CO Excitation in High-z Main-sequence Analogues: Resolved CO(4−3)/CO(3−2) Line Ratios in DYNAMO Galaxies

We make use of the CO(3−2) and CO(4−3) observations of nine DYNAMO galaxies with ALMA, associated with project code 2017.1.00239.S (PI: D. B. Fisher). Observations were taken in Band 7 (275−373 GHz) and Band 8 (385–500 GHz) between 2018 June 1 and 2018 July 10. The spectral windows were configured with bandwidths of 2.00 GHz and channel widths of 15.625 MHz (128 channels). In addition, we also make use of higher-resolution CO(3−2) ALMA observations of three DYNAMO galaxies (G04-1, G08-5, and G14-1) associated with project code 2019.1.00447.S (PI: R. Herrera-Camus). These observations were taken in Band 7 between 2019 October 9 and 2019 October 10. The spectral windows were configured with bandwidths of 1.875 GHz and channel widths of 7.8125 MHz (240 channels). The data associated with both projects were presented in Girard et al. (2021).

The visibilities were calibrated and flagged by the observatory with the Common Astronomy Software Application (casa; McMullin et al. 2007) pipeline versions listed in the fifth column of Table 1. After calibrating the visibilities, we imaged each observation using tclean in casa version 6.1.0.188 with the parameters deconvolver=''hogbom,'' weighting=''briggs,'' robust=0.5, usemask=''auto-multithresh,'' and restfreq set to the redshifted frequency of the observed CO line. We cleaned the data until the residuals were consistent with the rms noise levels that are listed in the fourth column of Table 1. To derive these thresholds, we consider data cubes with just a shallow clean, mask the emission (see below), and calculate the standard deviation of the masked cubes, i.e., nonline channels. These values are listed in column four of Table 1, and we reclean the data cubes to that rms level. For visualization purposes and ease of comparison to the Hα maps, we convolve the final cubes to a circular beam, listed in the second (angular size) and third (physical size) columns of Table 1, with the casa imsmooth function. At the redshifts of DYNAMO galaxies in our sample, the beam sizes correspond to physical scales of ∼1–2 kpc. Finally, we export all data cubes with the spectral axis in units of velocity, in the local standard of rest frame, adopting the radio convention. We present channel maps of CO(3−2) for DYNAMO G04-1 in Figure 1 to show an example of the final data, with the circularized beam shown at the bottom left corner of each panel. The complete figure set (14 images) is available in the online journal.

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View figure set (14 panels)

Tarball of figure set images

We produce moment-zero maps (integrated intensity) by first masking each cleaned data cube along both the spatial and spectral axes. To produce our masks, we first smooth each cleaned data cube to twice the circularized beam FWHM. We then compute the rms of the data cube and mask all pixels that are below 3× the cube rms. For the remaining pixels, we compute the integrated intensity over the channels that are not masked out. We do this for both the CO(3−2) and CO(4−3) observations. Figure 2 presents these moment-zero maps in the two rightmost panels.

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Finally, for the goal of calculating CO(4−3)/CO(3−2) line ratios, we match the pixel scale and resolution of all 2017 CO(4−3) observations to the pixel scale and resolution of the 2017 CO(3−2) observations, where data for both transitions are available. Similarly, we match the pixel scale and resolution of the 2019 CO(3−2) observations, where available, to the 2017 CO(4−3) observations. We match the pixel scales using the casa function imregrid, while to match the resolution, we use the casa imsmooth tool to convolve the higher-resolution data with a Gaussian kernel to produce the lower-resolution Gaussian beam. We note that these transformations are done on the cleaned data cubes with the original, noncircular beams, to ensure we are not introducing errors or artifacts in the data. Finally, we apply the masking of the CO(3−2) observations to the CO(4−3) to produce matching integrated intensity maps. This ensures that the intensities we derive for both lines are integrated over the same velocity ranges and regions.

