A 205 μm [N ii] MAP OF THE CARINA NEBULA

The South Pole Imaging Fabry-Perot Interferometer (SPIFI; Swain et al. 1998; Bradford 2001; Bradford et al. 2002) is a direct-detection imaging spectrometer which operates near the background photon noise limit in the submillimeter (submm; λ = 200 μm–1 mm) regime. After initial success measuring 370 μm [CI] and ¹²CO(7→6) emission lines from the James Clerk Maxwell Telescope (JCMT) on Mauna Kea (e.g., Bradford et al. 2003, 2005), SPIFI underwent a series of upgrades and modifications to optimize its performance in the 200 μm window (Oberst 2009) and was installed on the 1.7 m Antarctic Submillimeter Telescope and Remote Observatory (AST/RO; Stark et al. 1997b; Stark et al. 2001) at the South Pole in 2003 December.

SPIFI observed spectra containing the [N ii] 205 μm line (Table 1) in the Carina Nebula during 15 days (August 15–30) of the 2005 Polar winter, as previously reported in Oberst et al. (2006). During these observations, the 205 μm line-of-sight transmission ranged from 3%–6%, with an average value of 4.5% and standard deviation of 0.7% on ∼1 day timescales (Oberst 2009).

Table 1. Observed Spectral Lines

Species	Transition	λ	Beam	R  (λ/Δλ)b
		(μm)a	('')b
ISO:
[O i]	3P2 → 3P1	63.18372	87.2	223
[N ii]	3P2 → 3P1	121.8981	78.2	209
[O i]	3P1 → 3P0	145.52547	70.0	249
[C ii]	$^2P_{\frac{3}{2}}\rightarrow ^2P_{\frac{1}{2}}$	157.7409	70.1	270
SPIFI:
[N ii]	3P1 → 3P0	205.1782	54	4250

Notes. ^aThe references for λ are 63 μm [O i], Watson et al. (1984); 122 and 205 μm [N ii], Brown et al. (1994); 146 μm [O i], Saykally & Evenson (1979); and 158 μm [C ii], Cooksy et al. (1986) and Boreiko et al. (1990). ^bThe ISO beam diameters and spectral resolution elements, Δλ, have been taken from Gry et al. (2003).

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SPIFI mapped two separate areas in the nebula (Figure 2): (1) a ∼14' × 14' area containing the Car I H ii region and a portion of the GMC to the south and west, and (2) a ∼12' × 10' area containing the Car II H ii region and vicinity to the east. Each pixel in SPIFI's 25 (5 × 5) detector array of Winston cone-fed thermistor-sensed bolometers had a circular beam of ∼54'' FWHM and the array's inter-beam spacing was ∼65''. The entire array (∼325'' × 325'' field of view) was moved through a raster with a 130'' step size (a three-pixel overlap) to minimize flatfielding errors. The resulting map contains single-beam pointings at 236 distinct spatial positions with a ∼54% filling factor (where more extended spatial coverage was favored over denser spatial sampling). Two of SPIFI's 25 detectors were nonfunctional at the time of the Carina observations; as a result, seven of the 236 observed positions are lacking spectra (see Table 3). Pointing accuracy, refined by observing the limb of the Moon at 370 μm, was ≈1' (Oberst 2009).

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Each spectrum covered seven resolution elements of width Δλ ≈ 0.0483 μm (or 71 km s⁻¹ in terms of the relative Doppler velocity shift) slightly oversampled in 16 spectral bins of width ≈0.0211 μm (31 km s⁻¹). The resolving power at 205 μm was R = λ/Δλ ≈ 4250 ± 120. In each spectral bin, SPIFI measured the difference between the source and background sky using a three-position, 30'' azimuth throw, 2 Hz chop of the AST/RO's tertiary mirror. The total integration time for the Carina observations was 143 hr. Because SPIFI was spatially multiplexed by a factor of 25, this corresponds to an effective average integration time of ∼15 hr at each of the 236 distinct single-beam pointings, or ∼1 hr per spectral bin.

Wavelength calibration was achieved by measuring the CD₃OH 205.4229 μm laser line, which was used as the local oscillator for the Terahertz REceiver with NbN HEB Device (TREND; Yngvesson et al. 2004), also deployed on AST/RO in 2005. In terms of relative Doppler velocity shifts, the calibration uncertainty is estimated to be ±∼2.7 km s⁻¹ (Oberst 2009). However, a comparison of the centroids of SPIFI's 205 μm lines with previous radio recombination line observations of the Carina Nebula suggests an additional velocity offset in the SPIFI data of ∼−7.5 km s⁻¹ (a blueshift of ∼10% of an SPIFI resolution element, see Section 4.5). This is likely due to calibration against an imperfectly collimated laser (but observation of perfectly collimated astrophysical lines), since rays passing through a Fabry-Perot off-axis see shorter resonant wavelengths than those along the optical axis.

Intensity calibration was achieved by measuring the gain (mV K⁻¹) of hot and cold loads placed in the f-cone of the receiver and correcting by the efficiency of the AST/RO at 205 μm (51%; A. A. Stark 2004, private communication) and the measured transparency of the sky at the time of the observations. The final absolute calibration uncertainty in intensity is estimated to be ±26% (Oberst 2009).

