

<footnote n="17">¹⁷Department of Physics & Astronomy, Texas A&M University, College Station, TX, USA</footnote>

<footnote n="18">¹⁸Institut d'Astrophysique de Paris, Sorbonne Universités, Paris, France</footnote>
(i.e., the total luminosity over 5–1100 µm) with respect to various measures of luminosity or star-forming activity. Multiple studies of [C II]/TIR have found a decrease in this ratio as a function of increasing SFR surface density (Smith et al. 2017), infrared luminosity (Malhotra et al. 2001; Luhman et al. 2003), far-infrared color (Helou et al. 2001; Croxall et al. 2012; Parkin et al. 2013; Díaz-Santos et al. 2017), and the ratio of infrared luminosity to H₂ gas mass ($L_{IR}/M_{H_2}$) (Graciá-Carpio et al. 2011; Herrera-Camus et al. 2018a). Several mechanisms have been proposed and investigated to explain the observed relative decrease in [C II] emission. These include: (1) [C II] is optically thick or absorbed by dust in galaxies with the highest infrared luminosities (Abel et al. 2007; Neri et al. 2014), (2) that activity of active galactic nuclei (AGNs) in the host galaxies could produce higher infrared luminosity and lower [C II] emission due to the increased hardness of radiation in AGN host galaxies potentially changing the ionization states of carbon in the ISM (Langer & Pineda 2015; Herrera-Camus et al. 2018b), (3) the thermalization and saturation of the [C II] line in warm, high-density environments leads to the [O I] 63 µm line becoming the dominant cooling line in these regions (Muñoz & Oh 2016; Díaz-Santos et al. 2017), (4) in regions with high ionization parameters, a majority of the far-UV (FUV) radiation from young stars is absorbed within the H II regions rather than escaping to PDRs where [C II] is the primary coolant (Abel et al. 2009; Graciá-Carpio et al. 2011), or (5) that very small dust grains in the most infrared-luminous galaxies become highly charged by increased FUV emission from star formation, increasing the energy needed to photoeject additional electrons and thus reducing the number and energy of photoejected electrons per unit FUV radiation (Malhotra et al. 2001; Graciá-Carpio et al. 2011). The [C II] deficit has been measured across a wide range of galaxy samples, from low-metallicity dwarf galaxies (Cormier et al. 2019), to ultra/luminous infrared galaxies (U/LIRGS) with infrared luminosities above $10^{11} L_{\odot}$ (Díaz-Santos et al. 2017), to normal star-forming galaxies (Malhotra et al. 2001; Smith et al. 2017). These studies of multiple fine-structure cooling lines in a variety of galaxies and others like them have indicated that the third, fourth, and fifth explanations seem to be the most prominent causes of this deficit, although all five may play some part in creating the observed decline in the ratio of [C II] to TIR luminosity (Malhotra et al. 2001; Luhman et al. 2003; Croxall et al. 2012; Díaz-Santos et al. 2017; Smith et al. 2017).

Despite these difficulties, multiple groups have attempted to use [C II] alone as an SFR indicator (e.g., Stacey et al. 1991; Boselli et al. 2002; De Looze et al. 2011; Herrera-Camus et al. 2015). Although there are indications that [C II] emission primarily originates in and around star-forming regions (Stacey et al. 1985; Mookerjea et al. 2011), the relationships found between [C II] luminosity and other tracers of star formation such as extinction-corrected Hα (Boselli et al. 2002) and FUV luminosity (De Looze et al. 2011) often show a large scatter (as large as a factor of 10) and do a poor job of matching SFRs in extreme cases (Sargsyan et al. 2012; De Looze et al. 2014; Díaz-Santos et al. 2017). However, it has been found that by including additional spectral information it is possible to determine a better constrained [C II]–SFR relationship. For example, using [C II] surface brightness along with an infrared color correction can predict the SFR to within a factor of three for all but the most IR-luminous systems (Herrera-Camus et al. 2015). Other work has shown that the ratio of [C II] to TIR

luminosity exhibits a strongly nonlinear but quantifiable trend with SFR surface density (Smith et al. 2017).

In order to further decode any relationship between [C II] 158 µm emission and SFR, the [C II] emission can be separated by the ISM phase in which it originates. The [N II] 205 µm line is a powerful tool for separating [C II] emission into neutral and ionized ISM components. As the [N II] 205 µm line is also a far-infrared fine-structure line, it is typically unattenuated by dust, similar to the [C II] 158 µm line. Since neutral nitrogen has an ionization energy of 14.5 eV, slightly above that of hydrogen at 13.6 eV, $N^+$ mainly exists in environments where hydrogen is ionized; [N II] 205 µm emission is essentially from H II regions and other ionized phases of the ISM only. Due to this constraint on the origin of the [N II] 205 µm emission, [N II] can be used to constrain the fraction of [C II] emission arising from the ionized ISM. Since the [N II] 205 µm line has a similar critical density to the [C II] 158 µm line (~32 cm⁻³ for [N II] 205 µm and ~45 cm⁻³ for [C II] 158 µm, Oberst et al. 2006; Croxall et al. 2017), the ratio of [C II] 158 µm emission to [N II] 205 µm emission is nearly constant regardless of electron number density (see Figure 2, and Croxall et al. 2012). This consistency makes [N II] 205 µm derived measures of the fraction of [C II] 158 µm emission from the ionized ISM less dependent on electron number density ($n_e$) than when using the brighter [N II] 122 µm line, because the ratio of the [C II] 158 µm and [N II] 122 µm lines varies by a factor of three in conditions of normal ISM density (Croxall et al. 2012). Therefore, [N II] 205 µm emission is the preferred tool to distinguish between the [C II] originating from the ionized and neutral phases of the ISM.

With the added information from the [N II] 205 µm line, the [C II] 158 µm emission can be separated by ISM phase. Isolated [C II] emission from the ionized and neutral ISM phases can then be calibrated and tested as indicators of SFR. Unfortunately, due to the weakness of the [N II] 205 µm line and its location in the far-infrared part of the spectrum, it is notoriously difficult to detect in galaxies in the local universe. Fortunately, a collection of [N II] 205 µm detections was made with the Herschel Space Observatory (Pilbratt et al. 2010; Poglitsch et al. 2010).

An intriguing application of an improved [C II]-based SFR indicator lies in the realm of high-redshift galaxies. There have been many detections of the [C II] 158 µm line in galaxies from $z \sim 1$ to $z \sim 7$ (Hailey-Dunsheath et al. 2010; Ivison et al. 2010; Stacey et al. 2010; Graciá-Carpio et al. 2011; Valtchanov et al. 2011; Gullberg et al. 2015, 2018; Barisic et al. 2017; Malhotra et al. 2017; Rybak et al. 2019). The brightness of the [C II] line enables detections across a wide range of distances, making it a popular tool for probing the PDR properties and kinematics of galaxies in the high-redshift universe. In addition to the availability of high-redshift [C II] detections, the Atacama Large Millimeter/ submillimeter Array has already detected [N II] in multiple galaxies beyond a redshift of four (Decarli et al. 2014; Aravena et al. 2016; Pavesi et al. 2016; Lu et al. 2017). Other work has identified the [C II] and [N II] lines in larger samples of galaxies with $1 < z < 2$ (Stacey et al. 2010), where cosmic star formation peaks (Madau & Dickinson 2014). As the [C II] 158 µm emission line is now measurable both in the local universe and in distant galaxies, it can be used to trace star formation at nearly any cosmic epoch. Also, unlike ultraviolet and optical star formation tracers such as FUV and Hα, attenuation by dust is typically negligible at 158 µm.
<caption>Table 1</caption>

