POLYCYCLIC AROMATIC HYDROCARBON EMISSION IN SPITZER/IRS MAPS. I. CATALOG AND SIMPLE DIAGNOSTICS

We have selected the mapped H ii regions from the Spitzer archive, along with a subset of well-known RNe. Our objects span a variety of classes and physical properties, from the ultra-compact IRAS 12063-6259 to the giant star-formation complex W49A (summarized in Table 1). For each object we list its distance, the spectral type of its exciting star, and its size in both angular and physical units. In addition, we show the physical size of a Spitzer/IRS pixel, as the wide spread of distances evident in Table 1 corresponds to large changes (a factor of 30) in the physical area represented by the $1\buildrel{\prime\prime}\over{.} 8\;\mathrm{square}$ Spitzer IRS pixels. Each of the nebulae were observed using the spectral mapping mode of the IRS instrument and its SL module, which covers the 5–15 μm region at a spectral resolution of ∼128. All the pointing and exposure time information for each map is presented in Table 2. We also show the extent of each cube superimposed on optical/MIR imagery in Figure 1. Rather than discuss each source in detail here, we refer to final column of Table 2, where we list the papers that have previously examined these specific spectral cubes and discuss the various objects. As the G37.55-0.11, G11.94-0.62, M17, and NGC 1333 observations have not hitherto been presented, we give a brief overview of these sources here.

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Table 2.  Observation Properties

Object	IRS	Program	AORkey	Position Angle	Steps	Steps	Step Size	Step Size	Reference
	Module	ID		(°)	∥	$\perp$	∥ ('')	$\perp$ ('')
H ii Regions:
W49A	SL	63	16206848	84	5	100	40	1.8	1
G37.55-0.11	SL	20517	14799104	−93	1	9	⋯	3.6	⋯
IRAS 12063-6259	SL	20517	14798848	157	1	7	⋯	3.6	2
G11.94-0.62	SL	20517	14799360	86	1	9	⋯	3.6	⋯
M17	SL	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
Horsehead	SL	3512	12011520, 12017920, 12018688	101	1	23	⋯	1.8	9, 10
Reflection Nebulae:
NGC 2023 S	SL	30295	17977856	84	3	18	28	3.6	4
NGC 7023	SL1, SL2	28	3871744, 3871488	−1.2	2	15	7.3	3.6	6, 7
NGC 1333	SL	20378	14587648	−107	5	111	54.6	1.8	⋯

Note. The M17 and Horsehead IRS-SL AORs are combined to create the final maps. The NGC 7023 SL and SH cubes are sometimes analyzed after being stitched together (e.g., 6) because the cubes overlap to a high degree. For the other sources we have not merged the SL/SH cubes because this could involve discarding as much as 70% of the SL cubes.

References. (1) Stock et al. (2014), (2) Stock et al. (2013), (3) Peeters et al. (2012), (4) Peeters et al. (2016), (5) Rosenberg et al. (2011), (6) Boersma et al. (2014a), (7) Berné et al. (2007), (8) Shannon et al. (2015), (9) Ochsendorf et al. (2014), (10) Ochsendorf & Tielens (2015).

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G11.94-0.62 and G37.55-0.11—These sources, which are also known as IRAS 18110-1854 and IRAS 18577+0358, respectively, are both ultra-compact H ii regions (UC-H ii) that have been extensively studied in the radio. The radio observations provide us with measures of the distance, radius, and implied spectral type of the dominant exciting star (e.g., Table 1). Neither has been spectroscopically investigated in the MIR, although both objects have been imaged in the MIR. Crowther & Conti (2003) presented observations of both sources using MSX observations at a scale of around ∼20'', which revealed that the structure of the emission for G11.94 did not mirror the radio emission (which traces the ionized region), while for G37.55 the core-halo radio morphology was not contradicted by the "extended" appearance in the MIR. For G11.94, this conclusion was confirmed by De Buizer et al. (2003) who presented much higher resolution images taken at ground-based facilities. Their 20.8 μm image clearly shows that there is a very strong peak in the emission close to the south edge of the cometary halo that is observed in the radio (e.g., Wood & Churchwell 1989), with some extended emission to the north going well beyond the radio emission. In addition, there appears to be a secondary peak in the MIR emission on the northern edge of the radio halo. The Spitzer imagery presented in Figure 1 agrees with the MSX findings in that it shows distinct clumps of emission, in tension with the Wood & Churchwell (1989) categorization of the region as "cometary." On the other hand, the image we present of G37.55-0.11 matches the expected core-halo morphology very well.

