THE ARIZONA RADIO OBSERVATORY CO MAPPING SURVEY OF GALACTIC MOLECULAR CLOUDS. V. THE SH2-235 CLOUD IN CO J = 2 − 1, ¹³CO J = 2 − 1, AND CO J = 3 − 2

The subject of this paper is the molecular cloud that lies in the northern part of the Auriga OB1 association toward the galactic anti-center (R.A. (2000) = 05^h40^m, decl. (2000) = +35°50'; l = 1735, b = +26). Within or near this cloud are several visible H ii regions, cataloged by Sharpless (1959) as Sh2-231, -232, -233, and -235. (Sh2-234 lies to the south of the H ii region group within the molecular cloud and is not included in this study.) Of these four H ii regions, Sh2-235 is optically the most prominent because of its surface brightness and size, so the associated region is often referred to simply as the Sh2-235 complex. Observations (through 2008) of this "complex," and of the anti-center region in general, are summarized by Reipurth & Yan (2008). They present optical images showing the relationship among the nebulae and massive stars that recently formed there—see their Figures 1 and 5. The most probable distance to the molecular cloud and associated H ii regions is 2.0 ± 0.3 kpc (Montillaud et al. 2015), based on various published distances to the ionizing stars (Evans & Blair 1981; Porras et al. 2000; Ladeyschikov et al. 2015). This distance places the cloud in the middle of the Perseus spiral arm (Reid et al. 2014). We will assume a distance of 2.0 kpc in this paper. At this distance, 1' corresponds to a linear distance of 0.58 pc in the plane of the sky.

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For molecular cloud studies, the galactic anti-center has the advantage of being relatively clean in kinematic terms, in contrast to the first and fourth galactic quadrants. There are few molecular clouds that are seen along the line of sight yet lying at different distances from the object of interest, so interpretation of the maps is not significantly complicated by overlapping velocity components. The Sh2-235 complex is an excellent example of a GMC⁶ being substantially disrupted by the formation of massive stars that ionize H ii regions throughout the cloud. Besides direct dissociation and ionization of the molecular gas close to the ionizing stars, the subsequent expansion of the ionized gas has opened large cavities in the remaining molecular gas. In the Sh2-235 cloud complex, we see H ii regions with diameters from ∼30' to <1' (∼17 pc to <0.6 pc), indicating a range of ages and densities. Surrounding these are molecular features that appear to be partial shells or filaments possibly swept up by the expanding ionized gas. Our high spectral resolution allows us to assess the dynamical state of the cloud and to isolate features in three dimensions of six-dimensional position–velocity space. Such analyses will allow us to test whether star formation is being initiated by compression of the molecular gas, a process often referred to as "triggering." For example, Ladeyschikov et al. (2015) have argued, based in part on data from the present study, that a "collect and collapse" process at the compact H ii region Sh2-233 has led to recent star formation on the boundary of the ionized gas.

The Sh2-235 cloud complex has not been well-studied by the Herschel and Spitzer infrared satellites. Only selected areas, mostly concentrating on the bright H ii regions and immediate vicinity, have been observed, in contrast to the extensive set of Herschel and Spitzer data available for the other clouds that we have observed in this series (W51, W3, NGC 1333, Serpens Main). For example, a limited region of about 20' centered on the Sh2-235 H ii region was studied by Dewangan & Anandarao (2011), who cataloged young stellar objects (YSOs) and classified them according to evolutionary state, using Spitzer IRAC images and ground-based JHK band imaging. Chavarria et al. (2014) presented an extensive analysis of essentially the same field in the Spitzer images but with deeper JHK imaging, and thus were able to identify about three times as many YSO candidates as Dewangan & Anandarao (2011). These studies were limited to about 0.15 square degrees centered on Sh2-235. Infrared point-source catalogs with full-sky coverage now make it possible to identify at least the more luminous candidate YSOs within the entire ∼1 square degree region that we have mapped. We use the 2MASS and WISE databases, along with an algorithm by Marton et al. (2016), to find YSO candidates associated with the Sh2-235 molecular cloud. With at least the more massive YSO candidates identified, we can begin to examine the relationship between current star formation activity and the morphology of the CO emission and ionized gas.