Sample

<table><thead><tr><th>Galaxy</th><th>Alternative Name</th><th>Region Type</th><th>R.A. (J2000)</th><th>Decl. (J2000)</th><th>Distance (Mpc)</th><th>L<sub>TIR</sub> (L<sub>☉</sub>)</th><th>Morph. Type</th><th>BtP Data</th></tr></thead><tbody><tr><td>NGC 0337</td><td></td><td>Nuclear</td><td>00:59:50.200</td><td>-07:34:38.00</td><td>19.3</td><td>1.2 × 10<sup>10</sup></td><td>SBd</td><td>...</td></tr><tr><td>NGC 0628</td><td>[H76]292</td><td>Extranuclear</td><td>01:36:45.200</td><td>+15:47:49.00</td><td>7.20</td><td>8.0 × 10<sup>9</sup></td><td>SAc</td><td>...</td></tr><tr><td>NGC 1097</td><td>UGCA 041</td><td>Nuclear</td><td>02:46:19.200</td><td>-30:16:28.00</td><td>14.2</td><td>4.5 × 10<sup>10</sup></td><td>SBb</td><td>✓</td></tr><tr><td>NGC 1266</td><td></td><td>Nuclear</td><td>03:16:00.600</td><td>-02:25:39.00</td><td>30.6</td><td>2.5 × 10<sup>10</sup></td><td>SB0</td><td>✓</td></tr><tr><td>NGC 1377</td><td></td><td>Nuclear</td><td>03:36:39.500</td><td>-20:54:08.00</td><td>24.6</td><td>1.3 × 10<sup>10</sup></td><td>S0</td><td>...</td></tr><tr><td>IC 342</td><td>UGC 02847</td><td>Nuclear</td><td>03:46:48.200</td><td>+68:05:48.00</td><td>3.28</td><td>1.4 × 10<sup>10</sup></td><td>SABcd</td><td>...</td></tr><tr><td>NGC 1482</td><td></td><td>Nuclear</td><td>03:54:38.900</td><td>-20:30:09.00</td><td>22.6</td><td>4.4 × 10<sup>10</sup></td><td>SA0</td><td>✓</td></tr><tr><td>NGC 2146</td><td>UGC 03429</td><td>Nuclear</td><td>06:18:38.100</td><td>+78:21:23.00</td><td>17.2</td><td>1.0 × 10<sup>11</sup></td><td>Sbab</td><td>...</td></tr><tr><td>NGC 2798</td><td>UGC 04905</td><td>Nuclear</td><td>09:17:22.800</td><td>+42:00:00.00</td><td>25.8</td><td>3.6 × 10<sup>10</sup></td><td>SBa</td><td>✓</td></tr><tr><td>NGC 2976</td><td>[HK83]58</td><td>Extranuclear</td><td>09:47:07.300</td><td>+67:55:56.00</td><td>3.55</td><td>9.0 × 10<sup>8</sup></td><td>SAc</td><td>✓</td></tr><tr><td>NGC 3049</td><td>UGC 05325</td><td>Nuclear</td><td>09:54:49.600</td><td>+09:16:18.00</td><td>19.2</td><td>3.5 × 10<sup>9</sup></td><td>SBab</td><td>...</td></tr><tr><td>NGC 3077</td><td>UGC 05398</td><td>Nuclear</td><td>10:03:18.900</td><td>+68:44:03.00</td><td>3.83</td><td>6.4 × 10<sup>8</sup></td><td>I0pec</td><td>✓</td></tr><tr><td>NGC 3351</td><td>M095</td><td>Nuclear</td><td>10:43:57.900</td><td>+11:42:13.00</td><td>9.33</td><td>8.1 × 10<sup>9</sup></td><td>SBb</td><td>✓</td></tr><tr><td>NGC 3521</td><td>UGC 06150</td><td>Nuclear</td><td>11:05:48.600</td><td>-00:02:05.00</td><td>11.20</td><td>3.5 × 10<sup>10</sup></td><td>SABbc</td><td>✓</td></tr><tr><td>NGC 3627</td><td>MJV 14274</td><td>Extranuclear</td><td>11:20:16.500</td><td>+12:58:42.00</td><td>9.38</td><td>2.8 × 10<sup>10</sup></td><td>SABb</td><td>✓</td></tr><tr><td>NGC 4254</td><td>M099</td><td>Nuclear</td><td>12:18:49.500</td><td>+14:24:55.00</td><td>14.4</td><td>3.9 × 10<sup>10</sup></td><td>SAc</td><td>✓</td></tr><tr><td>NGC 4321</td><td>M100</td><td>Nuclear</td><td>12:22:54.900</td><td>+15:49:19.00</td><td>14.3</td><td>3.5 × 10<sup>10</sup></td><td>SABbc</td><td>✓</td></tr><tr><td>NGC 4536</td><td>UGC 07732</td><td>Nuclear</td><td>12:34:27.000</td><td>+02:11:19.00</td><td>14.5</td><td>2.1 × 10<sup>10</sup></td><td>SABbc</td><td>✓</td></tr><tr><td>NGC 4569</td><td>M090</td><td>Nuclear</td><td>12:36:49.800</td><td>+13:09:47.00</td><td>9.86</td><td>5.2 × 10<sup>9</sup></td><td>SABab</td><td>✓</td></tr><tr><td>NGC 4631</td><td>UGC 07865</td><td>Nuclear</td><td>12:42:07.700</td><td>+32:32:35.00</td><td>7.62</td><td>2.4 × 10<sup>10</sup></td><td>SBd</td><td>✓</td></tr><tr><td>NGC 4736</td><td>[HK83]004</td><td>Extranuclear</td><td>12:50:56.500</td><td>+41:07:09.00</td><td>4.66</td><td>5.8 × 10<sup>9</sup></td><td>SAab</td><td>✓</td></tr><tr><td>NGC 4826</td><td>M064</td><td>Nuclear</td><td>12:56:43.500</td><td>+21:41:03.00</td><td>5.27</td><td>4.2 × 10<sup>9</sup></td><td>SAab</td><td>✓</td></tr><tr><td>NGC 5055</td><td>M063</td><td>Nuclear</td><td>13:15:49.000</td><td>+42:01:44.00</td><td>7.94</td><td>2.2 × 10<sup>10</sup></td><td>SAbc</td><td>✓</td></tr><tr><td>NGC 5457</td><td>[HK83]033</td><td>Extranuclear</td><td>14:03:41.300</td><td>+54:19:03.00</td><td>6.70</td><td>2.3 × 10<sup>10</sup></td><td>SABcd</td><td>...</td></tr><tr><td>NGC 5457</td><td>UGC 09013</td><td>Nuclear</td><td>14:03:12.800</td><td>+54:20:52.00</td><td>6.70</td><td>2.3 × 10<sup>10</sup></td><td>SABcd</td><td>...</td></tr><tr><td>NGC 5713</td><td>UGC 09451</td><td>Nuclear</td><td>14:40:11.400</td><td>-00:17:22.00</td><td>21.4</td><td>3.2 × 10<sup>10</sup></td><td>SABbcp</td><td>✓</td></tr><tr><td>NGC 5866</td><td>UGC 09723</td><td>Nuclear</td><td>15:06:29.500</td><td>+55:45:44.00</td><td>15.3</td><td>5.7 × 10<sup>9</sup></td><td>S0</td><td>...</td></tr><tr><td>NGC 6946</td><td>UGC 11597</td><td>Nuclear</td><td>20:34:52.300</td><td>+60:09:13.00</td><td>6.80</td><td>8.6 × 10<sup>10</sup></td><td>SABcd</td><td>✓</td></tr><tr><td>NGC 6946</td><td>[HK83]003</td><td>Extranuclear</td><td>20:35:25.400</td><td>+60:10:00.00</td><td>6.80</td><td>8.6 × 10<sup>10</sup></td><td>SABcd</td><td>✓</td></tr><tr><td>NGC 6946</td><td>[HK83]066</td><td>Extranuclear</td><td>20:35:11.400</td><td>+60:08:59.00</td><td>6.80</td><td>8.6 × 10<sup>10</sup></td><td>SABcd</td><td>✓</td></tr><tr><td>NGC 7331</td><td>UGC 12113</td><td>Nuclear</td><td>22:37:04.000</td><td>+34:24:53.00</td><td>14.5</td><td>5.3 × 10<sup>10</sup></td><td>SAb</td><td>✓</td></tr></tbody></table>

Note. Sample selected based on availability of KINGFISH PACS [C II] 158 µm and [N II] 205 µm spectral maps. Measurements of distance, $L_{TIR}$, and morphological type are from Kennicutt et al. (2011).

This paper uses [C II] 158 µm and [N II] 205 µm measurements from the Key Insights on Nearby Galaxies: a Far-Infrared Survey with Herschel (KINGFISH) (Kennicutt et al. 2011) and Beyond the Peak (BtP) (Pellegrini et al. 2013) data sets to decompose the [C II] 158 µm emission into the ISM phases in which it originates. These samples include normal galaxies in the local universe ($D \le 30$ Mpc). This work builds on the previous studies of these data sets in Herrera-Camus et al. (2015), Croxall et al. (2017), and Abdullah et al. (2017).

In Section 2, the properties of the nuclear and extranuclear star-forming regions investigated and the observations used in this work are described. Section 3 explains the processing done to evaluate the data. In Section 4 we present the results of our analysis, comparing the measurements of [C II] from isolated ISM phases to TIR luminosity, emission from small dust grains measured by the strength of emission features of polycyclic aromatic hydrocarbons (PAHs), and SFR. Section 5 provides the conclusions drawn from this work.

## 2. Sample and Observations

### 2.1. KINGFISH Galaxies

Table 1 provides a brief description of the properties of the galaxies included in this study. This work uses the subset of the galaxies in the KINGFISH sample with Photoconductor

Array Camera and Spectrometer (PACS) [N II] 205 µm and [C II] 158 µm spectral maps (Kennicutt et al. 2011). The overall KINGFISH survey studied 61 galaxies in the local universe ($D < 30$ Mpc) spanning a wide range of morphological types, luminosities, metallicities, and levels of star formation activity. Of these 61 galaxies, 54 were observed at the [C II] 158 µm line. Within this smaller sample, Herschel PACS far-infrared spectral cubes targeting the [N II] 205 µm line were acquired for galaxies with the highest far-infrared surface brightnesses. This subsample contains 31 regions in 28 galaxies, with 24 centered on the brightest, central nuclear region of the galaxy and seven centered on extranuclear star-forming regions in the disk of the galaxy. All of the targeted galaxies in this sample are normal star-forming galaxies in terms of infrared luminosity, with no LIRGs included, i.e., all KINGFISH galaxies have $log_{10}(L_{IR}/L_{☉}) \le 11$. The galaxies included in this work cover a range of nebular metallicities ($12 + \log(O/H)$) spanning ~8.1–8.7 as measured by Moustakas et al. (2010) using the calibration of Pilyugin & Thuan (2005), and a distance range of 3–30 Mpc (Kennicutt et al. 2011). The physical scales of the [C II] 158 µm ~11" and the [N II] 205 µm ~14" 5 point-spread functions (PSFs) lie in the ranges 180–1700 pc and 200–2100 pc, respectively, across the sample. The proximity and properties of the galaxies included in this sample allow us to determine the nature of the [C II] emission in galaxies with a wide array of spectral coverage and compare
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Herschel PACS [C II] 158 µm (left) and [N II] 205 µm (right) maps of IC 342 with the 20" region where fluxes were extracted marked as black circles. Intensities are measured in nW m⁻² sr⁻¹. The nuclear region of IC 342 was selected as a typical region in this study, because the measured fluxes in both [C II] and [N II] are reliably detected.</figcaption></figure>

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

our results to the U/LIRGS studied in Díaz-Santos et al. (2017). Further, by only targeting normal, star-forming galaxies we are able to explore the behavior of the [C II] deficit without the complicating effects of AGNs or other extreme conditions. Establishing an understanding of the processes occurring in these well-studied galaxies will lay the groundwork for understanding measurements of more extreme cases.