NGC 1333—NGC 1333 is a large, active star-forming region in the Perseus molecular cloud (see Walawender et al. 2008 for a recent review). While the designation NGC 1333 has come to be used for the entire region, it originally referred to the bright reflection nebula in its core. The RNe is illuminated by the B8 type star BD+30°549, which lies around 35 (∼0.23 pc) to the northeast of the RNe and an early B star known as "SVS3"⁵ (Strom et al. 1976). SVS3 has been observed in the radio and MIR, and is found to have a very compact H ii region consistent with the central star being of spectral type B4-6 (Harvey et al. 1984; Snell & Bally 1986). The region around this source has also been spectroscopically observed in the MIR, with several studies in the 90s using such observations to make the first claims about the presence of ionized PAH molecules in the ISM (e.g., Joblin et al. 1996; Sloan et al. 1999). Both of these studies used ground-based observations of the 8–13 μm region, and so were limited in aperture. Despite that limitation, both studies found that the 8.6 μm band peaked in the center of the region (at around the location of SVS3), while the 11.2 μm band peaked around 10'' to the south (corresponding to a physical distance of about 0.64 pc).

The spectral maps for each object were processed using the Spitzer Science Center reduction pipeline for IRS/SL (generally Version 18.8, but 18.7 in some instances). CUBISM (Smith et al. 2007a) was employed to clean the individual BCDs. This primarily meant masking any rogue or otherwise "bad" pixels, initially using the CUBISM functions "AutoGen Global Bad Pixels" with settings "Sigma-Trim" = 7, "MinBad-Frac" = 0.5, and "AutoGen Record Bad Pixels" with settings "Sigma-Trim" = 7 and "MinBad-Frac" = 0.75, and subsequently by manual inspection of each cube. This process was repeated for each order (SL1, SL2, SL3) of each observation for each object. In order to combine the cubes of different orders, SL2 and SL3 were resampled to the same pixel grid as SL1 using CUBISM, then the scaling factors were calculated between the three orders for the now aligned pixels by comparing the average fluxes within the overlap regions. Subsequently the SL1 and SL2 cubes were stitched together using the derived scaling factors. For each of our maps, the scale factors between the orders were around 10%, with outliers being investigated and in some cases flagged as poor data.

As the IRS/SL pixels are around half the size of the beam, the final cubes were created by averaging 2 × 2 pixel apertures. This resulted in overlapping extraction apertures, in which one in every four pixels is independent. This was performed by taking the average of the next three adjacent pixels (i.e., ${F}_{1}(x,y,\lambda )$ = 0.25 × $({F}_{0}(x,y,\lambda )$ + ${F}_{0}(x+1,y,\lambda )$ + ${F}_{0}(x,y+1,\lambda )$ + ${F}_{0}(x+1,y+1,\lambda ))$), where ${F}_{1}(x,y,\lambda )$ is the resulting cube and ${F}_{0}(x,y,\lambda )$ is the observed cube. This process produces a new cube ${F}_{1}(x,y,\lambda )$ that has the same pixel scale as the old cube, however, each pixel represents a local beam average. Subsequent analysis masked out the non-independent pixels. While several of the maps were not Nyquist sampled, we adopted the same procedure such that we produced a uniform sample of spectral maps.

In general, molecular clouds and H ii regions contain copious amounts of dust, which combine to create continuous extinction from the UV to the MIR (although this is generally a small effect in the MIR), as well as strong absorption features associated with dust grains of specific compositions. The most important, from the point of view of measuring PAH band fluxes, is the silicate feature at 9.8 μm. This feature has significant width that overlaps two important PAH bands at 8.6 and 11.2 μm. Typically the 11.2 μm band is used to normalize measurements of the other bands, so its obscuration can strongly effect the interpretation of the PAH spectrum.

To correct our band measurements we adopt the "modified Spoon method" from Stock et al. (2013, 2014), which is an updated version of the method used by Spoon et al. (2007) that includes the silicate absorption profile given by Chiar & Tielens (2006). This procedure relies on the 5–15 μm continuum, displaying a strong rising power law toward the red, which is appropriate for the H ii regions. However, the RNe do not generally display spectra with rising power law continua, instead they seem to have roughly linear continua in physical units (i.e., W m⁻² μm⁻¹ versus μm). Therefore, for the RNe we used a modified version of our extinction measurement routine, in which we assume a linear continuum between 5 and 15 μm. This assumption is based on the observational results of samples of PDRs (e.g., Berné et al. 2007; Compiègne et al. 2008).

3.1.1. H ii Region Extinction

The extinction maps for the H ii regions presented (i.e., G11.94-0.62, G37.55-0.11, and M17) are shown in Figure 2 (along with the RNe, which will be discussed in the following section). The Horsehead PDR region was found to have essentially zero extinction measurable via the silicate feature.

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W49A and IRAS 12063-6259—The W49A and IRAS 12063-6259 extinction maps were shown and discussed at length by Stock et al. (2013, 2014), respectively. In general, each map was found to be consistent with prior measurements of stars on the line of sight or the nebulosity itself.

M17—The M17 extinction map displays reasonably consistent extinction levels throughout, ranging from A_K of 0.5 to a maximum of 2 in a region close to the main PDR in the northern half of the map. The northeastern corner of the map, which emits the majority of the PAH flux, has an average A_K of around 1. In the southern half of the map we masked out a protostar that dominated our extinction measurements.