SPIFI's sensitivity, as calibrated by SPIFI's chopper wheel over an hour-long integration, corresponded to a noise-equivalent power (NEP) of ∼2.5 × 10⁻¹⁵ W Hz^−1/2 (referred to the front end of the Dewar). This is within a factor of ∼1.4 of the fundamental limits imposed by the photon shot noise associated with the large thermal background from the (nearly opaque) sky at 205 μm (Oberst 2009). This NEP is also a factor of ∼10 better than the best NEPs achieved by direct-detection spectrometers using photoconductor detectors (see Colgan et al. 1993). SPIFI's equivalent double side-band (DSB) receiver temperature (T_rec(DSB) ∼ 150 K) is a factor of ∼7 better than the best temperatures achieved by heterodyne receivers near 200 μm (Yngvesson et al. 2004).

These observations constitute the first published ground-based detection of the [N ii] 205 μm line (Oberst et al. 2006) and the third detection overall since those collected by the Cosmic Background Explorer (COBE) Far Infrared Absolute Spectrophotometer (FIRAS; Wright et al. 1991) and the Kuiper Airborne Observatory (KAO; Colgan et al. 1993) in the early 1990s.

The Long Wavelength Spectrometer (LWS; Clegg et al. 1996) aboard the Infrared Satellite Observatory (ISO; Kessler et al. 1996) was used to obtain full bandwidth (43–197 μm) spectra of the Carina Nebula over four days—1996 July 23 and 24 and August 1 and 4—as part of a guaranteed time observation (GTO) by T. Onaka. Within the LWS band, fine-structure lines of [O i] 63 μm, [N ii] 122 μm, [O i] 146 μm, and [C ii] 158 μm (among others) were detected (Table 1), as previously reported by Mizutani et al. (2002, 2004).

These spectra were taken at 100 spatial positions within a ∼40' × 20' area centered at (l, b) = (2874, −06) and containing the Car I and Car II regions (Figure 2). The ISO beam had an average FWHM of 793 over the LWS band (Gry et al. 2003) and the pointings were spaced by 180'', resulting in a ∼16% map filling factor (with more extended spatial coverage favored over denser spatial sampling).

The grating was scanned in the AOT LWS01 mode (or "fast" mode), sampling every 1/4 of a spectral resolution element, where the spectral resolution element was Δλ ≈ 0.283 μm in the second grating order (detectors SW1–SW5, covering 43–93 μm) and Δλ ≈ 0.584 μm in the first grating order (detectors LW 1–LW 5, covering 84–197 μm; Gry et al. 2003). The resulting resolving powers for the detected species range from R ≈ 223 to 270 (Table 1). The effective integration time was 0.45 s per spectral bin, ∼13.2 minute per raster position, and ∼22 hr for the entire (100 raster positions) map.

The LWS data were run through the standard ISO Off-Line Processing version 11.1 (OLP v11.1) pipeline (see Swinyard et al. 1998 and Gry et al. 2003 for full details of LWS calibration) and were further processed with the LWS L01 pipeline to produce "highly processed data products" (HPDP; Lloyd et al. 2003). The OLP pipeline automatically corrects for diffraction losses from on-axis point sources. These losses do not occur for extended sources such as Carina, resulting in a flux overestimation. Thus, extended source correction factors (Salama 2000; Gry et al. 2003) were applied. Finally, the present authors manually removed (rare) remaining glitches.

The final LWS absolute calibration uncertainty in flux is estimated to be ∼20% (Oberst 2009), wavelength calibration was measured to have an accuracy better than 1/4 resolution element (0.07 μm for SW detectors and 0.15 μm for LW detectors; Gry et al. 2003), and the pointing accuracy of the ISO at the time of the Carina observations was <2'' (Kessler et al. 2003).

A Markov chain Monte Carlo (MCMC) χ² algorithm was used to fit linear baselines and Lorentzian profiles (SPIFI's Fabry-Perot profile is Lorentzian) to the 205 μm [N ii] lines in the spectra at each of the 236 positions in the Carina Nebula observed by SPIFI (Oberst 2009). After rejecting fits with signal-to-noise ratios (S/Ns) ≲ 3, ionized nitrogen emission was detected (i.e., lines with fits of S/N ≳ 3 were found) in over 40% of the positions mapped by SPIFI, with an average S/N at the detected positions of ∼5.

Sample spectra and fits are shown in Figure 3, and a full list of the line intensities derived from fits to SPIFI's spectra is provided in Table 3. The conversion between the main beam brightness temperature (T_MB) and velocity ($\mathsf {v}_{\mathrm{LSR}}$) values of the spectra in Figure 3 and the intensity (I) values of Table 3 is

$$\begin{equation} I=\frac{2k_{\mathrm{B}}}{\lambda ^3}\,\bigg (\frac{\pi }{2}\,T_\mathrm{MB} \Delta \mathsf {v}_\mathrm{LSR}\bigg), \end{equation} \tag{ 1 }$$

where k_B is Boltzmann's constant, and T_MB and $\Delta \mathsf {v}_\mathrm{LSR}$ are the height and FWHM of the fit to a spectral line, respectively.

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Statistical (1σ) noise values are also listed in Table 3, but do not include the absolute calibration uncertainty of ∼26%. At positions with intensities below the S/N ∼ 3 cutoff, theoretical upper limits to intensity have been calculated by taking the product of the noise and the width of a spectral resolution element (71 km s⁻¹).

The 205 μm [N ii] line intensities are plotted as a contour map in Figure 4. Because the SPIFI raster was spatially undersampled, intensities between observed positions were interpolated by averaging the intensities from surrounding observed positions weighted by both their noise and beam profiles. The final map was convolved with a two-dimensional (2D) Gaussian filter corresponding to the 54'' instrument beam size to smooth ersatz features with size scales smaller than the beam size. The interpolation and smoothing have somewhat attenuated the maxima of the map (theoretically, a ∼20% attenuation is expected from the convolution of two identical 2D Gaussians). Thus, while the maps are utilized for studying the morphology of the region, the original intensity values (Table 3) are used for any quantitative calculations.

