The Photodissociation and Ionization Fronts in M17-SW Localized with FIFI-LS on Board SOFIA

The FIFI-LS data reduction pipeline (Vacca et al. 2020) was used to reduce the raw data. The final data products of the pipeline (level 4) are data cubes with the observed flux regridded on an oversampled, regular, three-dimensional (x, y, λ)-grid with the x- and y-axes usually aligned with equatorial coordinates. However, for this data set, we kept the x- and y-axes aligned with the array and raster map axes, which were rotated by 60° relative to the equatorial coordinates.

The statistical uncertainties were estimated using an algorithm developed by one of us (D.F.) analogous to the way uncertainties were estimated for the PACS-spectrometer on board Herschel. ⁷ The uncertainty for each pixel in the data cube were based on the variance of all individual measurements in the spatial (within two times the full-width-half-maximum (FWHM) of the beam and within three times the FWHM for λ < 65 μm) and spectral (1/4 of FWHM of the line-spread function) vicinity of that pixel. The error is computed by weighting the contributions by the distance in space and wavelength.

The data is flux-calibrated in the pipeline processing using calibration factors derived as described by Fischer et al. (2018) achieving an absolute calibration of better than 15%. To avoid underestimating such systematic uncertainties, a relative uncertainty of 10% is added in quadrature to the propagated statistical uncertainties. The uncertainty for the atmospheric correction for the [O i]146 μm line is higher (possibly 20%) as the line is close to a narrow but deep telluric absorption feature (see Figure 3).

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To obtain the integrated line fluxes and continuum flux densities, we fit all spectra with a Gaussian and a baseline. The only free variable for the Gaussian was the line flux. Line center and width were fixed to the transition's wavelength and the instrument's resolution; the observed spectra did not exhibit any wavelength shifts or resolved line profiles. The baseline was a constant flux density F_ν multiplied with the atmospheric transmission modeled with ATRAN (Lord 1992) convolved to the instrument's spectral resolution.

The parameters for the ATRAN-model are altitude, zenith angle, and precipitable water vapor (PWV). While altitude and zenith angle are known from the observations, the PWV values are not directly available. Since the [O i]63 μm and the CO(14 → 13) lines are on the wings of broad telluric water absorption features and the spectra have strong continua, we were able to fit the atmospheric model to the spectra by letting PWV be a free parameter. We obtained values between 2 and 3 μm of PWV for these flights, which are consistent with those derived from satellite data (Iserlohe et al. 2021) for the 2016 data as well as the FIFI-LS measurements taken directly before and after the data acquisition in 2019 (Fischer et al. 2021). Thus we used 2.5 μm PWV for all observations. The only remaining free parameter for the baseline fit was the constant continuum flux density. Having determined the PWV for the observations allowed the correction of the observed line and continuum fluxes for atmospheric absorption.

An example for such a line and baseline fit is shown in Figure 3. Shown is the [O i]146 μm at a representative PDR position (position 2 of the discussion in Section 3 and Figure 4). The histogram with the errorbars shows the observed spectrum with its uncertainties computed as previously discussed. The solid lines show the fit (Gaussian emission line plus baseline) while the dashed line corresponds to the baseline. The dip in the baseline stems from a narrow atmospheric absorption feature broadened to the instrument's spectral resolution.

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Some data sets presented specific problems which were addressed in our analysis as explained in the following.

The continuum of the [O iii]52 μm observations was not used to estimate the FIR intensity (see Section 3) as the continuum map showed strong artifacts stemming from bad data at some map and especially reference positions. As the data from the reference position are used to subtract the sky emission at several map positions, a relatively large part of the map is affected. The [O iii]52 μm line intensity map is not affected as the bad reference data introduced only an offset in the continuum levels.