G11.94-0.62—Extinction in G11.94-0.62 is strongly peaked around the core of the H ii region (at around A_K = 4), which drops off very strongly to less than A_K = 2 within a few pixels. The center of the map is affected by CH₃OH absorption at 9.8 μm, which is much narrower than the silicate absorption and is clearly evident in the spectra (e.g., Skinner et al. 1992; van Breemen et al. 2011; also Figure 3). In order to measure the silicate absorption for G11.94-0.62, we modified the general method described in our previous papers (e.g., Stock et al. 2013, 2014) such that the wavelength of comparison between the observations and the interpolated power law spectra was outside the methanol band, in this case at 10.2 μm rather than 9.8 μm. The spectra that were strongly affected by methanol absorption are not used in the remaining analysis, because the methanol absorption created difficulties in defining an effective spline continuum for isolating the PAH bands.

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G37.55-0.11—An almost complete ring of silicate absorption is visible around the center of G37.55-0.11. This could represent the projection of a spherical dust shell, because the central region still retains a high extinction level of around A_K = 2 compared to the silicate absorption ring, which peaks at around 3.5.

3.1.2. RNe Extinction

The specifics of our implementation of the spline method are identical to those presented by Stock et al. (2014). In short, this process involves computing a spline fit to a set of continuum points at wavelengths λ = 5.37, 5.46, 5.86, 6.58, 6.92, 8.28, 9.15, 9.40, 9.64, 10.14, 10.33, 10.76, 11.82, 13.18, 13.49, 14.43, and 14.74 μm, and subtracting this spline from the measured data to create a continuum-subtracted spectrum. In Figure 4 we show an example of the spline method applied to a W49A spectrum, as well as examples of the techniques used to decompose the 7.7 μm complex and the blend between the 12.7 μm PAH band and the [Ne ii] 12.8 μm atomic line.

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In general, two splines were defined for each spectrum, and they differ from each other by the inclusion of a spline point at 8.28 μm (between the peaks of the 7.7 and 8.6 μm PAH bands). The first plateau, which we refer to as the 8 μm bump, is simply the difference between the two splines. The remaining plateaus that underlie the 5–10 μm and 10–14 μm regions are defined by drawing a straight line underneath the features and integrating all of the flux under the general spline. This process is displayed graphically in Figure 4. Measurement of the narrower emission features proceeds using continuum-subtracted spectra.

Measurement of the PAH bands then proceeds in three distinct ways. The fluxes of the strong bands at 6.2, "7.7," 8.6, and 11.2 μm are found by direct integration. For the 6.2 and 11.2 μm bands these measurements are supplemented with Gaussian profile fits to determine the strengths of the weak 6.0 and 11.0 μm bands with which each are blended. The final 6.2 and 11.2 band fluxes are then found by subtracting the weaker bands from the total flux. While we have measured the 6.0 μm PAH band, for the sake of brevity we do not discuss it or the other weak PAH bands at 5.7, 12.0, 13.5, and 14.0 μm.

For the "7.7" complex, the flux was directly integrated to produce measurements of the 7.7 and 8.6 μm bands. However, because there is some disagreement in the literature as to how the plateau underlying the "7.7" μm complex is related to the PAH bands, this measurement was repeated for spectra that had been continuum subtracted using both the local and general spline—producing two measurements for both the 7.7 and 8.6 μm bands: with and without a spline point at 8.3 μm.⁶

For the H ii regions,⁷ the blend between the 12.7 μm PAH band and 12.8 μm [Ne ii] line is decomposed using the method proposed by Stock et al. (2014; and subsequently used by Shannon et al. 2015) in which the 12.7 μm emission is assumed to have the same spectral profile as the average PAH emission spectrum given by Hony et al. (2001). The Hony profile is scaled to the continuum-subtracted emission in a small window between 12.4 and 12.6 μm, where the emission is assumed to be dominated by the PAH band (shown in Figure 4(c)). The PAH flux can then be recovered by integrating under the feature profile and the 12.8 μm atomic line can then be measured using a simple Gaussian profile fit after the PAH emission profile has been subtracted. While it would have been possible to directly integrate the remaining flux to obtain the 12.8 μm line flux, we chose to use a Gaussian profile fit in order to ensure that the method of subtracting a scaled 12.7 μm PAH emission band shape does not affect the shape of the 12.8 μm line. The possible systematics affecting this measurement (i.e., the presence of very strong [Ne ii] emission) are discussed in detail by Shannon et al. (2015). For the RNe, the 12.7 μm band flux was calculated by directly integrating the complex and subtracting the flux of the 12.3 μm H₂ line that was fitted using a Gaussian profile fit superposed on a rising polynomial continuum.

The other atomic lines, where present, are all measured using Gaussian profile fits with either flat or polynomial continua, depending on the line. For example, the 8.99 μm [Ar iii] line sits on the rising wing of the 8.6 μm PAH band, and so requires a second-order polynomial continuum.

