The Origin of [C ii] 158 μm Emission toward the H ii Region Complex S235

We observed [C ii] and [N ii] emission toward the S235 complex in SOFIA Cycles 4 and 5 in 2016 November and 2017 February using the SOFIA upGREAT instrument (Risacher et al. 2016). upGREAT is an enhanced version of the German Receiver for Astronomy at Terahertz Frequencies (GREAT; Heyminck et al. 2012). We used the upGREAT LFA channel (a 7 pixel array in 2016 and a 2 × 7 pixel array in 2017) to tune to [C ii] and the L1 (single pixel) channel to tune to the ${}^{3}{{\rm{P}}}_{1}\ -{}^{3}{{\rm{P}}}_{0}$ [N ii] 205 $\,\mu {\rm{m}}$ (1.46 THz) line. The total observing time for both cycles was 3.5 hr. We observed in total power on-the-fly (OTF) mapping mode and mapped a total area of 021 × 037 (α × δ), centered at $(\alpha ,\delta [{\rm{J}}2000])$ = (5^h41^m025, 35°51^m57^s). We employed a fast mapping mode for S235MAIN, which resulted in an undersampled map for [N ii], and a slow mapping mode for S235AB and S235C, which resulted in a fully sampled [N ii] map. The spatial resolution of the [C ii] data is 148, the velocity resolution is 0.385 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$, and the full velocity range is −60 to 20 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$. The spatial resolution of the [N ii] data is 202, the velocity resolution is 0.500 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$, and the full velocity range is −60 to 20 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$.

The final data cubes provided by the SOFIA Science Center (in units of main beam temperature T_MB) were processed using the Grenoble Image and Line Data Analysis Software (GILDAS).¹² The data were first scaled to ${T}_{A}^{* }$, the antenna temperature corrected for atmospheric opacity, using a forward efficiency of 0.97. Antenna temperature values were converted to main beam temperatures using the main beam efficiency of η_MB = 0.69. If the rms of an individual spectrum was higher than two times the radiometer noise, the spectrum was ignored. First-order (if rms < radiometer noise) or third-order (if rms < 2× radiometer noise) baselines were removed from all spectra.

Here, we frequently use the integrated [C ii] intensity, "moment 0," from the velocity range −29 to −12 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ (Figure 2). All significant [C ii] emission associated with S235 is found within this velocity range (see Figure 5). This figure shows strong [C ii] emission from the PDRs surrounding S235, but the most intense emission in the field is found toward S235AB and S235C.

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[N ii] is only weakly detected when averaged over the entire ionized hydrogen region. Because there is little spatial information on the distribution of [N ii], we limit analyses using these data.

3.1.1. Regions of Interest

To understand the distribution and velocity structure of the ionized gas, we create a fully sampled map in 6 $\,\mathrm{GHz}$ radio recombination line (RRL) emission using the Green Bank Telescope (GBT). The region has been observed previously in H-α by Lafon et al. (1983), who found a strong velocity gradient in the ionized hydrogen gas; the velocity is ∼−15 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ in the southeast of the region (near our "bg1" region) and ∼−25 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ in the northwest (near our "bg3" region). This strong gradient is unusual for an H ii region and may be due in part to absorption of H-α emission or to a bulk "champagne flow" of ionized gas.

We follow the same observing setup as in Anderson et al. (2018) and Luisi et al. (2018), tuning to 64 different frequencies at two polarizations within the 4−8 GHz receiver bandpass. Of these 64 tunings, 22 are Hnα transitions from n = 95 to n = 117. Carbon and helium RRLs fall within the same bandpass as that of hydrogen, shifted by −149.56 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ and −122.15 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ from hydrogen, respectively. Carbon RRLs are thought to arise from PDRs surrounding H ii regions, whereas helium RRLs come from the ionized hydrogen region.

There are 15 usable Hnα lines after removing those spoiled by radio frequency interference (RFI) or instrumental effects. Over the frequencies of the usable Hnα lines, the beam size ranges from 98'' to 183'', with an average of 141''. We calibrate the intensity scale of our spectra using noise diodes fired during data acquisition and assume a main beam efficiency of 0.94.