In addition to the KINGFISH measurements, 20 of the 28 galaxies in this sample were included in the BtP survey. The BtP survey used the Spectral and Photometric Imaging Receiver (SPIRE) on Herschel to obtain [N II] 205 µm maps with a larger area, extending this study to the more quiescent areas surrounding the bright regions of star formation included in the KINGFISH PACS 205 µm survey. The larger BtP maps introduce 127 additional 20'' regions within these 20 galaxies. For more information about the choice of 20'' regions, see Section 3. As the BtP regions cover a wider range of conditions, we split them into those centered nearest the galaxy nuclei and those further removed from the nuclei. We distinguish these "Inner" and "Outer" regions as those within one-quarter of $R_{25}$ and those outside of one-quarter of $R_{25}$. The numbers of each type of detection are listed in Table 1. Although the BtP regions do cover a wider range of properties, the centers of only ~14% fall outside of one-quarter of $R_{25}$.

## 2.2. KINGFISH PACS Line Maps

This work uses the KINGFISH program's Herschel/PACS far-infrared mapped spectral observations of the 158 and 205 µm lines. All PACS spectral maps were obtained in the unchopped mapping mode and reduced using the Herschel Interactive Processing Environment (HIPE) version 11.2637 (Smith et al. 2017). Standard data reductions were applied to all images and are summarized in Croxall et al. (2012). The resulting line maps cover a 47'' by 47'' square field of view with 2''6 pixels in both 158 and 205 µm lines and have calibration uncertainties of 20% and 30%, respectively (Beirão et al. 2010; Croxall et al. 2012). The detection of the [N II] 205 µm line in nearby galaxies at a spectral resolution of 150 km s⁻¹ is unique to the PACS instrument, making this data set invaluable for understanding the far-infrared fine-structure lines in the nearby

universe (Beirão et al. 2010). For two of the galaxies in this sample, NGC 5457 and NGC 6946, multiple star-forming regions were targeted; all others were observed only at the central nuclear region or at a single extranuclear star-forming region. As an example of the data from a typical nuclear pointing in this sample, the [C II] 158 µm and [N II] 205 µm maps of IC 342 can be seen in Figure 1. The flux measurements from the PACS line maps are shown in Table 2.

## 2.3. Beyond the Peak SPIRE-FTS Line Maps

In addition to the KINGFISH PACS [N II] 205 µm observations, the SPIRE-FTS on Herschel mapped the [N II] 205 µm line in 20 of the KINGFISH galaxies with PACS [N II] 205 µm detections as part of the Beyond the Peak program. These observations were obtained using the SPIRE-FTS intermediate mapping mode, which is a four-point dither (Croxall et al. 2017). These maps were calibrated using the extended-flux HIPE v10 package. The spectral resolution for these data is ~300 km s⁻¹ at the 205 µm wavelength. More information about the observations and data processing can be found in Pellegrini et al. (2013) and A. Crocker et al. (2019, in preparation). The SPIRE-FTS beam size at 205 µm is 16''6 (Makiwa et al. 2013), and the maps produced by this survey are significantly larger than the PACS [N II] 205 µm maps from the KINGFISH survey (2' × 2' versus 1' × 1' in most cases). The inclusion of these larger spectral maps extends the range of ISM conditions covered to cooler quiescent material surrounding the star-forming regions included in the KINGFISH sample. Some of the important properties of these maps are listed in Table 3.

## 2.4. PACS Imaging

As part of the KINGFISH survey, PACS images at 70, 100, and 160 µm were obtained in scan mode for each galaxy in this sample. These data provide valuable information about the dust temperatures of our sample and were used to determine the far-infrared colors and total infrared luminosities for our regions. These measurements were then used to quantify the [C II] deficit for our sample (see Section 4.1). Uniform surface brightness sensitivities of $\sigma_{sky} \sim 5, 5,$ and $2$ MJy sr⁻¹ at 70 µm, 100 µm, and 160 µm respectively, were achieved for
<table><caption>**Table 2**
PACS Line Measurements</caption><thead><tr><th>Galaxy Name</th><th>Region Type</th><th>L([C II] 158 µm) (erg s<sup>-1</sup>)</th><th>L([N II] 205 µm) (erg s<sup>-1</sup>)</th></tr></thead><tbody><tr><td>NGC 0337</td><td>Nuclear</td><td>774 (±77) × 10<sup>38</sup></td><td>&lt;6.44 × 10<sup>38</sup></td></tr><tr><td>NGC 0628</td><td>Extranuclear</td><td>491 (±49) × 10<sup>37</sup></td><td>52.3 (±16) × 10<sup>37</sup></td></tr><tr><td>NGC 1097</td><td>Nuclear</td><td>277 (±28) × 10<sup>39</sup></td><td>165 (±50) × 10<sup>38</sup></td></tr><tr><td>NGC 1266</td><td>Nuclear</td><td>116 (±12) × 10<sup>39</sup></td><td>108 (±33) × 10<sup>38</sup></td></tr><tr><td>NGC 1377</td><td>Nuclear</td><td>142 (±15) × 10<sup>38</sup></td><td>97.0 (±29) × 10<sup>38</sup></td></tr><tr><td>IC 342</td><td>Nuclear</td><td>196 (±20) × 10<sup>38</sup></td><td>178 (±53) × 10<sup>37</sup></td></tr><tr><td>NGC 1482</td><td>Nuclear</td><td>759 (±76) × 10<sup>39</sup></td><td>275 (±83) × 10<sup>38</sup></td></tr><tr><td>NGC 2146</td><td>Nuclear</td><td>178 (±18) × 10<sup>40</sup></td><td>48.0 (±14) × 10<sup>39</sup></td></tr><tr><td>NGC 2798</td><td>Nuclear</td><td>406 (±41) × 10<sup>39</sup></td><td>236 (±71) × 10<sup>38</sup></td></tr><tr><td>NGC 2976</td><td>Extranuclear</td><td>425 (±43) × 10<sup>37</sup></td><td>106 (±32) × 10<sup>36</sup></td></tr><tr><td>NGC 3049</td><td>Nuclear</td><td>604 (±60) × 10<sup>38</sup></td><td>24.4 (±7.7) × 10<sup>38</sup></td></tr><tr><td>NGC 3077</td><td>Nuclear</td><td>759 (±76) × 10<sup>38</sup></td><td>159 (±48) × 10<sup>36</sup></td></tr><tr><td>NGC 3351</td><td>Nuclear</td><td>443 (±44) × 10<sup>38</sup></td><td>33.8 (±10) × 10<sup>38</sup></td></tr><tr><td>NGC 3521</td><td>Nuclear</td><td>395 (±40) × 10<sup>38</sup></td><td>274 (±83) × 10<sup>37</sup></td></tr><tr><td>NGC 3627</td><td>Extranuclear</td><td>765 (±77) × 10<sup>38</sup></td><td>52.5 (±16) × 10<sup>38</sup></td></tr><tr><td>NGC 4254</td><td>Nuclear</td><td>103 (±10) × 10<sup>39</sup></td><td>84.5 (±25) × 10<sup>38</sup></td></tr><tr><td>NGC 4321</td><td>Nuclear</td><td>107 (±11) × 10<sup>39</sup></td><td>125 (±38) × 10<sup>38</sup></td></tr><tr><td>NGC 4536</td><td>Nuclear</td><td>300 (±30) × 10<sup>39</sup></td><td>39.5 (±12) × 10<sup>38</sup></td></tr><tr><td>NGC 4569</td><td>Nuclear</td><td>198 (±20) × 10<sup>38</sup></td><td>&lt;1.80 × 10<sup>38</sup></td></tr><tr><td>NGC 4631</td><td>Nuclear</td><td>670 (±67) × 10<sup>38</sup></td><td>223 (±67) × 10<sup>37</sup></td></tr><tr><td>NGC 4736</td><td>Extranuclear</td><td>104 (±10) × 10<sup>38</sup></td><td>27.7 (±8.4) × 10<sup>37</sup></td></tr><tr><td>NGC 4826</td><td>Nuclear</td><td>179 (±18) × 10<sup>38</sup></td><td>151 (±45) × 10<sup>37</sup></td></tr><tr><td>NGC 5055</td><td>Nuclear</td><td>227 (±23) × 10<sup>38</sup></td><td>227 (±68) × 10<sup>37</sup></td></tr><tr><td>NGC 5457</td><td>Extranuclear</td><td>194 (±19) × 10<sup>38</sup></td><td>5.29 (±2.9) × 10<sup>37</sup></td></tr><tr><td>NGC 5457</td><td>Nuclear</td><td>530 (±53) × 10<sup>37</sup></td><td>101 (±30) × 10<sup>37</sup></td></tr><tr><td>NGC 5713</td><td>Nuclear</td><td>349 (±35) × 10<sup>39</sup></td><td>151 (±45) × 10<sup>38</sup></td></tr><tr><td>NGC 5866</td><td>Nuclear</td><td>224 (±22) × 10<sup>38</sup></td><td>43.5 (±13) × 10<sup>38</sup></td></tr><tr><td>NGC 6946</td><td>Nuclear</td><td>606 (±61) × 10<sup>38</sup></td><td>302 (±91) × 10<sup>37</sup></td></tr><tr><td>NGC 6946</td><td>Extranuclear</td><td>216 (±22) × 10<sup>38</sup></td><td>109 (±33) × 10<sup>37</sup></td></tr><tr><td>NGC 6946</td><td>Extranuclear</td><td>965 (±97) × 10<sup>37</sup></td><td>157 (±47) × 10<sup>37</sup></td></tr><tr><td>NGC 7331</td><td>Nuclear</td><td>760 (±76) × 10<sup>38</sup></td><td>91.9 (±28) × 10<sup>38</sup></td></tr></tbody></table>

**Note.** Luminosities are measured for regions of 20'' radius smoothed to a 20'' FWHM PSF (see Section 3 for more information). 10% and 30% calibration uncertainties are included for [C II] 158 µm and [N II] 205 µm luminosities respectively.