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The ISO spectra were fit in the same manner as the SPIFI spectra except that Gaussian profiles were used in order to match the LWS profile. Lines of 63 μm [O i], 122 μm [N ii], 146 μm [O i], and 158 μm [C ii] were detected at all 100 positions observed by ISO, with average S/Ns of 40, 21, 8.4, and 71 for the four species, respectively. None of the fits fell below our S/N = 3 cutoff.

Sample spectra are shown in Figure 10 and intensities derived from the fits are reported in Table 4. The table lists statistical (1σ) errors for each measurement, but does not include the absolute calibration uncertainty of ∼20%. The conversion between the specific flux (F_ν) and wavelength (λ) values of the spectra in Figure 10 and the intensity (I) values in Table 4 is

$$\begin{equation} I=\sqrt{\frac{\pi }{4\ln 2}} F_\nu \, \Delta \lambda, \end{equation} \tag{ 2 }$$

where F_ν and Δλ are the height and FWHM of the fit to the spectral line, respectively.

Contour maps for each of the four spectral species are shown in Figures 6–9 (the gray-scale contours). These maps were created in the same manner as described above for the SPIFI contour map. The dimensions of the axes in these maps match those of Figure 1, with areas outside of the ISO raster (outlined by the solid line) grayed-out.

We find the 158 μm [C ii] intensities to be consistently ∼35% higher and the 122 μm [N ii] intensities to be consistently ∼25% lower than those reported by Mizutani et al. (2002, 2004) for the same raw data sets, while the 63 μm [O i] intensities were more or less the same. More significantly, we find good detections of 146 μm [O i] at all of the 100 raster positions observed by ISO, with an average S/N of ∼8.4 over the entire map. Mizutani et al., on the other hand, reported 146 μm [O i] detections at only 10 of the 100 positions, with marginal S/Ns of ∼2.5–3. While slight differences are to be expected between the reductions of Mizutani et al. and the current work due to improvements in the ISO LWS calibration (from OLP version 8–11), this cannot account for a tripling of the S/N of the 146 μm data. Unfortunately, the details of the Mizutani et al. fits are no longer available (T. Onaka 2007, private communication). Based on our analysis, they appear to suffer from systematic scaling errors in intensity. We contend that the present fits are a more robust and accurate representation of the raw data.

4.1.1. Ionized Component

In the region mapped, the 205 μm [N ii] emission observed by SPIFI (Figure 4) has two main peaks: a primary peak of intensity 51.7 × 10⁻⁸ W m⁻² sr⁻¹ at (l, b) = (287.3843, −0.6301) and a secondary peak of intensity 27.4 × 10⁻⁸ W m⁻² sr⁻¹ at (287.5519, −0.6182) (raster positions 27 and 195 in Table 3, respectively). The peaks are separated by 1008 (6.74 pc).

To compare morphologies, we overlay the 205 μm [N ii] map with the 122 μm [N ii] and 57 μm [N iii] line emission observed by ISO (Figures 7 and 5, respectively), and the 843 MHz radio continuum emission observed by the Molonglo Observatory Synthesis Telescope (MOST; Whiteoak 1994; Figure 12). (The [N iii] map, generated directly from the data of Mizutani et al. 2002, may suffer the intensity scaling error discussed in Section 3.2; it is considered here for morphology only.)

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The 205 μm [N ii] peaks line up fairly closely with the 843 MHz radio peaks: offset just 51'' (0.57 pc) eastward of Car I and 41'' (0.46 pc) southwest of Car II (see Figures 11 and 12). Given that the beam sizes of both maps and the SPIFI pointing accuracy were ∼1', and that the SPIFI map had a ∼50% filling factor, the two maps are in very good agreement. Nitrogen has an ionization potential of 14.53 eV, and can arise only in ionized regions. Radio emission can also arise in ionized regions due to thermal free–free transitions. From the agreement of the maps, it is clear that both the [N ii] lines and radio continuum emission originate in the ionized gas component of the Carina Nebula.

The closest morphological match to the SPIFI 205 μm [N ii] map among the ISO data is the 122 μm [N ii] map, as should be expected (Figure 7). Although the ISO beam is larger and its spatial sampling coarser (Section 2), the strong correlation of the two [N ii] maps shows that the two instruments are in good agreement.

We note two features of the ionized component evident in these maps.

• 1.  
  The lower ionization [N ii] gas has a Car I peak farther to the southwest and is also extended over a greater area of the sky to the south and west of Car I than is the more highly ionized [N iii] (compare Figures 7 and 5). The respective Car I peaks of 122 μm [N ii] and 57 μm [N iii] occur at (l, b) = (287.355, −0.686) (ISO raster position "Car 6:7" in Table 4) and (l, b) = (287.405, −0.637) ("Car 4:19"). This is consistent with the predominant view that the Car I emission peak is powered externally by the members of Tr 14 to the northeast (e.g., Retallack 1983; Whiteoak 1994; Mizutani et al. 2002; Brooks et al. 2003; Tapia et al. 2006) and that Car I sits just outside the edge of a GMC extending to the south and west (see Figure 11). (Embedded sources cannot be ruled out, however, Tapia et al. 2003 have detected an embedded stellar population in Car I which includes at least one O9/B0 star.) In other words, the more highly ionized gas exists primarily near the ionizing source, where the parent molecular cloud has been mostly ionized or swept away. The lower ionization gas, on the other hand, extends further from the ionizing source, and is either projected along the same line of sight as the molecular component or appears intermixed with it at the angular resolution of our beam.
• 2.  
  For all of the observed species discussed here which trace the ionized component ([N ii], [N iii], and the radio continuum), emission is extended over a fairly large area of the sky. In Section 4.2, we derive a density of n_e ∼ 28 cm⁻³ from the [N ii] emission, supporting the suggestion of Mizutani et al. (2002) that an extended low-density (ELD) H ii region spans 30 pc or more across the nebula.