In addition to the ALMA observations of CO, we make use of Hubble Space Telescope (HST) observations of Hα (PID 12977; P.I.: I. Damjanov) as a tracer of the star formation rate (leftmost panel of Figure 2). Observations were taken with the Wide Field Camera on the Advanced Camera for Surveys (WFC/ACS) using the FR716N and FR728N narrowband filters and were processed with the standard HST pipeline. Continuum observations with the FR647M filter were also taken and used to create continuum-subtracted Hα maps (for details, see Section 3.2 of Fisher et al. (2017a)). The final Hα maps have a pixel scale of ∼005 and a resolution corresponding to physical scales of ∼50–200 pc (Fisher et al. 2017a).

Our ability to make resolved measurements in these DYNAMO galaxies is limited by the resolution of the ALMA data; therefore, we match the pixel scale and resolution of the Hα observations to that of the CO(3−2), where available, and CO(4−3) otherwise. To achieve this, we convolve each Hα observation with a two-dimensional Gaussian function whose FWHM is equal to the circularized beam of the corresponding ALMA observation. Then, we reproject and regrid the Hα observations to match the WCS information and pixel scale of the CO observations using the Python astropy package reproject, ¹⁰ noting that the reproject functions assume that input images have surface brightness units.

Finally, we make use of observations from the Stratospheric Observatory for Infrared Astronomy (SOFIA) of DYNAMO galaxies taken by the Field-Imaging Far-Infrared Line Spectrometer (FIFI-LS; Colditz et al. 2018; Fischer et al. 2018) and High-resolution Airborne Wideband Camera Plus (HAWC+; Harper et al. 2018) instruments (PLAN ID 08_0238 and 09_158; P.I.: L. Lenkić) as part of Cycles 8 and 9. The FIFI-LS is an integral-field spectrometer with two channels observing simultaneously from 50 to 125 μm (blue channel) and 105−200 μm (red channel). The FIFI-LS observations targeted the [Cii] 158 μm fine-structure emission line in the red channel and the [Oiii] 88 μm fine-structure line (or [Oi] at 63 μm depending on atmospheric transmission) in the blue channel for six galaxies (DYNAMO B08-3, D10-4, D14-1, D15-3, F08-2, F09-1, and F12-4) at 156 resolution. These data cover a 1 × 1 arcmin² field of view (FOV) in the red channel and a 30 × 30 arcsec² FOV in the blue channel. FIFI-LS observations were taken on six nights in 2021 April in the nod-match-chop mode, and were reduced using the FIFI-LS pipeline ¹¹ (Vacca et al. 2020). The data reduction steps include ramp fitting and flagging bad pixels, subtracting the chops, wavelength, and spatial calibration, flat-field correction, atmospheric transmission correction using the ATRAN models (Lord 1992), flux calibration, and finally resampling to a regular grid to produce the final data cubes. The observations resulted in [Cii] detections for all galaxies in the sample, and an [Oiii] detection in DYNAMO F08-2 (see Figure 8 in Appendix A).

The HAWC+ instrument is an FIR camera and imaging polarimeter with a wavelength coverage of 50−240 μm. The HAWC+ observations targeted four galaxies (DYNAMO D14-1, D15-3, F08-2, and F12-4) in bands C, D, and E. These data provide measurements of the 89, 155, and 216 μm fluxes at a resolution of 78, 14'', and 19'', respectively. Observations were taken on three nights in 2021 May and one night in 2021 November in the on-the-fly mapping mode with a Lissajous scan pattern, and were reduced using the HAWC+ pipeline. ¹² The observations resulted in detections for all galaxies in the sample (see Figure 9 in Appendix A).

The typical sizes of galaxies in this sample are ∼4'', and our sources are thus point sources for both the FIFI-LS and HAWC+ observations. Appendix A presents the HAWC+ observations in Figure 9 and the FIFI-LS integrated intensity maps in Figure 8. While DYNAMO D13-5 is the only galaxy that overlaps with our ALMA sample, we make use of all SOFIA observations described here to measure the spectral energy distributions (SEDs) of DYNAMO galaxies, and place the measured dust temperatures within the global context of the line ratio measurements we will present. We also make use of these observations to measure the [Cii] luminosity and measure the [Cii]-to-total far-infrared luminosity ratios.