Procedures for the J = 2 − 1 line observations were identical to those described in Bieging et al. (2014). The receiver was the dual-polarization ALMA Band 6 prototype sideband-separating mixer system (Lauria et al. 2006). The spectrometer was a filterbank with 128 channels of 0.25 MHz bandwidth and separation (corresponding to a velocity resolution of ∼0.34 km s⁻¹ for the J = 2 − 1 lines), in each of the two polarizations and two mixer sidebands. The CO line at ∼230 GHz is detected in the mixer upper sideband and the ¹³CO line at ∼220 GHz in the lower sideband. Each line is observed in both horizontal and vertical linear polarizations, providing independent maps of the emission, which are averaged together to reduce the noise by $\sim 1/\sqrt{2}$. Observations were made during 2010 March–2010 April. The field to be mapped was divided into contiguous 10' × 10' "tiles," each of which was observed in the standard On-The-Fly (OTF) scanning mode. The data were calibrated and processed as described in Bieging et al. (2014). The line intensity calibrator was the compact molecular source W3(OH), with main-beam brightness temperatures and integrated line intensities as given in Bieging & Peters (2011). Telescope pointing was checked and corrected as necessary approximately every 2 hr. The typical pointing error was <5''. Since the transitions of CO and ¹³CO are observed simultaneously through identical telescope optics and separated in the sidebands of the mixer (see Lauria et al. 2006), the registration of the two isotopologue maps is guaranteed to be correct, ensuring the fidelity of CO/¹³CO line ratio maps, for example. The pointing errors are in any case a small fraction of the diffraction-limited beamsize (FWHM ≈ 32'').

We applied a modest amount of spatial smoothing to the J = 2 − 1 maps, as done in other papers in this series (see, e.g., Burleigh et al. 2013), by convolution of the maps with Gaussian kernels. The purpose of this smoothing was to make both the CO and ¹³CO maps have the same resolution (since the diffraction-limited beam sizes differ by the ratio of the line frequencies, ∼5%), and to reduce the noise per pixel. The effective resolution after convolution is 38'' (FWHM), or 0.37 pc at the cloud distance, for both isotopologues. All of the J = 2 − 1 data presented here have been smoothed to this resolution.

Both the CO and ¹³CO J = 2 − 1 lines were observed with 0.25 MHz filters yielding ∼0.34 km s⁻¹ velocity resolution, but since the line rest frequencies differ by ∼5%, the velocity sampling is not the same for the two isotopologues. Therefore, we resampled the maps by third-order interpolation in velocity on identical LSR values at 0.15 km s⁻¹ intervals, i.e., slightly better than Nyquist sampling.

The observed region of the molecular cloud extended over 70' × 50' (R.A. × decl.), or 41 pc × 29 pc at the cloud distance of 2.0 kpc. Our maps cover the bulk of the CO emission, though the bottom row of tiles was not completely filled out where the line emission appeared to be fading out, due to constraints on observing time. We also observed one additional tile above the topmost complete row, to follow an apparent extension of the emission, but did not fill out a full row due to time constraints. The rms noise in each pixel, computed over a velocity range that is free of CO emission, is uniform to about 30% over the map. The average rms is 0.10 K for CO and 0.12 K for ¹³CO.

Observations of the J = 3 − 2 line of CO, at a frequency of ∼345 GHz, were made using the same telescope with a new multi-pixel focal plane array of superconducting mixers ("SuperCam") during the period 2014 April 5–10. For a description of the instrument, see Kloosterman et al. (2012). In brief, the receiver consists of a square array of 8 × 8 superconductor-insulator-superconductor mixers, each with a cooled first-stage IF amplifier. The spectrometer was a custom-built digital Fourier transform spectrometer, which provided 900 spectral channels with a frequency spacing of 0.2686 MHz, or velocity resolution of 0.233 km s⁻¹, for each of the 64 mixers in the array.

Each mixer was calibrated with respect to a fiducial mixer near the center of the array by comparison of measured mixer responses on standard sources. The telescope beam efficiency at the fiducial mixer was measured by observations of Mars, which gave a value of 0.70, with an rms scatter of 1% over multiple measurements. Allowing for systematic calibration errors, we adopt a telescope beam efficiency of 0.70 with an estimated uncertainty of 5%. This value is applied to convert the map to main-beam brightness temperature.

The measured telescope beamwidth was 24'' (FWHM), consistent with the expected diffraction limit and mixer feed horn design. The beam pattern does not show any sign of an error beam or extended large sidelobes, consistent with the measured beam efficiency and the primary reflector surface accuracy, where the rms error of the 10 m paraboloidal surface is ∼25 μm.

