# The Calibration of Polycyclic Aromatic Hydrocarbon Dust Emission as a Star Formation Rate Indicator in the AKARI NEP Survey

Helen Kyung Kim, Matthew A. Malkan, Toshinobu Takagi, Nagisa Oi, Denis Burgarella, Takamitsu Miyaji, Hyunjin Shim, Hideo Matsuhara, Tomotsugu Goto, Yoichi Ohyama, et al.

► To cite this version:

Helen Kyung Kim, Matthew A. Malkan, Toshinobu Takagi, Nagisa Oi, Denis Burgarella, et al. The Calibration of Polycyclic Aromatic Hydrocarbon Dust Emission as a Star Formation Rate Indicator in the AKARI NEP Survey. The Astrophysical Journal, 2024, 974, 10.3847/1538-4357/ad72e6. insu-04846492

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https://insu.hal.science/insu-04846492v1

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Distributed under a Creative Commons Attribution 4.0 International License
# The Calibration of Polycyclic Aromatic Hydrocarbon Dust Emission as a Star Formation Rate Indicator in the AKARI NEP Survey

Helen Kyung Kim<fnref n="1" />, Matthew A. Malkan<fnref n="1" />, Toshinobu Takagi<fnref n="2" />, Nagisa Oi<fnref n="3" />, Denis Burgarella<fnref n="4" />, Takamitsu Miyaji<fnref n="5" />, Hyunjin Shim<fnref n="6" />, Hideo Matsuhara<fnref n="2" />, Tomotsugu Goto<fnref n="7" />, Yoichi Ohyama<fnref n="8" />, Veronique Buat<fnref n="4" />, and Seong Jin Kim<fnref n="7" />

Received 2023 June 27; revised 2024 August 18; accepted 2024 August 19; published 2024 October 16

## Abstract

Polycyclic aromatic hydrocarbon (PAH) dust emission has been proposed as an effective extinction-independent star formation rate (SFR) indicator in the mid-infrared, but this may depend on conditions in the interstellar medium. The coverage of the AKARI/Infrared Camera (IRC) allows us to study the effects of metallicity, starburst intensity, and active galactic nuclei on PAH emission in galaxies with $f_V$ (L18W) ≲ 19 AB mag. Observations include follow-up, rest-frame optical spectra of 443 galaxies within the AKARI North Ecliptic Pole survey that have IRC detections from 7 to 24 µm. We use optical emission line diagnostics to infer SFR based on $H\alpha$ and [O II]λλ3726, 3729 emission line luminosities. The PAH 6.2 µm and PAH 7.7 µm luminosities (L(PAH 6.2 µm) and L(PAH 7.7 µm), respectively) derived using multiwavelength model fits are consistent with those derived from slitless spectroscopy within 0.2 dex. L(PAH 6.2 µm) and L(PAH 7.7 µm) correlate linearly with the 24 µm dust-corrected $H\alpha$ luminosity only for normal, star-forming “main-sequence” galaxies. Assuming multilinear correlations, we quantify the additional dependencies on metallicity and starburst intensity, which we use to correct our PAH SFR calibrations at $0 < z < 1.2$ for the first time. We derive the cosmic star formation rate density (SFRD) per comoving volume from 0.15 ≲ z ≲ 1. The PAH SFRD is consistent with that of the far-infrared and reaches an order of magnitude higher than that of uncorrected UV observations at $z \sim 1$. Starburst galaxies contribute ≳0.7 of the total SFRD at $z \sim 1$ compared to main-sequence galaxies.

Unified Astronomy Thesaurus concepts: Star formation (1569); Polycyclic aromatic hydrocarbons (1280); Interstellar dust (836); Infrared galaxies (790); Infrared photometry (792); Spectral energy distribution (2129); Spectroscopy (1558); Photometry (1234); Galaxy evolution (594); Starburst galaxies (1570); Active galaxies (17)

Materials only available in the online version of record: machine-readable table

## 1. Introduction

The star formation rate (SFR) is one of the key parameters that describes a galaxy's growth and evolution, tracing the conversion of baryonic matter in the interstellar medium (ISM) into stellar radiation. The calibration of various SFR indicators across the electromagnetic spectrum has been extensively studied for the past three decades (R. C. Kennicutt & N. J. Evans 2012; D. Calzetti 2013). The Balmer recombination lines, most notably $H\alpha$ λ6563, and the rest-frame UV continuum emission from massive stars have been established as standard indicators at $z=0$ and $z \gtrsim 1$, respectively. However, the SFRs derived from rest-frame optical/UV lines are prone to large uncertainties in the presence of interstellar dust, which absorbs stellar photons and re-radiates in the infrared (IR). The total ISM luminosity, which measures the integrated dust continuum (~8–1000 µm) heated by O-, B-, A-, and F-type stars, is also commonly used to trace star formation, but may overestimate the SFR in post-starburst galaxies

(C. C. Hayward et al. 2014). Therefore, multiwavelength data are crucial for providing a “big picture” view of the energy generation in galaxies and for overcoming the limitations of relying on a single SFR indicator.

The brightness of the cosmic ISM background suggests at least half the luminous energy generated by stars has been reprocessed into the IR by dust (G. Lagache & H. Dole 2006; F. W. Stecker et al. 2016), and that dust-obscured star formation was more important at higher redshifts than today (V. Buat et al. 2007). At $z \sim 1$, ISM luminous galaxies ($L(8-1000 \mu m) \gtrsim 10^{11} L_\odot$) contribute ~70% of the cosmic IR luminosity density (E. Le Floc'h et al. 2005), but the individual dusty galaxies producing this IR light are not well understood, partly due to the requirement of deep wide-field mid-infrared (MIR) surveys to find them, and then the extreme difficulty of studying their dust spectra. The only mission able to accomplish these tasks was the AKARI space telescope with its Infrared Camera (IRC), which devoted a substantial fraction of its entire lifetime to intensive mapping of the 0.5 deg<fnref n="2" /> area of the North Ecliptic Pole (NEP)-Deep field (orange scalloped circle in Figure 1 of T. T. Takeuchi et al. 2007; K. Murata et al. 2013). AKARI NEP's >6000 faint galaxy the MIR nine-point spectra are a 1.5 order-of-magnitude increase over all other

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Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Department of Physics and Astronomy, University of California, Los Angeles, 475 Portola Plaza, Los Angeles, CA 90095, USA</footnote>

<footnote n="2">²Institute of Space and Astronautical Science, JAXA, Sagamihara, Kanagawa 252-5210, Japan</footnote>

<footnote n="3">³Faculty of Science Division II, Tokyo University of Science, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan</footnote>

<footnote n="4">⁴Aix Marseille Université, CNRS, CNES, LAM, Marseille, France</footnote>

<footnote n="5">⁵Instituto de Astronomía sede Ensenada, Universidad Nacional Autónoma de México, Km 107, Carret. Tij.-Ens., Ensenada, 22060, BC, Mexico</footnote>

<footnote n="6">⁶Department of Earth Science Education, Kyungpook National University, Daegu 41566, Republic of Korea</footnote>

<footnote n="7">⁷Institute of Astronomy, National Tsing Hua University, 101, Section 2. Kuang-Fu Road, Hsinchu, 30013, Taiwan (R.O.C.)</footnote>

<footnote n="8">⁸Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan (R.O.C.)</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Filter transmission curves from WISE and Spitzer/IRAC and MIPS (top) and AKARI/IRC (bottom) superimposed on a modeled MIR spectrum of a star-forming galaxy at $z = 0.308$.</figcaption></figure>

samples (e.g., Spitzer/IRS) combined. The NEP-Deep field is in a prime location that has been observed very intensively at all other wavelengths from the X-ray and UV to radio wavelengths (e.g., H. Matsuhara et al. 2006; S. J. Kim et al. 2021). Figure 1 highlights the continuous MIR coverage of AKARI/IRC photometry from 2 to 24 µm, compared to the Wide-field Infrared Survey Explorer (WISE), Spitzer/IRAC, and MIPS. The superimposed spectrum is that of a modeled star-forming galaxy at the median redshift of our spectroscopic sample ($z = 0.308$).

The luminosities of the 3.3, 6.2, 7.7, 8.6, and 11.3 µm polycyclic aromatic hydrocarbon (PAH) emission features have been proposed as extinction-independent SFR indicators (E. Peeters et al. 2004; B. R. Brandl et al. 2006; J. R. Houck et al. 2007; A. Castro et al. 2014; T. S. Y. Lai et al. 2020). The wavelength coverage from the IRC-derived spectral energy distributions (SEDs) is uniquely suited to study the strongest of these: the PAH 7.7 µm blend composed of emission features at 7.42, 7.60, and 7.85 µm, which can contribute ~42% of the total PAH luminosity in star-forming galaxies (H. V. Shipley et al. 2013). However, studies of ultraluminous infrared galaxies (ULIRGs: $L(8–1000~\mu\text{m}) \ge 10^{12}~L_{\odot}$) at $z < 0.9$ targeted by Spitzer/IRS have diverse MIR spectra, with the majority of ULIRGs having depressed PAH 6.2 and 7.7 µm equivalent widths (EWs), which is likely due to UV photons from buried active galactic nuclei (AGN) or compact star formation destroying small dust grains (H. W. W. Spoon et al. 2007; M. Imanishi et al. 2007; V. Desai et al. 2007). On the other hand, at $z \sim 1$, some ULIRGs have been observed with “enhanced” peak PAH 7.7 µm luminosities per total infrared (TIR) luminosity relative to local ULIRGs (T. Takagi et al. 2010).

The strength of PAH emission is also believed to depend on the gas-phase metallicity of the ISM. C. W. Engelbracht et al. (2005) found decreased 8–24 µm flux density ratios in local star-forming galaxies with $12+\log(O/H) \lesssim 8.2$, possibly due to decreased PAH contribution to the 8 µm bandpass. B. T. Draine et al. (2007) determined that the PAH index, defined as the fraction of the total dust mass in PAH grains with fewer than $10^3$ carbon atoms ($q_{PAH}$), is lower for galaxies with $12+\log(O/H) \lesssim 8.1$ observed in the Spitzer Nearby Galaxy Survey (SINGS). Some possible physical explanations for reduced PAH strength include UV dissociation of PAH molecules due to less dust shielding, increased destruction within shock-heated gas, and decreased efficiency in PAH production from carbon stars and planetary nebulae (B. T. Draine et al. 2007).

Given the effects of metallicity and radiation from AGN and starburst galaxies, observations of rest-frame UV/optical emission lines (e.g., ([O II], H$\beta$, [O III], H$\alpha$, [N II]) in MIR-detected sources are crucial for calibrating PAH dust emission as an SFR indicator. Emission line diagnostics provide the tools to classify sources, measure gas-phase metallicity and dust extinction, and measure accurate spectroscopic redshifts for SEDs.

In this work, we present SFR calibrations based on PAH luminosity, corrected for metallicity and starburst intensity. In Section 2, we describe our spectroscopic and photometric observations, data reduction processes, emission line measurements, galaxy classification, and SED fitting procedure. In Section 3, we present our methodology for measuring PAH luminosities. We confirm their validity by direct comparison with MIR spectra of the same galaxies. In Section 4, we discuss the effects of starburst intensity, metallicity, and AGN strength on PAH luminosity; we derive SFR prediction equations as a function of PAH luminosity calibrated against dust-corrected
Hα and [O II]λλ3726, 3729 line luminosities. In Section 5, we apply our SFR equations to estimate the cosmic star formation rate density (SFRD) from 0 ≲ z ≲ 1.2 and compare our results to UV and FIR-based calibrations. In Section 6 we discuss our PAH SFR results in the context of other studies, and how our calibrations may be used to analyze future James Webb Space Telescope (JWST) observations. Lastly, in Section 7, we provide a summary of conclusions.

## 2. Follow-up and Supporting Observations

To measure key physical properties of AKARI/IRC-detected sources, we obtained follow-up optical and near-infrared (NIR) spectra in the AKARI NEP-Deep and Wide fields. The main goals of our spectroscopic analysis include measuring reliable spectroscopic redshifts, classifying sources as star-forming galaxies or AGN, measuring metallicity, measuring dust extinction with the Balmer recombination lines, and calibrating the dust-corrected Hα and [O II]λλ3726, 3729 SFR against the PAH luminosity. In this section, we present our multiobject spectroscopy from Keck II/DEep Imaging Multi-Object Spectrograph (DEIMOS) and Keck I/MOSFIRE spectrographs, as well as supplementary spectra taken by the AKARI Collaboration from Keck II/Hectospec, WIYN/Hydra, and Subaru/FMOS.

### 2.1. Keck II/DEIMOS Spectroscopic Sample

From 2008 to 2016, we observed 19 slitmasks with Keck II/DEIMOS (S. M. Faber et al. 2003) targeting the AKARI NEP-Deep field. When selecting targets for each slit in the later years, we prioritized MIR AKARI/IRC sources with detected flux measurements at 9 and 18 µm, and assigned secondary priorities to high-redshift galaxies (photometric redshift $z_{phot} \sim 1$) (N. Oi et al. 2014) and optical counterparts of Chandra X-ray sources (M. Krumpe et al. 2015). The spectrograph was configured with the 600ZD grating and GG495 order-blocking filter (central wavelength $\lambda_c = 7500$ Å) for the two slitmasks observed on 2014 August 24, and the 900ZD grating and GG455 order-blocking filter ($\lambda_c = 6800$ Å) for the remaining four slitmasks observed in 2015–2016. A typical slitmask contained ~80 slits that were 1" in width. The spectral range covered approximately 4850 Å ≲ λ ≲ 10050 Å, depending on the location of the slit. The spectral resolution was $R \sim 2000$, which corresponds to the full width at half-maximum (FWHM) $\Delta\lambda \sim 3.75$ Å at the central wavelength $\lambda_c = 7500$ Å, as confirmed by the observed widths of night-sky lines. Prior to observing each night, we acquired one set of Ne, Ar, Kr, and Xe arc lamp spectra and three flat-field exposures of the detectors illuminated by an internal incandescent lamp. In addition, we observed standard star Feige 15 (R.A. 01h49m09s5, decl. +13°33′11″4) in the long-slit mode for flux calibration. We reduced the raw data from 2014 to 2016 using the UCB DEEP2 spec2d reduction pipeline (M. C. Cooper et al. 2012; J. A. Newman et al. 2013), which processed the flat fields and calibration arcs, fit a polynomial wavelength solution to the pixel locations of arc lines, subtracted night-sky emission, and extracted one- and two-dimensional spectra. The extended flux along the slit was included, but most spectra were unresolved in the spatial direction.

The AKARI NEP Collaboration observed eight DEIMOS slitmasks in 2011 July, with the focus of targeting galaxy

cluster candidates with AKARI/IRC MIR detections in the NEP-Deep field (PI: Tomotsugu Goto; A. Shogaki et al. 2018). 553 targets were selected based on Subaru/Suprime-Cam (K. Imai et al. 2007; T. Wada et al. 2008) R-band and Z-band brightness cuts such that $Z < 23$ mag and $R > 21.5$ mag. Slitmasks contained ~50–80 slits of 1" width. The instrument configuration consisted of the 600ZD grating and GG455 order-blocking filter, yielding a spectral resolution of $R \sim 2000$. A set of calibration images consisting of a Ne, Ar, Kr, and Xe arc lamp image and five flat field lamp images were acquired for each slitmask. Bright spectrophotometric standard stars BD +33°2642 and Feige 110 were observed for 90 s each in long-slit mode. Weather conditions were clear on both nights, with 0′′6 seeing. The data were reduced using the spec2d pipeline described above (A. Shogaki et al. 2018).

We then flux calibrated the one-dimensional object spectra from 2011 to 2016 using standard IRAF routines as follows. The raw frames were overscan trimmed and bias subtracted using the `mscred.ccdproc` routine. A normalized flat field was created using `mscred flatcombine`, `noao.twod-spec.longslit.response`, and `textttmscred.mscjoin`, and the standard star spectra were flat fielded with `mscred.ccdproc`. A wavelength-calibrated standard star image was produced using `noao.twodspec.longslit.identify`, `reidentify`, `fitcoordinates`, and `transform` on the arc images to determine the wavelength solution and `noao.imred.kpnoslit.doslit` on the standard star. Then, the sensitivity function was derived using `noao.twodspec.longslit.standar`, `sensfunc`, and `calibrate` on the standard star. Lastly, the sensitivity function was input into the routine `noao.onedspec.calibrate` to apply extinction corrections and flux calibrations to the reduced one-dimensional object spectra.