The map is 08 × 07, centered at $(\alpha ,\delta [{\rm{J}}2000])$ = (5^h40^m42^s, +35°48^m52^s). We create four complete maps, two in R.A. and two in decl., to mitigate in-scan artifacts, and average all together.

We average all lines at a given position to make one sensitive spectrum (Balser 2006), a technique that is well-understood (Anderson et al. 2011; Liu et al. 2013; Alves et al. 2015; Luisi et al. 2018). After removing transient RFI, we remove a polynomial baseline for each transition and shift the spectra so that they are aligned in velocity (Balser 2006). We regrid the 15 good Hnα lines to a velocity resolution of 0.5 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ and a spatial resolution of 1'. We then average the individual maps using a weighting factor of ${t}_{\mathrm{intg}}{T}_{\mathrm{sys}}^{-2}$ where t_intg is the integration time and T_sys is the system temperature.

We show the integrated intensity moment zero hydrogen RRL map in Figure 3. The emission is strongest for S235MAIN and peaked at the location of the ionizing source. S235AB also shows detected emission, but S235C does not. The other H ii regions in the field have some detected RRL emission. We show the peak line velocity derived from Gaussian fits in Figure 5, although due to the relatively poor spatial resolution we do not show the fit for S235PDR. For S235ION, the fit is to the average spectrum from our RRL map integrated over the entire region of interest. For S235AB and S235C, we use the pointed RRL results from Anderson et al. (2015), because the signal to noise in the RRL map is rather poor and the observational setup in Anderson et al. (2015) is the same as ours used here.

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We also use WISE MIR, 1.4 $\,\mathrm{GHz}$ NVSS radio continuum, and CO rotational transitions to investigate the S235 region (Figure 4). For later comparisons, we regrid all ancillary data to 10'' pixels, and do the same for the SOFIA [C ii] data. The CO data in panels (d)–(f) of this figure are of integrated intensity, integrated over −29 to −12 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ as we did for [C ii] (Figure 2).

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3.3.1. WISE 12 μm and 22 μm Data

3.3.2. NVSS 1.4 GHz Continuum Data

3.3.3. CO Data

The ancillary molecular line data used here of ¹²CO 2 − 1, ¹²CO 3 − 2, and ¹³CO 2 − 1 are from Bieging et al. (2016). The observations were made with the Heinrich Hertz Submillimeter Telescope¹⁵ in 2010 March to April. The two J = 2 − 1 lines were observed simultaneously. The ¹²CO emission line was observed in the upper sideband, while the ¹³CO line at 220.399 GHz was observed in the lower sideband. The maps cover ∼12 × 08 (α, δ), have a velocity resolution of 0.3 km s⁻¹, and have a spatial resolution of 38''.

The ¹²CO 3 − 2 line was observed in 2014 April, also with the Heinrich Hertz Submillimeter Telescope, using the multipixel focal plane array of superconducting mixers ("SuperCam"; Kloosterman et al. 2012). The FWHM beamwidth is 24''. The total area covered is ∼03 × 10 (α, δ) with 0.23 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ velocity resolution.

Kirsanova et al. (2008) distinguished three main velocity components in the S235MAIN region using ¹³CO 1 − 0 and CS 2 − 1 observations: a "red" component (−18 < V_lsr < −15 km s⁻¹), a "central" component (−21 < V_lsr < −18 km s⁻¹), and a "blue" component (−25 < V_lsr < −21 km s⁻¹). With additional observations of NH₃, Kirsanova et al. (2014) confirmed the existence of these different velocity components. Using ¹²CO 1 − 0 data, Dewangan & Ojha (2017) reported that the emission toward S235MAIN peaks in the velocity range −22 to −20, while the smaller H ii regions, S235A ("S235AB") and S235C, are at ∼−17 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$.

