Probing ISM Structure in Trumpler 14 and Carina I Using the Stratospheric Terahertz Observatory 2

We present the integrated intensity of the [C ii] emission in Figures 1 and 2 together with the Hα image from Hubble (Smith 2006), the 8 μm image from Spitzer (Smith et al. 2010; Povich et al. 2011), the 160 and 500 μm images from Herschel (Preibisch et al. 2012; Gaczkowski et al. 2013; Roccatagliata et al.2013), the integrated H i 21 cm image from ATCA (Rebolledo et al. 2017), the integrated CO 1–0 emission from Mopra (Rebolledo et al. 2016), and the integrated H92α emission from the Deep Space Network (DSN). Using multiple continuum and spectral line images, we describe here structures of the Tr 14/Carina I region and investigate the spatial distribution of the [C ii] emission with respect to different ISM phases.

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The overall morphology of the Tr 14 and Tr 16 region is as follows: the Tr 14/Carina I region is located in the western part of the CNC, while the Tr 16 region is located in the eastern part. The Tr 14 cluster is partially surrounded by dense clouds, including the dark V-shaped dust lane (see Hα in Figure 1) in the south of Tr 14 (aka Carina I) and dense CO clouds to the west and north of Tr 14 (see ¹³CO 1–0 contours in Figure 2). The east side of the Tr 14/Carina I region is open to the η Carinae and Tr 16 region, but there is another dust lane to the east of η Carinae, suggesting that the dust lane and dense clouds partially surround the η Carinae and Tr 14 region. The optical image shows that a majority of the members of the Tr 14 and Tr 16 clusters have low extinction (e.g., Smith 2006), which indicates that there is no significant foreground cold gas toward the two clusters and the H ii regions are exposed to us. On the other hand, the V-shaped dust lane appears as a high-extinction region in the Hα image, suggesting that the dust lane is in front of the H ii region (e.g., Wu et al. 2018).

We find that the [C ii] emission covers a significant fraction of the area mapped using STO2 (025 × 028, equivalent to 10.0 pc × 11.2 pc at a distance of 2.3 kpc). The fraction of the area with peak main beam temperatures >5 and >10 K are 83% and 58%, respectively. The [C ii] emission is expected from both the H ii region of Tr 14 and the PDRs. Looking at the Hα and 8 μm maps, we find that the upper half of our [C ii] map coincides with the H ii region of Tr 14, and the other half of the [C ii] map is coincident with the Carina I cloud and its PDRs, which confirms that there are multiple sources for the [C ii] emission. The brightest intensity peak of the [C ii] emission is 370 K km s⁻¹, located 7' south of Tr 14 (4.7 pc at the distance of 2.3 kpc), where the Carina I-E/Carina I-W clouds are located (indicated by green arrows in Figure 1). The brightest emission at Carina I-E/Carina I-W is because they are the densest clouds in Carina I and irradiated by a B1 supergiant only 0.5 pc away in projected distance, in addition to the main members of the Tr 14 cluster, thus resulting in a significantly high emission measure (the excitation condition of these clouds is further discussed in Section 5).

We compare the integrated [C ii] emission to the dust continuum emission and PAH observed using Herschel and Spitzer. The dust continuum emission at 160 and 500 μm shows warm and cold dust structures in the Tr 14/Carina I region. The 8 μm emission from Spitzer is typically dominated by PAH emission, which traces PDRs in star-forming regions. Overall, the strong [C ii] emission agrees better on a large scale with the bright structures seen in dust and PAH emission than with the bright structure of the Hα emission, suggesting that the strong [C ii] emission may originate from PDR and H ii regions near ionization fronts, while we still observe weak [C ii] emission coming from the inner part of the Tr 14 H ii region.

We show the integrated ¹²CO and ¹³CO 1–0 observed using Mopra in Figures 1 and 2 (Rebolledo et al. 2016), along with the integrated [C ii] emission. The ¹²CO 1–0 map reveals the cold molecular ISM, and the ¹³CO 1–0 map highlights the denser portions of the CO clouds in the Tr 14/Carina I region. The overall spatial distribution of the CO 1–0 emission, particularly ¹³CO 1–0, shows that CO clouds form a wall bounding the western part of the Tr 14/Carina I region. There is also weak, broad ¹²CO 1–0 emission from Tr 14, suggesting that there may be CO gas behind Tr 14, since we do not see significant extinction in optical bands. We find that, overall, the [C ii] emission is broadly distributed covering Tr 14 and nearby CO clumps, while the CO emission is bright 4' west and 5' south of Tr 14 (2.6 and 3.4 pc at a distance of 2.3 kpc) and extended to the western part of the Tr 14/Carina I region. There is a region with relatively bright [C ii] emission (121 K km s⁻¹) but quite weak CO emission (integrated intensity 34 K km s⁻¹ compared to 211 K km s⁻¹ from Carina I-E), which may indicate a CO-dark molecular region (Langer et al. 2014; indicated by a green arrow in the first panel of Figure 2). The intensity peaks of individual CO clumps are typically displaced a couple of arcminutes relative to the [C ii] and PAH (8 μm) intensity peaks, showing the locations of CO clumps relative to their PDRs and ionization fronts.

We probe the spatial distribution of the cold neutral medium using the integrated H i emission and the [C ii] emission (Figure 2). We integrate the H i emission from −40 to 0 km s⁻¹ because most of the CO and [C ii] emission is within this velocity range. The integrated H i 21 cm emission shows extended H i emission covering the CNC with clumpy H i clouds and with cavities in the H i emission near Tr 14 and η Carinae. Cavities may appear when neutral atomic hydrogen forms molecular hydrogen or becomes ionized, or if there is foreground absorption due to cooler H i gas. The cavities in the CNC are due to the absorption features in the H i spectra. We also find that the spatial distribution of the cavities agrees well with locations of the Keyhole Nebula and the dense CO clouds near Tr 14. To have absorption features, there must be a continuum background. In the CNC, the free–free emission of the H ii region provides a bright, hot background against which we see absorption. We find that the distribution of the H92α emission is broadly extended, including the H ii region and the cavities. Comparing H i 21 cm to [C ii] and ¹²CO 1–0, we find numerous bright CO clumps and [C ii] emission within the cavities in the Tr 14/Carina I region. In this part of the cavity, the cold H i in dense CO clumps may be the source of absorption, which was also discussed in Rebolledo et al. (2017). On the other hand, we do not see significant CO emission in the cavity west of η Carinae, where the Keyhole Nebula is located. This suggests that the Keyhole Nebula is a CO-dark cloud with relatively cold H i together with H ii gas.

Figure 3 shows the channel maps of [C ii] 158 μm and ¹²CO 1–0 (Rebolledo et al. 2016) overlaid on Hα (Smith 2006). The [C ii] emission is mostly found in the velocity range from −32 to −5 km s⁻¹ and is spatially localized near Tr 14. We find that the ¹²CO 1–0 emission also covers the velocity range from −32 to −5 km s⁻¹ but spans a wider area west of Tr 14 compared to the [C ii] emission. We find no significant CO emission between η Carinae and Tr 14 in any channel map. We find weak CO emission east of η Carinae but at slightly blueshifted velocity (−25 km s⁻¹) compared the CO emission west of Tr 14 (−20 km s⁻¹).

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Based on the distribution of the [C ii] 158 μm and ¹²CO 1–0 emission in PPV space, we may divide the dense structures into three velocity groups. The first group includes the ¹²CO and [C ii] structures in the local standard of rest (LSR) velocity range from −32 to −23 km s⁻¹, the second group includes the dense structures in the velocity range from −23 to −13 km s⁻¹, and the third group includes the dense structures in the LSR velocity range from −13 to −5 km s⁻¹.

The first group (−32 to −23 km s⁻¹) contains a few CO clumps south of Tr 14, including a part of Carina I-E/Carina I-W and the CO clumps east of η Carinae. This group is likely in front of Tr 14 relative to us, since CO clumps in this velocity range appear as dark clumps with respect to the bright Hα background (Haikala et al. 2017). Also, their blueshifted velocity compared to the LSR velocity of most of the CO clumps suggests that they are pushed toward to us by expanding H ii gas and in the foreground of the H ii region. The CO clumps in this group are relatively isolated from each other and have bright [C ii] layers on their outskirts (for more detail, see the maps at −28.5 and −23.5 km s⁻¹ in Appendix B), which indicates the presence of ionization fronts and PDRs surrounding those CO clumps due to high-mass stars in the Tr 14/Carina I region. We find that the [C ii] emission is mostly located in the eastern outskirts of the CO clumps rather than in the northern outskirts facing the center of Tr 14. This may be due to the B1 supergiant and O7 binary on the east side of Carina I (Wu et al. 2018). The spatial distribution of CO and [C ii] emission suggests that the CO clumps in the first group may not be at the same distance from us as Tr 14, which is consistent with silhouette globules at velocity ranges from −30 to −20 km s⁻¹ facing toward Tr 16 rather than Tr 14 (Smith et al. 2003).