To estimate the photometric accuracy of the flux-calibrated spectra, we calculated the average flux density of the spectra within the CFHT/MegaCam r-band filter (5690–6930 Å):

$$f_{\nu} [\text{erg s}^{-1} \text{cm}^{-2} \text{Hz}] = \frac{1 \int FT\lambda \, d\lambda}{c \int T\lambda \, d\lambda}, \quad (1)$$

where F is the galaxy spectrum in erg s⁻¹ cm⁻² Å⁻¹, T is the filter response function, λ is the wavelength in angstrom, and c is the speed of light in angstrom per second. We compared our measurements to observed photometric CFHT r-band flux densities and applied a typical offset correction of ~0.1–0.25 dex to account for slit losses. After applying the correction, the emission line fluxes have an uncertainty of ~10%.

The sample contains 68 Hα and 259 [O II] emission line candidates with at least four MIR detections/upper limits in the 7–24 µm filters. The ranges in redshift, stellar mass, and TIR luminosity of the combined unique 296 sources are 0.05 < z < 1.36, 2.1 × 10⁸ M☉ < M* < 9.3 × 10¹¹ M☉, and 1.1 × 10⁹ L☉ < L(TIR) < 2.2 × 10¹² L☉. Table 1 summarizes the newly reduced and calibrated multislit spectroscopy from this work.

### 2.2. Keck I/MOSFIRE Sample

In 2017, we targeted higher redshift galaxies in the AKARI NEP-Deep field, with the Multi-Object Spectrometer For Infrared Exploration (MOSFIRE; I. S. McLean et al. 2010, 2012) on the Keck I telescope. Based on photometric redshifts provided by the AKARI NEP team (N. Oi et al. 2014), we
<table><caption>**Table 1**
Summary of Observations Using the Keck I and Keck II Telescopes</caption><thead><tr><th>Instrument</th><th>UT Date<br>(yy:mm:dd)</th><th>R.A. (J200)<br>(hh:mm:ss.s)</th><th>Decl. (J200)<br>(dd:mm:ss.s)</th><th>PA<br>(deg)</th><th>FWHM<br>(")</th><th>t<sub>exp</sub><br>(min)</th><th>N<sub>r</sub></th></tr></thead><tbody><tr><td>DEIMOS</td><td>2008-08-01</td><td>17:57:21.3</td><td>+66:28:45.7</td><td>0.00</td><td>0.5</td><td>51.0</td><td>81</td></tr><tr><td>DEIMOS</td><td>2008-08-01</td><td>17:56:24.6</td><td>+66:32:26.1</td><td>-10.00</td><td>0.6</td><td>51.0</td><td>80</td></tr><tr><td>DEIMOS</td><td>2008-08-01</td><td>17:55:08.4</td><td>+66:42:34.5</td><td>-20.00</td><td>0.8</td><td>51.0</td><td>81</td></tr><tr><td>DEIMOS</td><td>2008-08-01</td><td>17:56:26.7</td><td>+66:45:40.0</td><td>-30.00</td><td>0.9</td><td>60.0</td><td>82</td></tr><tr><td>DEIMOS</td><td>2008-08-01</td><td>17:54:34.3</td><td>+66:29:37.4</td><td>-35.00</td><td>0.7</td><td>80.0</td><td>79</td></tr><tr><td>DEIMOS</td><td>2011-07-03</td><td>17:53:51.9</td><td>+66:44:55.6</td><td>359.82</td><td>0.6</td><td>120.0</td><td>66</td></tr><tr><td>DEIMOS</td><td>2011-07-03</td><td>17:55:49.7</td><td>+66:45:30.1</td><td>359.82</td><td>0.6</td><td>120.0</td><td>61</td></tr><tr><td>DEIMOS</td><td>2011-07-03</td><td>17:56:28.2</td><td>+66:41:00.1</td><td>359.83</td><td>0.6</td><td>120.0</td><td>55</td></tr><tr><td>DEIMOS</td><td>2011-07-04</td><td>17:57:01.8</td><td>+66:30:00.1</td><td>359.82</td><td>0.6</td><td>90.0</td><td>65</td></tr><tr><td>DEIMOS</td><td>2011-07-04</td><td>17:56:12.8</td><td>+66:30:05.8</td><td>359.80</td><td>0.6</td><td>90.0</td><td>64</td></tr><tr><td>DEIMOS</td><td>2011-07-04</td><td>17:54:54.9</td><td>+66:29:39.9</td><td>359.80</td><td>0.6</td><td>90.0</td><td>65</td></tr><tr><td>DEIMOS</td><td>2011-07-04</td><td>17:53:44.2</td><td>+66:27:54.6</td><td>359.82</td><td>0.6</td><td>90.0</td><td>83</td></tr><tr><td>DEIMOS</td><td>2011-07-04</td><td>17:57:08.4</td><td>+66:43:24.0</td><td>37.85</td><td>0.6</td><td>105.0</td><td>66</td></tr><tr><td>DEIMOS</td><td>2014-08-24</td><td>17:55:15.7</td><td>+66:38:36.3</td><td>130.07</td><td>0.6</td><td>120.0</td><td>83</td></tr><tr><td>DEIMOS</td><td>2014-08-24</td><td>17:54:37.8</td><td>+66:29:14.9</td><td>160.17</td><td>0.6</td><td>120.0</td><td>83</td></tr><tr><td>DEIMOS</td><td>2015-09-14</td><td>17:52:59.5</td><td>+66:30:37.7</td><td>145.04</td><td>0.8</td><td>120.0</td><td>78</td></tr><tr><td>DEIMOS</td><td>2015-09-15</td><td>17:55:01.9</td><td>+66:43:32.3</td><td>156.56</td><td>0.9</td><td>120.0</td><td>88</td></tr><tr><td>DEIMOS</td><td>2016-09-09</td><td>17:55:39.0</td><td>+66:29:59.1</td><td>150.03</td><td>0.9</td><td>80.0</td><td>77</td></tr><tr><td>DEIMOS</td><td>2016-09-10</td><td>17:53:26.0</td><td>+66:41:40.9</td><td>94.02</td><td>0.9</td><td>80.0</td><td>78</td></tr><tr><td>MOSFIRE</td><td>2017-08-02</td><td>17:55:46.3</td><td>+66:37:26.1</td><td>300.03</td><td>1.2</td><td>61.6</td><td>22</td></tr><tr><td>MOSFIRE</td><td>2017-08-02</td><td>17:55:35.4</td><td>+66:37:20.6</td><td>20.00</td><td>0.4</td><td>87.5</td><td>26</td></tr><tr><td>MOSFIRE</td><td>2017-08-03</td><td>17:53:43.9</td><td>+66:27:12.0</td><td>340.22</td><td>0.5</td><td>69.6</td><td>23</td></tr><tr><td>MOSFIRE</td><td>2017-08-03</td><td>17:52:39.6</td><td>+66:34:16.1</td><td>15.00</td><td>0.5</td><td>63.6</td><td>25</td></tr><tr><td>MOSFIRE</td><td>2017-08-03</td><td>17:55:40.8</td><td>+66:36:59.8</td><td>335.00</td><td>0.5</td><td>45.7</td><td>23</td></tr></tbody></table>

Note. The exposure time only includes reduced frames. $N_r$ is the number of targeted science objects (excluding alignment stars).

observed four slitmasks in the J band (1.153–1.352 µm) and one slitmask in the Y band (0.972–1.125 µm) to target Hα/ [N II] in AKARI/IRC sources at $0.7 < z < 1.1$ and $0.5 < z < 0.8$, respectively. Each mask had ~25 slits with a slit width of 0.7, and a resolution of R ~ 3300. Weather conditions were clear and dry on August 2 and mostly clear, with some high clouds on August 3. Calibration images consisted of Ne, Ar arc lamps (1.5 s each) and internal flat fields (11 s each). Slitmasks were observed in multiple correlated double sampling mode with 16 reads, and a dither position offset of ±1.5 was used. Standard stars FS 139 (R.A. 16h33m52s9, decl. +54°28′23″) and HD 162208 were observed in long-slit mode.

We used the standard MOSFIRE Data Reduction Pipeline to reduce the spectroscopic data. The pipeline creates a pixel flat field, performs slit edge tracing, calibrates the wavelength scale, performs background subtraction, rectifies the slits, and extracts the 1D spectra. We flux calibrated the 1D spectra by using the standard star. First we smoothed the standard star spectrum and interpolated over telluric absorption lines. Then we modeled the star as a blackbody based on its effective temperature, and normalized the curve to the star’s Ks-band magnitude from the Two Micron All Sky Survey, factoring in the filter response function. The factor to convert from counts s⁻¹ to erg s⁻¹ cm⁻² Å⁻¹ is then proportional to the ratio of the normalized blackbody function to the calibration star spectrum. We accounted for slit losses by comparing each galaxy’s average flux density to CFHT/WIRCAM J-band photometry.

Our MOSFIRE sample contains 14 Hα and 9 [O II] emission line candidates with at least four MIR detections/upper limits in the 7–24 µm filters. The ranges in redshift, stellar mass, and TIR luminosity of the combined unique 15 sources are 0.54 < z < 1.04,

$8.5 \times 10^9 M_{\odot} < M_{*} < 1.1 \times 10^{11} M_{\odot}$, and $5.5 \times 10^{10} L_{\odot} < L(TIR) < 8.6 \times 10^{11} L_{\odot}$.

## 2.3. T. Takagi et al. (2010) Sample

In addition to our 2011–2016 Keck II/DEIMOS observations, we obtained reduced DEIMOS spectra and emission line flux measurements from observations in semester 2008A through the AKARI NEP Collaboration (PI: Toshinobu Takagi). Targets included 242 AKARI NEP MIR-selected sources with Subaru/ Suprime-Cam R-band magnitude $\lesssim 24$ mag. Five slitmasks were observed using the 600ZD grating and GG495 order-blocking filter. Standard stars HZ 44 and Feige 110 were observed with a long slit (1.5 arcsec) using the same grating and filter setup as the targets. Data were reduced using the spec2d pipeline, and then flux calibrated with standard IRAF routines. [O II]λλ3726, 3729, Hβ, [O III]λ5007, Hα, and [N II]λ6584 emission lines were fit using Gaussian models with the IDL/MPFIT routine. Double Gaussians were used to fit the resolved [O II] doublet, Hβ emission with underlying absorption, and Hα with broad and narrow line components in AGN. The continuum was modeled with a linear fit. Hα and [N II]λλ6548, 6584 were fit simultaneously with three Gaussians. The T. Takagi et al. sample contains 48 Hα and 126 [O II] emission line candidates with at least four MIR detections in the 7–24 µm filters. The ranges in redshift, stellar mass, and TIR luminosity of the combined unique 152 sources are 0.09 < z < 1.35, $9.5 \times 10^8 M_{\odot} < M_{*} < 3.1 \times 10^{11} M_{\odot}$, and $8.3 \times 10^8 L_{\odot} < L(TIR) < 3.1 \times 10^{12} L_{\odot}$.

## 2.4. H. Shim et al. (2013) Sample

We also include spectroscopic redshifts and emission line fluxes from the H. Shim et al. (2013) sample, which consists of spectroscopy of hundreds of low-redshift galaxies and AGN
(z ≲ 0.4) in the AKARI NEP-Wide field. This provides rest-frame UV/optical emission line detections from Keck II/Hectospec and WIYN/HYDRA multiobject spectrographs. The authors primarily selected targets with MIR detections at 11 µm and 15 µm. Secondary target selection criteria are summarized in their Table 1, and include AGN candidates, Herschel FIR sources, and PAH-luminous galaxies. The Shim et al. sample contains 498 Hα and 571 [O II] emission line galaxies with at least four MIR detections/upper limits in the 7–24 µm filters and secure redshifts (i.e., the quality flag of 4). The ranges in redshift, stellar mass, and TIR luminosity of the combined unique 711 sources are 0.03 < z < 1.29, 1.9 × 10⁸ M⊙ < M* < 9.9 × 10¹¹ M⊙, and 4.3 × 10⁸ L⊙ < L(TIR) < 3.2 × 10¹² L⊙.

## 2.5. N. Oi et al. (2017) Sample

We supplement our high-redshift MOSFIRE data with NIR Hα detections from N. Oi et al. (2017), who studied the mass-metallicity relation in luminous infrared galaxies (LIRGs) at z ~ 0.9. Their sample consists of Subaru/FMOS Hα/[N II] multiobject spectroscopy in the J-long band (1.11–1.35 µm) of AKARI MIR sources in the NEP-Deep field. Target galaxies were selected to have detections at 11 µm, 15 µm, and/or 18 µm, and estimated photometric redshifts z<sub>phot</sub> ~ 1. Hα/[N II] fluxes are given for 28 secure Hα emitters and Hα fluxes are given for 36 “nonsecure” Hα detections (i.e., objects where a single emission line was observed and assumed to be Hα.) Some of the nonsecure Hα objects have since been reobserved in optical wavelengths by AKARI NEP collaborators using Keck II/Hectospec, WIYN/Hydra, Keck II/DEIMOS, and GTC/OSIRIS, allowing us to confirm that 10/36 are indeed Hα detections based on the detection of other strong emission lines at shorter wavelengths (e.g., [O II], Hγ, Hβ, [O III]). In addition, we find that the emission line from object 61016583, assumed by N. Oi et al. to be Hα, is [O III]λ5007 at z = 1.357. For reference, we list the updated secure Hα objects in Table 9 in Appendix A. Our SFR calibration sample includes 37 FMOS objects with Hα detections and at least four MIR detections/upper limits in the 7–24 µm filters. The ranges in redshift, stellar mass, and TIR luminosity are 0.70 < z < 1.03, 2.1 × 10⁹ M⊙ < M* < 1.5 × 10¹¹ M⊙, and 8.1 × 10¹⁰ L⊙ < L(TIR) < 1.5 × 10¹² L⊙.

## 2.6. Validation Sample: Y. Ohyama et al. (2018) SPICY Galaxies

The AKARI/IRC slitless SpectroscopIC surveyY (SPICY) obtained IR spectra of all sources with 9 µm flux density brighter than 0.3 mJy in 14 NEP fields of 10' × 10'. The primary goal was to study PAH emission in galaxies at z ≲ 0.5 (Y. Ohyama et al. 2018) within the NEP-Deep and Wide fields. Low-resolution spectra (R ~ 50) were acquired with the short-wavelength MIR camera on the IRC, which covers a wavelength range of 5–13 µm. Y. Ohyama et al. identified 48 galaxies with detectable PAH 6.2, 7.7, and 8.6 µm features. All 48 galaxies have AKARI/IRC photometry, with 83% having detections in the N2, N3, N4, S7, S9W, S11, L15, and L18W filters (~2–18 µm). Of the 48 PAH galaxies in the sample, 41 galaxies have optical spectroscopic detections and 33 galaxies have detected Hα emission from Keck II/DEIMOS (this work) or Keck II/Hectospec (PI: Ho Seong Hwang). Figure 2 illustrates typical SPICY spectra of star-forming galaxies from Y. Ohyama et al. (2018). We use these 41 galaxies as our validation sample to test the consistency and accuracy of our

photometrically derived PAH luminosity measurements. The ranges in redshift, stellar mass, and TIR luminosity of the 41 sources are 0.06 < z < 0.49, 2 × 10⁹ M⊙ < M* < 2 × 10¹¹ M⊙, and 2.1 × 10⁹ L⊙ < L(TIR) < 3.9 × 10¹¹ L⊙.

## 2.7. Emission Line Measurements

Figure 3 shows examples of the quality of our DEIMOS and MOSFIRE spectra. The top panel shows a MOSFIRE galaxy detected in the J band that has red- and blueshifted lines in Hα and [N II] due to rotational kinematics. The second panel is an example of a typical star-forming galaxy observed with DEIMOS with Hα, [N II], and [S II] emission lines. The third panel shows a Seyfert galaxy with double-peaked emission in Hβ and [O III]. The signal to noise is also high enough to resolve the doublet in Hγ (not shown). The fourth panel shows broad blue wings in [O III] emission, suggestive of outflows from an AGN.