Mapping of large areas was done by OTF scanning, with the raster pattern chosen to ensure that each independent pixel in the mapped field is sampled by several of the mixers. The area mapped was covered in several sections, where the telescope was scanned over ∼20'-wide sections in R.A., each extending typically 60' in declination. The sections overlapped in most cases, to reduce the noise. The sections were combined onto a single large map grid with 10'' × 10'' pixels. The data were processed in essentially the same manner as the J = 2 − 1 observations. Spectra were weighted by the inverse of the variance of the noise as determined by the rms of the baseline fit. Only those mixers whose scans sampled a given map position within the convolving kernel contributed to the weighted average spectrum in the final gridded map. Consequently, areas near the beginning and end of the telescope scan, and at the top and bottom rows of each map section, were not as well sampled as the inner parts of the OTF raster pattern, and therefore showed significantly higher noise (i.e., the map edges are vignetted). We trimmed the final map to omit the excessively noisy vignetted regions. Also, not all 64 mixers in the array were in operation, and some had excessive noise and thus were omitted from the data processing. These missing mixers produced some systematic variations in the noise level over the final map due to differences in the effective integration time at different pixels.

To mitigate the effects of non-uniformity in the noise, at least on small spatial scales, we have smoothed the images with a Gaussian kernel with a FWHM of 20'', or 2 pixels in diameter, to reduce the noise and improve the uniformity but without sacrificing much angular resolution. The effective resolution of the smoothed maps is 31'' (FWHM) or 0.30 pc. Figure 1 shows a map of the rms noise for the smoothed image, computed over a range of velocities without CO emission. The central part of the mapped area has the lowest noise due to substantial overlap in the OTF mapping sections. Other variations are a result of variable weather conditions during the observations. Horizontal striping is notable in sections that had no overlapping OTF regions, and where mixers omitted due to excessive noise created variations in the uniformity of the total integration at each pixel. It should be emphasized that even though the smoothed map has some pixel-to-pixel variation in the rms noise, the calibration of the spectra is uniform across the map. The spatial structure of the CO J = 3 − 2 emission is correctly represented, even if the noise levels vary somewhat with position.

Figure 2 shows the spectra of the three observed CO lines, averaged over the entire mapped areas, for CO and ¹³CO J =2 − 1 (left panel) and CO J = 3 − 2 (right panel). All three lines show a roughly Gaussian central component and a wing of emission on the redshifted side. The J = 2 − 1 ¹³CO line is about five times weaker and has a narrower Gaussian center than the CO line. These differences, largely a consequence of the differences in opacities between CO and ¹³CO, are typical of the CO and ¹³CO isotopologues as observed in other molecular clouds. The CO J = 2 − 1 and 3 – 2 lines have nearly the same line shape, though the redshifted wing in the J = 3 − 2 transition is weaker relative to the peak compared to the J = 2 − 1 transition.

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Since the lines of the most abundant isotopologue, CO, are generally quite optically thick for our observed transitions, the peak observed brightness temperature is a useful indicator of the cloud kinetic temperature, assuming that the lower CO rotational transitions are collisionally excited and near thermal equilibrium. Under typical molecular cloud conditions of density and temperature, these assumptions are likely to be reasonable. In Figure 3, we show a map of the maximum observed brightness temperature for the CO J = 2 − 1 transition. The CO map (left panel) may be considered as an indication of the gas temperature distribution. The abundant CO isotopologue is detected at low column densities such that the line may not be optically thick, but nevertheless indicates the presence of molecular gas. In the right panel of Figure 3, we show the Digital Sky Survey II red image of this region, with selected contours of peak CO J = 2 − 1 brightness temperature overlaid. The optical image is dominated by nebular emission from the H ii regions, as well as bright stars. One prominent feature in the left panel is the large hole centered near R.A. 05^h39^m30^s, decl. 35°56'. Figure 3 (left) shows the maximum CO brightness temperature regardless of velocity, so the lack of emission means that this area is nearly devoid of molecular gas. This gap in the molecular gas coincides with the location of the H ii region Sh2-231. In contrast, the brighter H ii region Sh2-235 is centered close to the brightest CO emission at R.A. 05^h41^m, decl. 35°50'. The peak CO brightness temperatures near this more compact, presumably younger H ii region are in the range ∼30–45 K, indicating that some significant heating of the molecular cloud is occuring close to the ionized gas.

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The peak brightness temperature of the CO J = 3 − 2 map is shown in Figure 4. The features are very similar to the J = 2 − 1 map, and have similar values for peak temperature, consistent with the J = 2 − 1 and 3 − 2 CO lines both being optically thick over the bulk of the molecular cloud.