4.1.2. Neutral Component

The 205 μm [N ii] emission contours observed by SPIFI (Figure 4) are overlaid on the 63 μm [O i], 146 μm [O i], and 158 μm [C ii] emission observed by ISO in Figures 6, 8, and 9, respectively. Oxygen has an ionization potential of 13.62 eV, so [O i] arises entirely in the neutral interstellar medium (ISM). Carbon, on the other hand, has an ionization potential of 11.26 eV, so [C ii] can arise from both the neutral and ionized phases of the ISM.

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However, in our contour overlays, [C ii] appears morphologically more akin to the neutral [O i] species than the ionized [N ii] species. This is supported quantitatively by the analysis of Section 4.3 below, in which we find that ∼63% of the observed [C ii] arises from the neutral medium. We conclude that [C ii] predominately traces the neutral component in the Carina Nebula.

We note two features of the neutral component evident in these maps.

• 1.  
  In the Car I region, [O i] and [C ii] both peak slightly (∼1 pc) to the southwest of the 205 μm [N ii] peak, at (l, b) = (287.355, −0.686) (raster position "Car 6:7" in Table 4). Thus, starting from Tr 14 and heading southwest in the plane of the sky, one encounters first the 57 μm [N iii] peak (tracing the highly ionized component), then the 205 μm [N ii] peak (tracing the lower ionization component), then the 63 μm [O i], 146 μm [O i], and 158 μm [C ii] peaks (all of which trace the neutral component), and then finally the GMC peak (tracing the molecular component). (The 122 μm [N ii] peak is near those of the neutral species—although this could be an artifact of coarse spatial sampling.) Observations of neutral 609 μm [CI] line emission (Zhang et al. 2001) and several polycyclic aromatic hydrocarbon (PAH) features (Rathborne et al. 2002, Kramer et al. 2008)—all of which trace the photodissociated neutral gas—also show peaks near those of our [O i] and [C ii] maps.This again supports the view of Tr 14 as the external ionizing source for Car I (cf. Section 4.1.1), with the neutral line emission ([O i] and [C ii]) arising from the photodissociated surface of the nearby GMC. The peak of the PDR emission occurs roughly at (l, b) ∼ (287.355, −0.686), corresponding to the northeastern surface of the GMC viewed edge-on along our line of sight—sandwiched between the ionized region near Tr 14 to the northeast and the greater GMC to the southwest. As was the case for the ionized gas, the tracers of photodissociated neutral gas extend well (several parsecs) to the south and west of Car I, indicating either that the FUV flux of Tr 14 penetrates deep into the GMC, or that a large fraction of the GMC surface (perpendicular to our line of sight) has undergone some photodissociation.
• 2.  
  The neutral gas peak near Car II is relatively much weaker compared to Car I than was the case for the ionized gas. This is consistent with Tr 16 being an older (age of ∼3 Myr; Smith 2006a) more evolved cluster which has ionized or swept away most of its parental cloud. On the contrary, the younger (age of ∼1.5 Myr; Smith 2006a) Tr 14 cluster is situated much closer (∼2 pc) from the northeastern edge of the remaining GMC, which also wraps behind Tr 14 along the line of sight. As evidenced by the PDR emission in its vicinity, Tr 14 is still actively eroding its parental cloud.

We conclude our study of the neutral morphology of Carina by pointing out the strong neutral peak (most evident in the 63 μm [O i] map) at (l, b) ∼ (287.405, −0.536) (raster position "Car 2:7" in Table 4) near the Tr 14 cluster. Since the 63 μm [O i] line can be enhanced in shocks, one might consider invoking shock excitation near Tr 14. However, the [O i]/[C ii] line intensity ratio there is similar to other positions in the map, and the [C ii] line is not enhanced by shocks. In terms of PDR parameters (see Section 4.4), this region is a peak not unlike other peaks in the neutral gas line maps. At low densities, the [N ii] line intensities should scale as the emission measure (n²_e d), as does the radio free–free emission flux. At Tr 14, there is no peak in the free–free emission, so the large [O i]/[N ii] line intensity ratio there likely just reflects less ionized gas in this region. Slightly enhanced PAH emission is seen near this position in the observations of Rathborne et al. (2002) and Kramer et al. (2008). This is consistent with PDR activity, possibly on the surface of the northeasterly portion of the GMC that wraps behind TR 14, relative to our line of sight (see Figure 11).

The ratio of the 122 μm to 205 μm [N ii] line intensities (hereafter "122/205") provides an excellent density probe of the diffuse weakly ionized gas in the ISM. Because it takes relatively low-energy photons (14.53 eV) to form N⁺, these lines arise in the lower ionization "outskirts" of H ii regions. Furthermore, the 122 and 205 μm [N ii] lines have critical densities of n_e ∼ 293 cm⁻³ and 44 cm⁻³ at T = 8000 K, respectively, so that the 122/205 ratio is sensitive to gas densities of n_e ≲ 300 cm⁻³. The theoretically expected curve of 122/205 as a function of electron density, n_e, is plotted in Figure 13 (solid line). The curve assumes electron-impact excitation and uses the collision strengths from Hudson & Bell (2004), scaled to an assumed electron temperature of 8000 K.