We used the SpecPro software (D. Masters & P. Capak 2011) to visually inspect each spectrum and to determine an initial redshift guess based on a template of emission and absorption lines. This initial redshift served as the seed for our Python routine that used nonlinear least-squares fitting. We used Gaussian fits to measure redshifts, emission line fluxes, and EWs for [O II]λλ3726,3729, Hγ, Hβ, [O III]λλ4959,5007, Hα, [N II]λλ6548,6584, and [S II]λλ6716,6731. In general, a linear local continuum was added. For Hγ and Hβ, the continuum was modeled with a Voigt profile in order to account for underlying stellar absorption.

For multicomponent Gaussian fits, the following constraints were used in order to limit the number of free parameters. When resolved, the [O II]λλ3726, 3729 doublet was fit with a double Gaussian, with the central wavelength and width of [O II]λλ3729 fixed relative to [O II]λλ3726. The [O III]λλ4959, 5007 lines were fit with a double Gaussian such that the width of [O III]λλ4959 was fixed to that of the stronger line λ5007, the central wavelength was fixed relative to the expected separation, and the amplitude was fixed to the theoretical value of [O III]λ5007/2.98 (D. E. Osterbrock 1989). For the Hα, [N II]λλ6548,6584 complex, a triple Gaussian was used; the amplitude of [N II]λλ6548 was fixed to be [N II]λλ6584/3.071 (D. E. Osterbrock 1989), the central wavelengths of [N II] were fixed relative to Hα, and the width of [N II]λλ6548 was fixed to be that of λ6584. For Seyfert galaxies where a broad Hα component was detected (FWHM ≳ 1000 km s⁻¹), an additional underlying Gaussian was added.

### 2.7.1. Metallicity Measurements

We estimate the oxygen abundance<fnref n="9" /> of the ionized ISM, 12 +log(O/H), by using the N2 (log [N II]λ6584/Hα), O3N2 (log ([O III]λ5007/Hβ)/([N II]λ6584/Hα)), and O32 (log ([O III]λ5007/[O II]λλ3726,3729) indicators. For the N2 and O3N2 indicators, we use the calibrations by M. Pettini & B. E. J. Pagel (2004), given by

$$12 + \log(O/H)_{\text{N2}} = 8.9 + 0.57 \times \text{N2}, \qquad (2)$$

$$12 + \log(O/H)_{\text{O3N2}} = 8.73 - 0.32 \times \text{O3N2}, \qquad (3)$$

where the 1σ calibration uncertainties are 0.18 dex and 0.14 dex for N2 and O3N2, respectively. When using the N2

<footnote n="9">⁹ We use the terms “oxygen abundance” and “metallicity” interchangeably in this work.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Examples of AKARI SPICY spectra of star-forming galaxies from Y. Ohyama et al. (2018) with PAH emission detections. Underlying curves represent Lorentzian fits to the PAH 6.2, 7.7, 8.6, and 11.3 µm emission features (Y. Ohyama et al. 2018).</figcaption></figure>

indicator, we limit measurements to objects with $N2 < -0.3$ to avoid saturation in nitrogen. For the O32 indicator, we use the calibration given by T. Jones et al. (2015):

$$12 + \log(O/H)_{O32} = 8.3439 - 0.4640 \times O32, \quad (4)$$

which has an uncertainty of 0.11 dex. For reference, solar metallicity is such that $12+\log(O/H) = 8.69$ (M. Asplund et al. 2009).

Table 2 lists the total number of $H\alpha$ and [O II] detections with at least four photometric detections (including upper limits from 7 to 24 µm) and empirical metallicity measurements using either the N2 index (for $H\alpha$- and [N II]-observed sources) and/or O32 index (for [O II] sources).

## 2.8. AGN Selection

To avoid contamination from AGN in our SFR calculations, and to study the impact that the presence of an AGN has on PAH dust luminosity, we classify our source spectra. We identify AGN candidates using a combination of spectroscopic diagnostics, MIR colors, and X-ray crossmatching. An object is considered to be an AGN if it meets at least one of the four following criteria:

1. the spectrum has broad permitted emission lines (i.e., FWHM $\gtrsim$ 1000 km s$^{-1}$) consistent with a Type 1 Seyfert galaxy;

2. the object is a Type 2 Seyfert galaxy or LINER identified with the Baldwin–Philips–Terlevich (BPT) line ratio diagram such that $\log([O III]/H\beta) > 0.61/(\log([N II]/H\alpha)-0.02-0.1833 \times z) + 1.2+0.03 \times z$ (L. J. Kewley et al. (2013), Equation (1));

<table><caption>**Table 2**
Number of $H\alpha$ and [O II] Detections from Combined Observations</caption><thead><tr><th>Instrument</th><th>Ref.</th><th>N(Hα)</th><th>N([O II])</th></tr></thead><tbody><tr><td>Keck/DEIMOS</td><td>...</td><td>72</td><td>196</td></tr><tr><td>Keck/MOSFIRE</td><td>...</td><td>9</td><td>7</td></tr><tr><td>MMT/Hectospec, WIYN/Hydra</td><td>(1)</td><td>334</td><td>422</td></tr><tr><td>Subaru/FMOS</td><td>(2)</td><td>22</td><td>...</td></tr><tr><td>Total</td><td></td><td>437</td><td>625</td></tr></tbody></table>

**Notes.** All galaxies have at least four photometric detections (including upper limits) from 7 to 24 µm and empirical metallicity measurements using the emission line ratios [N II]/$H\alpha$ (for $H\alpha$- and [N II]-measured sources) and/or O32 (for [O II] sources).

**References:** (1) H. Shim et al. (2013), (2) N. Oi et al. (2017).

3. for MIR-selected AGN, the AKARI/IRC colors are such that $N2-N4 > 0$ and $S7-S11 > 0$ [AB magnitude] (H. M. Lee et al. 2007; H. Shim et al. 2013); and/or

4. the object has a Chandra X-ray counterpart within $2''5$ (M. Krumpe et al. 2015).

The left panel of Figure 4 shows the usual BPT-[N II] emission line ratio diagram for our sources. Based on this diagram, there are 215 star-forming galaxies ("BPT-SF") and 154 AGN candidates ("BPT-AGN"). Based on the MIR colors, there are 779 star-forming galaxies ("MIR-SF") and 157 AGN candidates ("MIR-AGN"). BPT-classified SF galaxies with $N2$, $N4$, $S7$, and $S11$ filter detections are 99% consistent with their MIR color classifications; 160 BPT-SF galaxies are also MIR-SF galaxies, while only two BPT-SF galaxies are classified as MIR-
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Example observations illustrating the quality and variety of selected sections of our high-resolution spectra. The galaxy in the top panel was observed with Keck I/MOSFIRE in the J band, and the bottom three were observed with Keck II/DEIMOS. The Hα/[N II] complex is clearly detected in the top two spectra, while the Hβ/[O III] complex is seen in the bottom two.</figcaption></figure>

AGN. However, the likelihood that a BPT-AGN is classified as a MIR-SF galaxy is high: 121 BPT-AGN are classified as MIR-SF galaxies and eight are classified as MIR-AGN. This is probably because MIR color selection is stricter, tending to exclude objects with low AGN fraction and many Seyfert 2's, which the BPT diagram reveals. Thus, an MIR-selected AGN is powerful enough to be certainly identified as a BPT-AGN (left panel). The converse is not always true; some BPT-classified AGN have active nuclei that are too faint to contribute much MIR continuum. Both panels are color coded by their AGN fraction as determined through SED fitting (Section 3.1).

### 3. IRC Measurement of the PAH Luminosity

#### 3.1. SED Modeling

We matched our Hα detections with their multiwavelength photometric counterparts, using a matching radius of the FWHM

of the telescope point-spread function. When available, we merged photometry from the following telescopes: Chandra (M. Krumpe et al. 2015), GALEX far-ultraviolet (FUV) and near-ultraviolet (NUV; D. Burgarella et al. 2019), CFHT/MegaCam *u**, *g*', *r*', *i*'. *z*' (N. Hwang et al. 2007; N. Oi et al. 2014), Subaru/Hyper Suprime-Cam *g/r/i/z/Y* (N. Oi et al. 2021), CFHT/WIRCAM *J* and *K*<sub>s</sub> (N. Oi et al. 2014), KPNO/FLAMINGOS *J* and *H* (Y. Jeon et al. 2014), AKARI/IRC *N*2, *N*3, *N*4, *S*7, *S*9W, *S*11, *L*15, *L*18W, *L*24 (S. J. Kim et al. 2012; K. Murata et al. 2013), Spitzer/IRAC1 (3.6 µm) and IRAC2 (4.5 µm) (H. Nayyeri et al. 2018), WISE 12 µm and WISE 22 µm (E. L. Wright et al. 2010; T. H. Jarrett et al. 2011; R. M. Cutri et al. 2014), Herschel/PACS green (100 µm) and PACS red (160 µm) (C. Pearson et al. 2019), and Herschel/SPIRE 250 µm, 350 µm, 500 µm bands (C. Pearson et al. 2017). We note that some of these data sets do not cover the entire AKARI NEP-Wide field, but our multiwavelength coverage of the NEP-Deep field is reasonably complete.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Left: BPT-[N II] diagram based on the redshift-dependent L. J. Kewley et al. (2013) equation. The line that separates star formation from AGN at $z=0$ is shown for reference. Right: MIR classification with AKARI colors for objects with $S/N > 3$ detections in each filter. AGN candidates are found in the region where $N2-N4 > 0$ and $S7-S11 > 0$ (dashed lines). Both panels are color coded by their MIR-AGN fraction determined from CIGALE SED fits (Section 3.1).</figcaption></figure>

We modeled SEDs with the Code Investigating GALaxy Emission (CIGALE) software, which is based on the assumption of energy balance between stellar radiation absorbed by dust in the UV/optical and dust emission output in the mid to far-infrared (FIR; M. Boquien et al. 2019; G. Yang et al. 2020). This implicitly requires that our view of the extinction is similar to what observers along most other lines of sight to the galaxy would also measure. CIGALE uses Bayesian analysis that combines stellar population models, AGN and ISM templates,<fnref n="10" /> and various libraries to determine the best parameters across all possible spectra. We assumed an exponentially decaying star formation history, G. Chabrier (2003) initial mass function (IMF), D. Calzetti et al. (2000) dust attenuation model, B. T. Draine et al. (2014) dust emission template, and J. Fritz et al. (2006) AGN emission model. The dust emission model characterizes PAH emission strength based on the $q_{PAH}$ parameter, which is defined as the fraction of the total dust mass in PAH grains with fewer than $10^3$ carbon atoms. For reference, average Milky Way dust has $q_{PAH} \approx 4.6\%$ (B. T. Draine & A. Li 2007). We note that the Chandra X-ray data were only used to identify X-ray AGN and were not included in the CIGALE fits.

We define the AGN fraction, $frac_{AGN}$, as the ratio of the AGN luminosity to the total luminosity integrated between 5 and $10~\mu$m. For star-forming galaxies, we assume $frac_{AGN} = 0$. Otherwise, for AGN candidates and unclassified objects (i.e., objects with incomplete spectroscopic/photometric data), we allowed $frac_{AGN}$ to vary. Figure 4 is color coded by the AGN fraction. The median AGN fraction for BPT-AGN candidates is 0.05 with an interquartile range of 0.01–0.13, compared to a median of 0.33 for MIR-AGN candidates with an interquartile range of 0.12–0.48. This difference demonstrates the efficacy of the BPT diagram to select AGN with lower $frac_{AGN}$ than the AKARI color–color diagram.

We used a 32-core processor through Amazon Web Services cloud computing<fnref n="11" /> to run our models at a rate of ~30,000 models $s^{-1}$. For the final sample, we limit objects to those with $0.5 < reduced \chi^2 < 10$. Objects with reduced $\chi^2 < 0.5$ were excluded in order to avoid models with overfitting. Table 3 summarizes our input SED parameters. In Figure 5, we illustrate the multiwavelength coverage of our photometric data (purple circles) and show some diverse examples of CIGALE best-fit SEDs, which have a range of PAH strengths in the MIR. The light blue region from 2 to $24~\mu$m highlights the observed wavelength range of the AKARI/IRC, and the dotted vertical line indicates the observed wavelength for the PAH $7.7~\mu$m blend. The model spectrum (solid black line) represents the sum over the attenuated stellar emission, dust emission, and AGN emission components. Although we include the contribution from nebular emission when modeling SEDs, we omit it in the figure for simplicity.

The TIR, $L(TIR)$, has been extensively used in the literature as an SFR indicator, and is known to correlate with PAH luminosity (T. Takagi et al. 2010). We calculate $L(TIR)$ for individual objects by shifting the best-fit SED to the rest frame and integrating from 8 to $1000~\mu$m. In Appendix B, we test the dependence of FIR photometry on the integrated $L(TIR)$ and find that $L(TIR)$ measurements with and without FIR data are consistent with an rms dispersion of 0.096 dex (Figure 25). Therefore, we estimate that our $L(TIR)$ measurements are accurate to within ~20%.

## 3.2. Calibration Sample Characteristics

Our final PAH-derived SFR calibration sample consists of main-sequence and starburst galaxies with $H\alpha$ and/or [O II] emission lines and metallicities measured using the N2, O3N2, and/or O32 line ratio indices. The sample includes 319 galaxies with $H\alpha$ detections and 332 galaxies with [O II] detections. There are a total of 443 unique sources. We summarize the main properties of this sample in Figure 6. The redshift, stellar mass, and TIR luminosity range from $0.048 < z < 1.025$, $10^{8.7} M_{\odot} < M_{*} < 10^{11.2} M_{\odot}$, and

<footnote n="10">¹⁰ We note that CIGALE includes the option to include user-input nebular emission line fluxes (e.g., $H\alpha$, [N II]), which would further constrain the metallicity and $q_{PAH}$ parameters. However, we do not include emission line fluxes in this work, but recommend this option for future studies.</footnote>

<footnote n="11">¹¹ https://aws.amazon.com/</footnote>
<table><caption>**Table 3**
Input Parameters for CIGALE SED Fitting</caption><thead><tr><th>Parameter</th><th>Description</th><th>Value</th></tr></thead><tbody><tr><td colspan="3">Star Formation History: SFR(t) ∝ e<sup>-t/τ</sup></td></tr><tr><td>τ (Myr)</td><td>e-folding time of the main stellar population</td><td>100, 300, 1000, 2000, 3000, 5000, 10,000, 15,000, 30,000</td></tr><tr><td>age (Myr)</td><td>Age of the main stellar population</td><td>3, 8, 20, 50, 125, 300, 800, 2000, 5000, 13,000</td></tr><tr><td colspan="3">Stellar Populations</td></tr><tr><td>IMF</td><td>Initial mass function</td><td>G. Chabrier (2003)</td></tr><tr><td>Z</td><td>Metallicity</td><td>0.02 (solar)</td></tr><tr><td>Separation age (Myr)</td><td>Separation age between young and old stellar populations</td><td>10</td></tr><tr><td colspan="3">Nebular Emission</td></tr><tr><td>log(U)</td><td>Ionization parameter</td><td>-2.0</td></tr><tr><td>f<sub>esc</sub></td><td>Fraction of Lyman continuum photons escaping the galaxy</td><td>0.0</td></tr><tr><td>f<sub>dust</sub></td><td>Fraction of Lyman continuum photons absorbed by dust</td><td>0.0</td></tr><tr><td colspan="3">Dust Attenuation: D. Calzetti et al. (2000)</td></tr><tr><td>E(B-V)<sub>lines</sub></td><td>Color excess of nebular line emission</td><td>0.0-1.6 in steps of 0.2</td></tr><tr><td>f</td><td>Ratio of E(B-V)<sub>continuum</sub> to E(B-V)<sub>lines</sub></td><td>0.44</td></tr><tr><td>UV extinction bump wavelength</td><td>Central wavelength of UV bump in nanometers</td><td>217.5</td></tr><tr><td>UV bump width</td><td>FWHM of UV bump in nanometers</td><td>35.0</td></tr><tr><td colspan="3">Dust Emission: B. T. Draine et al. (2014)</td></tr><tr><td>q<sub>PAH</sub> (%)</td><td>Mass fraction of PAH</td><td>0.47, 1.12, 2.50, 3.90, 4.58, 5.26, 5.95, 6.63, 7.32</td></tr><tr><td>U<sub>min</sub></td><td>Minimum radiation field</td><td>1.0, 5.0</td></tr><tr><td>α</td><td>Power-law slope dU/dM ∝ U<sup>α</sup></td><td>2.0</td></tr><tr><td>γ</td><td>Fraction illuminated from U<sub>min</sub> to U<sub>max</sub></td><td>0.2</td></tr><tr><td colspan="3">AGN Emission: J. Fritz et al. (2006)</td></tr><tr><td>r ratio</td><td>Ratio of the maximum to minimum radii of the dust torus</td><td>60.0</td></tr><tr><td>τ<sub>9.7</sub></td><td>Optical depth at 9.7 µm</td><td>1.0, 6.0</td></tr><tr><td>opening angle</td><td>Opening angle of the dust torus</td><td>100°</td></tr><tr><td>ψ</td><td>Angle between the equatorial axis and line of sight</td><td>0°, 0.01, 89°</td></tr><tr><td>frac<sub>AGN</sub></td><td>AGN fraction</td><td>0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5</td></tr></tbody></table>

$10^{8.7} L_{\odot} < L(\text{TIR}) < 10^{12} L_{\odot}$, respectively. Table 4 lists the emission line fluxes and physical properties for a portion of galaxies within the calibration sample. The full table is published online.