Near η Carinae, we see that there are CO clumps to the east at −28.5 km s⁻¹, which comprises the east dust lane of the CNC. These CO clumps are blueshifted compared to the CO cloud to the west, and their LSR velocity is similar to that of the CO clumps in the dust lane south of Tr 14. This suggests that CO clumps to the east of η Carinae are likely in the foreground of the high-mass stars in the CNC. We do not see any strong CO emission near η Carinae in any channels, while there are CO clumps near Tr 14 in the redshifted velocity range of −16 to −8 km s⁻¹. It is likely that η Carinae may have cleared out the dense structures where it originally formed, while Tr 14 is still interacting with nearby dense clumps. This picture is consistent with the younger age of Tr 14 compared to Tr 16 (Walborn 1973; Morrell et al. 1988; Vazquez et al. 1996; Smith & Brooks 2008; Rochau et al. 2011), suggesting that Tr 14 has not lived long enough to clear out its surroundings. We will further discuss the three-dimensional structure of the Tr 14/Carina I region in Section 6.

The second group (−23 to −15 km s⁻¹) includes the CO clouds/clumps west of Tr 14. In this velocity range, we find that the CO emission is brighter and more extended than the [C ii] emission in the other groups, suggesting that the majority of the CO gas is within this velocity range. The spatial distribution shows highly clumpy CO structures but also includes a dense CO "wall" to the west of Tr 14 in the LSR velocity range from −20 to −15 km s⁻¹ with their central velocity near −17 km s⁻¹. The [C ii] emission reveals isolated structures associated with the CO clumps in the LSR velocity range from −23 to −20 km s⁻¹. The [C ii] emission associated with the CO clump is likely due to the PDRs of the clump. On the other hand, at velocities from −20 to −15 km s⁻¹, we find that the [C ii] emission forms a thick strip following the eastern outskirts of the CO wall. The bright [C ii] strip is the ionization front of the dense CO wall.

In the third group (−15 to −5 km s⁻¹), the ¹²CO emission is found on and around the center of Tr 14. Considering that the extinction from Hα is quite low in this direction (Smith 2006; Hur et al. 2015), we think that the CO gas in this group is likely behind Tr 14 along our LOS. In the [C ii] channel maps, we find that the majority of the [C ii] emission is found to be spatially associated with CO clumps (e.g., see channel map at −11 km s⁻¹ in Appendix B). This indicates that the [C ii] emission in this group comes from the PDRs of the CO clumps, which are behind Tr 14 and may be being pushed away from us.

Beyond −5 km s⁻¹, there is weak ¹²CO 1–0 emission around Tr 14, but we could not find a significant dense cloud. This suggests that the dense structures of Tr 14/Carina I are mostly within the −32 to −5 km s⁻¹ velocity range.

We compare the [C ii] 158 μm and ¹²CO 1–0 emission to the H92α emission in order to investigate the distribution of the ionized ISM in the Tr 14/Carina I region (right column of Figure 3 and channel maps in Appendix B). We find that ionized gas is distributed slightly asymmetrically between Tr 16 and Tr 14 in velocity space. The H92α emission near Tr 16 and η Carinae spans −60 to +15 km s⁻¹, while the H92α emission near Tr 14 is found from −40 to +10 km s⁻¹. This suggests that the H ii regions near Tr 16 and Tr 14 have different dynamics or spatial distributions. The spatial distribution of the H92α emission has intensity peaks at two different locations: one is the Keyhole Nebula, and the other is Carina I-E, which are both dense clouds near η Carinae and Tr 14. We see the brightest intensities toward the dense clouds rather than the inner H ii region of Tr 14 because the column densities of both the electrons and hydrogen atoms near the dense clouds are higher. The H92α emission is extended in the CNC, indicating that the ionized gas is widely distributed.

We first compare the H i 21 cm emission to the H92α, [C ii] 158 μm, and ¹²CO 1–0 emission to probe the distribution of the neutral medium to ionized and molecular media. The large-scale structure of H i in the CNC is discussed in Rebolledo et al. (2017), so we focus on the small-scale structures (<20 pc) of the H i emission within the Tr 14/Carina I region.

We find that there are cavities in the H i channel maps due to absorption features in the H i spectra, as shown in Rebolledo et al. (2017). Comparing the cavity to the [C ii] and CO emission, we find that the cavities have a strong correlation with CO and [C ii] in PPV space. In position space, we see that the western portion of the cavity coincides with Carina I-E, while the eastern portion of the cavity coincides with the Keyhole Nebula. In velocity space, the H i cavities are at two different velocity ranges: one at −50 to −20 km s⁻¹ and the other at −10 to 0 km s⁻¹. The CO gas is at LSR velocities between the two velocity ranges of the H i cavities (−30 to −5 km s⁻¹). These observations indicate that the neutral atomic medium is spatially associated with the cold molecular clouds but has different kinematics with respect to the dense molecular gas (e.g., cloud dispersal through stripping and photoevaporation).

To study the ISM structure, we select six positions representative of the H ii region in the CNC, the ionization front of the large CO cloud to the west of Tr 14, and molecular regions (Figure 4, numbers 1–6). We analyze the spectra including ¹³CO 1–0, ¹²CO 1–0 (Rebolledo et al. 2016), [C ii] 158 μm, H i 21 cm (Rebolledo et al. 2017), H92α, and optical lines of nitrogen and hydrogen (Damiani et al. 2016).

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Panels 1, 5, and 6 in Figure 4 present the spectra toward the three positions including the center of Tr 14, the middle position between Tr 14 and η Carinae, and η Carinae, respectively. We analyze these spectra to trace the kinematics of the H ii region because positions 1 and 6 are the centers of the H ii regions formed by Tr 14 and Tr 16, respectively, and position 5 is at the interface of the two H ii regions. We find three common features among the spectra of H92α, Hα, and [N ii] 6548 Å: wide velocity ranges compared to CO and [C ii], double intensity peaks, and long tails toward negative velocities. The H92α, Hα, and [N ii] 6548 Å spectra at all three positions cover velocities from −80 to +30 km⁻¹. These velocity ranges are at least a factor of 2 larger than those in the other three positions representing PDRs and ionization fronts.

We find double peaks in the H92α, Hα, and [N ii] 6548 Å profiles at positions 1, 5, and 6. The blueshifted intensity peaks are at −40 to −30 km s⁻¹, and the redshifted intensity peaks are at −5 to +5 km s⁻¹. As discussed in Damiani et al. (2016), the double intensity peaks likely indicate the red- and blueshifted boundaries/shells of the H ii region, since their emission measure is expected to be the highest toward the ionization front due to photoevaporation (e.g., Krumholz et al. 2007). We find that the line widths of the peaks are significantly larger (>30 km s⁻¹ for Hα and >25 km s⁻¹ for [N ii] 6548 Å) than the thermal broadening (21 km s⁻¹ for Hα and 5.7 km s⁻¹ for [N ii] 6548 Å at at 10,000 K), indicating the presence of considerable dynamical motions, such as expansion of the H ii regions and turbulence. We also find that the blueshifted portions of the spectra (<−20 km s⁻¹) typically have long tails toward negative velocities. For example, in the spectra at position 6 (η Carinae), we see that the blueshifted intensity peak is at −40 km s⁻¹ and the profile extends to −80 km s⁻¹, while the redshifted intensity peak is at 0 km s⁻¹ and the profile extends only to +20 km s⁻¹. We see similar profiles toward positions 1 and 5 but with smaller separations between the two intensity peaks and shorter tails compared to the spectra at position 6. The long tails on the negative velocity side of the spectra indicate that the blueshifted portion of the H ii region is likely larger and expanding faster than the redshifted portion. Considering that there is almost no blueshifted H i 21 cm emission and that most of the high-mass stars show low extinctions in Tr 14 and Tr 16, it appears that the blueshifted portion of the H ii region has burst through the dense gas and is freely expanding toward us, while the redshifted portion of the H ii region is confined by an H i cloud, similar to the Champagne model (Tenorio-Tagle 1979).

Comparing the spectra toward positions 1, 5, and 6, we find that there is CO emission toward positions 1 (Tr 14) and 5 (a middle position between Tr 14 and η Carinae), while we do not find any significant CO emission toward position 6 (η Carinae). This suggests that the CO clumps in Tr 14 are still confined and interacting with the H ii region, while Tr 16 has mostly cleared out nearby dense structures, except for the CO cloud east of η Carinae, which is consistent with their ages (Walborn 1973; Morrell et al. 1988; Vazquez et al. 1996; Smith & Brooks 2008; Rochau et al. 2011). We find that the CO emission at positions 1 and 5 is at a similar LSR velocity of −18 km s⁻¹, while the LSR velocities of the double peaks in H92α, Hα, and [N ii] 6548 Å are considerably different toward the two positions. The trend is almost the same throughout the entire Tr 14 region. This may indicate that the CO clouds at −18 km s⁻¹ are beyond the H ii boundary without getting much acceleration by the expanding H ii gas yet.