This work aims to investigate the CO(4−3)/CO(3−2) properties of DYNAMO galaxies resolved on a 1–2 kpc scale, and to relate this line ratio to the star formation rate surface density (Σ_SFR) on the same scale. Thus, we describe here our method for extracting these measurements from the data. For each of our resolution and WCS matched ALMA and HST data sets (excluding SOFIA observations because they are unresolved), we define two sets of "grids" of circular, beam-sized apertures: one that is centered on the galaxy, and a second that is offset from the center by 0.5 × the beam FWHM in both the x and y directions. This is to ensure that we cover the gaps of the first grid and results in measurements that are not entirely independent. Within each aperture, we measure the median brightness temperatures of both the CO(3−2) and CO(4−3) lines from the integrated intensity maps and take their ratio.

We measure the SFR surface density from our CO-matched Hα observations. We perform aperture photometry within each ALMA beam-sized aperture in our two grids, described above, to obtain the Hα flux (in electrons per second). We convert these fluxes to units of erg s⁻¹ cm⁻² Å⁻¹, apply a correction for extinction by relating A_V to A_Hα assuming the Cardelli et al. (1989) extinction law and the A_V measurements from Lenkić et al. (2021). Bassett et al. (2017) used Paα observations from the OH-Suppressing Infrared Integral-field Spectrographinstrument at Keck to make resolved extinction measurements in four DYNAMO galaxies. Their results show up to a magnitude difference in A_Hα ; however, strong variation in the adaptive optics point-spread function introduces significant systematic uncertainties in measuring the Paα flux. Furthermore, Bassett et al. (2017) also found that the average A_Hα in clump and nonclump regions are, within the uncertainties, consistent with one another (see their Table 3). This is consistent with the results of Lenkić et al. (2021), who found that within a given DYNAMO galaxy, the extinction-sensitive color they measure shows little variation between clumps, and the clump colors are consistent with their host disks (see their Figures 5 and 8). For these reasons, we choose to adopt a single A_V value for each galaxy. Finally, we calculate Hα luminosities and convert them to SFRs using the Hao et al. (2011) calibration for a Kroupa IMF, constant star formation history, and age of 100 Myr (see their Table 2):

$$\begin{eqnarray}&&\mathrm{SFR}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=5.53\times {10}^{-42}\times {L}_{{\rm{H}}\alpha }\,[\mathrm{erg}\,{{\rm{s}}}^{-1}].\end{eqnarray} \tag{ 1 }$$

In Section 2.1, we describe our process for matching our CO(4−3) and CO(3−2) observations and deriving integrated intensity maps. We adopt brightness temperature units, thus our integrated intensity maps have units of K km s⁻¹. To visually determine how this line ratio varies across each galaxy disk, if at all, we simply divide our CO(4−3) integrated intensity map by that of the CO(3−2). This is what we present in Figure 3, where the color scale indicates the ratio variations across each galaxy disk for which both line transitions were observed, and where the line ratio has S/N ≥ 3, and the black contours correspond to Hα emission in the pixel scale and resolution-matched HST observations. The contours span 1–10σ in increments of 1σ, where we take σ to correspond to the rms of each HST observation calculated in galaxy emission-free regions. We note that there are no HST Hα observations for DYNAMO C22-2 and SDSS 013527-1039. We derive uncertainties for the integrated intensity maps (σ_{J → J−1}) by summing in quadrature the rms of every channel over which we integrate, excluding line emission from the rms calculation, and multiplying by the channel width:

$$\begin{eqnarray}&&{\sigma }_{J\ \to \ J-1}={\rm{\Delta }}v\,\sqrt{\displaystyle \sum _{i}^{N}{({\mathrm{rms}}_{i})}^{2}},\end{eqnarray} \tag{ 2 }$$