In all cases, uncertainties were computed by comparing the integrated feature flux and the rms noise of featureless areas of the continuum between 9.3 and 9.5 μm, 13.3 and 13.5 μm, and 13.7 and 13.9 μm, respectively. We adopted this approach such that each flux measurement has an associated signal-to-noise ratio measurement that is calculated in a uniform way across the sample, rather than using, for example, the fit-parameter uncertainties for bands fit with Gaussian profiles. In all subsequent discussion, the uncertainties quoted or shown for a band measurement were calculated in this way.

The standard correlations between PAH ratios obtained by "normalizing" each PAH flux by dividing by the flux of another PAH band in the same spectrum are presented in Figure 5; we use the 11.2 μm band to normalize the data. This procedure is performed to cancel out the effects of, for example, PAH abundance and distance. In Figures 5, 6, and 7 we have chosen to present the majority of the data as contours for the sake of clarity. This was achieved by binning the data for each object into 50 bins in both x and y directions across the range of values present. Subsequently these binned data were slightly smoothed using a 2 pixel boxcar average routine and plotted as contours. The contour levels are given in Table 3 and were adjusted such that they only exclude isolated outliers. In Figure 5, we compare each MIR emission component to 7.7GS/11.2. For this figure we included only the points where the signal-to-noise ratio (S/N) for the combined bands is greater than three. In Figure 5 we represent the data by grouping the points of several of the sources that display the same overall trends. The rationale for these groupings is clearer in the flux versus flux plots presented in the subsequent section, however the overall behavior within each group is also consistent in the traditional correlation plots. The first group represents the H ii regions and contains W49A, IRAS 12063-6259, G11.94-0.62, and G37.55-0.11. The second major group represents the RNe and contains NGC 1333 and NGC 2023. Finally, three sources resist classification into these groups: the RN NGC 7023 and the H ii region PDRs of M17 and the Horsehead nebula.

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7.7 versus 6.2—For the most well-known correlation—between the 7.7 and 6.2 bands—the expected linear relationship is recovered in each case (albeit with a slightly different gradient for the H ii regions sample). For the NGC 7023 points in this plot we show that the majority of the points can be well explained by assuming that the 7.7 versus 6.2 μm band intensity ratio is essentially constant, and varying the 11.2 μm band intensity (indicated by the black line). Each of the other groups shown are also consistent with such a straight line, albeit with slight variations in the average 7.7 versus 6.2 μm band intensity ratio.

7.7 versus 8.6 and 11.0—For these correlations there are some splits by object type. For example, for the 7.7 versus 8.6 correlation, the RNe points have significantly better correlations than the H ii regions. M17 and the Horsehead PDR in particular display almost no correlation, while the grouped H ii regions display smaller variation than the RNe group (NGC 1333, 2023) by around a factor of two. The latter is repeated by the 7.7 versus 11.0 band correlation plot, where the grouped H ii regions also show no correlation and the RNe display strong, linear correlations. This may be a beam dilution effect whereby the range of variation in the H ii region data is squashed because the measurement represents the average over a much larger physical area because the distance to the H ii regions is much greater than our other sources (see Table 1). Interestingly, both correlations display some curvature in the correlation produced by the NGC 7023 points—indicating that either (a) our decomposition is not totally isolating the 8.6 or 11.0 μm bands from the surrounding emission (i.e., both are systematically low creating a slight upward curve on the plots), or (b) that the 8.6 and 11.0 μm bands do not follow the 7.7 μm band or the 6.2 μm band.

7.7 versus 12.7—For the final PAH band considered, at 12.7 μm, we see variations in behavior between the different groups. There is evidence of at least two different gradients, one of which is defined by the RNe (plus some of the W49A points) and another displayed best by M17. Curiously, the 12.7 band appears to be much weaker for the Horsehead PDR, with most of the points having a 12.7/11.2 value of around 0.2, which is well below the average of all the points (0.4–0.5). Interestingly, for both the 8.6 and 12.7 versus 7.7 correlation plots, there are also a significant number of points for which there is variation in the 12.7/11.2 and 8.6/11.2 band ratios without any progression in the 7.7/11.2 ratio. In fact, the 7.7/11.2 band ratio seems to be about 1.5 in both cases, with the 12.7/11.2 ratio varying from 0.2 to 0.9 and the 11.0/11.2 ratio varying from 0.01 to 0.18. For the 11.0 ratio, this is exclusive to the RNe sample,⁸ while this trend is also seen for the H ii regions sample for 12.7.

Plateaus—In Figure 6 we show the behavior of the 5–10 μm plateau features with respect to the 7.7 μm PAH band.⁹ Here we see some consistency between object-types with the H ii regions sample, M17, the RNe sample, and NGC 7023 all showing a similar trend for the 7 μm plateau versus the 7.7 band. However, there appears to be a difference in gradients between the RNe sample and the H ii regions (including M17). Interestingly, the Horsehead PDR points appear to support no correlation between the plateaus and the 7.7 μm PAH flux. A subset of the NGC 7023 points coincides with the RNe in the 5–10 μm plateau versus 7.7 plot. The remainder of the points originate in the region of low 11.2 μm band fluxes, and hence are being drawn out to the top-right of the diagram.