Position 2 shows the spectra toward a PDR in the north of Tr 14 (PDR N in Figure 1). This region is considered to be behind Tr 14, since it shows bright emission on its entire surface in Hα and 8 μm. We find ¹²CO and [C ii] emission around −20 km s⁻¹, indicating that the CO clump has a PDR. We do not find any significant ¹³CO emission toward this position, indicating that the CO clump may not have high column density. We also see emission of H92α, Hα, and [N ii] 6548 Å. However, the profiles of those lines show only a single intensity peak with a long tail toward negative velocities. We may not see the double peaks, since this clump is close to the edge of the H ii region and the expanding H ii gas motions are mostly tangential to our LOS. The long tail of the line profile toward to negative velocities may be due to the expansion of the H ii region toward us.

Position 3 is toward an ionization front of the dense CO wall in the west of Tr 14. We find multiple components of ¹²CO emission along the LOS and a single component of ¹³CO emission associated with the strongest ¹²CO component. We find relatively broad [C ii] emission coinciding with the CO components around −20 km s⁻¹. The H92α, Hα, and [N ii] 6548 Å lines show different profiles, but the velocities of their intensity peaks are around −18 km s⁻¹, which is near the velocity of the CO and [C ii] intensity peaks. This is likely due to the high emission measure of the ionized gas near the PDRs of the CO clumps. We find skewed profiles toward negative velocities as similar as the spectra toward Tr 14, which is likely related to the H ii region expanding toward us.

Position 4 is toward Carina I-E, where we observed the brightest CO and [C ii] emission. We find that there are at least two dense CO clumps along the LOS. The CO component at −23 km s⁻¹ is likely in front of Tr 14, since we see it as a dark clump in contrast against a bright H i background, but it also has bright [C ii] emission, which indicates that there is a PDR. The entire surface of Carina I-E has significant Hα and 8 μm emission, which confirms that we see the PDR of Carina I-E largely face-on but from the back (nonilluminated) side. Another CO component is at −12 km s⁻¹. This component has significantly brighter [C ii] emission with respect to the CO emission. The H92α line includes both of these velocities. The Hα and [N ii] 6548 Å lines show single intensity peaks and have their peaks at −25 km s⁻¹, which is different from the double intensity peaks in other positions. This may be mainly due to high optical depth toward dense clumps and obscuring the other intensity peaks. These observations indicate that the component at −12 km s⁻¹ is an H ii region interacting with a CO cloud. Comparing to positions 1, 5, and 6, we see that the H92α, Hα, and [N ii] 6548 Å lines at position 4 have narrower velocity ranges and single intensity peaks, while the line width (∼27 km s⁻¹ for H92α) is still significantly broader than the thermal line width (21 km s⁻¹ at 10,000 K). It is likely that the H ii region is in between dense clouds (foreground and background), or it may be near the edge of the H ii region, where we would not see the expansion of the H ii region along the LOS.

The H i 21 cm profiles toward positions 3 and 4 have complicated features including both emission and absorption. In the CNC, we find that there are two types of H i absorption features. One is H i absorption at the same velocity as ¹³CO emission. This is likely due to cold H i gas within the dense CO clumps, which may still have a relatively high H i column density due to high total column density in a CO clump combined with a modest fractional abundance of H i due to a relatively young age and incomplete conversion to H₂ (Wakelam et al. 2017, and references therein). The absorption feature associated with the ¹³CO intensity peak toward position 3 suggests that there is cold H i gas within the molecular clumps. The other absorption features are the ones that are red- or blueshifted relative to the ¹²CO components. One possible explanation is evaporation or stripping from a CO clump by extreme radiation, since the photoevaporating or radiation-stripped H i gas from the CO clumps can appear as absorption against the free–free emission background produced by the H ii region. We find that the velocity differences between the absorption features and the CO components in the Tr 14/Carina I region are typically ≤10 km s⁻¹. These velocity differences are similar to the photoevaporation or radiation-stripping velocity from the CO clouds predicted by numerical simulations (e.g., Bertoldi 1989; Bertoldi & McKee 1990; Lefloch & Lazareff 1994; Mellema et al. 1998; McLeod et al. 2016). In addition, the spatial distribution of the absorption features coincides with the dense clouds (e.g., Carina I-E/Carina I-W and Keyhole Nebula) in the CNC. It is thus likely that the absorption features are due to the dynamics related to the cloud dispersal by photoevaporation and radiation stripping.

One common feature in H i 21 cm lines at all positions is the asymmetric distribution of H i gas in velocity space seen in the channel maps. Looking at details of H i distribution in velocity, we find abundant neutral hydrogen at LSR velocities larger than −20 km s⁻¹ at all six positions, while we do not see significant H i emission at the LSR velocity smaller than −20 km s⁻¹. We find this behavior at all positions around the CNC. Considering the wide distribution of the H i emission at the same LSR velocity, we think that the H i cloud at >−20 km s⁻¹ confines the redshifted portion of the H ii region. This agrees with the consistent LSR velocity of the CO components at −18 km s⁻¹ across the Tr 14/Carina I region.

The basic Strömgren relation for an H ii region with no wind cavity and assuming constant electron density n_e inside the H ii region is

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{EUV}}{f}_{\mathrm{gas}}=\displaystyle \frac{4}{3}\pi {\alpha }_{r}{n}_{e}^{2}\,{d}^{3},\end{eqnarray} \tag{ 2 }$$

where Φ_EUV is the EUV photon luminosity of the source, f_gas is the fraction of the EUV absorbed by recombinations in the H ii gas (and not the dust in the H ii region), d is the Strömgren radius of the H ii region (and also the distance from the UV source to a PDR lying just outside the ionization front), and α_r is the recombination coefficient of electrons with protons in the H ii region. Using the on-the-spot assumption, so that only recombinations to the excited levels are counted, we take α_r = 2.6 × 10⁻¹³ cm³ s⁻¹, assuming the H ii region temperature is T = 10⁴ K. We define a proportional number f such that

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{FUV}}=f{{\rm{\Phi }}}_{\mathrm{EUV}},\end{eqnarray} \tag{ 3 }$$

where Φ_FUV is the FUV photon luminosity in the wavelength range 912–2000 Å. Typically, for large and young OB associations like Tr 14, with a number of very hot and early-type stars, f ∼ 1. For Tr 14, Smith (2006) found Φ_EUV = 2.2 ×10⁵⁰ EUV photons s⁻¹ and L_FUV = 2.0 × 10⁶ L_⊙. The latter luminosity can be approximately converted to a photon luminosity by assuming the average energy of an FUV photon is 10 eV; Φ_FUV = 4.8 × 10⁵⁰ FUV photons s⁻¹. This makes f = Φ_FUV/Φ_EUV = 2.18.

The incident FUV flux on the PDR just outside the H ii region is then written as

$$\begin{eqnarray}&&{G}_{0}=\displaystyle \frac{{{\rm{\Phi }}}_{\mathrm{FUV}}{f}_{\mathrm{PDR}}}{4\pi {d}^{2}{F}_{0}},\end{eqnarray} \tag{ 4 }$$

where F₀ ≃ 10⁸ photons cm⁻² s⁻¹ is the FUV flux appropriate for G₀ = 1, and f_PDR is the fraction of FUV photons that escape dust absorption in the H ii region: f_PDR ≃ f_gas. Here we assume that the PDR is a spherical shell that surrounds the H ii region or a cloud surface with a size greater than the distance d to the UV source. Once we find G₀ and f_PDR by comparing PDR models with observations, this equation can be used to determine d, the distance of the PDR from Tr 14. The thermal pressure in the H ii region is given by

$$\begin{eqnarray}&&{P}_{{\rm{H}}{\rm{II}}}=2{n}_{e}T,\end{eqnarray} \tag{ 5 }$$

where we have assumed that for each electron, there is one positive charge carrier, either H⁺ or He⁺.²¹ Assuming that T = 10⁴ K in the H ii region, we use Equations (2)–(5) to obtain

$$\begin{eqnarray}&&{P}_{{\rm{H}}{\rm{II}}}=2.3\times {10}^{4}{f}^{-3/4}{{\rm{\Phi }}}_{51}^{-1/4}{G}_{0}^{3/4}\,{\rm{K}}\ {\mathrm{cm}}^{-3},\end{eqnarray} \tag{ 6 }$$

where Φ₅₁ = Φ_EUV/10⁵¹ photons s⁻¹. Note that the dependence of P_{H ii} on G₀ (${P}_{{\rm{H}}{\rm{II}}}\propto {G}_{0}^{0.75}$) is close to but not quite the same as the empirical relation (${P}_{\mathrm{th}}\propto {G}_{0}^{0.9}$) given by Wu et al. (2018). We also note that the simplest assumption for a confined H ii region with a PDR that surrounds it is that P_{H ii} = P_PDR. However, the H ii region around Tr 14 does not appear confined but rather is a blister H ii region that is expanding away from the GMC. In this case, there is additional pressure on the PDR caused by the ram pressure of the photoevaporating H ii gas off the PDR surface. This additional pressure is of the order of the thermal pressure (Equation (A4) in Gorti & Hollenbach 2002), so that the applied pressure on the PDR P_PDR ≃ 2P_{H ii}, where P_{H ii} is the thermal pressure in the outflowing ionized gas from the PDR surface.