where Δv is the channel width, rms_i is the rms of the i^th channel, and N is the number of channels over which the emission is integrated. To obtain the final uncertainty on the line ratio per pixel, we propagate the integrated intensity uncertainties by taking:

$$\begin{eqnarray}&&{\sigma }_{{lr}}=\displaystyle \frac{\mathrm{CO}(4-3)}{\mathrm{CO}(3-2)}\sqrt{{\left(\displaystyle \frac{{\sigma }_{43}}{\mathrm{CO}(4-3)}\right)}^{2}+{\left(\displaystyle \frac{{\sigma }_{32}}{\mathrm{CO}(3-2)}\right)}^{2}},\end{eqnarray} \tag{ 3 }$$

which results in line ratio uncertainty maps.

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From Figure 3, we see that the line ratio for galaxies in our sample vary mildly across the disks, with typical values ranging from R₄₃ ∼ 0.4–0.7. However, galaxy DYNAMO G14-1 shows a strong gradient in the line ratio, with values approaching unity. The Hα image of G14-1 in Figure 2 shows two bright clumps with a fainter "stream" connecting the two. The Hα contours we overplot in Figure 3 show that these two bright features with the connecting filament coincide with the elevated line ratio values and the strong gradient. This may be indicative of an interaction taking place; however, the Hα kinematics of G14-1 show a rotating disk and no complex kinematics (Green et al. 2014). Overall, the line ratio maps we show in Figure 3 suggest a potential central enhancement in R₄₃. Such a central enhancement has been observed in the Milky Way and other nearby star-forming galaxies for CO(2−1)/CO(1−0) (see, e.g., Sakamoto et al. 1997; Sawada et al. 2001; Leroy et al. 2009, 2013; den Brok et al. 2021). To verify this, we separate pixels that are located within the central kiloparsec of each galaxy from pixels that lie outside this region, and compare the median line ratios. Indeed, we find enhanced CO(4−3)/CO(3−2) values in the central kiloparsec of all galaxies in Figure 3, except for G04-1 and G14-1, on the order of ∼10% (see Table 2). Finally, Figure 3 shows in particular for galaxy G04-1, variations in R₄₃ between the spiral arm and interarm region, a trend also observed for CO(2−1)/CO(1−0) in M51 (Koda et al. 2012).

Table 2. CO(4−3)/CO(3−2) Line Brightness Temperature Ratios Compiled from the Literature Compared to DYNAMO

Object(s)	Line Ratio	Reference
C22-2	0.62 ± 0.13	This work
C22-2 (≤1 kpc)	0.60 ± 0.10	This work
C22-2 (>1 kpc)	0.52 ± 0.08	This work
D13-5	0.57 ± 0.08	This work
D13-5 (≤1 kpc)	0.60 ± 0.08	This work
D13-5 (>1 kpc)	0.56 ± 0.09	This work
G04-1	0.50 ± 0.08	This work
G04-1 (≤1 kpc)	0.48 ± 0.20	This work
G04-1 (.1 kpc)	0.52 ± 0.16	This work
G14-1	0.71 ± 0.11	This work
G14-1 (≤1 kpc)	0.70 ± 0.13	This work
G14-1 (>1 kpc)	0.71 ± 0.16	This work
G20-2	0.61 ± 0.07	This work
G20-2 (≤1 kpc)	0.62 ± 0.10	This work
G20-2 (>1 kpc)	0.57 ± 0.10	This work
SDSS J013527.10-103938.6	0.44 ± 0.05	This work
SDSS J013527.10-103938.6 (≤1 kpc)	0.46 ± 0.06	This work
SDSS J013527.10-103938.6 (>1 kpc)	0.42 ± 0.06	This work
DYNAMO all	0.54${}_{-0.15}^{+0.16}$	This work
z = 1.5 MS Galaxies	0.74 ± 0.26	D15
ASPECS z = 1.0–1.6 SFGs	0.52 ± 0.16	B20
G1700-MD94 one component	0.92 ± 0.18	HB22
G1700-MD94 two component	0.77 ± 0.15	HB22
non-U/LIRGs (LFIR = 1010 L⊙)	0.25 ± 0.05	K16
LIRGs (LFIR = 1011 L⊙)	0.51 ± 0.10	K16
LIRGs	1.23 ± 0.38	P12
ULIRGs low CO excitation	1.08	R15
ULIRGs mid CO excitation	0.70	R15
ULIRGs high CO excitation	1.02	R15