The ¹²CO 2 − 1 data have a broad velocity component (centered at ∼ − 11.5 km s⁻¹) that is well-separated from the aforementioned velocity components, but is absent in the other molecular and [C ii] line data (see Figure 5). This redshifted component is possibly related to more diffuse gas not associated with S235; the component is also prominent in EBHIS H i emission (Winkel et al. 2016). As this component is redshifted relative to the overall velocity of the star-forming region S235, we likely observe the diffuse molecular gas component foreground or background to the star formation complex.

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The CO moment maps have similar spatial distributions (see panels (d)–(f) in Figure 4). The molecular emission is more extended than that of [C ii], but components associated with the ionized hydrogen zone and the PDR of S235MAIN are clearly visible. The spatial distributions of the observed molecular gas tracers shows a bridge between S235AB and S235C, especially in the case of the denser gas tracer ¹³CO 2 − 1. As these small H ii regions are essentially at the same velocity, this indicates that S235AB and S235C might be physically connected by a dense gas component.

In the S235PDR region the spatial correlation of the observed [C ii] and molecular gas is weaker than in the inner ionized hydrogen region. The CO emission appears clumpy compared to the emission of the other tracers. CO emission is absent toward the north. This "emission-free" part can also be seen in previous studies (e.g., Dewangan et al. 2016; Dewangan & Ojha 2017). This molecular deficit may be due to escaping ionized hydrogen gas in this direction (Dewangan et al. 2016). Although there is no indication that ionized hydrogen gas fills the evacuated space (see radio continuum map, panel (c) of Figure 4), the gas may be too rarefied to produce strong radio continuum emission.

We compare the spectra of [C ii] (Section 3.1), RRL (Section 3.2), and CO (Section 3.3.3) emission from the regions of interest in Figure 5. The [C ii] emission peaks near −20 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ for S235MAIN, and −18 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ for S235AB and S235C. All significant [C ii] emission is in the range −29 to −12 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$. Hydrogen RRL emission is much broader than that of the other tracers. It peaks near −23 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ for S235ION and near −16 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ for S235AB and S235C. Quireza et al. (2006) found that H RRLs toward S235ION peak at −23.07 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ and C RRLs peak at −19.82 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ (Silverglate & Terzian 1978; Vallee 1987, see also). Anderson et al. (2015) found that the RRL emission from S235A peaks at −15.3 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$, and that of S235C peaks at −16.6 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$. The CO emission has a similar velocity profile to that of [C ii], and carbon RRLs also peak near the velocities of strongest CO emission. We conclude that there is a real offset between the H RRL emission and that of other tracers in S235ION. This offset is not seen in the other regions of interest.

The [C ii] emission can be decomposed into three velocity ranges: −23 to −20 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ ("low"), −20 to −18 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ ("middle"), and −18 to −13 $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ ("high"). These three ranges have distinct emission components. We show moment maps of these three velocity ranges in Figure 6. The low velocity range contains bright compact [C ii] emission in the ionized hydrogen region of S235MAIN, emission from the eastern PDR, and a ridge of emission extending to the northwest. The middle velocity range contains multiple knots of compact [C ii] emission in the ionized hydrogen region of S235MAIN, and emission from the PDR to the northeast and to the west. The high velocity range mainly contains [C ii] emission from the western PDR of S235MAIN, and also compact emission from S235AB and S235C. Although S235AB and S235C are detected in the middle velocity range, this is just the blueshifted wing of emission (see Figure 5). All velocity components show excellent spatial agreement with ¹²CO 2 − 1 emission.

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We give the total fluxes for the regions of interest in Table 2. We find these values by integrating the emission over each aperture as defined in Table 1. For [C ii] and the molecular tracers, the data are in units of main beam temperature, T_MB, so the integrated intensity ${I}_{[}{\rm{C}}\,{\rm{II}}]=\int {T}_{\mathrm{MB}}{dv}$ has units of $\,{\rm{K}}$ $\,\mathrm{km}\ {{\rm{s}}}^{-1}$. We convert the [C ii] and CO data to the more useful quantity of flux in units of W m⁻² per pixel. For our SOFIA [C ii] maps with 7'' pixels, the conversion between integrated intensity and flux for each pixel is

$$\begin{eqnarray}&&\displaystyle \frac{{F}_{[{\rm{C}}{\rm{II}}]}}{{\rm{W}}\ {{\rm{m}}}^{-2}}=8.1\times {10}^{-18}\displaystyle \frac{{I}_{[{\rm{C}}{\rm{II}}]}}{\,{\rm{K}}\,\,\mathrm{km}\ {{\rm{s}}}^{-1}}.\end{eqnarray} \tag{ 1 }$$