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Because the ISO and SPIFI rasters are not spatially aligned (Figure 2), a direct division of the 122 and 205 μm maps was not possible. However, 27 of the ISO beams are overlapped by one or more SPIFI beams. By interpolating the 205 μm [N ii] intensities at the centers of these ISO beams (averaged and weighted by the SPIFI beam profiles and noises), the 122/205 ratio could be computed. Finally, to derive n_e, we matched our observed 122/205 ratios to the theoretical 122/205 curve (circles and solid line, respectively, in Figure 13). A full list of the 27 derived n_e values is provided in Table 5.

The average electron density (in the low-ionization gas) is found to be a modest n_e ∼ 28 cm⁻³, with little spatial variation over the nebula (n_e ∼ 0–100 cm⁻³). This average is close to the value of n_e ∼ 32 cm⁻³ previously determined at the Car II peak (Oberst et al. 2006).

Using the intensity ratio of the higher ionization 52 and 88 μm [O iii] lines, Mizutani et al. (2002) found two distinct components to the electron density in the Carina Nebula: a high-density (n_e ∼ 100–350 cm⁻³) component at Car I and II and an extended low-density (ELD; n_e < 100 cm⁻³) component detectable over the entire ∼30 pc mapped region. From the present analysis, it is thus clear that the ELD "halo" also contains gas of lower ionization states.

C⁺ has an ionization potential of 11.26 eV, and hence can arise from both PDRs and H ii regions. Because the 158 μm [C ii] line is often the brightest FIR line, and is a dominant coolant for much of the ISM, determining the fraction of the observed [C ii] line radiation that arises from the neutral and ionized gas components is critical to the study of star-forming regions. Our observations of the 205 μm [N ii] line provide a direct means to measure this abundance ratio: since the critical densities for electron-impact excitation of the 158 μm [C ii] and 205 μm [N ii] lines are very similar (40 and 44 cm⁻³, respectively), to a good approximation the 158/205 line intensity ratio is dependent only on the relative abundance of C⁺ and N⁺ in the ionized medium.

Using the collision rates for exciting the ground-state levels of C⁺ from Blum & Pradhan (1992), we plot the expected ratio of the two lines as a function of electron density in Figure 13 (dashed line). The temperature dependence is quite small, as the ²P_3/2 level of C⁺ and the ³P₁ level of N⁺ are only 91 and 70 K above ground, respectively—small compared with the temperature (8000 K) of an H ii region. For the calculation, we take the gas-phase abundances of C/H = 1.4 × 10⁻⁴ (Kaufman et al. 1999) and N/H = 7.8 × 10⁻⁵ (Savage & Sembach 1996).

As was done for the 122/205 ratio (Section 4.2), we determine the 158/205 ratio at the 27 positions in the ISO raster which are partially overlapped by SPIFI beams by interpolating the SPIFI 205 μm [N ii] intensities there. The resulting data points are plotted in Figure 13 (diamonds), where the electron densities for these points are taken as those derived from the 122/205 ratios.

For each point, the ratio of the expected to measured value represents the fraction of C⁺ which arises from the ionized gas. The remaining fraction must arise from the PDRs. All of the data lie above the theoretical curve, indicating that some fraction of the C⁺ arises from the neutral medium at every position. Spatially, we find, rather unsurprisingly, that a higher percentage of C⁺ arises from PDRs in locations where there are PDRs—e.g., over the surface of the GMC (a contour map of the percentage of C⁺ arising from PDRs, which demonstrates this effect, can be found in Oberst 2009). A lower percentage of C⁺ arises from PDRs in locations where there are no PDRs—e.g., in the vicinity of Tr 14 and 16, where winds from stellar members have driven away most of the gas and dust.

On average over these 27 positions in the nebula, we find that 63% of the C⁺ comes from PDRs and 37% from the ionized gas. This result agrees with previous studies which contend that the majority of the observed [C ii] line emission from Galactic star-forming regions, the Galaxy as a whole, and from external galaxies arises in warm dense PDRs on the surfaces of molecular gas clouds (e.g., Crawford et al. 1985; Stacey et al. 1985, 1991; Shibai et al. 1991; Wright et al. 1991).

The PDR model put forth by Tielens & Hollenbach (1985a) and refined by Kaufman et al. (1999) has shown good agreement with observations for a wide variety of astrophysical environments (e.g., Hollenbach & Tielens 1997, 1999, and references therein). In their model, the PDR is taken as a homogeneous infinite plane slab of hydrogen nuclei density n_H, with an incident FUV (6 eV <hν < 13.6 eV) flux parameterized in units of the local interstellar radiation field, G₀ (1.6 × 10⁻⁶ W m⁻²; Habing 1968). The model assumes a number of fixed parameters, including the elemental, PAH, and dust abundances, absorption properties, and a Gaussian turbulent velocity field. The defining aspect of the model is the gas heating mechanism: about 10% of the incident FUV photons eject hot photoelectrons from the dust grains and PAH molecules, and these electrons collisionally heat the gas. The gas subsequently cools via FIR fine-structure line emission. The model is solved simultaneously for chemical and energy equilibrium in the slab, and the fine-structure emission of the various chemical species is predicted. Observed intensities of fine-structure lines can be compared with model results to constrain n_H and G₀.