Figure 7 shows the specific star formation rate (sSFR) as a function of the redshift of all galaxy candidates with $H\alpha$ and/or [O II] detections. The sSFR, the mass-normalized SFR, is given by R. C. J. Kennicutt (1998) as

$$s\text{SFR} [\text{yr}^{-1}] = [1.72 \times 10^{-10} \times (L(\text{TIR})/L_{\odot})]/[(M_{*}/M_{\odot})/0.61], \quad (5)$$

where $L(\text{TIR})$ is the TIR luminosity of the best-fit SED integrated from rest-frame 8–1000 µm and $(M_{*}/M_{\odot})/0.61$ is the stellar mass converted from G. Chabrier (2003) to R. C. J. Kennicutt (1983) IMF. “Main-sequence” galaxies are defined as objects with $13 \times t_{\text{cosmic}}^{-2.2} \le s\text{SFR} [1/\text{Gyr}] \le 52 \times t_{\text{cosmic}}^{-2.2}$, where $t_{\text{cosmic}}$ is the cosmic time elapsed since the Big Bang in Gyr (D. Elbaz et al. 2011). “Starburst” galaxies and “quenched” galaxies lie above and below this region, respectively. To classify starburst galaxies, we adopt the $R_{\text{SB}}$ starburst parameter from D. Elbaz et al. (2011), which describes the “starburst excess” relative to main-sequence star formation and is defined as the ratio of the sSFR to the main-sequence sSFR. With their definition, starburst galaxies have $R_{\text{SB}} \gtrsim 2$ (blue-filled star symbols), main-sequence galaxies have

0.5 $\lesssim R_{\text{SB}} \lesssim 2$ (black-filled triangle symbols), and quenched galaxies have $R_{\text{SB}} \lesssim 0.5$ (red circle symbols).

In Figure 8, we plot the observed N3 and L18W magnitudes as a function of redshift for galaxies within our calibration sample (red-filled circle symbols). Of the 443 star-forming galaxies in the calibration sample, 424 galaxies have detected N3 magnitudes (left panel), and 369 galaxies have detected L18W magnitudes (right). For reference, photometric detections of galaxies in the AKARI/IRC NEP-Deep field with photometric redshifts are shown as black dots (N. Oi et al. 2014). The blue dashed lines in the figure indicate that our sample is flux-limited down to $\sim 20$ AB mag at 3 µm and $\sim 19$ AB mag at 18 µm up to $z \sim 0.7$, which corresponds to a stellar mass limit of $M_{*} \gtrsim 10^{9.5} M_{\odot}$.

### 3.3. Extinction-corrected $H\alpha$ and [O II] Luminosity

We calculate dust-corrected $H\alpha$ luminosities using three methods: the 24 µm rest-frame monochromatic luminosity ($\lambda L_{\lambda}(24 \mu m)$) correction, the Balmer decrement (BD) ($H\alpha/H\beta$), and the color excess $E(B-V)$ derived with CIGALE. The empirical 24 µm correction to $H\alpha$ defined by R. C. J. Kennicutt (1998) is given as

$$L(H\alpha)_{24\mu m} = L(H\alpha)_{\text{obs}} + 0.02 \times \lambda L_{\lambda}(24 \mu m) [\text{erg s}^{-1}], \quad (6)$$
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Examples of typical CIGALE SED fits, including (a) star-forming “main-sequence” galaxy with solar metallicity and strong PAH emission; (b) metal-rich starburst galaxy ($R_{SB} = 11$) with weak PAH emission; (c) metal-poor starburst galaxy ($R_{SB} = 18$) with weak PAH emission; (d) Type II BPT-AGN with weak PAH emission.</figcaption></figure>

where $L(H\alpha)_{obs}$ is the observed H$\alpha$ luminosity and luminosities are in erg per second We calculate $\lambda L_{\lambda}(24 \mu m)$ as the rest-frame luminosity density of the best-fit SED model at 24 $\mu m$ multiplied by the effective wavelength. The intrinsic H$\alpha$ luminosity is given by

$$L(H\alpha) = L(H\alpha)_{obs} \times 10^{0.4A(H\alpha)}, \quad (7)$$

where $A(H\alpha)$ is the attenuation in H$\alpha$ in magnitudes. For star-forming galaxies with H$\alpha$ and H$\beta$ flux measurements, $A(H\alpha)$ is given by the BD:

$$A(H\alpha)_{BD} [\text{mag}] = 3.33 \times 1.97 \times \log\left(\frac{(F(H\alpha)/F(H\beta))_{\text{obs}}}{2.86}\right), \quad (8)$$

where $(F(H\alpha)/F(H\beta))_{\text{obs}}$ is the observed flux ratio, and we assume the D. Calzetti et al. (2000) attenuation law and an intrinsic flux ratio of 2.86 (Case B recombination and $T = 10^4$ K (D. E. Osterbrock 1989). The SED-derived $A(H\alpha)$ is given by

$$A(H\alpha)_{\text{CIGALE}} [\text{mag}] = 2.45 \times E(B - V)_{\text{lines}}, \quad (9)$$

where $E(B - V)_{\text{lines}}$ is the color excess of the nebular lines' light, and we assume a standard Milky Way extinction curve.

Figure 9 shows a comparison of intrinsic H$\alpha$ luminosities for the galaxies in the calibration sample with H$\alpha$ and H$\beta$ flux measurements. Heavily dust-reddened objects with $A(H\alpha) > 3$ mag as calculated via the BD are shown by red squares. In these objects, the dust-corrected H$\alpha$ luminosity deviates significantly from those derived via the 24 $\mu m$ luminosity and predicted CIGALE extinction, as shown in panels (a) and (b). However, as shown by panel (c), the corrections given by the 24 $\mu m$ and CIGALE methods produce similar intrinsic H$\alpha$ luminosities, which is most likely due to their shared dependence on MIR photometry. The scatter between the Balmer decrement correction and 24 $\mu m$ luminosity correction has been observed in other studies (e.g., A. Boselli et al. 2015; H. V. Shipley et al. 2016). They attribute the discrepancy as being due to uncertainty in the underlying stellar absorption correction for objects with weak H$\beta$ emission.

To correct the [O II] luminosity for dust extinction, we adopt the calibration given in R. C. J. Kennicutt (1998):

$$L([\text{O II}])_{24 \mu m} = L([\text{O II}])_{\text{obs}} + 0.029 \times \lambda L_{\lambda}(24 \mu m), \quad (10)$$

where the luminosities are in erg per second. The [O II] SFR is then given by R. C. J. Kennicutt (1998) as

$$\text{SFR} [\text{M}_\odot \text{yr}^{-1}] = 8.1 \times 10^{-42} L([\text{O II}])_{24 \mu m} [\text{erg s}^{-1}], \quad (11)$$
<figure><img src="image_8.png" /><figcaption>Figure 6. Distributions of main properties of the final SFR(PAH) calibration sample with Hα and/or [O II] emission line detections. From left to right: spectroscopic redshift, stellar mass, TIR luminosity, metallicity based on N2 index, metallicity based on O32 index, and attenuation in Hα based on SED fitting.</figcaption></figure>

assuming a Salpeter IMF. We discuss the limitations of using the [O II] luminosity to measure SFR in Appendix D.

### 3.4. Measurement of PAH Luminosity

We input the rest-frame, best-fit SEDs from CIGALE into PAHFIT (J. D. T. Smith et al. 2007; J. D. Smith & B. Draine 2012) in order to model the dust emission and continuum from 5 to 35 µm, and to extract the PAH luminosities. The input best-fit SEDs include the attenuated stellar emission, nebular emission, and dust emission (i.e., modeled AGN emission is removed for AGN candidates). Then, we resample the model spectrum into the Spitzer/IRS wavelength grid. PAHFIT uses a physical decomposition model to simulate the MIR continuum with a sum of modified blackbodies and starlight, and the PAH dust blends with Drude profiles. Because it does not take AGN emission into account, we only consider SED components from the total attenuated stellar light, nebular emission, and dust emission. For the PAH features, we fixed the central wavelengths and FWHM to their standard values and allowed the amplitudes to vary. Figure 10 shows a typical PAHFIT result for a star-forming galaxy. The integrated intensity of the Drude profile is equal to

$$I^{(r)} = \frac{\pi c b_r \gamma_r}{2 \lambda_r}, \qquad (12)$$

where $\lambda_r$ is the central wavelength of the PAH feature, $\gamma_r$ is the fractional FWHM, and $b_r$ is the central amplitude (J. D. T. Smith et al. 2007). For example, the luminosities for the PAH 6.2 µm and 7.7 µm emission features are given by

$$L(\text{PAH } 6.2 \, \mu\text{m}) [\text{erg s}^{-1}] = 10^7 \times 4\pi d_L^2 \frac{\pi c}{2} \times \left( \frac{0.030 \, b_{6.22\mu\text{m}}}{6.22 \, \mu\text{m}} \right), \quad (13)$$

$$L(\text{PAH } 7.7 \, \mu\text{m}) [\text{erg s}^{-1}] = 10^7 \times 4\pi d_L^2 \frac{\pi c}{2} \times \left( \frac{0.126 \, b_{7.42\mu\text{m}}}{7.42 \, \mu\text{m}} + \frac{0.044 \, b_{7.60\mu\text{m}}}{7.60 \, \mu\text{m}} + \frac{0.053 \, b_{7.85\mu\text{m}}}{7.85 \, \mu\text{m}} \right), \quad (14)$$

with amplitudes $b_r$ in units of watt per square meter per hertz, luminosity distance $d_L$ in meters, and c in micron per second.

#### 3.4.1. Validation of PAH Luminosity Measurements

Figure 11 compares our PAH luminosity measurements for the 6.2 µm and 7.7 µm features to those by Y. Ohyama et al. (2018) in their SPICY spectra of the same galaxies. The figure demonstrates the validity of our method for measuring L (PAH 6.2 µm) and L(PAH 7.7 µm), with systematic offsets of only ~0.1 dex and ~0.2 dex, respectively. The small rms dispersions, $\sigma_{L(PAH 6.2 µm)} = 0.19$ dex and $\sigma_{L(PAH 7.7 µm)} = 0.14$ dex, represent the approximate errors in our PAH luminosity measurements. Our measurements of L(PAH 7.7 µm) have a larger systematic offset from Y. Ohyama et al.'s measurements compared to those of L(PAH 6.2 µm), which is likely due to the difficulty in constraining the underlying continuum beneath the wide 7.7 µm blend in noisy spectra. Their method uses a single broad Lorentzian to fit the 7.7 µm blend from low-resolution spectra, which may overestimate the flux somewhat. We note that although Y. Ohyama et al. (2018) initially fit some IRC spectra of brighter sources with PAHFIT, they adopted a simpler model that could better detect faint PAH features in low-resolution IRC spectra ($R \simeq 50$), compared to the Spitzer/IRS spectra ($60 < R < 130$) for which PAHFIT was designed.

We further tested the importance of MIR photometry on SED fitting by rerunning CIGALE on the sample of 48 SPICY galaxies without the MIR AKARI, WISE, and IRAC bands. We then compared the output $q_{PAH}$ and SFR values with and without the MIR data. When comparing the $q_{PAH}$ parameter, the results
<table><caption>**Table 4**
Calibration Sample Emission Line Fluxes and Physical Properties</caption><thead><tr><th>Object<br>(1)</th><th>R.A.<br>(2)</th><th>Decl.<br>(3)</th><th>Redshift<br>(4)</th><th>f([O II])<br>(5)</th><th>σ<sub>f([O II])</sub><br>(6)</th><th>f(Hβ)<br>(7)</th><th>σ<sub>f(Hβ)</sub><br>(8)</th><th>f([O III]<br>λ5007)<br>(9)</th><th>σ<sub>f([O III]λ5007)</sub><br>(10)</th><th>f(Hα)<br>(11)</th><th>σ<sub>f(Hα)</sub><br>(12)</th><th>f([N II]<br>λ6584)<br>(13)</th><th>σ<sub>f([N II]λ6584)</sub><br>(14)</th><th>log(<sup>M<sub>☉</sub></sup>/<sub>M<sub>☉</sub></sub>)<br>(15)</th><th>log(<sup>L(TIR)</sup>/<sub>L<sub>☉</sub></sub>)<br>(16)</th><th>L(PAH 6.2 µm)<br>(17)</th><th>L(PAH 7.7 µm)<br>(18)</th></tr></thead><tbody><tr><td>61017806</td><td>269.047</td><td>66.632</td><td>0.487</td><td>0.00</td><td>0.00</td><td>2.58</td><td>0.08</td><td>1.78</td><td>0.10</td><td>12.44</td><td>0.24</td><td>3.70</td><td>0.26</td><td>10.38</td><td>11.49</td><td>4.47 × 10<sup>42</sup></td><td>1.45 × 10<sup>43</sup></td></tr><tr><td>61018416</td><td>268.719</td><td>66.648</td><td>0.395</td><td>1.38</td><td>0.11</td><td>0.97</td><td>0.06</td><td>0.64</td><td>0.11</td><td>6.61</td><td>0.15</td><td>2.83</td><td>0.16</td><td>10.36</td><td>11.11</td><td>3.25 × 10<sup>42</sup></td><td>1.14 × 10<sup>43</sup></td></tr><tr><td>61019580</td><td>268.737</td><td>66.680</td><td>0.116</td><td>0.00</td><td>0.00</td><td>5.34</td><td>0.11</td><td>6.32</td><td>0.19</td><td>22.66</td><td>0.12</td><td>6.02</td><td>0.15</td><td>9.36</td><td>9.34</td><td>8.05 × 10<sup>40</sup></td><td>2.71 × 10<sup>41</sup></td></tr><tr><td>61019692</td><td>268.836</td><td>66.685</td><td>0.390</td><td>0.00</td><td>0.00</td><td>1.59</td><td>0.05</td><td>0.37</td><td>0.10</td><td>7.73</td><td>0.12</td><td>2.63</td><td>0.12</td><td>9.92</td><td>10.65</td><td>1.12 × 10<sup>42</sup></td><td>3.88 × 10<sup>42</sup></td></tr><tr><td>61020407</td><td>268.616</td><td>66.704</td><td>0.454</td><td>1.96</td><td>0.12</td><td>2.37</td><td>0.08</td><td>1.40</td><td>0.09</td><td>14.71</td><td>0.22</td><td>6.31</td><td>0.28</td><td>10.03</td><td>11.12</td><td>4.97 × 10<sup>42</sup></td><td>1.73 × 10<sup>43</sup></td></tr></tbody></table>

**Note.** Column names are as follows: (1) Object name; (2) Right ascension in degrees; (3) decl. in degrees; (4) Spectroscopic redshift; (5)–(14) Emission line fluxes and mean errors in $10^{-16}$ erg s$^{-1}$ cm$^{-2}$; (15) Stellar mass; (16) TIR; (17)–(18) PAH luminosities in erg per second. The errors in the PAH 6.2 µm and 7.7 µm luminosities are discussed in Section 3.4.1. This table is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.