<table><caption>**Table 3**
Summary of Spectral Map Data</caption><thead><tr><th>Telescope</th><th>Instrument</th><th>λ (μm)</th><th>~PSF FWHM (arcsec)</th></tr></thead><tbody><tr><td>Spitzer</td><td>IRS SL</td><td>5–14</td><td>2–3</td></tr><tr><td>Spitzer</td><td>IRS LL</td><td>14–38</td><td>3–10</td></tr><tr><td>Herschel</td><td>PACS</td><td>158</td><td>11.4</td></tr><tr><td>Herschel</td><td>PACS</td><td>205</td><td>14.5</td></tr><tr><td>Herschel</td><td>SPIRE</td><td>205</td><td>14.5</td></tr></tbody></table>

each region (Dale et al. 2012). The KINGFISH PACS images have a calibration uncertainty of $\epsilon_{cal,v}/f_v \sim 5\%$. For more information about these far-infrared images, see Dale et al. (2012). A summary of the details of these images can be found in Table 4.

## 2.5. Ancillary Infrared Observations

Most regions in the KINGFISH sample were also included in the Spitzer Infrared Nearby Galaxies Survey (SINGS) (Kennicutt et al. 2003; Dale et al. 2006; Smith et al. 2007b). This survey used the Spitzer Space Telescope to obtain infrared imaging and spectroscopy for 75 nearby galaxies. The Infrared

<table><caption>**Table 4**
Summary of Imaging Data</caption><thead><tr><th>Telescope</th><th>Band</th><th>Pixel Scale (arcsec)</th><th>~PSF FWHM (arcsec)</th></tr></thead><tbody><tr><td>GALEX</td><td>FUV</td><td>1.5</td><td>6.0</td></tr><tr><td>Spitzer</td><td>IRAC 3.6 µm</td><td>1.2</td><td>1.7</td></tr><tr><td>Spitzer</td><td>IRAC 8.0 µm</td><td>1.2</td><td>2.0</td></tr><tr><td>Spitzer</td><td>MIPS 24 µm</td><td>1.5</td><td>6.0</td></tr><tr><td>Herschel</td><td>PACS 70 µm</td><td>1.40</td><td>5.6</td></tr><tr><td>Herschel</td><td>PACS 100 µm</td><td>1.70</td><td>6.7</td></tr><tr><td>Herschel</td><td>PACS 160 µm</td><td>2.85</td><td>11.4</td></tr></tbody></table>

Spectrograph (IRS) on board Spitzer obtained low-resolution ($R \sim 50–100$) spectral maps in both the short-low (SL) (5–14 µm) and long-low (LL) (14–38 µm) modules for most of the nuclear regions in the KINGFISH sample (Smith et al. 2007b). This wavelength range includes several prominent PAH emission features. The availability of these data allows comparisons between the PAH emission and the [C II] emission for the regions in our sample (see Section 4.2). The extranuclear regions targeted by the KINGFISH survey were observed by Spitzer/IRS in only the SL module. In most cases, the larger BtP maps were covered with Spitzer/IRS by only the LL module. All observations were reduced with the CUBISM program to create spatially resolved spectral cubes and processed using the IRS pipeline version S14, producing an absolute flux calibration uncertainty of $\sim 25\%$ (Dale et al. 2006). For more information on these observations and data processing, see Smith et al. (2007a).

As part of the SINGS survey, 3.6, 8.0, and 24 µm images were also obtained for each galaxy using the Infrared Array Camera (IRAC) and the Multi-band Imaging Photometer (MIPS) (Rieke et al. 2004). These images were then processed using the MIPS Instrument Team Data Analysis Tool (Gordon et al. 2005). Calibration errors for these images are 10% at all three wavelengths (Dale et al. 2005). Four of the galaxies in this work, IC 342, NGC 2146, NGC 3077, and NGC 5457, were not included in the SINGS sample. For these galaxies 3.6, 8.0, and 24 µm images were obtained from other archival Spitzer surveys, namely the Local Volume Legacy (LVL, Dale et al. 2009) and MIPS GTO (Pahre et al. 2004). The 3.6 and 8.0 µm images provide alternative measurements of PAH feature strength for regions without both SL and LL coverage. For the purposes of this study, the 24 µm data were incorporated into the determination of the total infrared luminosities as well as in our measurements of SFR. More information about these images can be found in Table 4.

## 2.6. Ancillary Ultraviolet Data

In order to determine SFR, FUV maps were obtained from GALEX. 26 of the 31 regions in this sample were imaged as part of the GALEX Nearby Galaxy Survey (NGS) (Gil de Paz et al. 2005), and those that were not covered by NGS were imaged as part of the GALEX All-Sky Imaging Survey (AIS) or by other programs, with the exception of NGC 1377 which has no GALEX imaging. Priority was given to long-exposure data when available. Exposure times for this sample range from 110 to 21,177 s, with a median exposure time of $\sim 1700$ s. The GALEX images have a diffraction-limited FWHM of $\sim 6''$ (Gil de Paz et al. 2005). For more details on the GALEX images, see Table 4.
## 3. Data Analysis

To support a consistent analysis across the wide range of wavelength information we use (0.15–205 µm), we have extracted all fluxes according to an effective 20" resolution. This consistency in extraction is accomplished by taking each image (and each spectral slice within the IRS cubes) at its native resolution and, after centering on each targeted region, summing the pixel values using a Gaussian weighting $\sigma_{extraction}$ determined by the difference in quadrature between the desired 20" and native resolutions, namely

$$ \sigma_{extraction}^2 = \sigma_{20''}^2 - \sigma_{native}^2. \quad (1) $$

In this procedure the data are left at the native pixel sampling. This allows for streamlined convolution to an equivalent Gaussian resolution profile across the wide range of wavelength images we are working with. This method can be consistently used with both images and cubes, ensuring that all data are processed in the same manner. This process follows a similar method to that used in Contursi et al. (2002), which found little difference between this method and other methods of smoothed flux extractions.

### 3.1. Inner and Outer BtP Measurements

As multiple studies have found the [C II] deficit to be a local effect (Smith et al. 2017; Gullberg et al. 2018), we use the extended SPIRE coverage to determine whether there are significant differences between the behavior of the phase-separated [C II] deficit in the inner nuclear regions of these galaxies and in the more extended disks. In order to test these differences, we divide the BtP regions into “Inner” and “Outer,” with Inner regions centered within $0.25R_{25}$ and Outer regions as any falling outside this limit. As the [N II] 205 µm emission is faint, only ~14% of the BtP regions with [N II] 205 µm detections fall into our definition of Outer regions. To avoid biasing our data toward the conditions within galaxies with more regions, an average of the SPIRE detections for the Inner and Outer regions of each galaxy included in the BtP survey was performed to produce the BtP Inner and Outer measurements used throughout this study.

### 3.2. Neutral Fraction of [C II] Measurements

To determine the fraction of the [C II] emission originating in the neutral phase of the ISM, the following relation from Croxall et al. (2012) and Oberst et al. (2006) was used:

$$ f_{[C II],Neutral} = \frac{[C II]158 - (R_{Ionized} \times [N II]205)}{[C II]158}. \quad (2) $$

In this equation, $R_{Ionized}$ is the expected ratio of [C II] 158 µm to [N II] 205 µm emission in the ionized gas where both C$^+$ and N$^+$ are present, as represented by the solid cyan line in Figure 2. This ratio is derived using the collision rates of Tayal (2008) for [C II] and Tayal (2011) for [N II] and assuming Galactic gas-phase abundances of carbon and nitrogen ($1.6 \times 10^{-4}$ per hydrogen atom and $7.5 \times 10^{-5}$ per hydrogen atom respectively) (see Croxall et al. 2017 for further information). It has been found that there is a slight dependence of $R_{Ionized}$ on gas-phase abundances, but this dependence only results in shifts of $\le 5\%$ on measurements of $f_{[C II],Neutral}$ across the range of metallicities included in this sample, and therefore does not affect our results (Croxall et al. 2017). $R_{Ionized}$ is

<figure><img src="image_4.png" /><figcaption>Figure 2. Ratios of [C II] 158 µm to [N II] 122 µm and 205 µm emission for ionized regions where both C$^+$ and N$^+$ are present. Ratios are determined using the method described in Croxall et al. (2017).</figcaption></figure>

determined for each region individually based on measurements of electron number density made using ratios of the [S III] 18.7 and 33.4 µm lines (Dale et al. 2006) or the [N II] 122 and 205 µm lines (Herrera-Camus et al. 2016). Over the range of conditions covered by our sample, these two ratios both provide reliable measurements of $n_e$ (Rubin et al. 1995). Any slight differences in calculations of $n_e$ between these two methods will not affect our results, because $R_{Ionized}$ is nearly independent of $n_e$. Studies of local galaxies with high specific SFR (sSFR) have found that there is a correlation between $n_e$ and sSFR that could potentially affect the ionization parameter in the most dense regions in our study (Kewley et al. 2015; Bian et al. 2016; Holden et al. 2016), but we have not modified our calculation of $R_{Ionized}$ to account for this.

The values of $f_{[C II],Neutral}$ for the KINGFISH and BtP samples are shown in Figure 3, plotted against $\nu f_\nu$ (70 µm)/$\nu f_\nu$ (160 µm), a proxy for dust temperatures. Also shown in Figure 3 are the values determined using smaller subregions measured using Herschel SPIRE data in Croxall et al. (2017). The $f_{[C II],Neutral}$ values found for this sample follow a similar trend to those in the study of Croxall et al. (2017), with an average neutral fraction of ~67% and a decreasing dynamic range in $f_{[C II],Neutral}$ for the more actively star-forming galaxies that have increased $\nu f_\nu$ (70 µm)/$\nu f_\nu$ (160 µm) values. In this and all subsequent figures, the KINGFISH regions, shown as magenta squares, cover only higher $\nu f_\nu$ (70 µm)/$\nu f_\nu$ (160 µm) ratios because all KINGFISH regions are centered on warmer star-forming regions, while the BtP data with a wider field of view extend to the quiescent environments surrounding these star-forming regions.