We have modeled n_H and G₀ over the 100 ISO raster positions in the Carina Nebula using the observed line intensities of 63 μm [O i], 146 μm [O i], and 158 μm [C ii] (Section 3.2), as well as the FIR intensity derived from a graybody fit to the entire LWS spectrum by Mizutani et al. (2004). (It is possible that the latter suffers a calibration error similar to those of the ISO spectra fit by Mizutani et al. 2002, 2004; see Section 3.2.) The 158 μm [C ii] intensities at each spatial position were corrected for the average fraction (63%; cf. Section 4.3) arising from the ionized medium—i.e., [C ii] intensities were scaled by a factor of 0.63 at every spatial position. The calculations were performed with the online PDR Toolbox (PDRT; Pound & Wolfire 2008).⁶ The standard set of model parameters was assumed (see Kaufman et al. 1999), and the calculator searched for the best fit of n_H and G₀ to the combined observed intensity ratios of 63/146 μm [O i], 63/158 μm [O i]/[C ii], 146/158 μm [O i]/[C ii], and (63+158)/FIR.

Our PDR model results are shown in Figure 14. The solution space of the PDRT is quantized in four equal divisions per decade on a logarithmic scale, resulting in recurrences of the same n_H and G₀ values for several of the beam positions. To show this effect, circles are plotted around each data point, where the areas of the circles are proportional to the number of ISO raster positions yielding each solution. From the plot, we see that over most of the nebula 10 cm⁻³ < n_H < 1000 cm⁻³ and 10 < G₀ < 1000 × 1.6 μW m⁻². The maximum is (n_H, G₀) = (31600, 5620), but the average is (1250, 303). These data are near the low end of observed galactic star-forming regions, in which n_H and G₀ are both typically ∼10,000 or more. The goodness of fit varies substantially from one data point to the next, but over the entire data set averages $\sigma _{n_{\rm H}} \sim 150$ cm⁻³ and $\sigma _{G_0} \sim 40$ × 1.6 μW m⁻².

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The data of Figure 14 follow a clear trend, best fit by the power law G₀ = 4.84 n^0.74_H. This is somewhat in contrast to the correlation between G₀ and n_H theoretically predicted by Young Owl et al. (2002) for a PDR in pressure equilibrium with an ionization-bounded H ii region, namely G₀ = 0.00804 n^4/3_H. At high densities (n_H ∼ 6 × 10⁴ cm⁻³), both relations predict G₀ ∼ 17,000. But at low densities (<200 cm⁻³), we find a much (>10 times) higher G₀ at a given n_H. Larger G₀ at a given n_H means the star is much closer to the cloud than would be expected for an ionization-bounded H ii region in pressure equilibrium with the PDR. The obvious solution is that the widespread H ii regions in the Carina Nebula are not ionization-bounded, but rather well into the density-bounded stage so that the conditions of pressure equilibrium no longer apply. Establishing pressure equilibrium is relatively quick compared to the lifetime of the H ii regions. For example, at the ∼10 km s⁻¹ sound speed, changes in pressure equilibrium across a 1 pc H ii region take about 10⁵ yr.

Of the five highest density data points in Figure 14, three (ISO raster beams Car 4-17, 4-21, and 4-23; see Table 4) are found in close proximity to Car II. Car II has a higher average ratio of 63/158 than elsewhere in the nebula (Table 2), suggesting the possibility of shocks (cf. Section 4.1.2). In particular, the 63/158 ratio at position Car 4-23 ((l, b) = (287.605, −0.636)) is 1.35, about two times higher than average. Furthermore, the 35 μm [Si ii] line, measured by Mizutani et al. (2004), has an intensity at this position which is >3.5 times higher than average. The [Si ii] line is a good tracer of shocks since shocks can strip silicon atoms off of dust grains. These shocks are likely the result of winds from η Car (or other massive members of Tr 16).

Table 2. Parameters Averaged over Major Sources within the Carina Nebula

Parameter	Tr 16	η Car	Car II	Tr 14	Car I	GMC	Entire Nebulaa	Units
lb	287.63	287.5969	287.56	287.40	287.37	<287.33	...	deg
b	−0.65	−0.6295	−0.61	−0.58	−0.63	...	...	deg
Measured parameters:
I ([O i] 63 μm)	15.0	30.8	57.5	81.2	79.2	12.6	13.4	10−8 W m−2 sr−1
I ([N ii] 122 μm)	6.9	17.3	13.7	6.6	19.8	2.9	3.7	10−8 W m−2 sr−1
I ([O i] 146 μm)	0.6	1.2	2.4	3.2	6.4	0.6	0.7	10−8 W m−2 sr−1
I ([C ii] 158 μm)	28.3	32.1	46.7	83.5	80.8	27.8	29.2	10−8 W m−2 sr−1
I ([N ii] 205 μm)	12.3	< 2.6	16.2	12.2	18.7	9.5	11.3	10−8 W m−2 sr−1
RV ([N ii] 205 μm)	−34.7	...	−30.4	−32.2	−24.8	−27.9	−31.6	km s−1
Γ ([N ii] 205 μm)	52.8	...	55.3	47.1	40.9	35.6	37.7	km s−1
Derived parameters:
% [C ii] from PDRs	41	45	39	75	43	73	63	%
G0	119	<10	3310	580	1390	152	303	1.6 μW m−2
nH (PDRs)	78	17800	918	685	316	104	1250	cm−3
ne (H ii regions)	7	79	18	17	24	18	28	cm−3
NH (PDRs)	417	70	46	184	356	180	31	1020 cm−2
Ne (H ii regions)	22	6	18	9	19	4	3	1020 cm−2
Tsurface (PDRs)	263	71	432	295	486	332	234	K
(([O i] 63 + [C ii] 158)/FIR)	2.8	...	1.5	3.7	2.7	4.3	3.4	10−3