We subtract a local background value from the two WISE bands, computed as the median value surrounding the region, but perform no background correction for the other data.

The I_{[C ii]} and F_{12 μm} values appear in roughly the same ratio for all regions of interest. This correlation is less strong for the other tracers. We will explore this in more detail in Section 4.3.

We see from Table 2 that about half the emission from S235MAIN comes from the S235PDR region of interest for [C ii], the MIR bands, and all CO transitions. The [C ii] emission is strong south of the ionizing source (see Figure 2). The [C ii] emission in a central zone 15 in radius around the ionizing source has an integrated intensity of ∼0.6 × 10⁻¹² W m⁻², which is ∼40% that of S235ION and ∼20% that of the total emission from S235MAIN.

The values for all tracers are similar for S235AB and S235C, except for the radio continuum data. S235AB has ∼6 times higher flux density than S235C, indicating a higher Lyman continuum photon production rate in S235AB, a higher optical depth in S235C, and/or stronger dust absorption in S235C.

For S235MAIN, roughly half of the integrated intensity in all CO transitions is coming from the S235ION region, and half from the S235PDR region. In all the observed molecular transitions, the S235AB region is marginally brighter than S235C.

Because of emission from front- and back-side PDRs along the line of sight, it is difficult to accurately determine the percentage of [C ii] emission from the entire PDR of S235. Based on results from previous studies of H ii regions in [C ii] emission, we expect that nearly all the [C ii] emission arises from dense PDRs (e.g., Pabst et al. 2017).

In Figure 7 we show position–velocity (p–v) diagrams for S235MAIN. These diagrams show [C ii] emission from the S235ION region in red and from S235PDR in cyan. We create the orange (from H RRL data) and green (from C RRL data) crosses in this figure by integrating the RRL data along its position axes, and then fitting Gaussians spaxel by spaxel.

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Based on its coincidence with CO and the velocity offset of the ionized hydrogen gas with respect to all other tracers, we believe that the [C ii] emission seen toward the ionized hydrogen is from line-of-sight PDRs and not from the ionized hydrogen volume. The peak velocity of [C ii], CO, and C RRL emission toward the ionized hydrogen gas is redshifted relative to that of the ionized hydrogen gas itself, whereas [C ii] and CO emission from the PDR is at a similar velocity to that of the ionized hydrogen gas. In support of this, we note the excellent spatial agreement between [C ii] and CO emission in the three velocity ranges shown in Figure 6. This is consistent with an expansion of the ionized hydrogen gas preferentially toward us. In this scenario, the [C ii], CO, and C RRL emission are therefore due to back-side PDRs, as we draw in the cartoon model of Figure 8. This explanation is consistent with the fact that minimal absorption is seen across the face of the region in H − α maps (see Figure 1; also Dewangan & Ojha 2017, their Figure 10(b)). If there were dense foreground PDR material, we would see H-α absorption across the face of the region, which we do for H ii regions RCW120 (see Anderson et al. 2015, their Figure 1) and M20 (the Trifid Nebula; see Rho et al. 2006, their Figure 1). Our picture of S235 is similar to the model of Orion in Pabst et al. (2019, see their Figure 3). The main difference is that they observe a shell of [C ii] expanding toward us, whereas in S235 we see no evidence for such a feature.