The normalization constant in the P_PDR versus G₀ relation can be compared to the normalization constant in Wu et al. if we specify the Smith (2006) values of f and Φ_EUV in the Tr 14 cluster of OB stars and assume P_PDR = 2P_{H ii},

$$\begin{eqnarray}&&{P}_{\mathrm{PDR}}=3.7\times {10}^{4}\,{G}_{0}^{0.75}\,{\rm{K}}\ {\mathrm{cm}}^{-3}.\end{eqnarray} \tag{ 7 }$$

This equation appears very similar to the empirical relation P_th versus G₀ found by Wu et al. (2018). We need, however, to test it in the region of applicability of the Wu et al. relation. The relation found by Wu et al. (2018) was for PDRs where G₀ ∼ 3 × 10³–5 × 10⁴. The Wu et al. relation (Equation (1)) gives P_th = 3.6 × 10⁷ and 4.6 × 10⁸ K cm⁻³ for G₀ = 3 ×10³ and 5 × 10⁴, respectively, while our analytic relation (Equation (7)) gives P_PDR = 1.5 × 10⁷ and 1.2 × 10⁸ K cm⁻³, respectively. Thus, the analytic solution is indeed quite close, perhaps a factor of 3–4 lower than the P_th found by the best-fit PDR models in Wu et al. (2018).²²

We again stress here that P_th is the thermal pressure in the PDR gas, since PDR models often hold the thermal pressure constant, and it is this pressure that PDR modelers, including this paper, plot in their figures. With the exception of the applied pressure P_PDR in clumps discussed below, Equation (7) provides an upper limit to P_th because it assumes that the applied pressure to the neutral region is balanced by the thermal pressure of the PDR gas. If magnetic pressure supports the PDR gas, then, for a given G₀, P_th < P_PDR, since the sum of thermal pressure and magnetic pressure should equal the applied pressure in steady state. Since the neutral gas around H ii regions and in clumps inside H ii regions has been pressurized and compressed by the expanding, high-temperature H ii gas, one might expect larger ratios of magnetic pressure to thermal pressure in the compressed gas than in ambient gas because magnetic pressure generally increases more rapidly with compression than thermal pressure.

We show below that the PDR code provides 10 fits that have filling factors of essentially unity, suggesting a shell or partial shell just outside the H ii region. However, one fit requires a beam filling factor significantly smaller than unity. Such a small beam filling factor suggests neutral clumps inside the extended H ii region. Opaque clumps are certainly seen in the optical images, and clumps appear in the maps of CO we discussed above and are inferred in the Wu et al. (2018) study. The EUV evaporating clumps inside an H ii region have a different relation of P_PDR to G₀. In fact, another variable is introduced: the radius R of the clump. If R > d, where d is the distance of the clump from the EUV source Tr 14, then the solution given in Equation (7) still applies. However, if R ≪ d, then we have a small EUV evaporating clump inside the extended H ii region. A very similar computation to that described above applies, except that the incident EUV flux is absorbed by H atoms that have recombined in the evaporating flow off of the clump (see Bertoldi & McKee 1990, for a detailed analysis). Assuming that the flow is ejected at ∼10 km s⁻¹, the thermal speed of the 10⁴ K ionized gas at the surface of the clump, one finds that, analogous to the steps above for standard H ii regions, the applied pressure to the clump is

$$\begin{eqnarray}&&{P}_{\mathrm{PDR}}\simeq 4{T}_{{\rm{H}}{\rm{II}}}{\left(\displaystyle \frac{3{F}_{0}{G}_{0}}{{\alpha }_{r}{Rf}}\right)}^{1/2},\end{eqnarray} \tag{ 8 }$$

where T_{H ii} ∼ 10⁴ K is the temperature of the ionized gas streaming off the clump, cgs units are used, and the pressure is in units of K cm⁻³. Note that for a fixed G₀, the pressure now depends on the clump radius R. For R ≪ d, the derived pressure is higher than the P_PDR given in Equation (7). Small clumps require higher densities at the ionization front in order to absorb the incident EUV, since the characteristic distance R for the EUV to be absorbed is smaller. The higher densities produce higher applied pressures to the PDR. It is possible that some of the higher pressures found by Wu et al. (2018) are caused by clumps along their LOSs. Alternatively, the area mapped by Wu et al. (2018) may have localized sources of UV that can lead to a higher P_PDR for a given G₀ (see Equation (6)). Another possibility is differences in the chemistry and heating processes in the two PDR codes.

The analysis of the observations is carried out using a PDR model based on that of Wolfire et al. (2010) and Hollenbach et al. (2012), with additional updates noted in Neufeld & Wolfire (2016). The models calculate the steady-state chemical abundances and thermal balance gas temperature of a layer of gas of constant thermal pressure, P_th, exposed to an FUV radiation field, G₀, and cosmic-ray ionization rate ζ_CR. The radiation field is measured in units of the interstellar field of Habing integrated between 6 and 13.6 eV (=1.6 × 10⁻³ erg cm⁻² s⁻¹). To aid in the analysis, we have carried out a grid of models with G₀ varying in log steps of 0.25 in the range −0.5 ≤ log G₀ ≤ 6.5 and thermal pressure varying in log steps of 0.25 in the range 2 ≤ log P_th/(K cm⁻³) ≤ 8.

The cosmic-ray ionization rate and gas-phase abundances are held fixed as given in Table 2. The model output consists of integrated emission line intensities as functions of G₀ and P_th for lines that arise in the atomic and molecular gas in the PDR, including [C ii] 158 μm, CO 1–0, CO 4–3, CO 7–6, [C i] 610 μm, [C i] 370 μm, [O i] 63 μm, and [O i] 145 μm. The PDR models do include self-absorption inside the PDR region, as the lines emerge from the illuminated face. However, they neglect self-absorption by cool foreground clouds or for LOSs that approach the PDR from the nonilluminated (back) side. The [O i] 63 μm line has the highest optical depth and is the most prone to this effect. Therefore, in our best fits, we allow the PDR model to somewhat overpredict the integrated [O i] 63 μm line. However, in the models presented below, it is never more than a factor of ∼2–3. We emphasize that we do not allow our best-fit models to underpredict the [O i] lines by more than a factor of 2. We find that when there is overlap, the PACS observational [O i] line intensities (Wu et al. 2018), even when matched to the ISO beam sizes, give higher intensities than those quoted in Oberst et al. (2011). Our models suggest the higher values, and we therefore match our models to the integrated and convolved PACS data when they are available.

We use the Mopra ¹³CO J = 1–0 observations to estimate the total column of the PDR slab for each of our models. We take the PDR model temperature at A_V = 5 into the slab to estimate the average temperature of the ¹³CO in order to translate the integrated optically thin line emission into a column or a ΔA_V(CO) of gas that is both molecular H₂ and CO. We assume that the isotopic ¹²C/¹³C ratio is 60 (Szűcs et al. 2014). The PDR model allows us to compute the ΔA_V(atomic), which we define as the ΔA_V from the PDR surface to where the gas is half molecular H₂ and half atomic. Similarly, we obtain ΔA_V(dark), which we define as the ΔA_V from where the gas is half molecular to where the optical depth in the ¹²CO line is unity. The sum of these ΔA_V is the total A_V of the PDR slab.

An additional model parameter is the source area filling factor in the telescope beam, f_B. In practice, we compute f_B by comparing our model CO 1–0 intensity to the observed intensity and then fit all other lines by matching the ratio of the line to CO 1–0.