(This table is available in its entirety in machine-readable form in the online article.)
<figure><img src="image_9.png" /><figcaption>**Figure 7.** sSFR as a function of redshift for galaxies with Hα and/or [O II] detections in the calibration sample.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Observed AKARI/IRC magnitudes at 3 and 18 µm (N3 and L18W filters, respectively) as a function of redshift. Main-sequence and starburst galaxies from our calibration sample are shown as red-filled circles. Observations from the AKARI NEP-Deep field survey (N. Oi et al. 2014) are shown as faint black dots. Blue dashed lines indicate approximate flux limits.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Intercomparison of corrected Hα luminosities derived from our three different de-reddening methods (Equations (6)–(9)). The “BD” subscript refers to the Balmer decrement (Hα/Hβ).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Example of a typical PAHFIT result for a main-sequence galaxy at $z = 0.36$ (ID: J180123.2+654950.0; The SED is shown in Figure 5(a)), fit to the model SED (circle points). The solid red line shows the best-fit result. Drude profile fits to the PAH dust emission features are shown in blue. The solid purple line underlying the emission represents the continuum, which is the summation of the individual blackbody components shown in yellow.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Top panel: comparison between measured PAH luminosity from the Y. Ohyama et al. (2018) SPICY sample and inferred luminosity from our CIGALE and PAHFIT method for 6.2 µm (left) and 7.7 µm (right) blends. The solid line represents the least-squares linear fit to the data with the slope fixed to unity. Bottom panel: Residuals as a function of the measured PAH luminosity with the dotted lines indicating the rms dispersion in dex.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Comparison between the aromatic feature emission luminosities at 8 µm from A. R. Marble et al. (2010) and our PAH 7.7 µm luminosities (left panel) and those of Y. Ohyama et al. (2018) (right panel) for SPICY galaxies at $z < 0.1$. The rms scatter in the left panel is 58% (or approximately 10% after a 0.2 dex offset is applied to the residuals), while the rms scatter in the right panel is 32%.</figcaption></figure>

produced a scatter diagram, highlighting the necessity of including MIR data in determining $q_{PAH}$ (and PAH luminosity). The SFRs derived from CIGALE without MIR data were comparable to the original results for about 50% of the galaxies; however, for the remaining half, the SFRs calculated without MIR data were highly uncertain because these galaxies also lacked UV and FIR photometry.

In addition to the PAH luminosity, we also calculated the peak luminosity at 7.7 µm, $\nu L_{\nu}$ (7.7 µm), which is sometimes used as a proxy for the PAH luminosity in the literature because it can be estimated photometrically (e.g., T. Takagi et al. 2010). The relation for the peak luminosity is

$$ \nu L_{\nu}(7.7 \mu\text{m}) = F_{\nu}(7.7 \mu\text{m}) \times 4\pi d_{L}^{2} \nu(7.7 \mu\text{m}), \quad (15) $$

where $F_{\nu}(7.7 \mu\text{m})$ is the best-fit spectrum from PAHFIT evaluated at 7.7 µm (i.e., the sum of the blackbody continua and Drude profiles at 7.7 µm) and $\nu(7.7 \mu\text{m})$ is the frequency at 7.7 µm in hertz. We use these peak luminosities in Section 6 to compare our results to T. Takagi et al. (2010).

The convenience of estimating PAH flux from measurements in just a few broadband filters, particularly the IRAC-4 8 µm band, has been studied by many authors. For example, M. Figueira et al. (2022) attempted this with a limited set of IRAC and MIPS photometry. However, they found that the rest-frame 8 µm band luminosity did not correlate well with SFR, and the logarithmic slope they found, 0.81, was much less than linear. They speculated that their difficulty may have stemmed from their inability to separate the PAH 7.7 µm flux from the underlying continuum components in that wavelength region.

A. R. Marble et al. (2010) derived PAH fluxes for a local sample of SINGS galaxies based on the Spitzer/IRAC 3.6, 4.5, 5.8, and 8 µm bands and MIPS 24 µm. We compare our 7.7 µm PAH luminosity to their photometric-based PAH luminosity, known as the “aromatic feature emission” of the 8 µm blend ($L_{8}^{afe}$), by selecting SPICY galaxies with $z < 0.1$ and estimating the observed Spitzer flux densities with CIGALE. The resulting

subsample contains 13 objects. Figure 12 shows the comparison between $L_{8}^{afe}$ and our measured L(PAH 7.7 µm) (left panel) and L(PAH 7.7 µm) from Y. Ohyama et al. (2018). Our results are consistent with A. R. Marble et al. (2010), with a slight offset of ~0.15–0.2 dex. This offset is likely due to $L_{8}^{afe}$, including the 8.33 and 8.61 µm features in addition to the 7.7 µm blend, leading to an overestimation of the 7.7 µm luminosity. The result from Y. Ohyama et al. (2018) is likely more consistent with A. R. Marble et al. (2010) due to the simplified Lorentzian profile that was used to fit the 7.7 µm feature, again leading to a slight overestimate in the flux density.

### 3.4.2. Limitations on Constraining PA. Line Ratios

Throughout this work, we present our results using both the 6.2 µm and 7.7 µm luminosities. It is important to note that these luminosities and their resulting SFR calibrations are not completely independent of each other due to our use of the CIGALE templates. In all of these templates, $L(PAH 6.2 \mu m)/L(PAH 7.7 \mu m) \simeq 0.3$. A separate photometric approach would be needed to constrain the variability in 6.2 µm/7.7 µm. However, assuming that the SED templates give descriptions of the PAH dust emission in star-forming galaxies, which we tested with the SPICY sample, we believe that it is valuable to present both indicators for future research with this caveat. For example, the 6.2 µm feature is narrower than the 7.7 µm blend and may be easier to measure in some cases.

## 4. Analysis

### 4.1. Effects of Starburst Intensity, Metallicity, and AGN Fraction

To determine how well PAH luminosities predict SFR, we correlate the PAH 6.2 µm and 7.7 µm luminosities with the reddening-corrected $H\alpha$ and [O II] luminosities. Figure 13 shows the PAH 6.2 µm and 7.7 µm luminosity as a function of observed (reddened) $H\alpha$ and [O II] luminosity. The four panels
<figure><img src="image_15.png" /><figcaption>**Figure 13.** PAH 6.2 µm (left column) and 7.7 µm (right column) luminosities vs. observed $H\alpha$ and [O II] luminosities in star-forming galaxies, colored by the logarithm of the starburst intensity, $R_{SB}$.</figcaption></figure>

show a positive correlation between PAH luminosity and observed $H\alpha$ and [O II] luminosity, with considerable scatter due to reddening effects, which have not yet been taken into account. For reference, the symbols are colored by the logarithm of the starburst intensity, $R_{SB}$. Despite the large scatter, there is a visible trend such that galaxies with higher $R_{SB}$ generally have depreciated PAH luminosity for a given observed $H\alpha$ or [O II] luminosity (or enhanced $H\alpha$ or [O II] for a given PAH luminosity).

Figure 14 shows the PAH 7.7 µm luminosity as a function of the dereddened $H\alpha$ luminosity. We fit linear relations of the form $\log L(\text{PAH 7.7 µm}) = c_0 + c_1 \times \log L(H\alpha)$ to the star-forming sample. Quenched galaxies (i.e., $R_{SB} < 0.5$; see Section 3.2) are shown for reference as red-filled square symbols but are excluded from the fits. The three panels in Figure 14 show results for different methods of correcting the observed $H\alpha$ luminosity as discussed in Section 3.3. Compared to Figure 13, the scatter between $L(\text{PAH 7.7 µm})$ and $L(H\alpha)_{24~\mu\text{m}}$ is significantly reduced; the rms dispersion of the fit is 0.31 dex. The dotted line in panel (a) represents the linear relation from H. V. Shipley et al. (2016) derived from Spitzer/

IRS galaxies with solar metallicity at $z < 0.4$. For the majority of galaxies, $L(\text{PAH 7.7 µm})$ is linearly correlated with $L(H\alpha)_{24~\mu\text{m}}$ (i.e., slope ~1). However, we find that a small minority, 47/319 (15%), of the galaxies deviate from the fit by -0.4 dex, contributing to the uncertainty in the normalization and nonlinear slope. This deviation is consistent with D. Calzetti et al. (2007), who attribute it to low metallicity and decline to provide a calibration for 8 µm emission as a local SFR indicator on this basis. Panels (b) and (c) show that the correlations between $L(\text{PAH 7.7 µm})$ and $L(H\alpha)$ are nonlinear with the BD and SED fitting corrections, with the BD method resulting in the most scatter.

The majority of the quenched galaxies shown in panel (a) of Figure 14 (red-filled square symbols) lie along or slightly above the linear correlation between $L(\text{PAH 7.7 µm})$ and dust-corrected $L(H\alpha)$, which is consistent with the physical scenario where intense starbursts lead to the destruction of PAH dust grains due to UV dissociation (B. T. Draine et al. 2007); in an environment with low $R_{SB}$, there are significantly fewer young, massive O and B stars compared to actively star-forming galaxies. Based on a sample of local Sloan Digital Sky Survey
<figure><img src="image_16.png" /><figcaption>**Figure 14.** Comparison of PAH 7.7 µm luminosity vs. intrinsic Hα luminosity of main-sequence and starburst galaxies for different dust extinction correction methods: (a) rest-frame 24 µm luminosity correction from R. C. J. Kennicutt et al. (2009); (b) BD; (c) SED fitting. The solid lines represent linear fits.</figcaption></figure>

galaxies, A. Smercina et al. (2018) found that the dominant PAH emission in post-starburst galaxies can overestimate the SFR relative to traditional ionized gas tracers in the MIR that are typically present in H II regions (e.g., [Ne II]+[Ne III]). K. D. French et al. (2023) similarly found that the TIR luminosity overestimates the SFR relative to Hα, [Ne II] +[Ne III], and other ionized gas tracers when the star formation history is abruptly truncated, which is believed to be the scenario in post-starburst galaxies.

Figure 15 shows the correlations between the PAH 6.2 µm and 7.7 µm luminosities with the dust-corrected Hα luminosity for the star-forming sample, with main-sequence and starburst galaxies fit separately. For main-sequence galaxies, the linear and unity slope fits for the PAH 7.7 µm luminosities are consistent with the relations found by H. V. Shipley et al. (2016). The linear relations for L(PAH 6.2 µm) in main-sequence galaxies are also consistent within ~0.25 dex. The figure demonstrates that starburst galaxies have lower PAH luminosities for a given intrinsic Hα luminosity. If we assume unity slope in the linear fits, the trend for starburst galaxies has a systematic offset of ~0.35 dex relative to that of main-sequence galaxies for both PAH 6.2 µm and 7.7 µm features, suggesting that starburst galaxies are either PAH-deficient for fixed Hα luminosity or Hα-enhanced for fixed PAH luminosity.

The offset between starburst galaxies and main-sequence galaxies is also present in the correlation between PAH luminosity and dust-corrected [O II] luminosity, as shown in Figure 16. Starburst galaxies are systematically lower by a factor of 0.3 dex. We also find that linear fits to the main-sequence

sample of the form $\log L(\text{PAH}) = c_0 + c_1 \times \log L([\text{O II}])$ result in a shallower slope compared to fits with respect to $L(\text{H}\alpha)$ such that $L(\text{PAH}) \propto L([\text{O II}])^{0.9}$.

We further examine the dependence of PAH luminosity on starburst intensity and AGN strength by plotting the log ratio of PAH luminosity to intrinsic Hα and [O II] luminosity as a function of PAH EW in Figure 17. The EW is calculated as the flux of the PAH emission feature (given by PAHFIT) divided by the flux density of the continuum components, which includes the starlight, evaluated at the central wavelength of the feature. We note that it is difficult to constrain the values for EW(PAH 7.7 µm) for individual galaxies because the calculation relies heavily on assumptions for the underlying continuum shape and blend of Drude profiles. However, the exact EWs do not affect our overall interpretations. The top row of the figure shows the correlations for star-forming galaxies, color coded by starburst parameter. The bottom row shows the correlations for AGN candidates, color coded by AGN fraction. Objects with low PAH EW (i.e., EW(PAH 6.2 µm) ≲ 1 µm or EW(PAH 7.7 µm) ≲ 4 µm) scatter downward from the $L(PAH 6.2/7.7 µm)$ and dust-corrected $L(H\alpha)/L([\text{O II}])$ fits. The figure demonstrates that galaxies with higher starburst intensity ($R_{\text{SB}}$) have lower $L(PAH 6.2 µm)$ and $L(PAH 7.7 µm)$ for a given $L(H\alpha)_{24 µm}$ and that AGN with a higher AGN fraction have lower $L(PAH 6.2 µm)$ and $L(PAH 7.7 µm)$ for a given $L([\text{O II}])_{24 µm}$. The offset such that galaxies with high frac$_{AGN}$ have low $\log L(\text{PAH})/\log([\text{O II}])$ across all EWs is likely due to the destruction of PAH dust grains by hard radiation from AGN. Given that ionization from AGN limits the efficacy of using the intrinsic Hα and [O II]
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Relation between PAH 6.2 µm and 7.7 µm luminosities and intrinsic Hα luminosity for star-forming galaxies. Main-sequence galaxies (black triangles) are shown in the left column, and starburst galaxies (blue stars) are shown in the right column. “Extreme” starburst galaxies (i.e., $L(TIR)/L(8~\mu\text{m}) > 20$) are shown as red-filled triangles. The solid and dashed lines represent linear and fixed unity fits, respectively. The dashed-dotted line represents the linear relation given by H. V. Shipley et al. (2016).</figcaption></figure>

luminosities to trace star formation, we exclude AGN from all SFR calibrations.

To further illustrate the effect of starburstiness on PAH intensity, we show the kernel density estimate and marginal distributions of the PAH 7.7 µm luminosity to intrinsic Hα luminosity as a function of $R_{\text{SB}}$ on the left column of Figure 18. The log $L(\text{PAH 7.7 µm})/L(\text{H}\alpha)_{24~\mu\text{m}}$ ratio is anticorrelated with $R_{\text{SB}}$. In addition, galaxies with higher $R_{\text{SB}}$ are associated with lower PAH 7.7 µm EW (≤4µm), as shown by the orange contours. The Spearman rank-order correlation coefficient between EW(PAH 7.7 µm) and $R_{\text{SB}}$ is -0.48 with a p-value of $2 \times 10^{-26}$, indicating a moderate monotonically decreasing correlation. The anticorrelation between log $L(\text{PAH})/L(\text{H}\alpha)$ and $R_{\text{SB}}$ is consistent with the scenario in which PAH dust

grains are destroyed by UV dissociation in compact star-forming regions (E. Peeters et al. 2004; K. Murata et al. 2014). For example, K. Murata et al. (2014) observe a deficit in $\nu L(8)/\nu L(4.5)$ for star-forming galaxies with log $R_{\text{SB}} > 0.5$, which they interpret as a deficit of PAH emission in starburst galaxies.

The right column of Figure 18 illustrates the correlation between log $L(\text{PAH 7.7 µm})/L(\text{H}\alpha)_{24~\mu\text{m}}$ and $q_{\text{PAH}}$ parameter derived from best-fit SED models. The $q_{\text{PAH}}$ parameter is highly correlated with PAH EW; the Spearman rank-order correlation coefficient between EW(PAH 7.7 µm) and $q_{\text{PAH}}$ is 0.8 with a p-value of $1.6 \times 10^{-98}$. We note, however, that the strong linear correlation between log $L(\text{PAH 7.7 µm})/L(\text{H}\alpha)_{24~\mu\text{m}}$ and $q_{\text{PAH}}$ was to be expected given the correlation between L(PAH) and $q_{\text{PAH}}$ based on assumptions in the SED modeling.
<figure><img src="image_18.png" /><figcaption>**Figure 16.** Relations between PAH 6.2 µm and 7.7 µm luminosities and intrinsic (dereddened) [O II] luminosities for star-forming galaxies. Symbols and lines are the same as in Figure 15.</figcaption></figure>

In Figure 19, we investigate the dependence of PAH intensity on metallicity. Here, we calculate the PAH intensity as the ratio of L(PAH 7.7 µm) to SFR(Hα)₂₄ µm, both averaged over stellar mass. The stellar masses range from M/M☉ < 10⁹ to M/M☉ > 10¹⁰.⁵ in bins of 0.5 dex. The figure shows the correlation between PAH intensity and average metallicity, ⟨12 + log(O/H)⟩, calculated using either the N2 (top panel) or O3N2 (bottom panel) index. Main-sequence galaxies (i.e., 0.5 < R<sub>SB</sub> < 2) and starburst galaxies (i.e., R<sub>SB</sub> > 2) are shown as filled circle and star symbols, respectively. Table 5 lists the number of main-sequence and starburst galaxies included in each bin. There is a positive correlation between PAH 7.7 µm intensity and metallicity in both main-sequence and starburst galaxies, with starburst galaxies having systematically lower PAH 7.7 µm intensity per stellar mass.