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We can also use the measured [C ii] and [N ii] intensities to estimate the fraction of [C ii] emission that arises from neutral hydrogen regions. Croxall et al. (2017) found that the [C ii] to [N ii] intensity ratio has a value of I_{[C ii]}/I_{[N ii]} ≃ 4 for ionized gas, independent of electron density. Values of I_{[C ii]}/I_{[N ii]} > 4 indicate [C ii] emission from regions of neutral hydrogen. From the S235ION region, we measure I_{[N ii]} ≃ 2 × 10⁻¹³ W m⁻², which gives us I_{[C ii]}/I_{[N ii]} ≃ 10 (see Table 2). Using Equation (1) from Croxall et al. (2017), this results in a fraction of [C ii] emission from neutral hydrogen regions f_{[C ii],Neutral} ≃ 0.5. Because of the low quality of our [N ii] data, this value is only approximate. Our intensity ratio, however, is roughly consistent with that observed in the external galaxy sample of Croxall et al. (2017) and the study of Rigopoulou et al. (2013). If half of the [C ii] emission toward S235ION comes from locations of neutral hydrogen, just 25% of the emission from all of S235MAIN is from the ionized hydrogen volume.

We investigate the correlation between [C ii] intensity and that of the other tracers to help determine the origin of the [C ii] emission. We plot pixel-by-pixel correlations of the regridded data (Figures 9, 10, 13, and 14) to examine the relationships between the integrated intensity of [C ii] and that of the other tracers in the S235MAIN (S235ION and S235PDR), S235AB, and S235C regions. The bottom panel of each figure contains all data points, one per pixel of the regridded maps.

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To quantify the relationships between [C ii] and other observed tracers, we fit linear regressions of the form I_{[C ii]} = A + B × I_λ, where I_{[C ii]} is the integrated intensity of [C ii], I_λ is the integrated intensity of CO or the flux density for the IR and radio continuum data. We use a robust least-squares method to determine the fit parameters, with a Cauchy loss function. The robust least-squares fit minimizes the influence of outliers, which otherwise can skew the results. For data with few outliers, the choice of loss function has minimal impact on the fit parameters. We have left the data in their natural units, so B has units of K $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ mJy⁻¹ for the WISE and NVSS data, and is unitless for the CO data. We compute the coefficient of determination R² and list these values and the fit parameters in Table 3.

Table 3.  Correlations^a between [C ii] and Other Tracers

Tracer	Regions	Ab	B	R2
		$\,{\rm{K}}$ $\,\mathrm{km}\ {{\rm{s}}}^{-1}$	$\,{\rm{K}}$ $\,\mathrm{km}\ {{\rm{s}}}^{-1}$ mJy−1 or None
F12 μm	S235ION	−5.01	0.89 ± 0.02	0.70
	S235PDR	−12.44	1.02 ± 0.02	0.59
	S235AB	0.64	0.71 ± 0.03	0.51
	S235C	−3.86	0.61 ± 0.02	0.85
	S235BG	−9.71	0.59 ± 0.02	0.57
	Global	−6.99	0.89 ± 0.01	0.67
F22 μm	S235ION	20.44	0.38 ± 0.01	0.44
	S235PDR	−3.61	0.89 ± 0.02	0.64
	S235AB	14.95	0.22 ± 0.01	0.54
	S235C	−13.94	0.86 ± 0.01	0.68
	S235BG	−5.73	0.79 ± 0.13	0.04
	Global	16.19	0.45 ± 0.00	0.55
F1.4 GHz	S235ION	32.34	10.91 ± 0.30	0.36
	S235PDR	36.35	19.36 ± 0.89	0.15
	S235AB	28.55	14.86 ± 0.68	0.74
	S235C	26.69	62.88 ± 2.47	0.76
	S235BG	7.42	15.93 ± 6.66	0.04
	Global	36.74	11.14 ± 0.20	0.46
I12CO21	S235ION	19.80	0.62 ± 0.01	0.56
	S235PDR	9.39	0.33 ± 0.02	0.07
	S235AB	2.86	0.46 ± 0.21	0.18
	S235C	1.75	0.58 ± 0.16	0.00
	S235BG	3.00	0.02 ± 0.03	0.04
	Global	14.15	0.37 ± 0.02	0.23
I13CO21	S235ION	26.25	0.78 ± 0.02	0.57
	S235PDR	14.75	0.38 ± 0.02	0.12
	S235AB	−4.99	0.78 ± 0.23	0.20
	S235C	8.87	0.76 ± 0.20	0.00
	S235BG	5.18	−0.06 ± 0.11	0.01
	Global	16.08	0.47 ± 0.02	0.26
I12CO32	S235ION	30.36	1.44 ± 0.05	0.45
	S235PDR	18.66	1.06 ± 0.06	0.09
	S235AB	11.58	0.97 ± 0.39	0.04
	S235C	19.53	0.82 ± 0.38	0.00
	S235BG	3.39	0.02 ± 0.04	0.01
	Global	21.84	1.37 ± 0.05	0.23