Another important model constraint comes from the integrated IR continuum observations. We use the Herschel PACS (70 and 160 μm) and SPIRE (250, 350, and 500 μm) observations (Preibisch et al. 2012) convolved to the STO2 beam size. We fit each SED with a dust optical depth τ_D, dust temperature T_D, and emissivity index β and integrate under the resultant fit to find the integrated continuum intensity I_IR. We assume that this IR continuum arises from the sum of contributions from the PDR and the H ii region: I_IR = I_PDR + I_{H ii}. Using theoretical spectra from O stars (Parravano et al. 2003; Malkov 2007), we find that approximately half the dust heating in the PDR is from the FUV photons, and the rest is from photons outside this band. Therefore, I_PDR = 2 × 1.6 × 10⁻³f_BG₀/(4π) erg cm⁻² s⁻¹ sr⁻¹. Our best-fit models provide G₀ and f_B, and the observations provide I_IR. We can then estimate I_{H ii} = I_IR − I_PDR.

In the model fits, we vary only P_th, G₀, and f_B, although additional factors such as geometry, abundance variations, and depth of the PDR layer may affect the emitted line intensities. In light of these considerations and possible observational errors, we assume that fits to the observed line and continuum intensities to within factors of 2 are considered to be good fits, although we generally find agreement to better than a factor of 2. Below, we discuss each fit and the maximum difference between the good fit model and the observations.

To estimate the [C ii] line emission from ionized gas, we rely on the observed [N ii] line intensities. The [C ii] 158 μm/[N ii] 205 μm ratio is weakly dependent on electron density varying between 5.1 at the low-density limit and 6.0 at the high-density limit, with a minimum of 3.7 at n_e ≈ 50 cm⁻³. The [C ii] 158 μm/[N ii] 122 μm ratio has a stronger dependence on n_e varying monotonically between 0.62 (at the high-density limit, roughly n_e > 1000 cm⁻³) and 9.7 (at the low-density limit, roughly n_e < 1 cm⁻³). These ratios are calculated assuming the gas-phase abundances of C⁺ and N⁺ to be 1.6 × 10⁻⁴ (Sofia et al. 2004) and 7.5 × 10⁻⁵ (Meyer et al. 1997), respectively. The electron collision strengths are from Tayal (2011) for [N ii] and Tayal (2008) for [C ii] for T = 8000 K gas. We can estimate the electron density from the [N ii] 122 μm/[N ii] 205 μm ratio and then obtain the [C ii] line intensity from either of the [N ii] lines. This ratio varies from 0.53 in the low-density limit (n_e ≲ 1 cm⁻³) to 9.7 in the high-density limit (n_e ≳ 1000 cm⁻³). If either [N ii] line is not observed, an alternative approach to obtain the electron density is to use the best-fit thermal pressure in the PDR. From Equation (5), we find the electron density from

$$\begin{eqnarray}&&{n}_{e}=\displaystyle \frac{{P}_{{\rm{H}}{\rm{II}}}}{({\rm{K}}\,{\mathrm{cm}}^{-3})}\displaystyle \frac{1}{2T}=\displaystyle \frac{{P}_{\mathrm{PDR}}}{(2\times 2\times {\rm{10,000}})},\end{eqnarray} \tag{ 9 }$$

where we assume a gas temperature in the ionized gas of 10,000 K and P_PDR = 2P_{H ii}.

We have selected 10 spectral features from seven positions to analyze in detail (see Figures 4 and 5). These positions are labeled by the letters a−g in Figure 4. The points generally lie along a line from north of the Tr 14 cluster to southwest into the molecular ridge. For each spectrum, we integrate the line profiles over one or two likely velocity components, and we associate the (spectrally unresolved) [N ii] line intensity (i.e., the ionized gas) with the brighter [C ii] component. Often, the observed [C ii] line intensity in the bright component is brighter than what can be produced by the neutral PDR emission alone, and the expected contribution from the ionized gas is required to match the observations. When available, we use the theoretically expected ratio of [N ii] to [C ii] to estimate the [C ii] flux from the H ii region. We do not apply a filling factor correction to the ionized gas emission; i.e., we assume the ionized gas fills the beam. For observations with higher angular resolution than the [C ii] resolution, we convolve the observations to provide the integrated intensity in the [C ii] beam. If two velocity components are present along the LOS, then the observed continuum emission arises from the sum of both components. Using Equation (4), we also estimate a crude distance of the PDR layer, d, away from Tr 14 using the model G₀, the FUV luminosity estimate of Smith (2006), and the IR continuum intensities obtained by model and observation. Here we assume that f_PDR ≃ I_PDR/I_IR. The following gives a summary of our fits for each point. We follow the summary of each position with a short discussion of these results.

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(a) PDR North of Tr 14 (l, b) = 287.403, −0.537. The spectra indicate two basic velocity features, one from −11 to −4 km s⁻¹ and one from −25 to −11 km s⁻¹. However, the CO 4–3 and 7–6 and the [C i] observations suffer baseline problems and are not reliable, except possibly the CO 4–3 transition in the first velocity feature, which is fairly strong. We model this first feature because we have reliable CO 1–0, [C ii], [O i], and IR continuum observations. We find an excellent fit (the model fits the observation to within a factor of 1.2 for each line and the continuum) to all of these observations with a PDR model with log P_th = 7.25, log G₀ = 3.75, and f_B = 0.1. The ΔA_V values for the atomic, dark, and molecular CO gas are 1.1, 2.3, and 4.4, respectively. The beam filling factor suggests a clump or clumps in the beam. If a single clump dominates, then its diameter is about 0.3 of the beam diameter, or radius R = 0.1 pc. On the other hand, we may be observing just a portion of a larger cloud. The incident G₀ suggests a distance from Tr 14 of about 2.5 pc. This redshifted component compared to the H ii gas (whose emission centers at approximately −17 km s⁻¹) may be on the far side of the H ii region, traveling away from us. As we shall demonstrate below, out of the 10 features modeled, this is the only spectral feature that suggests a small clump in the beam. As seen in the Hα map, this position lies in a direction of unobscured optical emission and may be primarily ionized gas. This is borne out by the strong [C ii] emission from the second velocity feature, which likely arises in the ionized gas.

(b) The middle point between Tr 14 and the dust lane (l, b) = 287.392, −0.596. The spectra suggest a single velocity component: −24 to −7 km s⁻¹. The [C i] observations suffered baseline problems and were not used in this fit, which matched the CO 1–0, 4–3, and 7–6 and the two [O i] lines. The PDR model fit is log P_th = 5.5, log G₀ = 2.25, and f_B ≃ 0.5. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.6, 2.2, and 1.7, respectively. The ratio of the PDR model flux to the observed flux (henceforth "m/o") ranges from 0.5 for [O i] 63 μm to 1.9 for CO 7–6. The observed [N ii] scales to predict a [C ii] integrated intensity from the H ii region that is a factor of 0.54 of the observed; our PDR model fit only adds about 10% to the H ii contribution, so the H ii region dominates the [C ii] production in this case. The same is true of the IR continuum emission. We find that only 10% comes from the PDR and the rest from the H ii region. In general, we find that when the H ii region dominates the [C ii], it also dominates the IR, suggesting significant extinction of the UV as it traverses the H ii region to the PDR. Taking into account this extinction, we find d_PDR = 4.9 pc.

(c) CG South of Tr 14 (l, b) = 287.386, −0.604. We fit a single velocity component extending from −24 to −7 km s⁻¹. The PDR model fit is log P_th = 6.0, log G₀ = 2.5, and f_B ≃ 0.5. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.5, 2.2, and 2.4, respectively. The PDR fit is based on the CO, [C i], and [O i] fluxes. For [O i] 63 and 145 μm, the m/o = 1.1 and 1.3, respectively. The worst m/o = 1.8 is for CO 7–6. Our model fits the [C ii] if we scale the observed [N ii] 205 μm to estimate [C ii] from the H ii region. We find that about 90% of the [C ii] arises from the H ii region and 10% from the PDR. We note here that we have found another test besides [N ii] to determine if the [C ii] arises mostly from the ionized gas. If the flux ratio [C ii]/CO(1–0) ≳ 10⁴, then the H ii region dominates. The PDR dominates typically when the ratio is of order 1000–4000 (see also Wolfire et al. 1989). Again, just like the [C ii], we find that 15% of the IR comes from the PDR and the rest from the H ii region. Using the implied extinction in the H ii region, we find d_PDR = 4.5 pc.

(d) North surface of Carina I-E (l, b) = 287.376, −0.622. Here the spectra suggest two velocity components. The first component extends from −20 to −8 km s⁻¹. The PDR model fit is log P_th = 6.0, log G₀ = 2.0, and f_B ≃ 0.6. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.08, 1.9, and 1.8, respectively. The PDR model fit is based on the CO and [C i] observations. The worst m/o = 2.0 is for [C i] 2–1. The ionized gas is associated with this component, and, scaling from the [N ii], we find a match to the [C ii] from this component. Only about 8% comes from this PDR component. Similarly, this component only contributes about 3% of the IR continuum. As noted below, the IR comes from the other PDR velocity component, with a 10% contribution from the H ii region. Ignoring extinction in the H ii region in this case, we find d_PDR = 20 pc. This gas is somewhat redshifted relative to the ionized gas and may lie behind the H ii region, which apparently extends quite far back in this direction.