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By comparing on a pixel-by-pixel basis the peak intensities of the three observed transitions, we can assess whether the observed CO rotational levels are populated in near-LTE conditions. In the left panel of Figure 5 we plot the peak brightness temperature of the CO J = 3 − 2 versus the J = 2 − 1 lines. The J = 3 − 2 map has been smoothed and re-gridded to match the resolution (38'' FWHM) and spatial sampling of the J = 2 − 1 map. Pixels where the peak intensity is <5 × rms are omitted. The green diagonal lines show the loci of constant brightness temperature ratios. The red curved lines show the loci expected for optically thick emission where the excitation temperatures of the J = 3 − 2 and J = 2 − 1 lines are in the ratios of the red labels, i.e., the red curve for 1.0 corresponds to LTE, the lower curves correspond to sub-thermal excitation, and the higher curves correspond to super-thermal excitation. Here we have calculated the red curves using the definition for the "radiation temperature" in which the observed maps are calibrated, namely

$$\begin{eqnarray*}&&{T}_{R}=[{J}_{\nu }({T}_{\mathrm{ex}})-{J}_{\nu }({T}_{\mathrm{bgd}})][1-\exp (-\tau )],\end{eqnarray*}$$

where ${J}_{\nu }(T)\equiv (h\nu /k)/[\exp (h\nu /{kT})-1]$, τ is the line optical depth at the peak, and we assume the background radiation is only the CMB, so T_bgd = 2.73 K. For the left panel of Figure 5 we assume that both of the CO lines are optically thick so that $\exp (-\tau )\approx 0$. The majority of points in the graph cluster around the line with T_ex(3 − 2)/T_ex(2 − 1) = 0.9, suggesting that the CO energy levels are slightly sub-thermally populated for J > 2, but are not far from LTE. A handful of pixels appear to have somewhat super-thermal excitation, which may result from proximity to hot stars, as will be discussed below in Section 3.4.

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If the observed CO and ¹³CO transitions are close to LTE, then the intensities of the J = 2 − 1 isotopologues should indicate both the excitation temperature and the line optical depth. In the right panel of Figure 5, we compare the peak T_R values of the J = 2 − 1 CO and ¹³CO maps for each mapped pixel. (Pixels where the peak intensity is <5 × rms are omitted.) The red curves show the loci of values expected for constant T_ex, assumed to be the same for both isotopologues, for a range of CO optical depths from 1 to 100. The green lines are loci of constant CO J = 2 − 1 optical depth, and we assume a CO/¹³CO abundance ratio of 80 (discussed in Section 3.5 below).

The integrated intensity (or zeroth moment) is another useful quantity to show the distribution of the molecular emission. In Figure 6 we plot the integrated line intensity for the 2 isotoplogues in the J = 2 − 1 transitions. Both maps are integrated over the full range of velocities that show emission, from −28 to −2 km s⁻¹. These maps generally resemble those of the peak line intensity (Figure 4), but with differences that must depend on the width of the lines. For ¹³CO, the emission is not very optically thick, as will be shown in Section 3.5 below, so the integrated intensity is a fair measure of the total integrated CO molecular column density. If the ¹³CO abundances were constant throughout the cloud, then the integrated ¹³CO map would be an indicator of the total gas column density. We also show, as colored crosses and circles in Figure 6, the positions of candidate YSOs that were identified from analyses of the 2MASS and WISE all-sky infrared point-source catalogs (Marton et al. 2016). These objects will be discussed in more detail in Section 3.8.

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A map of intensity for the J = 3 − 2 line of CO, integrated over the same velocity range (−28 to −2 km s⁻¹), is shown in Figure 7 with the same set of symbols marking stellar objects as in Figure 6.

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Figure 8 shows CO J = 2 − 1 position–velocity maps in R.A. versus LSR velocity, for six cuts at constant declinations (cuts are shown by the horizontal white lines in Figure 6, left panel). This display of the data shows that the dominant CO feature, centered near −20 km s⁻¹ (LSR) extends over nearly the entire range mapped in R.A., with a velocity gradient from more to less negative velocities going from east to west (decreasing R.A.). For example, at decl. = +36° 07', the main CO emission shifts from −24 km s⁻¹ at R.A. = 05^h 42^m 30^s to −17 km s⁻¹ at 05^h 37^m 30^s, implying a velocity gradient of ∼0.2 km s⁻¹ pc⁻¹ in R.A. The structure of the position–velocity maps is more complex than can be described simply by linear gradients, however. Such complexity would be expected for a kinematically disturbed cloud being buffeted by multiple expanding H ii regions. Weaker CO emission is also evident at more restricted ranges of R.A. for velocities nearer to 0 km s⁻¹, which are presumably from smaller molecular clouds nearer to the Sun.