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Next, we perform ∼1–2 kpc sized sightline measurements of the line ratio across the disk of each galaxy, as described in Section 2.4. To characterize the typical line ratio we measure across the sample and the magnitude of the spread. To this end, we construct a global probability density function (PDF) by modeling each beam-averaged line ratio measurement with a kernel density estimate (KDE). We construct the individual KDEs by modeling each beam-averaged line ratio measurement as a one-dimensional Gaussian with a centroid corresponding to the measured line ratio and with width equal to the line ratio uncertainty. The area of each Gaussian is normalized to unity; then we sum all Gaussians to produce a final global PDF (see for example Section 4 and Figure 5 of Levy et al. (2018)). This is what we show in Figure 4. From this, we find that the median line ratio and 68% confidence interval for DYNAMO galaxies are: R₄₃ = 0.54${}_{-0.15}^{+0.16}$. These values are taken at the 15.9, 50, and 84.1 percentiles of the cumulative distribution function of the PDF.

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For comparison, we compile estimates of the CO(4−3) to CO(3−2) line ratio from the literature and include these in Figure 4. We describe our derivation of all line ratios compiled from the literature in Appendix B, and we summarize them along with the median line ratios we measure for each DYNAMO galaxy individually, and the median line ratio for the entire DYNAMO sample studied here in Table 2.

This comparison reveals that the CO(4−3)/CO(3−2) line ratio of non-ULIRGs from Kamenetzky et al. (2016; local galaxies with L_FIR ≤ 6 × 10¹⁰ L_⊙) is much lower and incompatible with what we find in our DYNAMO sample. In contrast, the U/LIRG line ratio estimate from Kamenetzky et al. (2016) for L_FIR = 10¹¹ L_⊙ is in much better agreement with what we find across the DYNAMO sample. Likewise, the CO(4−3)/CO(3−2) line ratios measured in main-sequence galaxies at z ∼ 1–2 (Daddi et al. 2015; Boogaard et al. 2020; Henríquez-Brocal et al. 2022) are, within the uncertainties, consistent with DYNAMO. In particular, the eight star-forming galaxies at z = 1.0–1.6 from the ALMA Spectroscopic Survey (ASPECS; Boogaard et al. 2020), are an especially good match to the R₄₃ we measure across our sample. DYNAMO galaxies lie on the star formation main sequence at z ∼ 2 (Fisher et al. 2019) and have gas fractions and velocity dispersions that are more similar to main-sequence galaxies of that epoch than local ones. Therefore, this result is consistent with lines of evidence that indicate DYNAMO galaxies are local analogues of high-z main-sequence systems. ULIRG samples (Rosenberg et al. 2015) have much larger line ratios than we observe in DYNAMO, and this too is consistent with previous observations. Using Herschel Photodetector Array Camera and Spectrometer (PACS) and Spectral and Photometric Imaging Receiver (SPIRE) observations of five DYNAMO galaxies, White et al. (2017) found that, despite their large FIR luminosities, L_FIR > 10¹¹ L_⊙, these galaxies have much lower dust temperatures (∼30 K) than ULIRGs. Therefore, unlike ULIRGs, the star formation in DYNAMO galaxies is more distributed throughout the disks; thus, colder dust temperatures would be expected and likewise lower CO(4−3)/CO(3−2) line ratios.