There has been some concern that these “strong-line” ratios might give systematically incorrect metallicities. One possibility, for example, is that the N/O ratio in strongly star-forming galaxies might deviate from the solar value (D. Masters et al. 2014; A. Henry et al. 2021; L. Spinoglio et al. 2022). However, we do not find any clear systematic differences between the metallicities estimated with or without the [O III] line in Figure 19. Another concern is that electron-temperature-based metallicities (using the [O III]4363 emission line, which is too weak to measure in our spectra) might yield systematically lower metallicities than our strong-line methods (C. Ly et al. 2016a, 2016b; K. Shin et al. 2021). However, even if a systematic offset of a few tenths of a dex were applied to all of our [O/H] estimates, our finding of a relative increase of PAH
<figure><img src="image_19.png" /><figcaption>**Figure 17.** Effects of starburstiness (log ratio of SFR to main sequence, $R_{SB}$, shown with color bar on top row) and AGN fraction (bottom row) on the correlation between PAH luminosity and intrinsic H$\alpha$ and [O II] luminosity.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 18.** Kernel density estimate of the PAH luminosity to intrinsic H$\alpha$ luminosity as a function of starburstiness (left) and $q_{PAH}$ (right) for main-sequence and starburst galaxies. The data are grouped according to the estimated PAH 7.7 µm EW. Marginal distributions are shown on the top and right sides of each plot.</figcaption></figure>

strength with metallicity is not significantly changed, other than in the normalization.

In Figure 20, we compare the PAH contribution to the TIR luminosity in star-forming galaxies and AGN by showing the distributions of the total PAH luminosity, $L(\text{PAH})$, to $L(\text{TIR})$ for objects with at least one Herschel FIR detection. We define $L(\text{PAH})$ as the sum of luminosities from PAH emission features at 6.2, 7.7, 8.6, 11.3, 12.6, and 17 µm. Star-forming galaxies

are shown in the top panel and AGN are shown in the bottom panels, with the bottom-most panel separating out “weak” AGN (i.e., $\text{frac}_{\text{AGN}} < 0.1$) from stronger AGN (i.e., $\text{frac}_{\text{AGN}} > 0.1$). We find that $L(\text{PAH} 7.7 \mu\text{m})$ contributes a median ~45% of the total PAH luminosity, and that the total PAH luminosity in turn can contribute up to ~20% of $L(\text{TIR})$. The median $L(\text{PAH})/L(\text{TIR})$ for star-forming galaxies (main-sequence and starburst galaxies) is 0.08 with an interquartile
<figure><img src="image_21.png" /><figcaption>**Figure 19.** Ratio of the PAH 7.7 µm luminosity to the dust-corrected Hα SFR, both averaged over stellar mass, as a function of average metallicity using the N2 (top) and O3N2 (bottom) indices. Average metallicity is calculated as $\langle 12 + \log(O/H) \rangle$. Symbols are color coded based on stellar mass bins as follows, with metallicity monotonically increasing with stellar mass: $M/M_{\odot} < 10^9$ (blue), $10^9 < M/M_{\odot} < 10^{9.5}$ (orange), $10^{9.5} < M/M_{\odot} < 10^{10}$ (green), $10^{10} < M/M_{\odot} < 10^{10.5}$ (red), and $M/M_{\odot} > 10^{10.5}$ (purple). Light gray horizontal lines indicate the metallicity ranges per bin.</figcaption></figure>

<table><caption>**Table 5**
Number of Star-forming Galaxies in Each Stellar Mass Bin to Calculate PAH Intensity as a Function of Average Metallicity in Figure 19</caption><thead><tr><th rowspan="2">Stellar Mass Bin</th><th colspan="2">N2 Index</th><th colspan="2">O3N2 Index</th></tr><tr><th>N<sub>MS</sub></th><th>N<sub>SB</sub></th><th>N<sub>MS</sub></th><th>N<sub>SB</sub></th></tr></thead><tbody><tr><td>M/M<sub>☉</sub> &lt; 10<sup>9</sup></td><td>2</td><td>6</td><td>2</td><td>6</td></tr><tr><td>10<sup>9</sup> &lt; M/M<sub>☉</sub> &lt; 10<sup>9.5</sup></td><td>15</td><td>28</td><td>7</td><td>23</td></tr><tr><td>10<sup>9.5</sup> &lt; M/M<sub>☉</sub> &lt; 10<sup>10</sup></td><td>62</td><td>52</td><td>37</td><td>48</td></tr><tr><td>10<sup>10</sup> &lt; M/M<sub>☉</sub> &lt; 10<sup>10.5</sup></td><td>69</td><td>44</td><td>37</td><td>31</td></tr><tr><td>M/M<sub>☉</sub> &gt; 10<sup>10.5</sup></td><td>18</td><td>3</td><td>14</td><td>0</td></tr></tbody></table>

range of 0.05–0.14. The median in the AGN sample is lower at 0.06 with an interquartile range of 0.03–0.10. Objects that are more AGN-dominant with $\text{frac}_{\text{AGN}} > 0.1$ have lower $L(\text{PAH})/L(\text{TIR})$ with a median of 0.04. For star-forming galaxies, the 10%–90% range in $L(\text{PAH})/L(\text{TIR})$ is 0.03 to 0.18, and is plotted as the pale blue shaded region in all three panels in Figure 20. Our results are consistent with those of H. V. Shipley et al. (2013). A simple interpretation is that up to half of the TIR luminosity in AGN may be produced by the AGN itself,

rather than from star formation. Previous detailed studies of the FIR suggest that most of this AGN luminosity emerges at wavelengths shortward of 100 µm (L. Spinoglio et al. 2002).

## 4.2. The PAH SFR Calibration

In this section, we develop our PAH SFR calibration based on the dust-corrected Hα and [O II] luminosities. Given that the AGN fraction is a significant driver of $L(\text{PAH})/L(\text{Hα})$ and $L(\text{PAH})/L([\text{O II}])$, as demonstrated in Figure 17, our calibration sample excludes AGN and is limited to the 443 unique star formation-dominated galaxies (Section 3.2). Therefore, $\text{frac}_{\text{AGN}}$ is not included in the following fits.

Assuming that PAH luminosity corrections for metallicity and starburst intensity are both simply linear, we perform a multilinear regression to the PAH luminosity with the dust-corrected Hα luminosity, $R_{\text{SB}}$ parameter, and metallicity as the independent variables in the form of $\log L(\text{PAH}) [\text{erg s}^{-1}] = c_0 + c_1 \times \log R_{\text{SB}} + c_2 \times (12+\log(\text{O/H})_{\text{index}} - 8.6) + c_3 \times [\log L(\text{Hα})_{24 \ \mu\text{m}} - 42] [\text{erg s}^{-1}]$, where the constant 8.6 is the median metallicity and 42 is the median logarithm of the intrinsic Hα luminosity. The relation for predicting the 7.7 µm
<figure><img src="image_22.png" /><figcaption>**Figure 20.** Distributions of the ratio of total PAH luminosity to the TIR luminosity for star-forming galaxies (top panel) and AGN (middle panel). The bottom panel shows the histograms of PAH/TIR separately for the “strong” and “weak” AGN that were shown together in the middle panel. For reference, the pale blue shaded region in all three panels represents the 10%–90% range in $L(\text{PAH})/L(\text{TIR})$ for the star-forming galaxies.</figcaption></figure>

PAH luminosity as the dependent variable is

$$ \begin{aligned} \log L(\text{PAH } 7.7 \, \mu\text{m}) [\text{erg s}^{-1}] = & (43.18 \pm 0.02) \\ & - (0.67 \pm 0.04)(\log R_{\text{SB}}) \\ & + (0.42 \pm 0.12)(12 + \log(O/H)_{\text{N2}} - 8.6) \\ & + (1.07 \pm 0.03)[\log L(\text{H}\alpha)_{24 \, \mu\text{m}} - 42] [\text{erg s}^{-1}], \end{aligned} \quad (16) $$

where $-0.30 \le \log R_{\text{SB}} \le 1.95$, $8.1 \le 12+\log(O/H)_{\text{N2}} \le 8.7$, $40.0 \le \log L(\text{H}\alpha)_{24 \, \mu\text{m}} [\text{erg s}^{-1}] \le 43.3$. The redshift range is $0.05 \le z \le 1.03$. Table 6 lists the results of the linear fits for $L(\text{PAH} \ 6.2 \, \mu\text{m})$ and $L(\text{PAH} \ 7.7 \, \mu\text{m})$ for both metallicity indicators. We note that the maximum threshold of $\log R_{\text{SB}} = 1.95$ is a result of the outliers with upper limits on the PAH luminosity; only nine objects in the SFR calibration sample have $R_{\text{SB}} > 10$. The median value of $R_{\text{SB}}$ is 1.94, with an interquartile range of 1.01–3.48. We note that C. M. Whitcomb et al. (2020) also found that increasing metallicity correlates with an increase in the PAH luminosity for a given SFR. Similarly, K. Kouroumpatzakis et al. (2021) found that

PAH luminosity for a given SFR increases with metallicity and decreases with the strength of star formation normalized by stellar mass (similar to our $R_{\text{SB}}$ parameter).

To calculate the $H\alpha$ SFR calibrations, we substitute the SFR equation given by R. C. J. Kennicutt (1998) into the multilinear fit results:

$$ \text{SFR} [M_{\odot} \text{yr}^{-1}] = 7.9 \times 10^{-42} L(\text{H}\alpha)_{24 \, \mu\text{m}} [\text{erg s}^{-1}], \quad (17) $$

where the normalization factor assumes an E. E. Salpeter (1955) IMF. We note that more modern SFR calibrations assume a P. Kroupa (2001) or G. Chabrier (2003) IMF; based on Equation (2) in J. S. Speagle et al. (2014), Equation (17) can be converted to a Kroupa or Chabrier IMF by dividing by a factor of 1.6 and 1.7, respectively. The form of the PAH SFR calibration is then

$$ \begin{aligned} \log \text{SFR} [M_{\odot} \text{yr}^{-1}] = & c_0 + c_1 \times \log R_{\text{SB}} \\ & + c_2 \times (12 + \log(O/H)_{\text{index}} - 8.6) \\ & + c_3 \times [\log L(\text{PAH}_n) - 42] [\text{erg s}^{-1}], \end{aligned} \quad (18) $$

where the index $n$ in $L(\text{PAH}_n)$ is equal to either 6.2 $\mu$m or 7.7 $\mu$m. To calculate the [O II] SFR calibrations, we similarly substitute Equation (11) into the multilinear fit results, where the $H\alpha$ luminosity is replaced with $L([\text{O II}])_{24 \, \mu\text{m}}$. The coefficients for the SFR calibrations are listed in Tables 6 and 7. The results show that the SFR is linearly predicted by the PAH luminosity (i.e., $c_3 \sim 1$) when corrected for starburst intensity and metallicity.

We additionally tested for dependence on redshift and TIR luminosity by including them as parameters in the multilinear fit. However, we found that there was no significant dependence on either parameter; the coefficients for both parameters were close to zero with large uncertainties. To investigate the relative contributions of starburst intensity versus metallicity in the multilinear fit, we tested fits by removing either parameter, resulting in fits in the form of $\log L(\text{PAH}) = c_0 + c_1 \times \log R_{\text{SB}} + c_3 \times [\log L(\text{H}\alpha)_{24 \, \mu\text{m}} - 42] [\text{erg s}^{-1}]$ for the “starburst-only” fit and $\log L(\text{PAH}) = c_0 + c_2 \times (12+\log(O/H)_{\text{index}} - 8.6) + c_3 \times [\log L(\text{H}\alpha)_{24 \, \mu\text{m}} - 42] [\text{erg s}^{-1}]$ for the “metallicity-only” fit. We found that for the starburst-only fit, the $c_1$ coefficients and uncertainties were consistent with those reported in our complete multilinear fit results, whereas for the metallicity-only fit, the $c_2$ coefficients were ~2.5–3 times higher than the original results, indicating that the correction for the $R_{\text{SB}}$ parameter is more dominant than that for $12+\log(O/H)$. However, both starburst-only and metallicity-only fits resulted in less linearity between $L(\text{PAH})$ and $L(\text{H}\alpha)$ (i.e., $c_3$ deviated more from 1). Therefore, we conclude that the complete multilinear fits that correct for both starburst intensity and metallicity as parameters provide the most reliable results.

Our methodology implicitly assumes that all of our galaxies have the same ratio of 7.7/6.2 $\mu$m PAH luminosity as in the CIGALE templates. This ratio can be determined from the $c_0$ coefficients in Table 6 to be about 3.4–3.6. This is an assumption that is not derivable from our AKARI MIR photometry. We are not able to independently determine the Table 6 correlations for the 6.2 $\mu$m PAH luminosity. There is evidence that stronger 6.2 $\mu$m emission is produced by more highly ionized PAHs. However, since the same trend is seen for the 7.7 $\mu$m emission (A. Maragkoudakis et al. 2022), it turns
<table><caption>**Table 6**
Multilinear Fit Results for the PAH 6.2 µm and 7.7 µm Luminosities and Hα SFRs</caption><thead><tr><th>y</th><th>c<sub>0</sub></th><th>c<sub>1</sub> (Starburstiness)</th><th>c<sub>2</sub> (Metallicity)</th><th>c<sub>3</sub></th><th>Metallicity Calibration</th></tr></thead><tbody><tr><td>log L(PAH 6.2 µm)</td><td>42.63 ± 0.02</td><td>-0.61 ± 0.04</td><td>0.38 ± 0.12</td><td>1.07 ± 0.03</td><td>N2</td></tr><tr><td>log SFR(PAH 6.2 µm)</td><td>-39.12 ± 0.02</td><td>0.57 ± 0.04</td><td>-0.35 ± 0.12</td><td>0.94 ± 0.03</td><td>N2</td></tr><tr><td>log L(PAH 6.2 µm)</td><td>42.61 ± 0.03</td><td>-0.60 ± 0.06</td><td>0.27 ± 0.12</td><td>1.09 ± 0.04</td><td>O3N2</td></tr><tr><td>log SFR(PAH 6.2 µm)</td><td>-38.15 ± 0.03</td><td>0.55 ± 0.05</td><td>-0.25 ± 0.12</td><td>0.92 ± 0.04</td><td>O3N2</td></tr><tr><td>log L(PAH 7.7 µm)</td><td>43.18 ± 0.02</td><td>-0.67 ± 0.04</td><td>0.42 ± 0.12</td><td>1.07 ± 0.03</td><td>N2</td></tr><tr><td>log SFR(PAH 7.7 µm)</td><td>-39.32 ± 0.02</td><td>0.62 ± 0.04</td><td>-0.39 ± 0.12</td><td>0.93 ± 0.03</td><td>N2</td></tr><tr><td>log L(PAH 7.7 µm)</td><td>43.15 ± 0.03</td><td>-0.65 ± 0.05</td><td>0.32 ± 0.12</td><td>1.09 ± 0.04</td><td>O3N2</td></tr><tr><td>log SFR(PAH 7.7 µm)</td><td>-38.59 ± 0.03</td><td>0.60 ± 0.05</td><td>-0.29 ± 0.12</td><td>0.92 ± 0.04</td><td>O3N2</td></tr></tbody></table>

**Note.** Luminosity equations are in the form of $y$ [erg s⁻¹] = $c_0$ + $c_1$ × log $R_{SB}$ + $c_2$ × (12+log(O/H)index - 8.6) + $c_3$ × (log L(Hα)₂₄ µm - 42) [erg s⁻¹]. SFR equations are in the form of $y$ [M⊙ yr⁻¹] = $c_0$ + $c_1$ × log $R_{SB}$ + $c_2$ × (12+log(O/H)index - 8.6) + $c_3$ × log L(PAHn) [erg s⁻¹], where L(PAHn) refers to either 6.2 µm or 7.7 µm PAH luminosities. The gas-phase metallicity 12+log(O/H) is calculated via the N2 or O3N2 index (M. Pettini & B. E. J. Pagel 2004). The SFR equations assume a Salpeter IMF; to convert to a Kroupa or Chabrier IMF, the constant $c_0$ would be subtracted by log(1.61) ≈ 0.21 (Kroupa) or log(1.71) ≈ 0.23 (Chabrier).