Normalization—Boersma et al. (2013) showed that there is useful information regarding local physical conditions along the line of sight encoded into the PAH band flux to PAH band flux correlation. Hence, we examine our sample in such a way as well. However, in order to visualize each of the sources in the same parameter space, we scaled the fluxes from each object, because the pixel by pixel band fluxes between the sources vary more than three orders of magnitude. The weakest and strongest emission is associated with the Horsehead PDR and W49A, respectively. Using the 11.2 μm PAH band flux as an example, the W49A peak flux is 2.4 × 10⁻¹⁸ W m⁻², while the brightest Horsehead 11.2 μm PAH band measurement is 5.4 × 10⁻²¹ W m⁻². In order to consider the interrelationships of the fluxes of the PAH bands, we scaled each source's fluxes by the peak 11.2 μm flux, so as to yield 11.2 μm fluxes in the range of 0–1 for each source, while the 7.7 μm band fluxes, for example, vary from 0 to ∼4. This process maintains the intrinsic relationships between each band and is very different from the usual process of normalization (discussed in the previous section). So to summarize, the peak 11.2 μm PAH flux was used as a scale factor for all of the flux measurements for each pixel of each source, rather than dividing each pixel, for example, by its own 11.2 μm flux measurement as is traditionally done.

The peak 11.2 μm band fluxes used as scaling factors are presented in Table 4. The flux relationships between the MIR PAH emission components are presented in Figure 7. In these figures we only included points for which the band was detected with an S/N greater than three for both axes.

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NGC 7023—The reflection nebula NGC 7023 has been examined in terms of its flux–flux correlations by Boersma et al. (2014a). Therefore, we will not repeat the detailed findings of that paper here, although, we do make some comparisons later on. In general though, the NGC 7023 points agree with those found for the other RNe, with the exception of an additional component in many cases. This component is defined by weak 11.2 emission and thus forms the lower trend in the top panels of Figure 7. In the third panel of the top row of Figure 7, we show the two general trends identified for NGC 7023 by Boersma et al. (2014a), which they label the "PDR" line (upper) and the "diffuse" line (lower). Where appropriate, we adopt this convention throughout. Boersma et al. (2014a) attributed the observed bifurcation to changes in the 11.2 μm complex profile, specifically the appearance of extra emission appearing redward of 11.3 μm, which they refer to as the "red wing." In general, this split is evident for all of the relationships between ionized PAH bands (at 6.2, 7.7, 8.6, and 12.7 μm) and the neutral band at 11.2 μm, albeit very weakly for 12.7 versus 11.2. In addition, Boersma et al. (2015) found that the different gradients on this plot could be ascribed to different degrees of ionization, with the PDR line representing an ionized fraction of 0.4 and the diffuse correlation having an ionized fraction of around 0.7. Our figure shows that the Horsehead points seem to adopt a slightly steeper gradient than the PDR line, perhaps suggesting that the PAH molecules in the Horsehead nebula possess an ionization fraction even lower than the 0.4 found for the PDR correlation.

Groupings—In general, all of the H ii region points follow the "PDR" component identified by Boersma et al. (2014a), with the exception of some outliers seen for M17 and the Horsehead. There are some small inconsistencies in gradient though, with the H ii regions and M17 points forming slightly different gradients in the 11.2 versus 6.2 plot, and the Horsehead points forming an almost vertical trend in the 11.2 versus 11.0 plot. The NGC 1333, 2023 points (grouped together as "RNe") also follow the "PDR" component, albeit with a distinct bulge toward the diffuse component seen in the NGC 7023 points. In some cases, this bulge overlaps with the diffuse trend (particularly when considering the 11.0 μm band). In terms of the Boersma et al. (2014a) interpretation of this diagram, this would imply that a subset of the RNe points possess ionization fractions similar to that seen in NGC 7023. Finally, in the 11.2 versus 12.7 plot, we see that the Horsehead points actually follow the RNe points much better than the H ii regions or M17 samples, contrary to what might be expected.

Trends with the 7.7 μm band—The middle-right panel and bottom row of Figure 7 feature the relationships between the 7.7 μm PAH band fluxes (7.7GS) and the other PAH bands. For 6.2 and 8.6GS, all of the points are consistent with linear relationships between the bands; for 11.0 we see what amounts to a curve, where every increase in 7.7 leads to a slightly smaller increase in 11.0. This shape is effectively the same as that seen for the 11.2 versus 11.0 correlation (middle left panel of Figure 7), implying that either the 7.7 or 11.0 μm band measurement features a neutral component.¹⁰ The most interesting result is that the slope of the trend in the 7.7 versus 12.7 plot is different for each source, possibly reflecting the physical conditions. Again, this suggests that the 12.7 μm PAH band is composed of emission from both neutral and ionized PAH molecules. This idea has been suggested by several groups, particularly Candian et al. (2014) who showed that both ionized and neutral PAHs with an armchair structure could contribute to emission at around 12.7 μm. Subsequently, Boersma et al. (2014a) found observational evidence of this effect in NGC 7023, which we show here as a general behavior.