The second velocity component extends from −35 to −20 km s⁻¹. The PDR model fit is log P_th = 7.25, log G₀ =3.5, and f_B = 0.6, and d_PDR = 3.5 pc. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.8, 2.2, and 4.7, respectively. The PDR model fit is based primarily on the CO, [C i], and [C ii] fluxes, but the [O i] fluxes help drive the fit to high P_th and G₀. The m/o flux ratios vary from 0.63 for [C i] 2–1 to 1.4 for CO 7–6, while the more suspect [O i] lines have m/o = 3.7 and 0.64 for 63 and 145 μm, respectively. Since the 63 μm line can be self-absorbed, as discussed, we discount the mismatch to the 63 μm line. We cannot get higher values for the 145 μm line without ruining the fits to the CO and [C i] lines. Essentially, all of the [C ii] and IR emission arises from the PDR. This blueshifted gas is likely on the near side of the H ii region, moving toward us. We note that this velocity component dominates the line intensity integrated over all velocity and that this position is close to that modeled by Kramer et al. (2008). Our model result for G₀ is in exact agreement with Kramer et al., but our density at A_V = 1 is 6 × 10⁴ cm⁻³, whereas they obtained 2 × 10⁵ cm⁻³ in their constant density clumpy model.

(e) The Oberst et al. Car I position (l, b) = 287.370, −0.630. The spectra suggest two velocity components. The first extends from −20 to −7 km s⁻¹. The PDR model fit is log P_th = 6.5, log G₀ = 2.5, and f_B ≃ 0.5. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.2, 2.1, and 2.4, respectively. The worst m/o = 2.0 for the [C i] 2–1 line. The other four lines have m/o values from 0.7 to 1.5. The ionized gas is associated with this component, and the [C ii] in this velocity range must come from the ionized gas, as the PDR component only contributes roughly 5%. The scaled [N ii] lines support this, if we use the electron density estimated from the thermal pressure. Likewise, the [C ii]/CO 1–0 flux ratio is high, 1.7 × 10⁴, suggesting [C ii] from the H ii region. Similarly, this PDR component only supplies about 6% of the IR continuum. Taking extinction in the H ii region into account, the distance to the PDR is d_PDR = 3.4 pc.

The second velocity component extends from −35 to −20 km s⁻¹. The PDR model fit is log P_th = 6.75, log G₀ =3.25, and f_B ≃ 0.8 based on CO, [C i], [C ii], [O i], and IR continuum observations. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.8, 2.2, and 4.3, respectively. The fits to the CO and [C i] lines have m/o values that range from 1.0 for CO 1–0 and 4–3 and [C i] 2–1 to 1.4 for CO 7–6. As in case (d) above, our fit to the [O i] lines matches the 145 μm line satisfactorily (m/o = 0.7), but the model overestimates the 63 μm line by a factor of 2.5. The latter misfit may be caused by self-absorption.²³ The PDR model fit provides ∼90% of the [C ii] emission, so little arises from the ionized gas in this case. This PDR velocity component supplies roughly 0.5 of the observed IR emission. Taking into account moderate extinction in the H ii region, we find d_PDR ≃ 3.4 pc. This blueshifted gas likely lies in the foreground, between the observer and the H ii region.

(f) South shell of Carina I-E (l, b) = 287.370, −0.636. The first velocity component extends from −20 to −8 km s⁻¹. The PDR model fit is log P_th = 6.75, log G₀ = 3.0, and f_B ≃ 0.5, based primarily on fits to the CO and [C i] lines but also considering the [O i] lines (see below). The ΔA_V values for the atomic, dark, and molecular CO gas are 0.5, 2.2, and 3.1, respectively. The m/o ranges from 1.0 for CO 1–0 and 4–3 to 1.8 for [C i] 2–1. The observed [N ii] 205 μm scales to predict [C ii] from the H ii region that is 70% of the observed. The PDR model only supplies about 10% of the observed emission. Therefore, the H ii region dominates the [C ii] production. This PDR component supplies only 17% of the observed IR continuum. We show below that the other PDR velocity component contributes about 31%; thus, the H ii region contributes about 52% of the IR continuum. We find then that the first velocity component lies roughly d_PDR = 4.6 pc from Tr 14. The PDR gas may be somewhat redshifted with respect to the H ii gas and therefore may lie somewhat behind UV source Tr 14.

The second velocity component extends from −35 to −20 km s⁻¹. The PDR model fit is log P_th = 6.5, log G₀ =3.0, and f_B ≃ 0.9, based on CO, [C i], [C ii], and, to some extent, [O i] and IR continuum. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.7, 2.2, and 3.4, respectively. The m/o for CO and [C i] ranges from 1.0 for CO 1–0 and 4–3 to 1.4 for CO 7–6. The models predict about equal amounts of [O i] emission from each velocity component. When summed, the m/o = 2.7 for 63 μm and 0.85 for 145 μm. Most of the [C ii] in this component comes from the PDR; the PDR model predicts 0.83 of the observed [C ii]. In addition, about 31% of the IR continuum comes from this component. The derived distance to Tr 14 is d_PDR = 4.9 pc. The blueshift suggests that this PDR is on the near side of the H ii region.

(g) West shell of Carina I-E (l, b) = 287.355, −0.639. We fit a single velocity component from −30 to −10 km s⁻¹. Here we have no [O i] observations to guide us, but we get an extremely good fit with log P_th = 6.5, log G₀ = 2.75, and f_B ≃ 1.7. The ΔA_V values for the atomic, dark, and molecular CO gas are 0.4, 2.1, and 2.9, respectively. The three CO lines and the two [C i] lines are all fit to within a factor of 1.05. However, the PDR model fit only provides 28% of the observed [C ii] emission and 31% of the IR continuum, suggesting that both [C ii] and IR arise mostly from the H ii region. Using the inferred extinction in the H ii region, we then estimate d_PDR ≃ 4.8 pc. The blueshifted velocity range suggests that the PDR lies on the near side of the H ii region.

Figure 6 plots pressure P versus G₀. The asterisks show our PDR code fits of the PDR thermal pressure P_th and G₀ for 10 spectral features along seven sight lines. The solid line shows the analytic relation of the applied pressure P_PDR to G₀ for the case where the size scale of the PDR (or clump radius R) is large compared to the distance to the UV source. The best fits that fall below this line suggest that magnetic pressure helps support the PDR, and that the applied pressure is matched by the sum of the magnetic and thermal pressure. Seven of the 10 fits fall below but within a factor of ∼2 of the applied pressure line. These suggest that the magnetic pressure is only comparable to or smaller than the thermal pressure. Two points fall slightly (much less than a factor of 2) above the relation. Within the errors, these are consistent with thermal pressure dominating. However, one fit (the middle point between Tr 14 and the dust lane) lies a factor of 6 below the applied pressure line. This extreme case may indicate errors in observation (the observations indicate an extremely low CO 7–6/4–3 ratio of ∼0.1, much lower than the other nine observations). However, taking the observations and model fit at face value, it implies a magnetic pressure five times the thermal pressure.

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The dotted line at G₀ = 3000 indicates how much the applied pressure would rise if the PDR were a clump with radius R = 0.1 pc that is much smaller than the distance to the source (d ∼ 5 pc for this FUV field). There are two motivations for showing this result. The first is that the dashed line shows the relation of P_th to G₀ found by the PDR modeling of Wu et al. (2018). Their fits fall factors of 2–4 above the analytic relation for a shell or clumps with a size larger than d. One explanation is that they more often see small clumps in their observations than we do along our LOS. The dotted line shows that clumps of size ∼0.1 pc would raise the applied PDR pressure by a factor of about 6 for a given G₀ = 3000. The other motivation is that we have one LOS (a, north of Tr 14) that is the only one in our analysis that appears to be a clump with a size smaller than d. As noted above, its beam filling factor suggests a clump of radius R ≃ 0.1 pc. If this is the case, note that our fit falls below the predicted applied pressure on this clump. This suggests magnetic support for this clump. Indeed, one can compute that if this clump were solely thermally supported, it would gravitationally collapse in a time much shorter than the ∼1 Myr life of the H ii region/PDR complex. Therefore, it must be dominated by magnetic pressures.

We conclude this subsection by summarizing the main points of the PDR modeling. The PDRs are observed at both blueshifts and redshifts from the H ii region gas, suggesting both foreground and background PDRs. The PDRs on the molecular ridge may have a more edge-on geometry. The distances of the PDRs from the H ii region generally are somewhat greater than 2.3 pc, which is the projected distance of the molecular ridge from the Tr 14 OB association. This seems reasonable, given the three-dimensional aspect of this blister H ii region and the neutral gas that surrounds it.