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A critically important feature of this study is the combination of sensitivity and high spectral resolution, which permits an analysis of the kinematics and dynamical state of the molecular gas. Such an analysis is not possible with observations of the dust thermal continuum, as measured by spacecraft such as Spitzer and Herschel, where the observed emission may originate from a whole range of kinematically distinct dust components with different positions, physical properties, and velocities along a single line of sight.

In Figures 9–11, we show maps of CO and ¹³CO J = 2 − 1, and CO J = 3 − 2 emission, respectively, in selected LSR velocity channels indicated in the top left corner of each panel. The J = 2 − 1 maps are sampled at 1.35 km s⁻¹ intervals and averaged over 0.45 km s⁻¹. The CO maps (Figure 9) cover a larger velocity range than the ¹³CO maps (Figure 10) because the CO line has a greater velocity width, but the same sampling of velocity space is presented for both isotopologues. The CO J = 3 − 2 maps (Figure 11) are averaged over 0.7 km s⁻¹, and also spaced by 0.7 km s⁻¹, i.e., the velocity coverage is contiguous. In all three figures, the intensity scale has a square-root stretch to emphasize the lower brightness emission. All of the figures are calibrated in main-beam brightness temperature in Kelvin. The J = 2 − 1 images have an angular resolution of 38'' (FWHM) and a typical rms noise of 0.10 K for the displayed velocity width. The J = 3 − 2 images have a 31'' resolution and an rms noise of 0.31 K for the displayed velocity width of 0.7 km s⁻¹ (averaging over three independent velocity channels).

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All of the velocity channel maps show that the molecular gas is in a highly disturbed state, with numerous small-scale clumps and filaments, as well as large holes or gaps between the molecular gas. The most prominent holes are at the positions of the dominant H ii regions, especially at Sh2-231 as noted above, but the other ionized regions also appear to be affecting the associated molecular gas. The structure of the cloud changes significantly with radial velocity, as expected if the gas is in a highly turbulent state, or has organized motions such as expanding shells at the boundaries of the H ii regions. The highest brightness CO is associated with the more luminous stars as shown in Figures 6 and 7.

Besides numerous small-scale features, there are regions of extended diffuse emission at velocities near the line center (e.g., in the range −21 to −15 km s⁻¹) extending over ∼10'–20' (corresponding to 6–12 pc at the cloud distance of 2.0 kpc), where the CO brightness temperature is ∼7–10 K. This diffuse, extended cold gas likely contains most of the cloud mass, as has been shown for other GMCs mapped in lines of CO (e.g., Heyer et al. 1996). The diffuse gas shows up best in the main CO isotopologue, in both the J = 2 − 1 (Figure 9) and J = 3 − 2 (Figure 11) lines. The ¹³CO J = 2 − 1 line (Figure 10) does not reveal this diffuse cold material as well because of the lower abundance and optical depth of ¹³CO compared to CO. In contrast to the diffuse emission, all of the compact, bright features are clearly seen in all three of the mapped lines, consistent with high optical depths and excitation temperatures.

If we assume that both the J = 2 − 1 and J = 3 − 2 lines of the main isotopologue (CO) are optically thick and at the same excitation temperature everywhere in the cloud, then the maps should have the same brightness temperatures everywhere. Comparing the line intensity ratios as a function of position and velocity can in principle show areas where one or both of these assumptions fails. In Figure 12, we present ratio maps of the CO J = 3 − 2/J = 2 − 1 brightness temperatures. The J = 3 − 2 map has been convolved to match the resolution of the J = 2 − 1 map (38'' FWHM), and resampled on the same velocity grid. The panels in Figure 12 show velocity channels, averaging over 0.45 km s⁻¹, at representative LSR velocities to illustrate the behavior of the line ratio. Pixels are blanked where the denominator, the J = 2 − 1 line, falls below 0.5 K (5σ). We also show in Figure 12 the locations of (1) the ionizing stars of the 4 H ii regions, (2) compact H ii regions, and (3) some luminous embedded IR sources with associated molecular outflows, all as white crosses with black outlines. The identifications of these objects and their coordinates are given in Table 1. Coordinates are from the SIMBAD database, with ionizing stars as given by Reipurth & Yan (2008), Boley et al. (2009), and Ladeyschikov et al. (2015). The ionizing stars and bright compact IR sources will likely act as heating sources for the associated molecular gas.