Our results can be summarized as follows.

• 1.  
  The H ii regions behave differently from the RNe. This was clearest when we consider the range of variations between the PAH ratios (Figure 5) where for the 8.6/11.2 and 11.0/11.2 ratios the RNe span a dynamic range twice that of the H ii regions. We note that our H ii region sample is systematically more distant than the RNe sample, and suspect that this compresses the dynamic range of the H ii region data by spatial dilution.
• 2.  
  There are systematic differences between the slopes recovered for the different groups present in many of the found correlations. For example, even in the most well-known correlation—6.2/11.2 versus 7.7/11.2—the H ii region and M17 samples have steeper slopes than the RNe.
• 3.  
  The data suggest that the 11.0 and 12.7 μm bands may arise from a combination of neutral and ionized PAH species. For the 12.7 μm band this effect is very clear in Figure 7, where the different groups have different slopes.
• 4.  
  NGC 7023 has unique PAH emission characteristics that seem to be driven by the weaker 11.2 μm band emission in the diffuse region (around a factor of four weaker for a constant intensity of the 6–9 μm bands), which causes the traditional correlation plots to have extended ranges (by at least a factor of two) and the flux versus flux correlation plots to split into two branches (labeled diffuse and PDR).

In Figure 7 we showed that the scaled flux correlations between most of the PAH bands had a variety of shapes, ranging from linear to bifurcated. The bifurcated correlations belong exclusively to NGC 7023, and this is likely due to its unique geometry with respect to our line of sight, producing a very sharp edge between two distinct PAH emitting regimes (e.g., Boersma et al. 2013, 2014a, 2015). The shapes seen in the scaled correlation plots for the other objects seemed to take two forms: linear and linear plus an offset peak (this pattern is clearest in the 11.2 versus 11.0 panel of Figure 7, where the offset peak is centered around x = 0.06, y = 0.5 for the RNe). In the following discussion we use the naming convention of Boersma et al. (2014a) and refer to the upper linear trend as the PDR material and the lower trend as the diffuse material. In these terms then, the linear component evident for most of the objects is very close to the "PDR" line defined by Boersma et al. (2014a), although different sources seem to have slightly different slopes. The second pattern consists of a section of the PDR line at lower intensity levels and an offset peak for the brighter regions. We understand this second pattern as being a mixture of environments along the line of sight, with the points within the offset peak being dominated (although to what degree we cannot say) by ionized PAH spectra from regions that are similar to the diffuse region seen for NGC 7023, and the linear component dominated by colder material behind the PDR front (i.e., experiencing a lower radiation field similar to the PDR regions of NGC 7023).

This observation can help us understand the seemingly uniform nature of the H ii region-scaled flux correlations, which all seem to fall into the category of "linear" correlations (i.e., dominated by emission from the PDR surrounding the H ii regions). However, if we assume that the much more distant H ii regions could possess environments similar to the NGC 7023 "diffuse" component, then one may expect a slight curvature in the linear correlations because the pixels containing the diffuse component would be diluted with normal "PDR" material to a greater extent—with the overall effect being a slight shift rather than forming a separate peak. In this case the PDR material is still the major component of the spectrum. We can test this idea immediately by examining Figure 7 for evidence of a curvature in the "linear" trends, with the expectation that the curvature would increase (i.e., move toward the combination of PDR and diffuse components seen for the RNe) for the closer objects with pixels covering smaller spatial areas (see Table 1 for the area of 1 IRS/SL pixel in square parsecs for each object). This trend is evident if we compare the H ii region sample (generally very distant, dominated by W49A points at distance >10 kpc) and M17 (almost a factor of 10 closer) in Figure 7; indeed, the M17 trend is curved toward the RNe points (this is especially evident in the top row, where 11.2 μm band is plotted versus 6.2, 7.7, and 8.6 μm band measurements). Interestingly, the Horsehead points match this pattern for the 6.2GS and 7.7GS bands versus the 11.2 μm band scaled flux correlation, but not the 8.6GS versus 11.2 μm scaled flux correlation.