### 3.3. PAH Measurements

The PAHFIT program was used to determine the strength of the PAH emission features from the fluxes extracted from
<figure><img src="image_5.png" /><figcaption>**Figure 3.** $f_{[C_{II},Neutral]}$ measurements for the nuclear regions in the KINGFISH sample (magenta squares), extranuclear regions in the KINGFISH sample (cyan diamonds), averaged inner regions in the BtP sample (orange stars), averaged outer regions in the BtP sample (blue plus marks), and all individual BtP regions (green crosses), plotted along with the data from Croxall et al. (2017), shown as gray points. Both samples show a similar pattern of increased neutral fraction with far-infrared color as measured by the $v_{f_{\nu}}(70~\mu\text{m})/v_{f_{\nu}}(160~\mu\text{m})$ ratio.</figcaption></figure>

the IRAC spectral maps (Smith et al. 2007b; Gallimore et al. 2010). This program separates emission from PAH features, far-infrared emission lines, warm dust, and stars. For the KINGFISH nuclear regions with IRAC spectral maps in both SL and LL large enough to cover the [C II] 158 µm and [N II] 205 µm emission, the total PAH power was determined by summing the emission from all the PAH emission features measured by PAHFIT (Croxall et al. 2012). For regions covered only in SL (KINGFISH extranuclear regions) or only in LL (BtP regions), the total PAH power was determined using a combination of the IRAC spectral maps and the 8.0 and 3.6 µm IRAC imaging. The bandpass used for the 8.0 µm images contains one of the strongest PAH features (Croxall et al. 2012). Stellar contributions can be removed from the 8.0 µm flux through the use of the 3.6 µm IRAC images. The total PAH power can thus be calculated photometrically using the result determined from the LVL survey (Marble et al. 2010):

$$PAH_{\text{Phot}}^{*} = \nu S_{\nu}(8.0) - 0.24 \times \nu S_{\nu}(3.6). \quad (3)$$

With the added information from either the SL or LL bands, this photometrically determined PAH power can be improved using the results from Croxall et al. (2012):

$$PAH_{\text{SL}}^{*} = 0.497 \times [PAH_{\text{Phot}}^{*} + 3.59 \times \nu S_{\nu}(11.3)] \quad (4)$$

$$PAH_{\text{LL}}^{*} = 0.7472 \times [PAH_{\text{Phot}}^{*} + 3.25 \times \nu S_{\nu}(17)]. \quad (5)$$

With the *Spitzer* IRAC imaging and spectral maps, estimates of the total PAH emission for most regions in our sample were determined, allowing for comparisons of the PAH emission and [C II] emission in both actively star-forming regions and the more quiescent environments surrounding these regions. For our sample, the total PAH emission strength of the KINGFISH extranuclear regions is determined using Equation (4) and that of the BtP regions is determined with Equation (5). These three methods produce similar measurements of total PAH emission power with $1\sigma$ scatters of 0.15 dex and 0.09 dex compared to the summation of all PAH features for Equations (5) and (4) respectively (Croxall et al. 2012).

<figure><img src="image_6.png" /><figcaption>**Figure 4.** [N II] 205 µm/TIR plotted against the far-infrared color measured by $v_{f_{\nu}}(70~\mu\text{m})/v_{f_{\nu}}(160~\mu\text{m})$. The decreasing trend as a function of warmer regions shows that the [N II] 205 µm line has a deficit in our sample. Lines of best fit are shown for the trend found with all the individual regions in the KINGFISH and BtP samples (black line), the KINGFISH nuclear regions and the averaged BtP inner regions (orange dashed line), and the KINGFISH extranuclear regions and the averaged BtP outer regions (blue dotted line).</figcaption></figure>

# 4. Results and Discussion

## 4.1. [N II] and [C II] Deficits

The [N II]/TIR measurements for our sample are displayed as a function of the far-infrared color as measured by the $v_{f_{\nu}}(70~\mu\text{m})/v_{f_{\nu}}(160~\mu\text{m})$ ratio in Figure 4. This ratio is used because it is a proxy for dust temperature, and increased dust temperatures often indicate increased star formation activity. TIR luminosity was determined for each individual region using Equation (4) from Dale et al. (2014) (Equation (6) in this work) with the *Spitzer* 24 µm luminosities and *Herschel* PACS 70 and 160 µm luminosities:

$$L_{\text{TIR}} = 1.548\nu L_{\nu}(24~\mu\text{m}) + 0.767\nu L_{\nu}(70~\mu\text{m}) \\ + 1.285\nu L_{\nu}(160~\mu\text{m}). \quad (6)$$

Similar to the findings of Díaz-Santos et al. (2017), we find that the [N II] 205 µm line ratio with TIR shows a clear decreasing trend in warmer regions, and this trend holds irrespective of whether the inner or outer portions of the galaxies are sampled. Using the form

$$\log_{10} \frac{[\text{N II}]}{\text{TIR}} = m v_{f_{\nu}}(70~\mu\text{m}) / v_{f_{\nu}}(160~\mu\text{m}) + b \quad (7)$$

we perform a linear regression for all the individual regions in our sample, the averaged inner BtP measurements and the KINGFISH nuclear regions, and the averaged outer BtP measurements and the KINGFISH extranuclear regions. For these and all following fits, the KINGFISH extranuclear region from NGC 5457 has been ignored because it is a faint source with significant noise contamination at the edges of the image, making it an outlier in each plot (see the cyan diamond with
<table><caption>**Table 5**
Linear Fits from Figure 4</caption><thead><tr><th>m</th><th>b</th><th>Rms Scatter</th></tr></thead><tbody><tr><td colspan="3">All Individual Regions</td></tr><tr><td>-0.381 [±0.03]</td><td>-3.05<br>All Inner Regions</td><td>0.174</td></tr><tr><td>-0.355 [±0.04]</td><td>-3.09<br>All Outer Regions</td><td>0.181</td></tr><tr><td>-0.317 [±0.22]</td><td>-3.08</td><td>0.246</td></tr></tbody></table>

Note. Properties of the lines of best fit for our [N II] deficit measurements, displayed in Figure 4. We divide our fits by region type, with a fit for all individual regions, a fit for the averaged BtP inner regions and the KINGFISH nuclear regions, and a fit for the averaged BtP outer regions and the KINGFISH extranuclear regions.

$\log_{10} \frac{[\text{N II}]}{\text{TIR}}$ just below -3.0 in Figure 4). The slopes and intercepts for each fit are listed in Table 5 and displayed in Figure 4. Each fit has an equivalent slope within error, showing that the location of the region within the galaxy does not significantly affect our results.

In Figure 5, the [C II]/TIR measurements are displayed as a function of $v f_{\nu}$ (70 µm)/$v f_{\nu}$ (160 µm). In this figure, the left panel is the combined ionized and neutral [C II] emission ([C II]$_{I+N}$), the middle panel is the [C II] emission from only the ionized ISM ([C II]$_{Ionized}$), and the right panel is the [C II] emission from only the neutral ISM ([C II]$_{Neutral}$). The trend we notice in our [C II]$_{Ionized}$ measurements is a scaled version of the [N II] 205 µm measurements by nature of our method for determining [C II]$_{Ionized}$. Each [C II]/TIR measure is fit by a linear regression of the form

$$ \log_{10} \frac{[\text{C II}]}{\text{TIR}} = m v f_{\nu} (70 \mu\text{m}) / v f_{\nu} (160 \mu\text{m}) + b. \quad (8) $$

These fits are displayed in Figure 5 and the properties of each fit are listed in Table 6. For our sample, we find an average of $\log_{10} \frac{[\text{C II}]_{I+N}}{\text{TIR}} = -2.53$, $\log_{10} \frac{[\text{C II}]_{Ionized}}{\text{TIR}} = -3.07$, and $\log_{10} \frac{[\text{C II}]_{Neutral}}{\text{TIR}} = -2.73$. These results match well with other studies, which find the [C II] line emission to account for approximately 1% of the total infrared emission (Smith et al. 2017). As expected from previous work (Croxall et al. 2012; Smith et al. 2017), the ratio of combined ionized and neutral [C II] luminosity to TIR luminosity shows a decline with warmer far-infrared color. As there are no extreme cases in this study, the decreasing trend in the combined ionized and neutral [C II]/TIR ratio is slight, as shown by the slope of -0.127 for our line of best fit. While the [C II] deficit is pronounced for the [C II] emission from the ionized ISM, it disappears when only [C II] emission from the neutral ISM is considered, as shown in the middle and right panels of Figure 5.

By separating our detections by ISM phase, we are able to narrow down the possible causes of the [C II] deficit in our sample. Using this method, we determine that the decreasing trend in [C II]/TIR for warmer, more actively star-forming environments is greatly reduced when only the [C II] emission from the neutral phases of the ISM is considered. On the other hand, the ratio of [C II] emission from the ionized phases of the ISM to TIR luminosity shows a steep decrease as a function of

far-infrared color. This can also be seen in the combined ionized and neutral [C II]/TIR measurements, where the slight decrease observed is driven by the regions from the BtP survey, which have lower $f_{[CII,Neutral]}$ values and therefore more emission from the ionized phases of the ISM (see Figure 5). This trend suggests that the cause of the [C II] deficit occurs predominantly in the ionized phases of the ISM, a conclusion that is supported by the work done in the GOALS survey (Díaz-Santos et al. 2017).