<table><caption>**Table 7**
Multilinear Fit Results for the PAH 6.2 µm and 7.7 µm Luminosities and [O II] SFRs</caption><thead><tr><th>y</th><th>c<sub>0</sub></th><th>c<sub>1</sub> (Starburstiness)</th><th>c<sub>2</sub> (Metallicity)</th><th>c<sub>3</sub></th><th>Metallicity Calibration</th></tr></thead><tbody><tr><td>log L(PAH 6.2 µm)</td><td>42.59 ± 0.02</td><td>-0.61 ± 0.04</td><td>0.33 ± 0.14</td><td>1.06 ± 0.04</td><td>N2</td></tr><tr><td>log SFR(PAH 6.2 µm)</td><td>-39.19 ± 0.02</td><td>0.57 ± 0.05</td><td>-0.31 ± 0.14</td><td>0.94 ± 0.04</td><td>N2</td></tr><tr><td>log L(PAH 6.2 µm)</td><td>42.51 ± 0.02</td><td>-0.51 ± 0.04</td><td>0.39 ± 0.12</td><td>1.00 ± 0.03</td><td>O32</td></tr><tr><td>log SFR(PAH 6.2 µm)</td><td>-41.53 ± 0.02</td><td>0.50 ± 0.04</td><td>-0.39 ± 0.12</td><td>1.00 ± 0.03</td><td>O32</td></tr><tr><td>log L(PAH 7.7 µm)</td><td>43.13 ± 0.03</td><td>-0.66 ± 0.05</td><td>0.40 ± 0.15</td><td>1.06 ± 0.04</td><td>N2</td></tr><tr><td>log SFR(PAH 7.7 µm)</td><td>-39.82 ± 0.03</td><td>0.63 ± 0.05</td><td>-0.38 ± 0.15</td><td>0.94 ± 0.04</td><td>N2</td></tr><tr><td>log L(PAH 7.7 µm)</td><td>43.05 ± 0.02</td><td>-0.54 ± 0.04</td><td>0.43 ± 0.13</td><td>1.00 ± 0.03</td><td>O32</td></tr><tr><td>log SFR(PAH 7.7 µm)</td><td>-41.97 ± 0.02</td><td>0.54 ± 0.04</td><td>-0.43 ± 0.13</td><td>1.00 ± 0.03</td><td>O32</td></tr></tbody></table>

**Note.** Luminosity equations are in the form of $y$ [erg s⁻¹] = $c_0$ + $c_1$ × log $R_{SB}$ + $c_2$ × (12+log(O/H)index - d) + $c_3$ × (log L([O II])₂₄ µm - 42) [erg s⁻¹]. SFR equations are in the form of $y$ [M⊙ yr⁻¹] = $c_0$ + $c_1$ × log $R_{SB}$ + $c_2$ × (12+log(O/H)index - d) + $c_3$ × log L(PAHn) [erg s⁻¹], where L(PAHn) refers to either 6.2 µm or 7.7 µm PAH luminosities, and d = 8.6 for the N2 index and d = 8.5 for the O32 index. The gas-phase metallicity 12+log(O/H) is calculated via the N2 or O32 index (M. Pettini & B. E. J. Pagel 2004; T. Jones et al. 2015). The SFR equations assume a Salpeter IMF; to convert to a Kroupa or Chabrier IMF, the constant $c_0$ would be subtracted by log(1.61) ≈ 0.21 (Kroupa) or log(1.71) ≈ 0.23 (Chabrier).

out that the 7.7/6.2 µm ratio has little variation with PAH ionization or other galaxy properties. Larger PAH molecules are thought to emit slightly higher 7.7/6.2 µm ratios. However, in LIRGs and ULIRGs, which are the main targets of this study, the observed 7.7/6.2 µm ratios are all close to 3.6. The small scatter in this ratio, of ~0.05 dex (J. McKinney et al. 2021), indicates that CIGALE is indeed giving us reasonably accurate 6.2 µm luminosities. We, therefore, include the 6.2 µm PAH/SFR correlations in Tables 6 and 7 as a convenient aid for future researchers who will measure that emission feature.

The PAH SFR calibrations highlight four main results:

1. The PAH luminosity per intrinsic Hα or [O II] luminosity is increasingly deficient (or the Hα and [O II] luminosities per PAH luminosity are enhanced) as $R_{SB}$ increases or metallicity decreases.

2. The PAH SFR calibration does not depend on the TIR luminosity.

3. There is no apparent redshift evolution in the PAH SFR calibration from the local Universe out to z ~ 1.2.

4. Although starburst intensity, $R_{SB}$, has a stronger effect than metallicity on the correlation between PAH luminosity and intrinsic Hα or [O II] luminosity, both are important for reliably calibrating the PAH SFR.

### 4.3. Possible Physical Interpretation

Although this paper has focused on empirical analysis of observational data, the results described above may shed light on possible physical mechanisms that can suppress PAH emission. In particular, we can offer two speculations about why the PAH luminosity—for a given SFR—is significantly reduced in galaxies with active starbursts ($R_{SB}$), and in those having AGN (fracAGN ≥ 0.05). PAHs are very large molecules, and are therefore vulnerable to destruction by various energetic processes that can occur in the ISM. In the nearby Orion star-forming complex, there is direct evidence for PAH destruction by sputtering and/or by photo-dissociation (M. Giard et al. 1994). Observations and models of H II region spectra indicate that PAH destruction occurs in regions of elevated strength and hardness of the interstellar radiation field (V. Lebouteiller et al. 2011), both of which are expected in AGN and extreme starbursts.

### 5. SFRD from 0 < z < 1.2

The largest source of uncertainty in UV-based cosmic SFRD measurements arises from correcting for dust attenuation (D. Burgarella et al. 2005; M. A. R. Kobayashi et al. 2013). For example, S. Salim et al. (2007) show that there is
<figure><img src="image_23.png" /><figcaption>**Figure 21.** Top panels: correlations between PAH 7.7 µm luminosity and monochromatic luminosity at 8 µm (left) and 12 µm (right) for star-forming galaxies. Dashed lines represent linear fits with a fixed unity slope. Bottom panels: residuals of the fit as a function of monochromatic luminosity with dotted lines indicating the rms dispersion in dex. Each galaxy is color coded by the relative abundance of its small PAH dust grains, shown by the vertical scale on the right. The outliers correspond to low $q_{PAH}$ sources and represent upper limits.</figcaption></figure>

significant scatter between $A_{FUV}$ and the rest-frame FUV-NUV color for their sample of ~50,000 local, optically selected galaxies with GALEX photometry. The scatter is especially prominent for starburst galaxies, which can deviate from the trend found for normal star-forming galaxies by ≳1 mag. SFRD indicators based on IR observations are particularly invaluable toward the epoch of peak cosmic star formation when much of this activity was heavily dust obscured. T. T. Takeuchi et al. (2007) estimate that the FIR luminosity density is approximately 15 times higher than that of the FUV at $z \sim 1$. However, studies have shown the FIR SFR to be less certain for galaxies whose UV to optical emission is dominated by old stellar populations or AGN (R. C. J. Kennicutt 1998).

We apply our extinction-independent PAH 7.7 µm SFR calibrations to estimate the SFRD to $z \sim 1.2$ for star-forming galaxies with metallicity detections. We use the rest-frame 8 µm and 12 µm luminosity functions (LFs) from T. Goto et al. (2010), which were derived using AKARI/IRC sources in the NEP-Deep field. The LFs assume a double power law given by

$$ \Phi(L)dL/L^* = \Phi^*\left(\frac{L}{L^*}\right)^{1-\alpha} dL/L^*, \quad (L<L^*), \quad (19) $$

$$ \Phi(L)dL/L^* = \Phi^*\left(\frac{L}{L^*}\right)^{1-\beta} dL/L^*, \quad (L>L^*), \quad (20) $$

where $\Phi^*$ is the normalization in Mpc$^{-3}$ dex$^{-1}$, $L^*$ is the characteristic luminosity or “knee” of the LF in $L_\odot$, $L$ is the monochromatic luminosity $\nu L_\nu(8 \mu m)$ or $\nu L_\nu(12 \mu m)$, and $\alpha$ and $\beta$ are the slopes of the LF at the low- and high-luminosity sides. We adopt the best-fit parameters given in Table 2 of T. Goto et al. (2010). The luminosity density is then given as

the integral

$$ \Omega = \int_{0.1L^*}^{10L^*} L\Phi(L)dL, \quad (21) $$

where we define the lower and upper limits to be within an order of magnitude of $L^*$. We calculate the 8 µm luminosity density in redshift bins of $0.38 < z < 0.58$ (S11) and $0.65 < z < 0.90$ (L15), and the 12 µm LF in bins of $0.15 < z < 0.35$ (L15), $0.38 < z < 0.62$ (L18W), and $0.84 < z < 1.16$ (L24), where the corresponding AKARI/IRC filters are given in parentheses. At $0 < z < 0.3$, we use the 8 µm luminosity density given by J. S. Huang et al. (2007) where $\Omega_{8\mu m} = 3.1 \times 10^7 L_\odot$ Mpc$^{-3}$.

We use linear fits with fixed unity slope to convert PAH luminosity to monochromatic luminosity at 8 and 12 µm, as shown in Figure 21. The correlations are given by

$$ \log L(\text{PAH 7.7 µm}) = (-0.70 \pm 0.01) + \log \nu L_\nu(8 \mu\text{m}), \quad (22) $$

$$ \log L(\text{PAH 7.7 µm}) = (-0.57 \pm 0.01) + \log \nu L_\nu(12 \mu\text{m}), \quad (23) $$

where $\nu L_\nu(8 \mu m)$ and $\nu L_\nu(12 \mu m)$ are in erg per second. The scatter in the linear fits represented by the rms dispersion in the residuals is approximately 0.13 and 0.18 dex for the 8 µm and 12 µm relations, respectively (bottom panels). These relations suggest that the PAH 7.7 µm luminosity may be estimated to within 30% by multiplying the rest-frame broadband luminosity at 8 µm by a factor of 0.2 (unless the galaxy is an extreme starburst). The outliers with residuals $\lesssim -0.5$ are starburst galaxies with exceptionally high IR8 (=L(TIR)/L(8 µm) $\gtrsim$ 20) and represent only 7% of the overall starburst galaxy sample.
<figure><img src="image_24.png" /><figcaption>**Figure 22.** SFRD as a function of redshift for the N2 (top) O3N2 (bottom) metallicity indicators, using the PAH 7.7 µm calibration tied to metallicity, R<sub>SB</sub>, and dust-corrected Hα. Three dotted lines of different colors connect the estimates based on the 8 and 12 µm and FUV LFs. The best-fit function from P. Madau & M. Dickinson (2014) is shown in light gray.</figcaption></figure>

However, as shown by the color bar, these PAH-weak outliers also have SEDs, which CIGALE fitted with the minimum $q_{PAH}$ value ($q_{PAH} \approx 0.47$), and therefore represent upper limits due to modeling constraints.

Then, we substitute Equations (22) and (23) for L (PAH 7.7 µm) into our SFR calibrations to derive a function of SFR(R<sub>SB</sub>, 12+log(O/H), $\nu L_{\nu}(8~\mu\text{m})$) or SFR(R<sub>SB</sub>, 12+log(O/H), $\nu L_{\nu}(12~\mu\text{m})$). The SFRD ($\rho_{SFRD}$) is calculated in each redshift bin as

$$ \rho_{SFR} = c_0 + c_1 \times \langle \log R_{SB} \rangle + c_2 \times \langle (12 + \log(\text{O/H}) - 8.6) \rangle + c_3 \times (c_4 + \Omega_{8\mu\text{m}}), \quad (24) $$

$$ \rho_{SFR} = c_0 + c_1 \times \langle \log R_{SB} \rangle + c_2 \times \langle (12 + \log(\text{O/H}) - 8.6) \rangle + c_3 \times (c_5 + \Omega_{12\mu\text{m}}) \quad (25) $$

in $M_{\odot}~\text{yr}^{-1}~\text{Mpc}^{-3}$, where the constant coefficients $c_0, \dots, c_3$ are given by the SFR calibrations in Table 6, $c_4$ and $c_5$ are the best-fit intercepts from Equations (22) and (23), respectively. $\Omega_{8\mu\text{m}}$ and $\Omega_{12\mu\text{m}}$ are the luminosity densities in $L_{\odot}~\text{Mpc}^{-3}$ calculated from Equation (21) based on $\nu L_{\nu}(8~\mu\text{m})$ and $\nu L_{\nu}(12~\mu\text{m})$ and converted to $L_{\odot}$ units. The averages $\langle \log R_{SB} \rangle$ and $\langle 12 + \log(\text{O/H}) \rangle$ are averaged over each redshift bin. Table 8 shows the number of

star-forming galaxies integrated in each bin for a given PAH 7.7 µm and optical emission line calibrator.

Figure 22 shows the redshift evolution of the PAH 7.7 µm-derived SFRD based on the Hα calibration and N2/O3N2 metallicity indicators. We calculate the SFRD for the combined main-sequence and starburst galaxy sample in each redshift bin (filled circles) and show the separate contributions from main-sequence galaxies only (triangle symbols) and starburst galaxies only (star symbols). The redshifts plotted are the median redshifts per bin. The SFRDs derived from either the 8 µm and 12 µm LFs are consistent with each other within the uncertainties.

For reference, we plot the best-fit cosmic star formation history from P. Madau & M. Dickinson (2014, hereafter MD14; gray line). In addition, we plot the SFRD calculated from FUV and FIR observations from D. Burgarella et al. (2013, hereafter B+13), who use calibrations from R. C. J. Kennicutt (1998). We find that the PAH 7.7 µm SFRD includes a significant contribution from dust-obscured star formation absorbed in the UV. In fact, at $z \sim 1$, the PAH SFRD is an order of magnitude higher than the FUV SFRD. Our results are consistent with the total (UV+FIR) SFRD, and suggest that when corrected for metallicity and starburst intensity, the PAH 7.7 µm luminosity traces the total star formation (i.e., obscured and unobscured) in actively star-forming galaxies. In addition, the contribution from starburst galaxies to the SFRD becomes more significant at higher z relative to main-sequence galaxies. Our results are consistent with past attempts to estimate the
<figure><img src="image_25.png" /><figcaption>**Figure 23.** SFRD as a function of redshift for the N2 (top) O32 (bottom) metallicity indicator using the PAH 7.7 µm calibration tied to metallicity, $R_{SB}$, and dust-corrected [O II]. Symbols and lines are the same as in the previous figure.</figcaption></figure>

<table><caption>**Table 8**
Number of Star-forming Galaxies Integrated in Each Redshift Bin to Calculate the SFRD</caption><thead><tr><th rowspan="2">LF</th><th rowspan="2">Redshift Bin</th><th colspan="3">N<sub>tot</sub> (N<sub>MS</sub>, N<sub>SB</sub>)</th></tr><tr><th>Hα N2</th><th>Hα O3N2</th><th>[O II] N2</th><th>[O II] O32</th></tr></thead><tbody><tr><td>8 µm</td><td>0.02 &lt; z &lt; 0.3</td><td>203 (129, 74)</td><td>131 (70, 61)</td><td>120 (77, 43)</td><td>98 (59, 39)</td></tr><tr><td>8 µm</td><td>0.28 &lt; z &lt; 0.47</td><td>105 (51, 54)</td><td>89 (38, 51)</td><td>85 (46, 39)</td><td>135 (66, 69)</td></tr><tr><td>8 µm</td><td>0.65 &lt; z &lt; 0.90</td><td>10 (1, 9)</td><td>3 (1, 2)</td><td>1 (1, 0)</td><td>17 (8, 9)</td></tr><tr><td>12 µm</td><td>0.15 &lt; z &lt; 0.35</td><td>183 (106, 77)</td><td>132 (67, 65)</td><td>131 (80, 51)</td><td>112 (67, 45)</td></tr><tr><td>12 µm</td><td>0.38 &lt; z &lt; 0.62</td><td>30 (10, 20)</td><td>29 (7, 22)</td><td>23 (8, 15)</td><td>120 (39, 81)</td></tr><tr><td>12 µm</td><td>0.84 &lt; z &lt; 1.16</td><td>7 (1, 6)</td><td>1 (0, 1)</td><td>1 (0, 1)</td><td>0</td></tr></tbody></table>

SFR based on Herschel/PACS detections. The SFR calibration with the O3N2 index (bottom panel) is consistent with that of the N2 index. The MD14 cosmic SFRs are ~20%–30% lower than ours.