The [C ii] line intensity map showed clear indication of [C ii] emission in the off-beam for the chop-pairs especially in the northern corner of the mapped area. The [C ii] emission in the off-beam was stronger than in the on-beam so that the resulting spectra showed the [C ii] line in absorption rather than in emission there. To obtain a [C ii] map, the data were reduced in the same way as the other data sets except that the data from the off-beam from each chop-pair were not subtracted, but ignored. Only the on-beams of the reference positions were subtracted from the on-beams in the source positions. That allowed us to recover the [C ii] flux. ⁸ Similarly, a map of the [C ii] emission in the off-beams relative to off-beams at the reference position could be made. That showed that the off-beams were free of [C ii] emission in all parts of the map except in the northern corner of the mapped area, where the off-beams saw up to 1.5 × 10⁻³ erg cm⁻² s⁻¹ sr⁻¹ of [C ii] in a ridge roughly at a decl. of $-16^\circ 11^{\prime}$ seen from R.A. 18^h20^m55^s to 18^h21^m10^s matching the far eastern end of M17 north (just outside of Figure 1).

The absolute continuum level in this virtually un-chopped observation was not used, as the atmospheric background subtraction is much less certain due to the about 2 orders of magnitude slower nod frequency compared to the chopping frequency. The 158 μm continuum map was obtained from the normally reduced [C ii] observations. At no wavelengths were there any indications of significant continuum emission in the off-beams.

Four of the maps are displayed in Figure 2 as colored overlays at their original resolutions. Before calculating intensity ratios for the PDR modeling, each map is convolved with a Gaussian to match the spatial resolution of the longest-wavelength map. The individual line maps at their original resolution and the smoothed version are shown in the Appendix together with a FIR intensity (I_FIR) map. We created the I_FIR map by creating spectral energy distributions (SEDs) for each map pixel in our continuum maps and available Herschel continuum maps and then integrated the SEDs to obtain the I_FIR at each position. We estimate a 40% uncertainty for this map. The FIR continuum is shown together with the line maps that enter the PDR model, [O i]146 μm and CO(14 → 13), in the left panel of Figure 4. For the convolved maps, the uncertainties are propagated taking the correlation in the original maps into account (Klein 2021). We assume that the correlation between pixels in the original maps is on spatial scales of the respective beam sizes.

Comparing directly to the Kuiper Airborne Observatory (KAO) observations of M17-SW by Stutzki et al. (1988) and Meixner et al. (1992), we find a general agreement with our SOFIA/FIFI-LS observations of fine-structure lines. For example, along the two scans done by Stutzki et al. (1988), the [C ii]-emission smoothed at the same resolution as the KAO data also peaks at 3.5 × 10⁻³ erg cm⁻² s⁻¹ sr⁻¹ and is about 0.5 pc wide. However, we find the location of the [C ii]-peak about 05 further southwest along the scan.

The FIFI-LS [C ii]-map matches the integrated intensity [C ii]-map obtained with SOFIA/GREAT (Pérez-Beaupuits et al. 2012) very well in shape, position, and relative intensity of the emission. The absolute flux calibration of our [C ii]-data seems to be about 20% lower than the SOFIA/GREAT observations, which is within the combined uncertainties of both observations.

The PDRT assumes that all UV radiation is absorbed and remitted in the FIR. This is the reason why the derived UV-field closely follows the FIR intensity as indicated by the contours in the right panel of Figure 6. It looks as if the contours represent the UV-field but actually they represent the FIR intensity.

The H-density map derived by the PDRT shows a distinct jump separating the high densities in the molecular cloud and the low densities in the [H ii] region. A dotted contour is drawn as reference to the jump in some figures including Figure 6, left panel, enclosing densities of more than 10⁵ cm⁻³ with an uncertainty better than 1 dex. This discontinuity may partly be the result of the modeling being limited to three input quantities and the model properties. To understand the appearance of the discontinuity, the general anatomy of the reduced χ² in the n–G_UV-plane needs to be explained.