We show this effect in Figure 8, in which we replicate the RNe contours of the 11.2 versus 8.6 μm scaled band intensity correlation plot and show best fits for the H ii regions and M17 data using both straight line and polynomial ($f(x)=a+{bx}+{{cx}}^{2}$) models, taking into account both x and y uncertainties calculated from the S/Ns. For the H ii region sample, the curved fit follows the straight line almost exactly, showing that there is almost no curvature; conversely for M17, a significant deviation from the straight line toward the secondary RNe peak is seen (with an accompanying increase in reduced ${\chi }^{2}$). There is a significant amount of scatter around these trends, which shows that even in pixels that have similar dispositions of environments along the line of sight, there can be significant changes in flux. Simple models like our polynomial fit cannot capture these changes (in fact, the scatter for the Horsehead points forces the best fitting curve model to turn over entirely). However our model does seem to capture the small changes that are present in more distant objects like M17. For the H ii regions that are around a factor of 10 more distant than M17, the diffuse component cannot be detected in this way, because if it is present its emission is overwhelmed by the PDR-like material dominating the beam.

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Earlier we commented that the Horsehead PDR points do not seem to follow the expected pattern of curvature despite being nearby, where it would be expected that the increased spatial resolution would yield a clearer detection of any diffuse component. The likely reason for this is, again, the size of the beam used to make our map, but in the opposite sense from the other H ii regions—the Horsehead region is so large on the sky that the diffuse region is not present in our map. Ochsendorf & Tielens (2015) show IRS/SL spectra for a selection of positions between the IC 434/Horsehead PDR interface and the ionizing star (their Figure 4), in which they show that the spectrum of their region 6, which several arcminutes outside our map, seems to have a PAH spectrum reminiscent of that seen for the "diffuse" emission from NGC 7023.

We have seen that the observed PAH band intensity ratios can be attributed mainly to changes in the overall ionization state of the emitting PAH molecules within the beam of each observation. These feature ratios should therefore be related to the physical conditions¹¹ in which the PAH molecules find themselves. Three studies have attempted empirical calibrations between the band ratios and physical conditions (e.g., Bregman & Temi 2005, Galliano et al. 2008 and Boersma et al. 2015), with each taking very different approaches: Bregman & Temi (2005) estimated the physical conditions in their sample based on other information (e.g., spectral types and geometry), Galliano et al. (2008) used only well-studied sources for which the physical conditions were known beforehand, and Boersma et al. (2015) used observations to calibrate the ionization fractions found using NASA Ames PAH database (Bauschlicher et al. 2010; Boersma et al. 2014b) with γ, using only the PAH spectra. We adopted a mixture of the first two approaches, using literature values where present and estimating other parameters with simple relationships between, for example, the stellar spectral types, G₀, and continuum radio emission measurements and the nebular n_e. Given the very different strategy employed by Boersma et al. (2015) to compute physical conditions, we present their results as a point of comparison because we would not necessarily expect their methodology to produce the same results as those presented here or by Galliano et al. (2008).

First, we restrict our sample to those sources where we believe that a simple estimate is physically meaningful (i.e., where we believe that the simple estimates of physical conditions correspond to the location of the dominant emitting PAH population). In some cases this is relatively straightforward because the geometry of the system is obvious. For example, the IC 434/Horsehead PDR front is at a known (large) distance from its exciting star and so experiences no strong gradients in G₀. Conversely, objects such as M17 are very difficult to treat in a spatially resolved way, because while there exists a prescription for the varying of G₀ throughout our field of view (based on the spectral types and distances of the stars in the central cluster; Sheffer & Wolfire 2013), we do not have any corresponding spatially resolved measurements of density or temperature. As such, we concentrate on including the geometrically simplest sources in our sample: the UC-H ii regions, including those measured as part of the W49A map, the ultra-compact H ii regions CC and DD (see, for example, De Pree et al. 1997; Stock et al. 2014).

The UC-H ii regions can be characterized using only radio observations of the free–free hydrogen emission continuum. Such observations typically provide us with (a) the stellar spectral type, (b) the radius of the H ii region, and (c) the hydrogen density of the H ii region. In order to convert these values into a measurement of the physical conditions in the PDR region, we employ the following relationships. First, the density of a PDR (in terms of the number of hydrogen nuclei n_H, regardless of ionization or molecular state) is about a factor of 30 higher than the electron density of the ionized region (e.g., Tielens 2010). We can convert this n_H into the election density, n_e, of the PDR by assuming that the dominant source of electrons is the ionization of neutral carbon atoms (e.g., that ${n}_{e}\;\simeq$ (C/H)n${}_{{\rm{H}}}\;\simeq$ 1.6 × 10⁻⁴n_H if we assume galactic abundances). Here we are explicitly following the method of Galliano et al. (2008), although this relationship is a fundamental part of the structure of PDRs. An average value for G₀ can be calculated from the stellar spectral type if we know the radius of the PDR. This relationship is given by Tielens (2010) as

$$\begin{eqnarray}&&{G}_{0}=625\displaystyle \frac{{L}_{*}\chi }{4\pi {d}^{2}},\end{eqnarray} \tag{ 1 }$$

where L_* is the stellar luminosity, χ is the fraction of far-UV photons, and d is the diameter of the H ii region. Using the relationships provided by Parravano et al. (2003) we can translate the stellar spectral type into the FUV luminosity ${L}_{*}\chi$, and thereby arrive at the results presented in Table 5 for our UC-H ii regions. This process is performed routinely in order to calculate G₀ for PDRs (e.g., Meixner et al. 1992; Stock et al. 2015). The final parameter, T, only appears in its square root, which means that variations within the small range of temperatures physically plausible for PDRs, such as those studied here, only change γ by around 10%, with a typical temperature being around 400 K. Therefore we adopted a value of 10% as the uncertainty of the calculated γ factors. For each source we calculated the 6.2/11.2 band intensity ratio by finding the average and standard deviations of the 6.2/11.2 band intensity ratios of all of the associated spectral pixels.