We make use of existing CO(1−0) measurements from the PdBI and NOEMA (angular resolution ∼5''–10''; Fisher et al. 2014; White et al. 2017; Fisher et al. 2019) to derive the CO(4−3)/CO(1−0) and CO(3−2)/CO(1−0) line ratios across our sample. We measure the total CO(4−3) and CO(3−2) fluxes by summing all pixels with S/N ≥3 in our integrated intensity moment maps and then scaling by the number of pixels per beam. We then convert the total fluxes to luminosities ($L^{\prime} ;$ K km s⁻¹ pc²) using Equation (3) in Solomon et al. (1997). We present these results in Table 3.

Table 3. Galaxy Integrated CO(3−2)/CO(1−0) and CO(4−3)/CO(1−0) Line Ratios and Model Predictions

Galaxy	$L{{\prime} }_{\mathrm{CO}(1-0)}$	$L{{\prime} }_{\mathrm{CO}(3-2)}$	$L{{\prime} }_{\mathrm{CO}(4-3)}$	R31	R41	R31	R41
	(109 K km s−1 pc2)			Observed		Predicted
C13-1	1.91 ± 0.05	0.47 ± 0.05	⋯	0.40 ± 0.05	⋯	⋯	⋯
C22-2	0.66 ± 0.05	0.47 ± 0.04	0.23 ± 0.02	0.71 ± 0.08	0.35 ± 0.04	⋯	⋯
D13-5	2.69 ± 0.08	1.48 ± 0.03	0.87 ± 0.03	0.55 ± 0.02	0.32 ± 0.01	0.63	0.39
D15-3	3.02 ± 0.06	⋯	0.49 ± 0.02	⋯	0.16 ± 0.01	0.57	0.32
G04-1	5.41 ± 0.39	2.90 ± 0.10	1.54 ± 0.08	0.54 ± 0.04	0.28 ± 0.02	0.56	0.31
G08-5	2.29 ± 0.26	1.83 ± 0.08	⋯	0.80 ± 0.10	⋯	0.57	0.32
G14-1	1.59 ± 0.19	0.77 ± 0.08	0.427 ± 0.001	0.48 ± 0.08	0.27 ± 0.03	0.56	0.31
G20-2	1.68 ± 0.19	0.97 ± 0.03	0.56 ± 0.03	0.58 ± 0.07	0.33 ± 0.04	0.61	0.36
SDSS 013527-1039	3.45 ± 0.16	1.48 ± 0.05	0.65 ± 0.02	0.43 ± 0.02	0.19 ± 0.01	⋯	⋯

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We find line ratio values across our sample that range from R₃₁ ∼ 0.4–0.8, with a mean (median) R₃₁ = 0.56 (0.55) and R₄₁ ∼ 0.2–0.4, with a mean (median) R₄₁ = 0.27 (0.28). Our R₃₁ result is consistent with multiple studies of CO excitation in z ∼ 1–3 star-forming galaxies: Daddi et al. (2015) found that the brightness temperature line ratio of CO(3−2) to CO(1−0) ranges from R₃₁ ∼ 0.4–0.6, with an average R₃₁ = 0.42 ± 0.07, for their three star-forming BzK z ∼ 1.5 galaxies; Dessauges-Zavadsky et al. (2015) found R₃₁ = 0.57 ± 0.15 for five lensed star-forming galaxies (SFR < 40 M_⊙ yr⁻¹) at z ∼ 1.5 galaxies; Riechers et al. (2020) found R₃₁ = 0.84 ± 0.26 for six galaxies at z ∼ 2–3; Birkin et al. (2021) found R₃₁ = 0.63 ± 0.12 for a large sample of SMGs at z ∼ 1.2–4.8; and Harrington et al. (2021) found R₃₁ = 0.69 ± 0.12 for 24 dusty star-forming galaxies at 1 < z < 3. However, we note that Bolatto et al. (2015) found R₃₁ ∼ 1 for two main-sequence galaxies at z ∼ 2; however, one of the two galaxies is classified as an AGN, and the other may host a weak AGN. In contrast, Leroy et al. (2022) analyzed the global R₃₁ for nearby normal star-forming galaxies and find a mean (median) of R₃₁ = 0.30 (0.29), which are lower and inconsistent with the DYNAMO results, but similar to the Milky Way (Fixsen et al. 1999). We illustrate this comparison in Figure 5 where we plot the brightness temperature ratios of DYNAMO galaxies as a function of the upper-J number, along with the ratios of z ∼ 1–2 star-forming galaxies (Daddi et al. 2015; Boogaard et al. 2020), nearby star-forming galaxies (Leroy et al. 2022), and the Milky Way inner disk (Fixsen et al. 1999). We can see that the ratios of nearby galaxies and the Milky Way are incompatible with those of DYNAMO. The CO SLED of the ASPECS galaxies and two of the three BzK galaxies are in agreement with DYNAMO, while the third galaxy (referred to as BzK-16000 in Daddi et al. 2015) shows overall lower line ratios. Interestingly, Daddi et al. (2015) describe this galaxy as the most evolved in their sample, with no massive clumps.