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Table 1.  Ionizing Stars, Compact H ii Regions, and IR Sources in the Sh2-235 Complex

Identifier	R.A. (J2000)	Decl. (J2000)	Sp. Type	Comment
HD 37737	05h42m3116	36°12'01''	O9.5IIIa	Ionizing star of Sh2-232
BD+35°1201	05 40 59.45	35 50 46.	O9.5Vb	Ionizing star of Sh2-235
Sh2-235A	05 40 53.33	35 42 22.	B0.5c	Compact H ii region
Sh2-235B	05 40 52.37	35 41 29.	B1Vd	Compact H ii region
Sh2-235C	05 40 50.3	35 38 23.	B0.5	Compact H ii region
CGO 103	05 39 45.64	35 53 56.	O9Vb	Ionizing star of Sh2-231
IRAS 05361+3539	05 39 27.7	35 40 43.	...	IR/outflow sourcee
IRAS 05358+3543	05 39 10.4	35 45 19.	...	IR/outflow sourcef
USNO-A2 1200-03588518	05 38 31.5	35 51 19.	B0.5Vg	Ionizing star of Sh2-233

Notes.

^abinary. ^bGeorgelin et al. (1973). ^cThompson et al. (1983). ^dBoley et al. (2009). ^eShepherd & Watson (2002). ^fBeuther et al. (2002, 2007). ^gLadeyschikov et al. (2015).

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The velocity moments of the spectrum can be useful for characterizing the gross properties of the emission, without assuming a specific line shape (e.g., Gaussian). The first moment (centroid) is a measure of the intensity-weighted mean velocity of the emitting gas. In Figure 13, we show the distribution of centroid velocities for the CO and ¹³CO J = 2 − 1 emission. The moment integral was calculated over the LSR velocity range (−28, −2) km s⁻¹. Pixels where the maximum line intensity within that velocity range was less than 0.5 K (5 × rms noise) are blanked. Most of the CO map (left panel) has a mean velocity of ∼−17 km s⁻¹, but a large area in the northeast of the map has a mean some 5 km s⁻¹ more negative, while a region to the south of Sh2-235 is redshifted relative to the bulk of the cloud, with a mean velocity of about −13 km s⁻¹. There are smaller regions with mean velocities discrepant from the cloud average, by ∼4–5 km s⁻¹.

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The CO J = 2 − 1 line is generally very optically thick, however, so the velocity centroid is not necessarily a good measure of the true bulk motion of the gas along a line of sight. The ¹³CO J = 2 − 1 line should be a better measure of the gas motions. In the right panel of Figure 13 we show the ¹³CO velocity centroid, also integrated over the same range of LSR velocities as the CO map. The ¹³CO centroid distribution shows more small-scale structure, perhaps consistent with the disturbed morphology of the velocity channel maps, and with turbulent motions resulting from the expansion of H ii regions. Gradients on the order of 5 km s⁻¹ over distances of ∼1'–2' (0.6–1.2 pc) are evident at several locations, especially near the dominant H ii region Sh2-235.

The second velocity moment, or dispersion (σ_V), gives a measure of the line width at each pixel. In Figure 14, we show maps of the CO and ¹³CO J = 2 − 1 velocity dispersions, where the moment integrals are computed over the same velocity range as for the first moment, and pixels with peak intensity ⩽5× rms are blanked. The moment integral makes no assumption about the line shape, though if the line profile were a Gaussian, then the FWHM equals 2.355σ_V. A large dispersion could indicate a broad single velocity component, but could also result from two or more narrow components with different velocities along one line of sight. Comparison of the left (CO) and right (¹³CO) panels in Figure 14 confirms that the CO line is generally broader than the ¹³CO line, shown in the distribution of second moment values plotted in Figure 15.