Notes.

^aFits made using I_{[C ii]} = A + B × I_λ. ^bThe A-values for the WISE correlations are uncertain due to the absolute flux calibration of the WISE data.

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Based on previous results, we expect that this linear relationship can approximate the correlation between [C ii] and the other tracers, as Pabst et al. (2017) found between [C ii] and 8.0 $\,\mu {\rm{m}}$ emission in L1630. For example, Malhotra et al. (1997) show that the [C ii]/IR ratio for galaxies is roughly constant at 2–7 × 10⁻³ for L_IR < 10¹¹ L_⊙. De Looze et al. (2011) claim that the L_{[C ii]}/_FIR ratio is typically linear within normal galaxies, but that it shows nonlinearities for ultraluminous galaxies. Although more complicated forms of the relationship are also found in the literature (e.g., $\mathrm{log}({L}_{[{\rm{C}}{\rm{II}}]})=A\times \mathrm{log}({L}_{\mathrm{IR}})+B;$ Ibar et al. 2015), we prefer the simplicity of the linear relationship.

4.3.1. [C ii] and MIR Data

4.3.2. [C ii] and Radio Continuum Data

4.3.3. [C ii] and Molecular Gas

We investigate spatial differences in the correlation between [C ii] emission and that of the other tracers in the percentage difference maps of Figure 11. The maps give the difference between the actual [C ii] intensity and the [C ii] intensity that would be expected from the other tracers if they strictly followed the correlation measured for S235ION (Table 3), normalized by the measured [C ii] integrated intensity. We do, however, adjust the offset (the "A" parameter in the fits) so that emission from S235ION has an average difference of zero. These maps show locations where the [C ii] emission is bright relative to that expected from the other tracers (red) and where the [C ii] emission is faint compared to that of the other tracers (blue). The values of the maps are therefore less important than the distribution of values.

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These maps support our results from the preceding subsections. The [C ii]/12 $\,\mu {\rm{m}}$ difference is nearly uniform across the map, indicating that there is little change in the relative intensities in the field. The [C ii] versus 22 $\,\mu {\rm{m}}$ difference map shows that the relative intensities in the ionized hydrogen and PDR zones differ. Locations within S235ION of bright IR emission from point sources (IRS1, IRS2, and the ionizing source) appear as [C ii] deficits in these panels. For the [C ii]/radio continuum difference map, the ionized hydrogen zone again has different values compared with the rest of the map. Compared with [C ii], there is a negligible amount of CO gas in the cavity located to the north. In the ionized hydrogen region (S235ION) and most of the PDR region (S235PDR), the CO difference maps do not show a large difference between the ionized and molecular gas components.

We can use the correlations established above to investigate the implications for studies of galaxy-wide [C ii] emission. The 158 $\,\mu {\rm{m}}$ [C ii] emission line is known to be an excellent tracer of ongoing star formation, as are CO, radio continuum, and MIR emission. Therefore, we would expect a correlation between all these measures of active star formation.