This decreasing trend in [C II] from the ionized phases of the ISM holds both for the star-forming regions targeted in the KINGFISH study, shown as magenta squares, and for the more extended coverage from the BtP survey, shown as green crosses, and is true for both regions within $0.25R_{25}$ and those outside this boundary, as seen in Figure 5 and in the consistency of our measured slopes within error for each location. The decreasing trend measured for the [C II]$_{I+N}$/TIR luminosity ratio is much shallower than the steep trend found in the [N II] 205 µm and [C II]$_{Ionized}$ measurements, shown in Figure 4. This difference indicates that the lack of a measured deficit in the [C II] emission from the neutral ISM is not solely caused by identical decreases in the [C II] 158 µm and [N II] 205 µm fluxes. If this were the case we would then expect similar slopes in our line fits to the [C II]$_{I+N}$ and [N II] deficits. Instead, there must be some differing physical processes in the neutral and ionized ISM driving the observed deficit.

With this new insight into the nature of the [C II] deficit, we can narrow down the possible causes of the deficit in our sample. We suggest that the [C II] deficit is caused by changes in the fraction of UV light absorbed by dust within H II regions and PDRs. Compact/nuclear regions with warmer far-infrared colors have fractionally higher UV absorption by dust. $v f_{\nu}$ (70 µm)/$v f_{\nu}$ (160 µm) traces TIR/FUV for centrally concentrated distributions of dust (Dale et al. 2007); therefore higher $v f_{\nu}$ (70 µm)/$v f_{\nu}$ (160 µm) indicates regions where UV light is being proportionally more quenched by dust in PDRs and H II regions. The resulting dearth of UV emission leaking into the diffuse ISM leads to a decrease in [C II] emission from the ionized phases of the ISM. Previous studies have suggested that a majority of the [C II]$_{Ionized}$ emission must originate in the diffuse ISM because there should be little [C II] emission originating in H II regions where the [C II] line is often thermally quenched by high temperature and densities, and the availability of photons with energies above the 24.38 eV necessary to ionize C+ limits the emission of the 158 µm line (Díaz-Santos et al. 2017; Herrera-Camus et al. 2018a). Thus, the decrease in [C II]$_{Ionized}$ as a fraction of the total infrared emission may be due to (1) a smaller fraction of the ultraviolet radiation from stars being above the Lyman limit (i.e., a deficiency in recent star formation) and (2) a smaller fraction of the H-ionizing radiation being absorbed in low-density ($n_e < 30 \text{ cm}^{-3}$) H II where [C II] emission is not collisionally quenched, i.e., the diffuse ionized ISM. Under these conditions, [C II]$_{Neutral}$ should remain unaffected because it primarily originates in PDRs, where UV photons with energies above 11.3 eV have not been significantly quenched and are still available to ionize the carbon atoms present. This interpretation is consistent with the explanations of the [C II] deficit described in Abel et al. (2009) and Graciá-Carpio et al. (2011) and suggests that the third and fourth explanations of the deficit listed in Section 1 (i.e., the thermalization of [C II] in H II regions and increased FUV absorption leading to [O I])
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Left: [C II] 158 µm/TIR plotted against the far-infrared color measured by $v_{f,70}$ (70 µm)/$v_{f,160}$ (160 µm). The [C II] deficit is observed as a slight decrease in the [C II] 158 µm/TIR ratio at warmer far-infrared colors in our sample. Our sample covers a limited range of conditions, and therefore only a small deficit effect is observed. The lines represent predicted neutral fractions based on the relationship determined by the [C II] emission from only the ionized phase of the ISM (shown in the middle panel). Middle: the ratio of [C II] 158 µm emission from the ionized ISM to TIR plotted against the far-infrared color measured by $v_{f,70}$ (70 µm)/$v_{f,160}$ (160 µm). Right: the ratio of [C II] 158 µm emission from the neutral ISM to TIR plotted against the far-infrared color measured by $v_{f,70}$ (70 µm)/$v_{f,160}$ (160 µm). Notice the disappearance of the observed decrease in [C II] 158 µm/TIR when only the neutral ISM is considered.</figcaption></figure>

<table><caption>**Table 6**

Linear Fits from Figure 5</caption><thead><tr><th>[C II] Component</th><th>m</th><th>b</th><th>Rms Scatter</th></tr></thead><tbody><tr><td colspan="4">All Individual Regions</td></tr><tr><td>Ionized + Neutral</td><td>-0.127 [±0.03]</td><td>-2.33</td><td>0.175</td></tr><tr><td>Ionized</td><td>-0.360 [±0.03]</td><td>-2.49</td><td>0.173</td></tr><tr><td>Neutral</td><td>-0.024 [±0.03]</td><td>-2.69</td><td>0.270</td></tr><tr><td colspan="4">All Inner Regions</td></tr><tr><td>Ionized + Neutral</td><td>-0.113 [±0.05]</td><td>-2.36</td><td>0.197</td></tr><tr><td>Ionized</td><td>-0.356 [±0.04]</td><td>-2.49</td><td>0.171</td></tr><tr><td>Neutral</td><td>-0.024 [±0.06]</td><td>-2.69</td><td>0.287</td></tr><tr><td colspan="4">All Outer Regions</td></tr><tr><td>Ionized + Neutral</td><td>-0.050 [±0.08]</td><td>-2.30</td><td>0.083</td></tr><tr><td>Ionized</td><td>-0.304 [±0.26]</td><td>-2.50</td><td>0.250</td></tr><tr><td>Neutral</td><td>0.018 [±0.16]</td><td>-2.57</td><td>0.147</td></tr></tbody></table>

**Note.** Properties of the lines of best fit for our [C II] deficit measurements. A line of best fit is displayed for each component of the [C II] emission (combined ionized and neutral, ionized, and neutral). We further divide our fits by region type, with a fit for all individual regions, a fit for the averaged BtP inner regions and the KINGFISH nuclear regions, and a fit for the averaged BtP outer regions and the KINGFISH extranuclear regions.

becoming a major coolant in the diffuse ionized ISM) are the most likely for our sample. It is also possible that the other mechanisms described in Section 1 have an effect on the deficit measurements for our sample, but do not explain the changes in trends between measurements of the ionized-phase [C II] and the neutral-phase [C II].

## 4.2. [C II] 158 µm and PAH Emission

PAHs are the dominant source of the photoejected electrons that heat the neutral ISM, which is in turn cooled through channels such as the [C II] 158 µm line (Bakes & Tielens 1994;

Weingartner & Draine 2001). The mid-infrared PAH emission features are a result of vibrational and bending transitions that have been excited by the absorption of far-ultraviolet photons. We thus compare the strength of the PAH emission features to the [C II] emission from both the neutral and ionized phases of the ISM to better understand the microphysics underlying the gas heating by photoelectric ejection of electrons from PAHs and gas cooling by [C II] 158 µm emission. Previous works have found that while the [C II] 158 µm/TIR decreases in warmer regions, the ratio of [C II]/PAH emission is more constant (Helou et al. 2001; Croxall et al. 2012). By measuring this ratio in the separated ISM phases we can test the relationship between gas heating by small grains and gas cooling by [C II] emission.

The ratio of [C II] luminosity to the strength of PAH features for the combined ionized and neutral [C II] emission and the [C II] emission from only neutral and ionized phases of the ISM can be found in Figure 6. KINGFISH nuclear regions where both SL and LL IRS cubes are available are shown as magenta squares, KINGFISH extranuclear regions where only SL IRS cubes are available are shown as blue squares, and BtP regions where only LL IRS cubes are available are shown as green crosses. It should be noted that the slight separation between the different region types is likely driven by the different methods for determining PAH emission strengths, and not by any differences between the regions themselves (see Section 3.3 for more information).

The middle and right panels of Figure 6 show the [C II] to PAH emission ratio when only the [C II] emission from the ionized and neutral ISM are considered, respectively. Similar to results of the deficit observed when comparing the [C II] and TIR luminosity, the ratio of [C II] emission from only the ionized ISM to PAH emission feature strength shows a clear decrease as a function of far-infrared color, while the ratio of [C II] emission from only the neutral ISM to PAH emission feature strength remains fairly constant across the range of
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Left: the ratio of combined ionized and neutral [C II] emission to PAH feature emission strength plotted against far-infrared color. Notice a small decline in the warmer, more actively star-forming regions at higher 70 µm/160 µm ratios. Middle: the ratio of [C II] emission from only the ionized ISM to PAH feature emission strength plotted against far-infrared color. Right: the ratio of [C II] emission from only the neutral ISM to PAH feature emission strength plotted against far-infrared color. Notice the sharp decline in this ratio in the ionized emission and the lack of decline in the neutral emission. Markers are the same as in previous figures.</figcaption></figure>

far-infrared color included in this sample. This holds for both the warmer KINGFISH nuclear and inner BtP regions as well as the slightly cooler outer BtP regions and the KINGFISH extranuclear star-forming regions.

We find that the neutral [C II] emission traces the total PAH emission well (Figure 6, right panel). We interpret this result as naturally arising from the ubiquity of PAHs in the neutral ISM (e.g., PDRs) and their comparative paucity in ionized portions of the ISM such as H II regions (e.g., Helou et al. 2004). This result is consistent with [C II] being a major cooling channel, and PAHs providing a majority of the heating through the photoelectric effect, for the neutral ISM. Therefore, in a scenario where ISM heating is balanced by ISM cooling, [C II]$_{Neutral}$ emission should trace PAH emission. As a majority of the [C II] emission in our sample originates in the neutral ISM (Figure 3), the ratio of combined ionized and neutral [C II] emission to PAH feature strength (Figure 6, left panel) shows a similar trend with a slight decrease in the ratio of [C II] to PAH emission in regions with the highest $v_{f_ν}$ (70 µm)/$v_{f_ν}$ (160 µm) values. The ratio of [C II] emission from the ionized phases of the ISM to PAH emission feature strength shows a decrease with respect to far-infrared color (Figure 6, middle panel). This observed decrease is due to an increasing [C II]$_{Neutral}$ fraction in the warmer, more actively star-forming regions (i.e., higher $v_{f_ν}$ (70 µm)/$v_{f_ν}$ (160 µm)), making [C II]$_{Ionized}$ lower in these regions. Such a decrease could be due to a fractionally higher absorption of UV photons within H II regions for warmer, more actively star-forming environments as described in Section 4.1.