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The relative abundance of the CO and ¹³CO isotopologues is on the order of 50–80 for molecular clouds in the vicinity of the Sun (Milam et al. 2005). Therefore the ¹³CO line will have a correspondingly lower optical depth compared to the CO line, so even if the CO J = 2 − 1 line is optically thick, the ¹³CO line may be optically thin, or only marginally thick (τ ≈ 1). If we assume that both isotopologues have similar excitation conditions for the lower rotational levels, and that their relative abundances are constant throughout the cloud, then the observed intensity ratio is a nonlinear function of the CO line optical depth given by

$$\begin{eqnarray*}&&R\equiv \displaystyle \frac{{T}_{\mathrm{mb}}(\mathrm{CO})}{{T}_{\mathrm{mb}}{(}^{13}\mathrm{CO})}=\displaystyle \frac{1-\exp (-{\tau }_{\mathrm{CO}})}{1-\exp (-{\tau }_{\mathrm{CO}}/{f}_{12/13})}.\end{eqnarray*}$$

Here the intrinsic ratio of abundances is ${f}_{12/13}=n(\mathrm{CO})/n{(}^{13}\mathrm{CO})$, where n(X) is the density of molecular species X. An estimate of the ¹²C/¹³C isotope ratio in the interstellar gas at the galactocentric radius of Sh2-235 (∼10.5 kpc) is 80 ± 10 (Milam et al. 2005). Taking f_12/13 = 80, the observed line intensity ratio can be used to estimate τ_CO and ${\tau }_{13{CO}}$. For example, a ratio of R = 10 would imply τ_CO ≈ 8 for the simple homogeneous cloud model. R = 3 gives τ_CO = 32, and R = 1.58 would imply τ_CO = 80 and therefore τ_13CO ≈ 1, i.e., the ¹³CO J = 2 − 1 line is becoming optically thick for R ⩽ 1.6.

Figure 16 shows the CO/¹³CO intensity ratio for selected velocity channels, averaged over 0.45 km s⁻¹, and spaced at 1.35 km s⁻¹ intervals. The "heat" color palette is dark brown at R < 2, indicating very optically thick CO emission, with ¹³CO becoming moderately optically thick (τ ≳ 1). Positions of the YSOs extracted from the WISE and 2MASS catalogs (Marton et al. 2016—see Section 3.8 below) are marked with symbols indicating the evolutionary class. Generally, the youngest classes, class I and "flat," tend to lie within the high-CO opacity regions at some velocity. For example, note the cluster of class I objects at −16.55 km s⁻¹, associated with the Sh2-235A, B, and C compact H ii regions listed in Table 1.

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The comparison of the CO J = 3 − 2 and J = 2 − 1 intensities in Figures 5 and 12 indicates that the lower rotational levels of CO are not far from thermal equilibrium. We have therefore analyzed the CO and ¹³CO J = 2 − 1 maps using an LTE model that assumes that both lines have the same excitation temperature, and that optical depths along each line of sight are in the ratio of the adopted relative abundance of the two isotopologues, namely, CO/¹³CO = 80 and CO/H₂ = 1 × 10⁻⁴. We employed the task colden in the MIRIAD software package (Sault et al. 1995), using as input data the maps of peak CO and ¹³CO J = 2 − 1 brightness temperature (Figure 3), the ¹³CO integrated intensity (Figure 6), and the ¹³CO velocity second moment (Figure 14) multiplied by 2.355 to approximate a Gaussian FWHM. The task produces maps of the CO (and ¹³CO) excitation temperature, the ¹³CO optical depth, and the molecular hydrogen column density as outputs. We multiplied the total hydrogen density by 1.40 to correct for He and heavier elements in converting to a total gas column density.

The resulting map of CO (and ¹³CO) excitation temperature is shown in Figure 17. The bulk of the cloud has temperatures between 10 and 20 K, with smaller regions in excess of 30 K. These warmer areas are mainly associated with gas near the locations of the OB stars, compact H ii regions, and embedded luminous IR sources, marked with white crosses in the figure. The ¹³CO optical depth distribution is shown in Figure 18. The ¹³CO optical depth is ⩽1 over most of the map, and exceeds 2 in only a few pixels. We conclude that the ¹³CO line is not very optically thick anywhere in the cloud, so this basic LTE analysis using the relations plotted in the right panel of Figure 5 is reasonable. The total gas column density from this analysis is given in Figure 19. The total gas mass for the mapped region is 5.2 × 10⁴ M_⊙. Because our J = 2 − 1 maps have rms noise levels of ∼0.1 K, even with a 5× rms cutoff in the LTE calculation, the column density map has an excellent dynamic range (≲5–1400 M_⊙ pc⁻²). The distribution is far from uniform, with holes and voids located at the positions of the larger H ii regions (Sh2-231 and -232), and clumpy, high gas column density regions that are evidently associated with ongoing star formation, as indicated by the distribution of YSOs, which are discussed in the next section. It is striking that the ¹³CO optical depth map (Figure 18) shows a kind of "skeleton" of higher optical depth gas embedded within the relatively uniform excitation temperature map (Figure 17).