The colored solid lines in Figure 5 mark the (n, G_UV)-pairs predicting the observed line ratios and I_FIR, respectively, with colored dotted lines indicating the 1σ uncertainty of each quantity. The observed FIR intensity (red) defines the range for the UV field intensity, but sets no constraint on the H-density (horizontal I_FIR line). The (n, G_UV)-pairs predicting the observed CO(14 → 13) to [O i]146 μm ratio (green) lie on an L-shaped line. A high ratio requires high densities and UV radiation fields, while low densities or low UV fields lead to a low CO(14 → 13) to [O i]146 μm ratio. The intersection of the green with the red line would set the density, if we disregarded the [O i]146 μm to I_FIR ratio (blue). The (n, G_UV)-pairs satisfying a given [O i]146 μm to I_FIR ratio form an oval. In the PDR, where we observe higher [O i]146 μm to I_FIR ratios, the oval is relatively small. Together with the high I_FIR there are no intersections of the blue and red line, but their 1σ neighborhoods intersect. The minimum χ² is found in this intersection region on the green line resulting in a H-density around 10⁶ cm⁻³. Position 1 (peak of the continuum emission and most PDR transitions) and position 2 (a representative location in the PDR with relatively weak CO(14 → 13) emission) in Figures 5 and 6 are examples of how the high densities come about.

Toward the [H ii] region, the CO(14 → 13) line gets weaker and is not detected at all away from the molecular cloud (except around position 6, which will be discussed in Section 4.3.1). At position 4 the CO(14 → 13) to [O i]146 μm ratio is so low that the lower dotted 1σ line for this ratio transition is missing in that panel in Figure 5. For most of the [H ii] region including position 5, the observed CO(14 → 13) to [O i]146 μm ratio is zero and the ratio's uncertainty becomes its upper limit. Only that 1σ upper limit can be plotted in the (n, G_UV)-plane and the ratio becomes effectively an upper limit for the hydrogen density.

The sharp drop from densities 10⁶ cm⁻³ to about 10⁴ cm⁻³ happens in the model because as I_FIR and the ratio I([O i]146 μm)/I_FIR drop, there are two (n, G_UV)-pairs that match the measurements (the red line and the blue oval intersect twice), one at a density higher than 10⁶ cm⁻³ and one around 10⁴ cm⁻³. Due to the CO(14 → 13) to [O i]146 μm ratio serving as an upper limit, only the lower-density solution is compatible with the observations. This transition is illustrated by positions 3 and 4 in Figures 5 and 6.

While the PDRT derives a solution for the area where no CO(14 → 13) was detected, the applicability of the PDR model is questionable. The model assumes that we are looking at a PDR, but in the edge-on PDR in M17-SW, we are looking past the PDR in the upper parts of the maps, where no CO(14 → 13) but [O iii] is detected. The sight lines cross the [H ii] region, but do not hit the PDR. Thus, the model may not even be applicable there. The model-derived low densities should therefore seen only as upper limits for the densities in the [H ii] region. We postpone further discussion of the [H ii] region to a future paper.

How do the derived H-densities compare to other density estimates? Pérez-Beaupuits et al. (2015a) derived densities for four locations in the molecular cloud. Their HCN and CO peak locations are close to our position 1. Their southern and western locations are within the area where the PDRT fitting leads to high-density solutions. They estimate for the warm H₂ component, which is the dominant one, densities between 10^5.7 and 10⁶ cm⁻³ for these four locations.

We derived very similar densities in the molecular cloud, which we define here as the region where the modeling finds a high-density solution with an uncertainty better than 1 dex excluding the area around the O-stars at the top of the map. The range of densities in the molecular cloud is 10^5.6–10^6.1 cm⁻³ (excluding 5% of the pixels as outliers), with a median of 10^5.9 cm⁻³ matching the findings of Pérez-Beaupuits et al. (2015a). Our densities also fall into the range of densities found by Stutzki & Guesten (1990) for the clumps in their clumpy PDR model (10^4.5–10⁷) cm⁻³. Using pure-rotational lines of H₂ in the mid-IR (MIR), Sheffer & Wolfire (2013) even find densities of a few 10⁷ cm⁻³ adding that the H₂ emission is produced "in high-density clumps immersed in an interclump gas of density lower by two or three orders of magnitude."