### 4.3. [C II] as an SFR Indicator

The top panel of Figure 7 shows star formation surface densities ($\Sigma_{SFR}$) as a function of [C II] surface brightness ($\Sigma_{[C II]}$) for the [C II] emission from both the neutral and ionized phases of the ISM (left), the [C II] emission arising from only the ionized phase of the ISM (middle), and [C II] emission arising from only the neutral phases of the ISM (right). The

SFRs were determined using the hybrid FUV+24 µm local SFR indicator (Hao et al. 2011; Liu et al. 2011; Calzetti 2013):

$$ SFR(M_{\odot} \text{ yr}^{-1}) = 4.6 \times 10^{-44} \left[ \frac{L(\text{FUV})}{\text{erg s}^{-1}} + 6.0 \frac{L(24 \text{ µm})}{\text{erg s}^{-1}} \right]. \quad (9) $$

After calculating the SFR using Equation (9), $\Sigma_{SFR}$ was calculated by dividing by the deprojected area of the 20" regions. The area was deprojected by dividing by $\cos i$ where $i$ is the inclination of the galaxy disk. $\cos i$ was determined using

$$ \cos^2 i = \frac{(1 - \epsilon)^2 - q^2}{1 - q^2} \quad (10) $$

from Dale et al. (1997), where $\epsilon$ is the disk's ellipticity as measured by de Vaucouleurs et al. (1991) and $q$ is an adopted intrinsic axial ratio (i.e., the ratio of the minor axis to the major axis), with a value of $q = 0.13$ for galaxies of morphological class Sbc and later and $q = 0.2$ for galaxies earlier than Sbc (Dale et al. 1997; Murphy et al. 2018). The same deprojected area was used to determine $\Sigma_{[C II]}$, which is the luminosity of the [C II] emission from each region and each separated phase divided by the deprojected area.

As found in previous studies (Stacey et al. 1991; Boselli et al. 2002; De Looze et al. 2011, 2014; Sargsyan et al. 2012; Herrera-Camus et al. 2015; Díaz-Santos et al. 2017; Smith et al. 2017), there are clear trends with increasing [C II] surface brightnesses indicating increasing star formation. The lines in Figure 7 represent the lines of best fit to our data for all individual regions as well as the combination of the KINGFISH nuclear regions and the inner BtP regions and the combination of the KINGFISH extranuclear star-forming regions and the outer BtP regions, determined using the method described in Kelly (2007). This method uses a Bayesian linear regression that takes into account both detections and upper limits. Between 5000 and 10,000 Markov chain Monte Carlo (MCMC) steps through the
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Top: the [C II] surface brightness plotted vs. SFR surface density for the combined ionized and neutral [C II] emission from each region (left), only the [C II] emission from the ionized phase of the ISM (middle), and only the [C II] emission from the neutral phase of the ISM (right). Black lines represent the fits determined using MCMC fitting and blue shaded regions show the full range of lines attempted in the MCMC fitting. Bottom: the difference in the measurements of SFR using FUV+24 µm measurements and using the derived combined ionized and neutral [C II] surface brightness SFR relationship (left), [C II] surface brightness from only the ionized ISM SFR relationship (middle), and [C II] surface brightness from only the neutral ISM SFR relationship (right).</figcaption></figure>

parameter space are then tested to determine the best-fit relationship. The relationships found for each component of the [C II] emission are described using Equation (11) and the values displayed in Table 7:

$$ \log_{10} \Sigma_{\text{SFR}}(M_{\odot} \text{ yr}^{-1} \text{ kpc}^{-2}) = m \log_{10} \Sigma_{\text{[C II]}}(\text{erg s}^{-1} \text{ kpc}^{-2}) + b. \quad (11) $$

To test our measurement of SFR, the SFR indicator of Hao et al. (2011) determined using a lower dust attenuation coefficient, which is identical to Equation (9) but with a proportionality constant for the 24 µm luminosities of 3.89 instead of 6.0, was also applied to each region in our sample. We that find our linear fit parameters have no dependence on the coefficient we use.

The bottom panels of Figure 7 show the differences between $\Sigma_{SFR}$ measured with the FUV and 24 µm hybrid star formation indicator (Equation (9)) and $\Sigma_{SFR}$ measured using the relationships we determined with all the individual regions and using the different components of the [C II] emission (Equation (11) and Table 7). The median value of the difference for $\Sigma_{SFR}$ measured by the summation of the ionized and neutral [C II] emission is -0.024 dex with a range of 0.80 to -0.36 dex. The range for the differences in $\Sigma_{SFR}$ measured by the [C II]$_{Ionized}$ surface brightness is 1.87 to -0.54 dex with a median value of -0.058 dex, and for the $\Sigma_{SFR}$ measured by [C II]$_{Neutral}$ surface brightness it is 0.025 dex with a range of

<table><caption>**Table 7**
Linear Fits from Figure 7</caption><thead><tr><th>[C II] Component</th><th><i>m</i></th><th><i>b</i></th><th>Rms Scatter</th></tr></thead><tbody><tr><td colspan="4">All Individual Regions</td></tr><tr><td>Ionized + Neutral</td><td>1.04 [±0.053]</td><td>-42.74</td><td>0.230</td></tr><tr><td>Ionized</td><td>0.91 [±0.085]</td><td>-37.11</td><td>0.332</td></tr><tr><td>Neutral</td><td>0.90 [±0.050]</td><td>-37.01</td><td>0.269</td></tr><tr><td colspan="4">All Inner Regions</td></tr><tr><td>Ionized + Neutral</td><td>1.11 [±0.112]</td><td>-45.15</td><td>0.270</td></tr><tr><td>Ionized</td><td>0.88 [±0.180]</td><td>-35.65</td><td>0.405</td></tr><tr><td>Neutral</td><td>1.02 [±0.104]</td><td>-41.78</td><td>0.271</td></tr><tr><td colspan="4">All Outer Regions</td></tr><tr><td>Ionized + Neutral</td><td>1.23 [±0.185]</td><td>-50.00</td><td>0.152</td></tr><tr><td>Ionized</td><td>0.90 [±0.400]</td><td>-36.68</td><td>0.314</td></tr><tr><td>Neutral</td><td>0.96 [±0.198]</td><td>-39.55</td><td>0.235</td></tr></tbody></table>

**Note.** Properties of the lines of best fit for our $\Sigma_{SFR}-\Sigma_{[C II]}$ relationships determined using the method of Kelly (2007). A line of best fit is displayed for each component of the [C II] emission (combined ionized and neutral, ionized, and neutral). We further divide our fits by region type, with a fit for all individual regions, a fit for the averaged BtP inner regions and the KINGFISH nuclear regions, and a fit for the averaged BtP outer regions and the KINGFISH extranuclear regions.

0.80 to -0.39 dex. We plot these differences (logarithmic ratios) to better illustrate the scatter about our best-fit lines.

The [C II] luminosity is plotted against the SFR for the combined ionized and neutral [C II] emission and the [C II] from
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Same as Figure 7, but with SFR plotted against the [C II] luminosity from the different ISM phases. Orange stars are measurements of LIRGS from the GOALS survey (Díaz-Santos et al. 2017). Gray squares represent the limited sample of published high-redshift ($z \ge 4$) galaxies from Lu et al. (2017) and Pavesi et al. (2016, 2019) where $R_{\text{Ionized}}$ was set to four because measurements of $n_e$ are unavailable.</figcaption></figure>

the isolated ionized and neutral ISM phases in the top panels of Figure 8. In these plots, the LIRGS from the Great Observatory All-sky LIRG Survey (GOALS) are included to expand the range of parameter space covered (Díaz-Santos et al. 2017). The LIRGS in this survey were similarly covered at the [C II] 158 µm line with PACS on Herschel and at the [N II] 205 µm line with SPIRE-FTS on Herschel. More information about the observations and processing of these maps can be found in Díaz-Santos et al. (2013) and Zhao et al. (2013, 2016). The inclusion of this sample extends our study to include the more extreme infrared ($L_{IR} \ge 10^{11} L_{\odot}$) LIRGS that were part of the GOALS sample. In addition to the GOALS sample, the handful of high-redshift ($z \ge 4$) galaxies with [N II] 205 µm detections are plotted in Figure 8 (Pavesi et al. 2016, 2019; Lu et al. 2017). As measurements of $n_e$ were unavailable for these sources, we used an average value of $R_{\text{Ionized}} = 4.0$ to determine $f_{\text{Neutral}}$ for these sources. None of the high-redshift sources were included in the line fitting. Similar linear fits were performed on these data and are shown in Figure 8. These trends are described using Equation (12) and the values listed in Table 8:

$$ \log_{10} \text{SFR}(M_{\odot} \text{ yr}^{-1}) = m \log_{10} L([\text{C II}]) (\text{erg s}^{-1}) + b. \quad (12) $$

The bottom panels of Figure 8 show the differences between the SFR measured by the FUV+24 µm hybrid star formation indicator (SFR(FUV+24), Equation (9)) and the SFR determined using the relationships found for the [C II] luminosity, labeled