Notes. ^aThe "entire nebula" consists of all the observed raster positions, which differ between the ISO and SPIFI data (Figure 2). ^bCoordinates refer to the nominal centers of the sources, listed in order of decreasing l (Röser & Bastian 1988 for η Car, Whiteoak 1994 for Car I and II, and Kharchenko et al. 2005 for Tr 14 and 16). The areas of the sources (over which the parameters were averaged) were determined by a multi-wavelength comparison with previous observations and are limited by the observed raster positions (see Table 6).

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The modeled G₀ and n_H values have been plotted spatially as contours in Figures 15 and 16. Quantitative averages of G₀ and n_H over six spatial subregions of the nebula (corresponding to the sources Car I and II, Tr 14 and 16, η Car, and the GMC) are listed in Table 2 (Section 4.6). The morphology of the G₀ distribution roughly follows the PDR emission (Figures 6, 8, and 9) with the G₀ fields peaking near the positions of Car I, Car II/η Car, and just north of Tr 14. The strongest G₀ is found in the vicinity of Car II, as would be expected from the collection of massive early-type stars there (η Car and Tr 16). Little G₀ flux is seen westward of l ∼ 287.3, in the GMC. In its lower level contours, n_H shows a similar morphology to G₀. However, the eastern peaks (in the vicinity of η Car and Car II) are significantly larger relative to those at Car I and Tr 14. One explanation is the proximity of the dense Homunculus nebula and Car II molecular cloud remnant to the strong G₀ flux in these locations, so relatively higher density PDRs might be expected near these sources.

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As a check on our PDR model for Carina (Section 4.4), it is instructive to compare the FUV flux predicted by the model with the FUV flux expected from the total luminosity of the nebula's known O and B spectral-type stars. It is now generally accepted—and further supported by the present work—that Car I is excited externally by the Tr 14 cluster to its northeast, and that Car II is excited externally by the Tr 16 cluster to its southeast. The O and B members of Tr 14 have a total FUV luminosity of L_FUV = 7.84 × 10³² W (Smith 2006a), and the distance from Tr 14 to Car I is d ∼ 2.34 pc =7.22 × 10¹⁶ m (using the nominal source center positions from Table 2). Therefore, the expected FUV flux at Car I is G₀ = L_FUV/(4πd²) ∼ 7480 × 1.6 μW m⁻². The O and B stars of Tr 16 have a combined FUV luminosity of L_FUV = 2.37 × 10³³ W, and a distance to Car II of d ∼ 3.24 pc =10.0 × 10¹⁶ m. Therefore, the expected FUV flux at Car II is G₀ = L_FUV/(4πd²) ∼ 11800 × 1.6 μW m⁻².

For both Car I and II, the expected FUV flux from O and B stars (7480 and 11800, respectively) is a few times larger than the FUV flux predicted by our PDR model (1390 and 3310, respectively; Table 2). Thus, our findings agree with the established hypothesis that there is more than enough radiation from the O and B members of Tr 14 and 16 to externally excite Car I and II, respectively, without the need invoke embedded sources.

Previous kinematic studies of the Carina Nebula have consistently found two large-scale effects.

• 1.  
  Spectral lines near Car II show strong line splitting, while spectral lines near Car I are single-profiled. The double-peak profiles near Car II have been interpreted as arising from an expanding bubble of hot ionized gas, likely centered on Tr 16 or η Car. Car I, on the other hand, which shows only single spectral profiles, has been interpreted as an H ii region which is expanding only into the GMC which wraps beneath and behind it (mostly receding along our line of sight), while the foreground is largely devoid of gas and dust (see Figure 11). Using the highly spectrally resolved radio recombination line observations of Huchtmeier & Day (1975), we estimate the average centroids of the two peaks of the nebula's double-peaked profiles near Car II to occur at −32.5 km s⁻¹ and −5.4 km s⁻¹, with an average peak separation of 27.1 km s⁻¹ and average individual peak width of 27.9 km s⁻¹. The single-profiled peaks near Car I have an average width of 45.0 km s⁻¹. Line splitting near Car II has also been observed by Zhang et al. (2001, in the submm lines of ¹²CO(4→3) and [CI]), Deharveng & Maucherat (1975, in several optical lines), and Gardner et al. (1970, in several radio recombination lines).
• 2.  
  Radial velocities measured near Car II are more negative than those near Car I (for the split profiles, the radial velocity referred to here is the average centroid of the two peaks). Thus, it appears that Car II is approaching slightly faster than Car I along our line of sight. Huchtmeier & Day (1975) report a radial velocity of ∼−24 km s⁻¹ at Car II and ∼−16 km s⁻¹ at Car I, with a monotonic gradient between the two positions. Velocity channel maps of the radio recombination line observations of Brooks et al. (2001) show peak emission in Car II in the velocity channel centered at −28 km s⁻¹, and peak emission in Car I in the velocity channel centered at −16 km s⁻¹ (the velocity resolution of these channel maps is 4 km s⁻¹).