Of 10 spectral features analyzed along seven LOSs, we find six spectral features in which the [C ii] and IR continuum mainly comes from the H ii region and four where both arise mostly from the PDR. If unresolved spectra had been used, so that we could not separate features along an LOS, we find that out of the seven LOSs, three would have [C ii] dominated by PDR emission, two by H ii emission, and two with comparable contributions. As would be expected, the PDRs dominate when the LOSs are directed at the molecular ridge. It is noteworthy that [C ii] and IR correlate in this way: if one comes primarily from the H ii region, then so does the other. Intuitively, this makes sense. High dust extinction in the H ii region leads to much lower FUV fields incident on the PDR, and thus less [C ii] emission. Like other authors (e.g., Oberst et al. 2011), we find that [C ii] often has a significant contribution from the ionized gas in this region around Tr 14. Summing the [C ii] luminosities over the seven LOSs, we find that 3.7 times more [C ii] luminosity comes from the H ii region than from the PDR. The edge-on geometry of the molecular cloud with respect to Tr 14 and the blister geometry leading to expanding H ii gas toward and away from us may help explain the importance of the H ii region. The high EUV luminosity of Tr 14 leads to larger columns in the H ii gas and therefore stronger [C ii] emission from the ionized gas; it also contributes to the possibility of significant dust extinction in the H ii region and therefore dominant contributions to the IR continuum.

The PDR model fits provide a measure of the mass in atomic gas, dark gas (H₂ but little CO), and CO gas. Summing the 10 PDRs found on these seven sight lines, we find a beam-averaged mass proportion going as 1:4.1:5.6 for atomic:dark:CO. If these 10 regions are representative, this gives an estimate of the mass budget in this Tr 14 region.

The correlation of the thermal pressure in the PDR with the incident FUV field, observed by Wu et al. (2018) and confirmed by our PDR models presented here, finds some theoretical basis using a simple analytic model of evaporating ionizing gas pressurizing the PDR surface of a molecular cloud or clump. The good correlation of observation and theory suggests that our PDR models are reasonably correct.

We show a schematic picture of the Tr 14/Carina I region in Figure 7 illustrating the following six findings about the three-dimensional morphology of the Tr 14/Carina I region.

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1. The H ii region in Tr 14/Carina I is expanding and likely to be asymmetric where the redshifted portion of the H ii region is confined by the H i cloud, while the blueshifted portion of the H ii region is freely expanding toward us. We find that the H92α, Hα, and [N ii] 6548 Å lines near Tr 14 and Tr 16 typically have highly asymmetric profiles with long tails to negative velocities relative to the CO clumps around −20 km s⁻¹ (e.g., the spectra toward positions 1, 5, and 6 in Figure 4). The H i emission in velocity space over the entire CNC is observed mainly at LSR velocities greater than −20 km s⁻¹, while we do not find significant H i emission at LSR velocities lower than −20 km s⁻¹, indicating that the H i gas impedes the H ii region from expanding away from us.

2. The CO and H i clumps partially confine the H ii regions of Tr 14 and Tr 16. The channel maps in Figures 9–12 show that molecular and H i clouds/clumps partially surround Tr 14 and Tr 16 in PPV space. We see that there are CO clouds/clumps surrounding the north, west, and south of Tr 14 and the east of Tr 16.

3. The Tr 14 and Tr 16 clusters have made their own H ii regions that have partially merged as they expanded. Figure 8 shows the LSR velocities of the red- and blueshifted peaks of Hα lines observed using Gaia (Damiani et al. 2016). The small separation between the red- and blueshifted peaks indicates that there are either H i or CO clumps that confine the H ii regions or the edge of the H ii bubble. We find that the separation is reduced between Tr 14 and Tr 16. In the H i 21 cm map, we see that there are numerous H i clumps between Tr 14 and Tr 16 separating the H ii regions of the two clusters.

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4. The H ii region of Tr 16 is likely more extensive than that of Tr 14. A large separation between the red- and blueshifted peaks of the Hα lines (Figure 8) indicates a faster expansion of the H ii region in Tr 16 compared to Tr 14. The expansion speed increases with the radial distance from the ionizing source (e.g., Krumholz et al. 2007); thus, a larger H ii region is expected to have a faster expansion speed. We found that Tr 16 has a roughly three times larger projected area and a factor of 2 larger velocity separation between two intensity peaks compared to Tr 14, suggesting that the H ii region of Tr 16 is significantly larger than Tr 14 along the LOS as well. In addition, CO clouds still confine Tr 14, while Tr 16 seems to have cleared out the nearby dense structures, except the east side.

5. The CO clouds/clumps have PDRs that show a hint of cloud dispersal by photoevaporation and radiation stripping. We find that most of the [C ii] emission is spatially correlated with the CO clouds/clumps, but the intensity peaks of the [C ii] emission are slightly displaced from the CO intensity peaks. In the channel maps, we also found that the morphology of the [C ii] emission often has arc-shaped clumps surrounding or a strip adjacent to a CO cloud, suggesting that there are PDRs and ionization fronts on many of the CO clouds/clumps. Toward dense clumps (e.g., Carina I-E), most of the H i spectra show absorption features (e.g., positions 3 and 4 in Figure 4). The H i absorption features either red- or blueshifted relative to ¹²CO emission are likely due to photoevaporation and radiation stripping of the exposed CO clumps as predicted from theories (e.g., Bertoldi 1989; Bertoldi & McKee 1990; Lefloch & Lazareff 1994; Mellema et al. 1998; McLeod et al. 2016). This suggests that dense CO clumps subjected to strong external radiation show a multilayered structure.

6. Some of the CO clumps are located within the H ii regions. The locations of the ionized, neutral, and molecular gas along the LOS are not trivial to determine, but we think that the H i absorption features and the [C ii] emission provide information about the locations of CO clumps relative to the H ii regions. Near Tr 14, most of the H i spectra show both red- and blueshifted absorption features with respect to CO clumps at ∼−20 km s⁻¹ (see Figures 9–12). If massive stars powering H ii regions are in front of and behind the CO clouds/clumps along the LOS, we may observe H i absorption features red- and blueshifted relative to the CO clouds/clumps originating from their evaporating surfaces. The strongest double absorption features are found near Carina I-E and the Keyhole Nebula, suggesting that they are cold dense clumps or pillars located within the H ii regions.

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The schematic in Figure 7 presents the six findings on the ISM structure in the Tr 14/Carina I region in addition to the descriptions of Tr 16 in Brooks et al. (2000). The H ii region is mostly open to us, and the CO clumps are within the H ii region or partially confine the H ii region. The CO clumps exposed to the H ii regions have layered structures with evaporating surfaces. There is an H i cloud enclosing and confining the far-side/redshifted portion of the H ii region, while the near/blueshifted side is expanding more freely, similar to the Champagne model (Tenorio-Tagle 1979) but with some of the dense CO clumps still being left within the H ii regions.

The GMC, which mostly lies to the west of Tr 14, has an estimated mass of about ∼10⁶ M_⊙ (e.g., Grabelsky et al. 1988; Smith & Brooks 2007). Grabelsky et al. (1988) also estimated the radius of the GMC to be R_GMC ∼ 66 pc. Smith (2006) estimated the total present-day EUV photon luminosity produced by the 65 O stars and the three WNL stars in Carina to be Φ_EUV ∼ 10⁵¹ EUV photons s⁻¹ (see Smith & Brooks 2007). Of this, about 6 × 10⁵⁰ EUV photons s⁻¹ come from Tr 16, and 2.2 × 10⁵⁰ EUV photons s⁻¹ come from Tr 14. Our STO2 region mostly encompasses the region illuminated by Tr 14, but we examine photoevaporation from our smaller region and also consider the photoevaporation caused by both Tr 14 and Tr 16 as they illuminate the GMC.

We consider a blister configuration for the GMC; that is, Tr 14 and Tr 16 are assumed at some distance from the surface of the GMC but at a distance that is small compared to the radius of the GMC, R_GMC, as well as to the radius R of the illuminated surface. The EUV-induced mass-loss rate from a surface area of radius R is given by

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{evap}}\simeq \pi {R}^{2}{n}_{e}\bar{m}{v}_{\mathrm{evap}},\end{eqnarray} \tag{ 10 }$$

where n_e is the typical electron density at radius R, $\bar{m}\sim 2\,\times {10}^{-24}$ gm is the gas mass per electron, and v_evap ∼ 10 km s⁻¹ is the speed at which the ionized gas moves off the surface of the GMC.