Meixner et al. (1992) analyzed FIR fine-structure and molecular lines observed by the KAO with lower spatial resolution than our maps obtained with SOFIA. In their paper, the density and the UV intensity is derived for four positions. Their first position is about 15'' east of our position 1. Our position 2 is about 15'' south of the midpoint between their second and third positions, which are separated by 40'' in a nearly east–west direction. Their fourth position is at the southeastern edge of our maps. All their position fall into the region, where our method finds a high-density solution. The densities derived from the [C ii] to [O i]146 μm ratio only by Meixner et al. (1992) are about a factor of four below our densities at these positions with a similar relative trend between the positions. Later in that paper, Meixner et al. (1992) adopt, similar to Stutzki & Guesten (1990), a clumpy PDR model with a density of 10^5.7 cm⁻³ in the clumps embedded in a core with a density of 10^3.5 cm⁻³.

4.2.1. Predictions for the [O i]63 μm and [C ii] Lines

According to the literature and our analysis, the PDR is clumpy and allows the UV to penetrate the molecular cloud relatively deeply, exciting more C⁺ than in a homogeneous medium. Still the PDR looks edge-on as seen by the layering in Figures 2 and 8, but there is also some overlap of the ionized and molecular phase as traced by, e.g., the ionized and atomic oxygen emission. There is also the big clump hosting M17-UC1 protruding very obviously into the [H ii] region, and that clumpiness and projection effect seen there would also be expected down to at smaller spatial scales. So, the overlapping could be explained alternatively by a projection effect as in the model by Sheffer & Wolfire (2013) (also a clumpy PDR model) where the PDR surface is behind the molecular material from our vantage point to explain extinction effects.

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Can we still identify the locations of the ionization and photodissociation fronts? While the density jump in the PDR model indicates the magnitude of the density ratio between the [H ii] region and the molecular cloud, its abruptness may be an artifact of modeling with just the three input quantities and, thus, its exact location is dependent on the model parameters, too.

The left panel of Figure 8 shows a three-color image of M17-SW in three MIR tracers. There is a color change showing where the conditions change in this layered edge-on PDR. There is the red–blue region with strong 8 μm and [O iii]52 μm emission with a quick transition to the green–blue region with strong 37 μm and some 8 μm but vanishing [O iii]52 μm emission. Similarly, the near-IR H₂ and Brγ observations by Burton et al. (2002) show a sharp transition from ionized to molecular material. The H₂ and Brγ both form ridges next to each other, especially prominent as layers on the clump containing M17-UC1 (lower right panel of Figure 4 in Burton et al. 2002).

The yellow line in Figure 8, denoting the density jump, follows the above-mentioned color change fairly well, and thus also the transition from the [H ii] region to the molecular cloud, except around the clump containing M17-UC1. There, the yellow contour is well in front of the sharp edge of the clump toward the [H ii] region, which can be seen in the IRAC Band 4 and the FORCAST 37 μm images in Figure 8. Since the PDRT modeling is based on the FIR maps smoothed to a resolution of about 17'' the location of the density jump can easily be pushed out by a good fraction of the maps' resolution around the flux peaks of these maps, which all peak around M17-UC1. The pillar in the background (see Section 4.3.1) contributes further to an additional notch in the contour into the [H ii] region.

Below the yellow line, the modeling tells us that the gas, even if clumpy, has mostly a density around 10⁶ cm⁻³. The atomic layer of PDRs forming on the surface of molecular clouds has a hydrogen column density typically of about (2–4) × 10²¹ cm⁻² (Hollenbach & Tielens 1999). That means the atomic layer here has a thickness on the order of only 10⁻³ pc. Further, Hollenbach & Tielens report in their section on "Time-dependent and nonstationary PDRs" that for relatively high gas densities (≈10⁶ cm⁻³) and UV intensities (10^4.5 G₀), as derived here for the PDR region, the ionization and dissociation fronts can even merge as H₂ flows fast enough toward the [H ii] region. Thus in M17-SW, the ionization and photodissociation fronts on the clumpy PDR-medium may even be merged. Even with a clumpy structure and projection effects, the density jump in the model and the layered appearance of the various tracers indicate that both fronts should be where the red and yellow contours drawn in Figure 8 are close together. On the M17-UC1 clump, the contours diverge as the geometry departs significantly from the a simple edge-on geometry due to the high-density clump protruding into the [H ii] region.

4.3.1. The Pillar