SPIFI cannot spectrally resolve the line splitting discussed above. However, one might expect unresolved (single-profile) 205 μm [N ii] peaks at Car II, which are wider than single-profile peaks elsewhere in the nebula. In particular, one might expect line widths near Car II of 27.9 km s⁻¹ (the average width per peak in the split radio profiles) + 27.1 km s⁻¹ (the average peak separation in the split radio profiles) = 55.0 km s⁻¹. Near Car I, on the other hand, we might expect to see line widths similar to the average radio line width at Car I of 45.0 km s⁻¹. After de-convolving the spectral and instrument profiles to recover the intrinsic line widths (Oberst 2009), the 205 μm [N ii] SPIFI data yield an average intrinsic line width of 55.3 km s⁻¹ at Car II and 40.9 km s⁻¹ at Car I (Table 2), in good agreement with the radio data.

Furthermore, we find the average radial velocities of the 205 μm [N ii] lines near Car I and Car II to be −24.8 km s⁻¹ and −30.4 km s⁻¹, respectively (Table 2). (Average line widths and velocities for other regions of the nebula can also be found in Table 2.) These values are somewhat more negative than the average velocities of the radio data of Huchtmeier & Day (1975, −16 km s⁻¹ and −24 km s⁻¹, respectively). However, both data sets are in agreement that Car II is approaching slightly faster than Car I along our line of sight. It is likely that this ∼−7.5 km s⁻¹ (∼10% of an SPIFI resolution element) blueshift of the SPIFI data relative to the radio data is the result of imperfect velocity calibration in our system (see Section 2.1). Taking into account such effects, the radial velocities observed in the SPIFI data are in very good agreement with those of the radio data.

To compare the contributions from various sources within Carina to one another and to other Galactic and extragalactic sources, we have averaged our data over six spatial subregions of the nebula corresponding to the sources Car I and II, Tr 14 and 16, η Car, and the westerly GMC. The results are shown in Table 2, where the sources are listed in order of decreasing galactic longitude, l. We have also included averages over the whole nebula. With the exception of η Car, all of these sources are extended relative our beam sizes, and thus had to be averaged over several beams in both the SPIFI and ISO rasters. The raster beams assigned to each source were chosen by proximity to the nominal central position of the source (Table 2) and multi-wavelength morphological considerations (Section 4.1). The beam assignments are listed in Table 6. Given the coarse spatial sampling of both SPIFI and ISO, and the lack of strictly defined boundaries for extended sources in general, there is some subjectivity in these assignments. However, the results of Table 2 are not overly sensitive to them.

For each of the sources within Carina, Table 2 lists the average measured line intensities (I) of the spectral species observed by SPIFI and ISO (Sections 3.1 and 3.2) and the average measured radial velocities (RV) and intrinsic line widths (Γ) of the 205 μm [N ii] lines (Section 4.5). In addition to these measured parameters, Table 2 includes averages of several derived parameters: the electron density (n_e, Section 4.2); the percentage of the 158 μm [C ii] emission arising from PDRs (Section 4.3); and the FUV flux (G₀), hydrogen nuclei density (n_H), PDR surface temperature (T_surface), and photoelectric heating efficiency (, Section 4.4).

Finally, we have calculated the hydrogen and electron column densities, N_H and N_e, for PDRs and H ii regions, respectively, using the measured intensities of 146 μm [O i] for PDRs (since this line is typically optically thin) and 122 μm [N ii] for H ii regions. We assumed a PDR temperature equal to the PDR surface temperature (which will be higher than that in the bulk of the PDR), so that our column densities for PDRs are likely to be underestimates. From these column densities we find a relative mass fraction for PDRs/(PDRs + H ii regions) of ∼91%–98% for all sources except Car II, where it is 72%. Thus, despite the fact that the [C ii] emission from PDRs is only ∼2 times greater than that from H ii regions, the mass of PDR gas greatly exceeds that of ionized gas. This is not surprising, as it takes very little ionized gas to produce nearly as much [C ii] emission as arises from the neutral gas. This is because the collision strengths for the electron-/ion-impact excitation of [C ii] in H ii regions are much greater than those in the neutral gas regions. These large PDR/H ii region mass ratios are reminiscent of the high ratios observed in the Galaxy as a whole and in external galaxies (cf. Crawford et al. 1985; Stacey et al. 1985, 1991).

In Figure 17, we have plotted the data for Car I, Car II, and the entire Carina Nebula (taken from Table 2) on n_H and G₀ axes with several other Galactic and extragalactic sources. The data points are overlaid on contours of the line intensity ratio of 63 μm [O i] to 158 μm [C ii] from the PDR model of Kaufman et al. (1999). The Carina sources have lower densities and FUV fields (n_H < 10⁴ and G₀ < 10⁴) than most other Galactic star-forming regions—e.g., the Orion Nebula, M17, and W49. Instead, Carina may be more akin to 30 Doradus (as previously suggested by Brooks et al. 2003).

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The physical separation between Tr 14 and the Car I PDR is similar to the distance between the [C ii] peak and star cluster R136 in 30 Dor (Israel et al. 1996). In both of these regions, the bulk of the molecular matter in the vicinity of the early-type stars has been destroyed or swept away, and the PDRs we see are forming on the peripheral edges of the remaining GMCs. On the other hand, in the case of Orion, the parent molecular cloud (OMC-1) still appears to be relatively intact, resulting in PDRs which have formed much closer to the exciting stars. We also notice that the conditions in Carina are similar to those in large (∼500 pc scale) beam studies of the nearby starburst galaxies NGC 253, NGC 3256, and M82. The very high rates of star formation over large scales in Carina have resulted in FUV fields and gas excitation conditions that mimic those in starburst galaxies as a whole.