We also show the redshift evolution for the PAH 7.7 µm-derived SFRD, based on the dereddened [O II] luminosity calibration and N2 (top panel) and O32 (bottom panel) metallicity indicators in Figure 23. Although more data are needed at $z \gtrsim 0.8$ to constrain the shape of the SFRD, the PAH SFRD derived from the L[O II] calibration is consistent with that of Hα.

# 6. Discussion

## 6.1. Comparison with Previous Studies

To our knowledge, this study is the first to derive PAH SFR calibrations from AKARI/IRC 2–24 µm photometry. We extend

the relationship between PAH luminosity and SFR by determining the dependence of the SFR calibration on metallicity and starburst intensity. H. V. Shipley et al. (2016) derived PAH SFR calibrations using a sample of Spitzer/IRS galaxies at $z < 0.4$. We find that their linear fits to L(PAH) versus L(Hα) are consistent with our results for main-sequence galaxies up to $z \sim 1.2$, but must be corrected in starburst galaxies, which have systematically higher L(TIR)/L(8 µm) ratios. This discrepancy is most likely because starburst galaxies were excluded from their sample due to having low signal-to-noise ratios (S/Ns). Based on Figure 17, we estimate that H. V. Shipley et al.'s calibration sample is limited to main-sequence galaxies with EW(PAH 6.2 µm) $\gtrsim 1$ µm and EW(PAH 7.7 µm) $\gtrsim 4$ µm.

T. Takagi et al. (2010) studied “PAH-luminous” starburst galaxies at $z \sim 0.5$ and $z \sim 1$ in the AKARI NEP-Deep survey that
<figure><img src="image_26.png" /><figcaption>**Figure 24.** Peak photometric monochromatic PAH 7.7 µm luminosity as a function of TIR luminosity for star-forming galaxies in the NEP-Deep region. The points in the boxes meet the selection criteria of “PAH enhancement” from T. Takagi et al. The solid line represents the relation found by J. R. Houck et al. (2007) for local starburst galaxies. Symbols are color coded by the logarithm of the starburst intensity.</figcaption></figure>

were selected using color cuts based on the 15 µm/9 µm and 11 µm/7 µm flux ratios. Applying the same color criteria to our star-forming galaxies in the NEP-Deep region, we select 22 such galaxies at $0.39 < z < 0.62$ ($z̃ = 0.47$) and 16 galaxies at $0.76 < z < 1.23$ ($z̃ = 1.01$). Figure 24 shows the correlation between the photometric monochromatic luminosity at 7.7 µm, $νL_{ν,phot}(7.7~µm)$ and $L(TIR)$, color coded by $R_{SB}$. Galaxies shown by square symbols represent “PAH-selected galaxies” that satisfy T. Takagi et al.’s criteria. To calculate the photometric monochromatic luminosity, we scaled our peak luminosity measurements by a factor of $10^{-0.24}$ (see Appendix C). Most objects lie along the local relation for less luminous starbursts, indicating that MIR-selected galaxies up to $10^{12} L_⊙$ are “PAH normal” rather than “PAH enhanced” for a given TIR luminosity.

## 6.2. Applications with JWST

The JWST Mid-Infrared Instrument has an observing wavelength range of 5–28 µm, which includes spectroscopy that resolves the PAH 6.2 µm and 7.7 µm features to $z \sim 3$. To apply our PAH SFR calibrations to JWST observations, follow-up spectroscopy in the NIR such as with Keck I/MOSFIRE (I. Shivaei et al. 2017) or JWST/NIRSPEC would also be useful to determine the gas metallicity with rest-frame optical emission lines. FIR photometry would be needed to measure the TIR luminosity and infer the starburst intensity/compactness of star formation, although extrapolations from multi-wavelength SED fitting may be used provided there are sufficient data in the observed optical to NIR wavelengths. In addition, joint observations with the Hubble Space Telescope will be able to constrain the sSFR. PAH-based SFR calibrations that do not correct for metallicity or starburstiness would underestimate the true SFR in metal-poor and starburst galaxies.

## 7. Summary

In this work, we explore PAH dust emission as an extinction-independent SFR indicator, a major scientific goal of the AKARI

mission. We combine ground-based, optical and NIR spectroscopy with AKARI/IRC multiband photometry to measure the IR spectra of ~500 galaxies in the AKARI NEP field. We present the first results of PAH 6.2 and 7.7 µm SFR calibrations with corrections for metallicity and starburst intensity, applicable to star-forming galaxies. Our calibration sample consists of 443 main-sequence and starburst galaxies from the AKARI/IRC NEP survey at $0.05 \le z \le 1.03$, with a broad range of stellar masses ($M_{25} \sim 10^{8.7}-10^{11.2} M_⊙$), TIR luminosities ($L(TIR) \sim 10^{8.7}-10^{12} L_⊙$), and SFRs (~0.06–500 $M_⊙$ yr$^{-1}$). These MIR-selected galaxies were observed to have strong emission lines with optical/NIR spectroscopy, including Keck II/DEIMOS and Keck I/MOSFIRE observations, which we newly presented in this work. A summary of our main conclusions are as follows:

1. To measure the PAH luminosity of AKARI/IRC galaxies, we first derive best-fit SEDs with CIGALE to model the MIR dust emission. Then from the best-fit, rest-frame SEDs, we decompose the PAH emission features by using PAHFIT. Our photometrically derived PAH 6.2 and 7.7 µm luminosities are consistent with AKARI/IRC slitless spectroscopic measurements to within 20%–40%.

2. The PAH luminosity per dust-corrected $H_α$ and [O II] $\lambda\lambda3726, 3729$ luminosity increases as a function of metallicity, and decreases as a function of starburst intensity ($R_{SB}$) and AGN fraction. Starburst galaxies (i.e., galaxies with $R_{SB} > 2$) are systematically deficient in $L(\text{PAH})$ per dust-corrected $L(H_α)$ and $L([\text{O II}])$ relative to main-sequence galaxies by a factor of 0.34 and 0.3 dex, respectively. Based on multilinear fits, we derive, for the first time, corrections for metallicity and starburst intensity to the PAH luminosity and SFR. Due to the effect of AGN on $L(\text{PAH})$ per dust-corrected $L(H_α)$ and $L([\text{O II}])$, our PAH SFR calibrations may not be applicable to AGN systems. In addition, we find that the PAH SFR calibration is independent of TIR luminosity and redshift (at least up to $z \sim 1$).

3. We apply our PAH SFR calibrations to the extensive data set of AKARI to study the dust-obscured cosmic SFRD per comoving volume. We combine our correlations between $L(\text{PAH} 7.7~µm)$ versus $νL_ν(8~µm)$ and $νL_ν(12~µm)$ with LFs at 8 and 12 µm to derive the SFRD as a function of PAH luminosity. The SFRD as predicted by our PAH 7.7 µm SFR calibration is a factor of 5 higher at $z \sim 0.15$ and a factor of ~10 higher at $z \sim 1$ than observed FUV estimates due to dust attenuation, with significant contribution from starburst galaxies at $z \gtrsim 0.6$. Compared to infrared-based SFR indicators, our PAH SFRD is consistent with FIR and TIR estimates from $0.15 \lesssim z \lesssim 1$ (D. Burgarella et al. 2013).

4. Future studies that involve PAH luminosity as an SFR indicator, such as those conducted with JWST, would need to correct for the effects of metallicity and starburst intensity; otherwise, the PAH SFR would be underestimated in metal-poor or starburst galaxies.

## Acknowledgments

We wish to thank the anonymous referee whose helpful comments greatly improved this work. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the
California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The analysis pipeline used to reduce the DEIMOS data was developed at UC Berkeley with support from NSF grant AST-0071048. H. K. gratefully acknowledges financial support from the S.O.S. program of the National Radio Astronomy Observatory, grant number SOSPA6-024. T. M. is supported by UNAM-DGAPA PAPIIT (IN111319, IN114423) and CONACYT Grant Ciencias Básicas 252531.

# Appendix A
## Subaru/FMOS Hα Detections

Table 9 lists the 10 additional Hα sources from N. Oi et al. (2017) that are newly identified as secure detections based on other emission line detections that confirm the spectroscopic redshift.

<table><caption>**Table 9**
Updated Additional Secure Hα Detections from Subaru/FMOS</caption><thead><tr><th>AKARI ID</th><th>R.A.<br>(deg)</th><th>Decl.<br>(deg)</th><th>Redshift</th><th>F(Hα)<br>(10<sup>-16</sup> erg s<sup>-1</sup> cm<sup>-2</sup>)</th></tr></thead><tbody><tr><td>61021137</td><td>269.24127</td><td>66.72676</td><td>0.949</td><td>0.34 ± 0.13</td></tr><tr><td>61014814</td><td>269.13637</td><td>66.55578</td><td>1.030</td><td>0.22 ± 0.11</td></tr><tr><td>61016430</td><td>269.00271</td><td>66.59490</td><td>1.003</td><td>1.45 ± 0.27</td></tr><tr><td>61009352</td><td>268.98370</td><td>66.40349</td><td>0.902</td><td>0.82 ± 0.14</td></tr><tr><td>61023314</td><td>268.83595</td><td>66.80321</td><td>0.925</td><td>0.78 ± 0.23</td></tr><tr><td>61010363</td><td>268.77946</td><td>66.43416</td><td>0.902</td><td>0.58 ± 0.12</td></tr><tr><td>61023651</td><td>268.71468</td><td>66.81580</td><td>0.715</td><td>0.68 ± 0.09</td></tr><tr><td>61023133</td><td>268.64746</td><td>66.79599</td><td>0.714</td><td>0.55 ± 0.12</td></tr><tr><td>61012206</td><td>268.34379</td><td>66.48484</td><td>1.026</td><td>0.63 ± 0.22</td></tr><tr><td>61015448</td><td>268.91175</td><td>66.57122</td><td>1.003</td><td>1.02 ± 0.23</td></tr></tbody></table>

# Appendix B
## Measurement of TIR Luminosity

In this section, we describe our procedure for testing the dependence of our *L*(*TIR*) measurements on FIR photometry. We selected 82 star-forming galaxies from the NEP-Wide survey with one to five FIR flux density measurement(s) from Herschel/PACS and/or SPIRE. Then, using the same input parameters described in Table 3, we modeled SEDs using CIGALE twice—including and excluding the FIR data. Figure 25 shows the resulting comparison between *L*(*TIR*) when the FIR data are included and excluded. For 78% of galaxies, the *L*(*TIR*) measurements agree to within ≲12%. In a minority of galaxies, removing the FIR data results in a significant underestimation of the TIR luminosity. There was no correlation between the scatter and the number of FIR filter detections. We conclude that our estimates of *L*(*TIR*) are generally accurate, even for those galaxies that lack Herschel detections.

<figure><img src="image_27.png" /><figcaption>**Figure 25.** Comparison between *L*(*TIR*) measurements when including and removing Herschel FIR photometry in SED fitting. The dashed line represents a perfect 1:1 correlation, and has not been fitted to the data.</figcaption></figure>

# Appendix C
## Measurement of Peak PAH 7.7 µm Luminosity

The PAH luminosity measurements presented in Y. Ohyama et al. (2018) are determined by the integrated Lorentzian fits to the SPICY spectra. To compare their measurements to other works that rely on rest-frame SEDs, Y. Ohyama et al. (2018) define the “photometric monochromatic luminosity,” *ν*<sub>L<sub>v,photo</sub></sub>(7.7 µm), and the “spectroscopic monochromatic luminosity,” *ν*<sub>L<sub>v,spec</sub></sub>(7.7 µm). Both the photometric and spectroscopic monochromatic luminosity include contributions from the underlying continuum and measure the peak PAH 7.7 µm luminosity. However, the photometric monochromatic luminosity at 7.7 µm is the peak PAH 7.7 µm luminosity based on broadband SED fitting (T. Takagi et al. 2003), while the spectroscopic monochromatic luminosity is based on the SPICY spectra. According to the scaling relation in their Section 3.3.1, *ν*<sub>L<sub>v,photo</sub></sub>(7.7 µm) is a factor of 0.6 dex higher than their integrated PAH 7.7 µm luminosity due to the different luminosity definitions and continuum contribution. Based on our *L*(*PAH* 7.7 µm) measurements, *ν*<sub>L<sub>v,photo</sub></sub>(7.7 µm) as measured by Y. Ohyama et al. is ~0.7 dex higher than our integrated PAH 7.7 µm luminosities, which is consistent with the errors.

Figure 26 shows a comparison of our method for measuring the peak 7.7 µm luminosity versus the monochromatic spectroscopic and photometric luminosities given by Y. Ohyama et al. (2018) in 41 SPICY galaxies in our sample. We find that our peak *ν*<sub>L<sub>v</sub></sub>(7.7 µm) measurements are consistent with Y. Ohyama et al.'s spectroscopic monochromatic 7.7 µm luminosities within 13% (left panel). In contrast, there is a 0.24 dex offset between our peak *ν*<sub>L<sub>v</sub></sub>(7.7 µm) measurements and the photometric monochromatic 7.7 µm luminosities (right panel), indicating that our values should be multiplied by a factor of 10<sup>-0.24</sup> when comparing to photometric-based methods that rely on broadband SED fitting.
<figure><img src="image_28.png" /><figcaption>**Figure 26.** Comparison between our measured peak PAH 7.7 µm luminosity vs. spectroscopic monochromatic luminosity (left) and photometric monochromatic luminosity (right) by Y. Ohyama et al. (2018) for SPICY galaxies. Linear fits are shown as solid lines. The dotted lines show the exact agreement between the two luminosity estimates.</figcaption></figure>

## Appendix D
### Comparison between [O II] and Hα SFR

Although the [O II] luminosity calibration from R. C. J. Kennicutt (1998) is commonly used as an alternative SFR diagnostic in galaxies where Hα is redshifted out of the visible range (0.4 ≲ z ≲ 1.5), the [O II] emission line is sensitive to reddening and metallicity, which can cause disagreement

between SFR([O II]) and SFR(Hα) (L. J. Kewley et al. 2004). In light of these effects, we compare SFR([O II]) and SFR(Hα) in Figure 27, where we correct for reddening using the rest-frame 24 µm luminosity calibration given in R. C. J. Kennicutt (1998). For the majority of galaxies, the SFR calibrations are consistent with a 0.06 dex offset and dispersion of 20%.
<figure><img src="image_29.png" /><figcaption>**Figure 27.** Comparison between [O II] and Hα SFR for calibration sample, dust-corrected assuming the monochromatic 24 µm luminosity correction given by R. C. J. Kennicutt (1998) equations. A linear fit to the data is shown by the solid line.</figcaption></figure>

## ORCID iDs

Helen Kyung Kim https://orcid.org/0000-0003-2352-8636

Matthew A. Malkan https://orcid.org/0000-0001-6919-1237

Toshinobu Takagi https://orcid.org/0000-0002-8053-4357

Denis Burgarella https://orcid.org/0000-0002-4193-2539

Takamitsu Miyaji https://orcid.org/0000-0002-7562-485X

Hyunjin Shim https://orcid.org/0000-0002-4179-2628

Yoichi Ohyama https://orcid.org/0000-0001-9490-3582

Veronique Buat https://orcid.org/0000-0003-3441-903X

Seong Jin Kim https://orcid.org/0000-0001-9970-8145

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