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We extract background-subtracted 89, 155, and 216 μm fluxes for four DYNAMO galaxies, including D15-3, which overlaps with our ALMA sample, from our HAWC+ SOFIA observations using the Photutils software (Bradley et al. 2021). We define the flux extraction apertures to correspond to the FWHM beam size of each corresponding HAWC+ band, while we define the background annuli to have an inner radius equal to 5 × beam FWHM and an outer radius of 7 × beam FWHM (see Figure 9 in Appendix A). We record these flux measurements in Table 4. To fit the SED, we combine the HAWC+ fluxes with Wide-field Infrared Survey Explorer (WISE) measurements at 22 μm (which is not contaminated by line emission and traces the warm dust continuum; Cluver et al. 2017), and use the modified blackbody (MBB) SED fitting tool mbb_emcee, ¹³ described in Riechers et al. (2013) and Dowell et al. (2014). The MBB is joined to a power law of the form ν^α at short wavelengths. mbb_emcee fits the dust temperature, T_d, the extinction curve power-law slope, β, the power-law slope of the blue side, α, the wavelength where the optical depth reaches one, λ₀, and the normalization. We impose a prior on β to constrain it between 1.5 and 2, and leave all other parameters unconstrained. We record the resulting fit parameters and total infrared luminosity (TIR; 8–1000 μm) in Table 4.

Table 4. SOFIA [C ii] and IR Measurements

Galaxy	22.2 μm	89 μm	155 μm	216 μm	Td	TIR	log10 L[Cii]
	(mJy)	(mJy)	(mJy)	(mJy)	(K)	(1010 L⊙)	(erg s−1)
B08-3	⋯	⋯	⋯	⋯	⋯	⋯	41.82 ± 0.46
D10-4	⋯	⋯	⋯	⋯	⋯	⋯	41.91 ± 0.46
D14-1	12.3 ± 3.5	148 ± 19	423 ± 47	209 ± 25	25.94${}_{-4.88}^{+5.10}$	3.48${}_{-0.78}^{+0.69}$	⋯
D15-3	8.1 ± 2.8	282 ± 33	393 ± 44	685 ± 73	29.56${}_{-2.89}^{+3.06}$	4.26${}_{-0.49}^{+0.52}$	41.74 ± 0.46
F08-2	⋯	522 ± 57	326 ± 37	563 ± 61	46.15${}_{-6.72}^{+7.66}$	6.27${}_{-1.34}^{+1.30}$	41.95 ± 0.46
F09-1	⋯	⋯	⋯	⋯	⋯	⋯	42.20 ± 0.46
F12-4	15.3 ± 3.9	224 ± 27	279 ± 32	594 ± 64	23.43${}_{-7.05}^{+7.65}$	4.11${}_{-1.02}^{+0.74}$	42.21 ± 0.46