Using Equation (2), we derive

$$\begin{eqnarray}&&{n}_{e}(R)\simeq {\left(\displaystyle \frac{3{{\rm{\Phi }}}_{\mathrm{EUV}}}{4\pi {\alpha }_{r}{R}^{3}}\right)}^{1/2}\simeq 30{{\rm{\Phi }}}_{51}^{1/2}{R}_{20}^{-3/2}\ {\mathrm{cm}}^{-3},\end{eqnarray} \tag{ 11 }$$

where R₂₀ ≡ R/10²⁰ cm and Φ₅₁ ≡ Φ_EUV/10⁵¹ EUV photons s⁻¹. Note that R here is really the distance from the ionizing source to the GMC cloud surface. This is somewhat larger than the radius R of the illuminated surface. However, because we assume that the distance of the stars from the cloud surface is small compared to R, these two distances are approximately the same.

Substituting Equation (11) into Equation (10), we obtain

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{evap}}\simeq 3\times {10}^{-2}{R}_{20}^{1/2}{{\rm{\Phi }}}_{51}^{1/2}\ {M}_{\odot }\ {\mathrm{yr}}^{-1}.\end{eqnarray} \tag{ 12 }$$

Note that although the GMC surface very close (R ∼ 3 pc) to Tr 14 and Tr 16 is illuminated with a higher EUV flux and produces a higher mass flux loss, the more distant (R ∼ 30 pc) regions of the GMC actually dominate the evaporative mass loss from the cloud because they have so much more area.

The existence of a large area of the cloud being illuminated and ionized by the massive stars in Tr 14 and Tr 16 has been observed by numerous investigators. Mizutani et al. (2004) detected fine-structure IR lines of [O iii], [N iii], and [N ii] and inferred the existence of diffuse (n_e < 100 cm⁻³) ionized gas over at least 30 pc. Considering just the region dominated by Tr 14, we see from Equation (11) that although the electron density at the GMC surface at R ≃ 3 pc is n_e ≃ 450 cm⁻³, the electron density on the GMC surface at R ≃ 15 pc is n_e ≃ 40 cm⁻³, in accordance with the results of Mizutani et al. (2002).

If we substitute Φ_EUV ∼ 10⁵¹ s⁻¹ for the total of Tr 14 and Tr 16 and estimate that their EUV flux covers R ∼ 10²⁰ cm ≃ 30 pc of the GMC surface, then we obtain ${\dot{M}}_{\mathrm{evap}}$ ≃ 3 × 10⁻² M_⊙ yr⁻¹. If the GMC mass is M_GMC ≃ 10⁶ M_⊙, then the lifetime of the cloud is t_GMC ≡ M_GMC/${\dot{M}}_{\mathrm{evap}}$ ≃ 30 Myr. This is close to the estimated lifetimes of GMCs. Note, however, that this assumes that the cloud is illuminated by Φ_EUV ∼ 10⁵¹ s⁻¹ for the entire 30 Myr, which implies that other associations will form to replace Tr 14 and Tr 16, once their massive stars die in ∼3–5 Myr. If we just use the Φ_EUV ≃ 2.2 × 10⁵⁰ s⁻¹ of Tr 14 and just consider the region mapped by STO2, which is R ∼ 5 pc, then the evaporative mass-loss rate from this region is only ${\dot{M}}_{\mathrm{evap}}$ ≃ 5 ×10⁻³ M_⊙ yr⁻¹. We will compare this below with the neutral mass loss caused by the expansion of the H ii region in this region.

The escape speed v_esc of a shell or clump of mass m from a GMC is given by

$$\begin{eqnarray}&&\displaystyle \frac{1}{2}{{mv}}_{\mathrm{esc}}^{2}=\displaystyle \frac{{{GmM}}_{\mathrm{GMC}}}{{R}_{\mathrm{GMC}}}.\end{eqnarray} \tag{ 13 }$$

Thus,

$$\begin{eqnarray}&&{v}_{\mathrm{esc}}\,\simeq \,16{\left(\displaystyle \frac{{M}_{6}}{{R}_{20}}\right)}^{1/2}\ \mathrm{km}\ {{\rm{s}}}^{-1},\end{eqnarray} \tag{ 14 }$$

where M₆ ≡ M_GMC/10⁶ M_⊙. Assuming M₆ ≃ 1 and R₂₀ ≃ 2 (Grabelsky et al. 1988; Smith & Brooks 2007), we find v_esc ≃11 km s⁻¹. Assuming the LOS rest velocity of the GMC is −17 km s⁻¹ (Brooks et al. 2003), we then associate all observed CO, [C ii], and H i that is traveling at LOS speeds v < −23 or v > −11 km s⁻¹ as being liberated from the gravitational potential of the GMC.

We proceed to make a very rough estimate of the mass of neutral gas that is not bound to the GMC and therefore may be considered to be evaporating off the cloud, perhaps pushed by the expanding H ii gas. First, we estimate the mass in neutral gas that is not traced by CO but by the [C ii] from the PDRs. This includes atomic PDR gas but also gas that is H₂ but has little CO due to photodissociation, sometimes called the hidden molecular gas or the dark gas. We assume that most of the [C ii] emission comes from the PDRs and not from the H ii ionized gas, and that the [C ii] emission is optically thin. This probably gives a lower limit to the mass, since the PDR models show that the [C ii] often has a line optical depth of order unity but only a lower limit by a factor of a few. We also assume that the PDR densities are sufficiently high that the level populations are in LTE and that the temperature of the PDR is T > 92 K (as the PDR models suggest). If the densities or temperature are lower, then again, our estimate is a lower limit. With these caveats, we then obtain a mass of escaping gas (hydrogen and helium included) that is directly related to the [C ii] luminosity from the whole region mapped by STO2:

$$\begin{eqnarray}&&M=1.2\left(\displaystyle \frac{{L}_{[{{\rm{C}}}_{\mathrm{II}}]}}{1\ {L}_{\odot }}\right)\ {M}_{\odot }.\end{eqnarray} \tag{ 15 }$$

The observed STO2 [C ii] luminosity from the LOS velocity range −40 to −23 km s⁻¹ is ${L}_{[{{\rm{C}}}_{\mathrm{II}}]}$ = 583 L_⊙. This then corresponds to 707 M_⊙ of atomic and H₂ gas (but no CO gas). The observed STO2 [C ii] luminosity from the LOS velocity range −11 to 0 km s⁻¹ is ${L}_{[{{\rm{C}}}_{\mathrm{II}}]}=205$ L_⊙. This then corresponds to 246 M_⊙ of atomic and H₂ (but no CO) gas. So, in sum, we find a lower limit of about 1000 M_⊙ of evaporating or nonbound gas traced by [C ii].

We use the ¹³CO J = 1–0 luminosity to estimate the mass of the evaporating gas traced by CO. This gas is almost certainly optically thin in this isotopic line, so the mass derives directly from the luminosity in the line, the temperature of the emitting gas, and the assumption that the gas density is above the critical density, which the PDR models confirm:

$$\begin{eqnarray}&&M=9.6\times {10}^{4}\left(\displaystyle \frac{T}{30\ {\rm{K}}}\right)\left(\displaystyle \frac{{L}_{{}^{13}\mathrm{CO}}}{1\ {L}_{\odot }}\right)\ {M}_{\odot }.\end{eqnarray} \tag{ 16 }$$

In the 10 spectral features that we modeled in detail, the average temperature of the gas at A_V = 5, typical of the ¹³CO gas, was 22 K, with a range of 18–33 K. The observed Mopra ¹³CO luminosity from the LOS velocity range −40 to −23 km s⁻¹ is ${L}_{{}^{13}\mathrm{CO}}=0.0077$ L_⊙. These numbers then correspond to roughly 540 M_⊙ of H₂ gas associated with this blue CO component. The observed Mopra ¹³CO luminosity from the LOS velocity range −11 to 0 km s⁻¹ is ${L}_{{}^{13}\mathrm{CO}}=0.0022$ L_⊙. This then corresponds to roughly 155 M_⊙ of H₂ gas associated with the red CO component. In sum, we find about 700 M_⊙ of evaporating or nonbound gas traced by CO. Adding the neutral gas traced by [C ii], we find ∼1700 M_⊙ of neutral gas in the STO2 mapped region that is unbound to the Carina GMC and possibly evaporating from it.

This range can be compared to the mass in ionized H ii gas that is evaporating from the GMC in the region mapped by STO2. In the previous subsection, we derived that the ionized mass-loss rate in the STO2 region is ${\dot{M}}_{\mathrm{evap}}$ ≃ 5 ×10⁻³ M_⊙ yr⁻¹. Brooks et al. (2001) and Smith (2006) suggested an age for Tr 14 of about 1 Myr. Thus, roughly 5000 M_⊙ of ionized gas has evaporated from the surface of the GMC during this time and would mostly still lie inside the STO2 mapped area. This appears to dominate the neutral evaporation by a factor of about 3. In summary, the mass-loss rates we estimate lead to GMC lifetimes of 20–30 Myr if they persist for the cloud lifetime, a result consistent with observational estimates of GMC lifetimes.