Table 5.  Physical Conditions for UCH ii Regions

Object	Spectral Type	PDR Radius (pc)	H ii Density (cm−3)	log(G0)	${n}_{e,\mathrm{PDR}}$	T (K)	γ
W49A/CC	O6	0.09	2700	4.67	13	400	2270
W49A/DD	O6	0.09	3100	4.67	15	400	1977
G37.55-0.11	O6	0.06	12000	4.38	58	400	1070
IRAS 12063-6259	O6	0.13	1000	4.31	5	400	2746
G11.94-0.62	O7.5	0.02	61000	5.14	293	400	1192
Horsehead PDRa	O9	3.7	⋯	2	0.15	400	105
Galliano et al. (2008) Sources:
NGC 2023	B1.5	⋯	⋯	4.17	16	750	800
NGC 7027	WD	⋯	⋯	5.77	1600	2000	520
Orion Bar	O6	⋯	⋯	4.60	8	500	3519

Note.

^aAll values from Ochsendorf & Tielens (2015).

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The data from Table 5 are shown in Figure 9, along with the points and linear regression from Galliano et al. (2008). Four of our UC-H ii regions are consistent with the Galliano et al. (2008) data: W49A/CC, W49A/DD, G37.55-0.11, and IRAS 12063-6259. The remaining sources (G11.94-0.62 and the Horsehead) deviate from the trend, appearing above the line (by factors of 2 and 4, respectively). We first investigate possible systematics affecting our calculation of γ. The key parameter that could strongly influence the γ values is the size of the H ii region as measured from the radio data. This parameter strongly affects the value of G₀ without changing n_e. For the UC-H ii region radii we used observations by Wood & Churchwell (1989) for G11 and G37, De Pree et al. (1997) for the W49A sources, and Martín-Hernández et al. (2003) for IRAS 12063-6259. IRAS 12063-6259 is a complex source with three separate peaks in the radio map (Martín-Hernández et al. 2003). In order to include this source, we measured the approximate size of the northern peak, which shows the strongest emission and is roughly circular. For the W49A sources, we did not use the radii quoted for the regions directly, because the low resolution radio observations of those regions gave very different values (a factor of three larger) than the radii given for the very similar sources (in terms of stellar spectral type and density) observed in high-resolution mode. The numbers adopted and quoted in Table 5 refer to this average of the high-resolution observations of similar sources in W49A (i.e., same spectral types and densities). In order to force the G11.94-0.62 point to match the Galliano et al. (2008) trend, we need to reduce the radius of the H ii region by 40%. While Wood & Churchwell (1989) do not quote uncertainties on their measurements, it is clear from inspection of their imagery (Wood & Churchwell 1989, Figure 5(a)) that the emission region is larger than the 05 radius implied by a 40% reduction in size. In addition, for the Horsehead PDR, the γ value that was calculated by Ochsendorf & Tielens (2015) is even more strongly discrepant, with no similar arguments regarding size, temperature, or G₀; it is clear that some objects can strongly deviate from the Galliano et al. (2008) trend.

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This idea is further demonstrated by the Boersma et al. (2015) calibration of the PAH ratio and γ (shown in Figure 9 as a blue line). The relationship found by Boersma et al. (2015) does not match any of the points used by Galliano et al. (2008) or our H ii regions sample. That said, the Horsehead and G11 are closer to the Boersma et al. (2015) relationship than the Galliano et al. (2008) fit. Boersma et al. (2015) attribute this to differences in the decomposition of the bands (i.e., that Galliano et al. 2008 include the 11.0 μm band flux in their 11.2 μm band measurement). However, our decomposition does differentiate between the two bands, and we find that the 11.0 μm band is on average around 5%–10% of the strength of the 11.2 μm band (e.g., Figure 5). This is not enough to explain the difference in Figure 9, which is about 50%. The elevated NGC 7023 PAH band ratios found by Boersma et al. (2015) are consistent with those found for NGC 7023 in this paper (and largely at greater 6.2/11.2 values than we have shown in Figure 9). This observation leaves us with two options: either the physical conditions in NGC 7023 are far more extreme than predicted by Boersma et al. (2015) or the relationships between the PAH ratios and physical conditions are more complex than that expressed by γ. Given that other sources in our sample—noticeably the Horsehead PDR with its extremely low radiation field strength—do not fall on the Galliano et al. (2008) trend, it seems that the second scenario is the most likely.