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We present the resulting SEDs in the left panel of Figure 6, where the filled colored data points represent fluxes from the HAWC+ (three longest wavelength data points), open colored data points represent WISE bands (shortest wavelength point) for each of the four galaxies, and the matching colored line represents the SED fit for that galaxy. The dust temperatures derived from these SEDs are shown in the upper left corner. For DYNAMO D14-1 and D15-3, the resulting dust temperatures are T_d = 25.94${}_{-4.88}^{+5.10}$ K and T_d = 29.56${}_{-2.89}^{+3.06}$ K, respectively, consistent with the dust temperature measurements of T_d = 28.09 ± 0.86 K and T_d = 25.64 ± 0.52 K from SED fitting of Herschel PACS and SPIRE observations by White et al. (2017).

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The SEDs provide us with estimates of the TIR for four out of the seven galaxies in the SOFIA sample. We combine these measurements with the SOFIA FIFI-LS observations to explore the "[Cii] deficit": the observed decreasing fraction of [Cii] emission with respect to the TIR in increasingly more infrared luminous objects (see, e.g., Malhotra et al. 2001; Brauher et al. 2008; Smith et al. 2017; Herrera-Camus et al. 2018a). For the remaining four galaxies in the SOFIA sample where no HAWC+ observations are available, we instead use the SFRs reported in Green et al. (2014) to estimate the TIR and the calibration in Equation (3) of Cluver et al. (2017):

$$\begin{eqnarray}&&\mathrm{SFR}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=2.8\,\times \,{10}^{-44}\,{L}_{\mathrm{TIR}}\,[\mathrm{erg}\,{{\rm{s}}}^{-1}],\end{eqnarray} \tag{ 4 }$$

which is derived from Starburst99 for solar metallicity, continuous star formation over 100 Myr, and a Kroupa IMF, and assumes that the ultraviolet (UV) component of stellar emission is completely absorbed and reradiated in the infrared (see also Calzetti 2013).

To determine the [Cii] luminosities, we produce integrated intensity maps from the FIFI-LS observations (see Figure 8 in Appendix A) and take the peak value within a beam located at the position of each galaxy. In the right panel of Figure 6, we present the [Cii]/TIR as a function of the TIR measured in this sample of DYNAMO galaxies. The magenta squares represent galaxies for which SEDs were used to derive the TIR, while the teal diamonds represent the galaxies for which the SFRs were used instead. In both cases, we show error bars where the errors on the [Cii] and TIR luminosities have been propagated into the ratio. The two approaches to estimating the TIR luminosities yield consistent results. To illustrate this, we join with black dashed lines the data points for which we have SEDs and SFRs. When we compare DYNAMO to existing measurements in different types of galaxies (Herrera-Camus et al. 2018a), we find that DYNAMO galaxies do not exhibit a [Cii] deficit. Herrera-Camus et al. (2018a) showed that at a fixed IR luminosity, the [Cii]/FIR ratio decreases as galaxies become more compact, and Lutz et al. (2016) showed that the line-to-FIR ratios form a much tighter relation with the FIR surface brightness than with luminosity. To investigate this, Herrera-Camus et al. (2018b) constructed two toy models with the PDR toolbox (Kaufman et al. 2006): one where OB stars are closely associated with molecular gas clouds, and another where OB stars and clouds are randomly distributed. They found that as galaxies become more compact, a combination of effects give rise to the [Cii] deficit. These include a reduction in the photoelectric heating efficiency, an increase in the ionization parameter, and as the interstellar radiation field increases, the [Cii] line saturates and becomes nearly independent of the far-UV flux. Although DYNAMO galaxies generally lie above the star-forming main sequence at z ∼ 0.1, their star formation is distributed throughout their disks within numerous star-forming clumps, rather than being confined to a compact region. Their low dust temperatures and lack of a [Cii] deficit are consistent with this morphology.