We create a catalog of galaxies observed in [C ii], CO, radio continuum, and WISE emission. We take [C ii] emission line data from Brauher et al. (2008), who observed 227 galaxies in far-IR continuum and [C ii] line emission using the Infrared Space Telescope. These [C ii] data have an angular resolution of ∼85''. We supplement the [C ii] data set with [C ii] observations by Stacey et al. (1991) using the Kuiper Airborne Observatory, which have an angular resolution of ∼55''. We compile ¹²CO (1 − 0) data from the FCRAO Extragalactic CO Survey (Young et al. 1995), which have an angular resolution of 46''. For galaxies with more than one observed CO position, we choose the position closest to that of [C ii]. We complement our CO and [C ii] data with NVSS 1.4 GHz continuum emission data (at a resolution of 45'') and WISE 12 and 22 μm data (at resolutions of 6'' and 12''), both compiled through spatial searches of the public point-source catalogs. We attempt to remove the stellar contribution to the 12 and 22 $\,\mu {\rm{m}}$ fluxes by subtracting the flux at 3.5 $\,\mu {\rm{m}}$, since for stars the 3.5 $\,\mu {\rm{m}}$ band flux is similar to that in the 12 and 22 $\,\mu {\rm{m}}$ bands (Nikutta et al. 2014). We determine galaxy types and angular diameters using the SIMBAD database.

The galaxies have a range of diameters from ∼30'' to ∼1°. Observations of each galaxy will therefore be sensitive to emission from different galactic components. For the largest galaxies, the data will contain emission only from the central region. This emission may be dominated by contributions from an older stellar population or the presence of a black hole. Observations of smaller galaxies will contain a better sampling of the total emission. To ensure that our comparisons deal with similar portions of all galaxies, we restrict our sample to those with diameters <150''.

Our combined data set includes 32 galaxies: 9 active galaxies (which we call "AGN"; Simbad classifications "LIN," "Sy1," "Sy2," and "SyG"), 3 H ii and starbursting galaxies (which we call "H ii"; Simbad classifications "H2G" and "SBG"), 19 normal spiral galaxies, (which we call "Gal"; Simbad classifications "G," "GiC," "GiG," "GiP," and "IG") and 1 of other type (Simbad classification "EmG"). Nearly all galaxies in our sample have measured intensities for all tracers.

We fit a linear regression to the compiled data of the same form as before (I_{[C ii]} = A + BI_λ) using an orthogonal distance regression (ODR), and show the results in Figure 12. An ODR minimizes the summed squared distances between the fit and the data points, and therefore simultaneously takes into account errors on the dependent and independent variables. We perform this fit individually for AGN and normal spiral galaxies. In these figures, the asterisk on the 12 and 22 $\,\mu {\rm{m}}$ data represents that it is point-source corrected. We expect that the [C ii] emission from H ii galaxies would show good correlations with all tracers if there were sufficient data for a fit, because the [C ii] emission traces ongoing star formation. The normal spirals should also have good correlations, and due to the potentially intense emission from the active nuclei themselves, the AGN correlations should be poorer.

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These hypotheses are only partially born out. There are positive correlations between [C ii] and the other tracers for the normal galaxies. The strongest such correlations are between [C ii] and NVSS or [C ii] and CO. There is no correlation between [C ii] strength and that of the other tracers for the AGN sample. There are only three H ii galaxies, so although we do not perform fits, the trends appear consistent with our expectations.

All the tracers provide a measurement of star formation activity. The WISE bands, however, may contain contributions from stars that are not removed in our method, the 1.4 $\,\mathrm{GHz}$ flux densities are potentially contaminated by the emission from central black holes (even in galaxies that are not active, like the Milky Way), and the CO integrated intensities may include contributions from CO that is not currently in the process of forming stars. That all these tracers are correlated with the integrated [C ii] emission is not surprising. It is encouraging, however, that we find similarly strong correlations for the single high-mass star-forming region S235 as we do for the integrated intensities from galaxies.

We are comparing results from our [C ii] observations of a single H ii region complex at subparsec resolution with those integrated over entire galaxies. Results obtained at such different spatial scales should not be overinterpreted. It does, however, appear that correlations between [C ii] and other SFR tracers may only exist because they all trace star formation when averaged over large areas, not because the small-scale emission properties are related.