<table><caption>**Table 8**
Linear Fits from Figure 8</caption><thead><tr><th>[C II] Component</th><th><i>m</i></th><th><i>b</i></th><th>Rms Scatter</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center;">All Individual Regions</td></tr><tr><td>Ionized + Neutral</td><td>0.96 [±0.036]</td><td>-39.46</td><td>0.229</td></tr><tr><td>Ionized</td><td>0.92 [±0.057]</td><td>-37.32</td><td>0.332</td></tr><tr><td>Neutral</td><td>0.92 [±0.035]</td><td>-36.03</td><td>0.237</td></tr><tr><td colspan="4" style="text-align: center;">All Inner Regions</td></tr><tr><td>Ionized + Neutral</td><td>1.05 [±0.079]</td><td>-42.91</td><td>0.272</td></tr><tr><td>Ionized</td><td>1.10 [±0.145]</td><td>-44.32</td><td>0.414</td></tr><tr><td>Neutral</td><td>0.96 [±0.075]</td><td>-39.42</td><td>0.270</td></tr><tr><td colspan="4" style="text-align: center;">All Outer Regions</td></tr><tr><td>Ionized + Neutral</td><td>0.97 [±0.176]</td><td>-39.86</td><td>0.167</td></tr><tr><td>Ionized</td><td>0.63 [±0.182]</td><td>-25.81</td><td>0.235</td></tr><tr><td>Neutral</td><td>0.88 [±0.227]</td><td>-36.31</td><td>0.228</td></tr><tr><td colspan="4" style="text-align: center;">With GOALS</td></tr><tr><td>Ionized + Neutral</td><td>1.02 [±0.022]</td><td>-41.64</td><td>0.309</td></tr><tr><td>Ionized</td><td>1.02 [±0.030]</td><td>-41.11</td><td>0.406</td></tr><tr><td>Neutral</td><td>0.98 [±0.022]</td><td>-40.05</td><td>0.313</td></tr></tbody></table>

**Note.** Properties of the lines of best fit for our SFR-L([C II]) relationships determine using the method of Kelly (2007). A line of best fit is displayed for each component of the [C II] emission (combined ionized and neutral, ionized, and neutral). We further divide our fits by region type, with a fit for all individual regions, a fit for the averaged BtP inner regions and the KINGFISH nuclear regions, and a fit for the averaged BtP outer regions and the KINGFISH extranuclear regions.
SFR([C II]) (Equation (12) and Table 8). We find a median value of −0.036 dex in the differences between the SFR measured using the hybrid FUV+24 µm indicator and the combined ionized and neutral [C II] luminosity, −0.051 dex in the differences between SFR(FUV+24) and the SFR measured by only [C II]$_{Ionized}$ luminosity, and 0.031 dex in the differences between SFR(FUV+24) and the SFR measured by only the [C II]$_{Neutral}$ luminosity. The high-redshift sources seem to follow similar trends with greater scatter, potentially due to the large uncertainties in the [N II] 205 µm detections.

We find that the combined ionized and neutral [C II] emission and the [C II] emission from only the neutral phases of the ISM trace SFR as measured by the FUV+24 µm hybrid SFR indicator with a scatter of ~0.23 dex. The measured slope of 0.96 [±0.036] for the combined ionized and neutral [C II] luminosity–SFR relation is consistent with the relationship found by De Looze et al. (2014), where a slope of 1.01 [±0.02] was found for a sample of dwarfs, ULIRGs, AGNs, and starburst galaxies, and the relationship found by Pineda et al. (2014), with a slope of 0.98 [±0.07] for [C II] luminosity within the Milky Way. Using Equation (2), and our result for the SFR measured by the [C II]$_{Neutral}$ luminosity, we can write an equation for SFR measured by [C II] 158 µm and [N II] 205 µm luminosities:

$$ \log_{10} \text{SFR}(M_{\odot} \text{ yr}^{-1}) = 0.99 \log_{10}[L([\text{C II}] 158 \text{ erg s}^{-1}) - R_{\text{Ionized}} L([\text{N II}] 205 \text{ erg s}^{-1})] - 40.49. \quad (13) $$

This equation has potential to be used in both the local and high-redshift universe without the need for dust corrections.

As the [C II] emission from the neutral phases of the ISM accounts for most of the [C II] emission from these regions, it is expected that the combined ionized and neutral [C II] emission and [C II] emission from only the neutral phases of the ISM follow similar trends, as shown by the similar slopes measured by our lines of best fit. Although both components of [C II] emission rise with higher star formation surface densities, the [C II] emission from the neutral ISM shows a more tightly constrained relationship than the [C II] emission from the ionized ISM. This increased rms of 0.33 for [C II]$_{Ionized}$, 0.1 dex above the rms for [C II]$_{Neutral}$, is likely due to the sharp decrease in [C II]$_{Ionized}$/TIR as a function of far-infrared color. As described in Section 4.1, this result could indicate that a large fraction of the [C II] emission from ionized phases of the ISM is not coming from star-forming H II regions, but originates instead in the diffuse ionized ISM (Díaz-Santos et al. 2017; Herrera-Camus et al. 2018a). The large scatter in the [C II]$_{Ionized}$–SFR relationship indicates that any attempt to use [C II] emission as a tracer of SFR must be treated with caution in galaxies that will have a large fraction of [C II] emission from ionized phases of the ISM, such as high-redshift Lyα emitter galaxies. This conclusion is supported by analysis of the kiloparsec-resolution [C II] detections from the SHINING survey (Herrera-Camus et al. 2018a). We also find no difference in the slopes within error when we separate our regions by location within the galaxy, suggesting that these results hold in a variety of conditions. The inclusion of the GOALS sample raises the slope slightly, which we believe is due to the elevated SFRs of these U/LIRGS, which causes them to fall above the galaxy main sequence (Elbaz et al. 2011; Murphy et al. 2013).

## 5. Conclusions

With the recent availability of [N II] 205 µm detections in galaxies in the local universe from the KINGFISH and BtP

surveys, we are able to distinguish emission from the [C II] 158 µm line from the ionized and neutral phases of the ISM. The sub-kiloparsec resolution of these [N II] 205 µm spectral maps makes them an ideal resource for separating [C II] emission by ISM phase. Our main conclusions are:

1. The [C II] emission from our sample primarily originates from the neutral ISM, with an average neutral fraction $f_{[C II],Neutral}$ of 67%. The [C II] emission from the ionized ISM only dominates in a few regions where far-infrared color temperatures are coolest.

2. The trend of decreasing [C II]/TIR as a function of far-infrared color, commonly referred to as the [C II] deficit, is most prominent when only the [C II] emission from the ionized phases of the ISM is considered, and is almost non-existent in the [C II] emission from the neutral ISM.

3. The differences in the behavior of the [C II] deficit are likely due to the majority of the ionized [C II] emission originating in the diffuse ionized ISM. In warmer regions with increased deficit, the FUV radiation required to heat the diffuse ionized ISM is proportionally more absorbed by dust and therefore unavailable to ionize carbon, decreasing the [C II] emission we observe from this phase.

4. The ratio of [C II] emission from the neutral ISM to PAH emission strength is fairly constant in our sample, suggesting that in the neutral ISM gas heating is controlled by PAHs.

5. The ratio of [C II] emission from the ionized ISM to PAH emission strength decreases sharply as a function of infrared color. This result is consistent with a majority of the [C II] emission from the warmer regions originating in the neutral ISM, decreasing the strength of [C II]$_{Ionized}$.

6. We find that the [C II] emission from the neutral phases of the ISM traces the SFR with a scatter of ~0.23 dex, while the [C II] emission from the ionized phases of the ISM trace SFR with a scatter of ~0.33 dex. The smaller scatter in the neutral [C II]–SFR relationship is inherently tied to the lack of a [C II]$_{Neutral}$ deficit.

7. We do not find strong dependences on spatial location within the galaxies. However, 85% of the regions sampled lie with $0.25R_{25}$, limiting the interpretation of this result.

The work presented here is limited to the normal star-forming galaxies observed with the PACS spectrometer in the KINGFISH survey. Studies of the [C II] emission in AGNs and LIRGs have found that [C II]–SFR relationships are more scattered in extreme conditions (De Looze et al. 2014; Herrera-Camus et al. 2015). Despite this increased scatter for infrared-luminous and accretion-powered environments, there is reason to believe that the SFR–[C II]$_{Neutral}$ relationship presented here will hold in a wide variety of environments. Additional measurements of the [C II] and [N II] lines in LIRGs produce similar trends in the deficit behaviors for [C II] emission from the ionized and neutral phases of the ISM (Díaz-Santos et al. 2017). We plan to further investigate the samples presented, particularly with respect to any trends that may depend on quantities such as metallicity and photoelectric efficiency. Better understanding in detail of the nature of the [C II] deficit in local galaxies, where we can disentangle the contributions from different ISM phases, is critical to interpreting [C II] observations of galaxies at higher redshifts.
We would like to thank George Privon and Tanio Díaz-Santos for enlightening discussions and contributions. D.A.D. would like to thank IPAC/Caltech for hosting him during the beginning stages of this research. This work was supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program, Grant #80NSSC18K1107, as the Wyoming NASA Space Grant Consortium, NASA Grant #NNX15AI08H. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. IRAF, the Image Reduction and Analysis Facility, has been developed by the National Optical Astronomy Observatories and the Space Telescope Science Institute.

## ORCID iDs

Jessica Sutter https://orcid.org/0000-0002-9183-8102

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

Kevin V. Croxall https://orcid.org/0000-0002-5258-7224

J. D. T. Smith https://orcid.org/0000-0003-1545-5078

Philip N. Appleton https://orcid.org/0000-0002-7607-8766

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

Daniela Calzetti https://orcid.org/0000-0002-5189-8004

Alison Crocker https://orcid.org/0000-0001-8513-4945

Bruce Draine https://orcid.org/0000-0002-0846-936X

Maud Galametz https://orcid.org/0000-0002-0283-8689

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

Rodrigo Herrera-Camus https://orcid.org/0000-0002-2775-0595

Leslie K. Hunt https://orcid.org/0000-0001-9162-2371

Mark G. Wolfire https://orcid.org/0000-0003-0030-9510

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