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The borders of the visible H ii regions are outlined by moderately high gas column densities, which suggests that the expansion of the ionized gas is compressing the molecular cloud where the two gas phases are in contact. This effect is particularly notable around Sh2-231, the large H ii region centered near R.A. 05^h39^m30^s, decl. 35°55'. There is also a prominent ridge of high gas column density that extends some 40' (∼25 pc) along a southeast–northwest line that is roughly tangentential to the shell around Sh2-231. This ridge contains several YSO candidates.

If we employ only an LTE excitation model in this analysis, the J = 2 − 1 transition has the virtue that the line emissivity is relatively insensitive to gas temperature, compared to the J = 1 − 0 or J = 3 − 2 transitions. This lack of strong temperature dependence results from the compensating effects of gas temperature on the line excitation temperature versus the CO partition function. For example, Ginsburg et al. (2011—see their Figure A1) calculate that the total LTE column density derived from a measurement of the ¹³CO J = 2 − 1 integrated intensity changes by a factor of only 1.25 for excitation temperatures between 10 and 40 K, about the range indicated by our CO J = 2 − 1 peak intensity map for the bulk of the cloud. The line emissivity goes through a shallow minimum at T_ex ≈ 17 K (corresponding to the upper state energy, E(J = 2)/k), so the derived LTE column densities are very insensitive to excitation temperature at typical cloud gas kinetic temperatures.

Although this LTE analysis may be a fair representation of the molecular gas distribution in the dense parts of the cloud, an important caveat is the effect of stellar radiation on the gas. The Sh2-235 complex has produced several OB stars, as evidenced by the H ii regions associated with the molecular cloud. These stars must also have an effect on the neutral gas by their UV radiation, which should have created photodissociation (or "photon dominated") regions in the outer parts that surround the dense molecular cores. An analysis of UV radiation effects is beyond the scope of this paper but we will present a more detailed treatment of radiation effects in a future work. It is almost a certainty that in a GMC such as the Sh2-235 complex, there is a substantial amount of mass that is not accounted for by a simple LTE analysis. The masses and gas column densities derived in this section must therefore be considered as only lower limits.

Molecular clouds in the galactic anti-center have received relatively less attention in wide-field infrared and submillimeter wavelength studies, compared to regions in the inner Galaxy, or in nearby clouds (d < 1 kpc). As a result, the census of candidate YSOs associated with clouds like the Sh2-235 complex is much less complete than those for regions included in the Spitzer Legacy surveys or the Herschel Key Projects. In recent work utilizing the all-sky infrared surveys of 2MASS (Cutri et al. 2003; Skrutskie et al. 2006) and the WISE satellite (AllWISE, Cutri et al. 2013), Marton et al. (2016) have identified ∼134,000 candidate YSOs over the entire sky. Their analysis uses a support vector machine (SVM) approach, based on artificial intelligence algorithms, to identify candidate YSOs and to differentiate them by spectral class, as an indicator of evolutionary stage. Marton et al. (2016) argue that their method is robust and very effective at rejecting contaminant objects such as external galaxies and galactic red giants (AGB stars), resulting in a clean list of YSO candidates over our CO mapping field. Based on the infrared spectral indices calculated from the 2MASS and WISE data, we use the classifications of Lada (1987) to identify (1) class 0/I (the youngest category, except that we cannot distinguish between the deeply embedded class 0 from class I, so these are lumped together); (2) "flat" SED sources; (3) class II; and (4) class III candidates. We have plotted symbols showing the positions of these four YSO categories in several of the preceding figures, including Figure 6 (CO and ¹³CO J = 2 − 1 integrated intensity), Figure 7 (CO J = 3 − 2 integrated intensity), and Figure 16 (velocity channel maps of CO/¹³CO J = 2 − 1 intensity ratio). Figures 6 and 7 show that almost all of the candidate YSOs are found at positions with large CO integrated intensities (in both J = 2 − 1 and 3 – 2 transitions), and most lie on bright ¹³CO integrated intensities. Figure 19 (LTE-derived gas column density) confirms that most of the youngest YSO classes (class I and "flat") are located at positions of high gas column density. The velocity channel maps of CO/¹³CO line ratios (Figure 16) allow us to identify the radial velocity of the gas that is associated with the YSOs, and to estimate the CO optical depth at those locations.

The all-sky survey by Marton et al. (2016), however, is limited by the sensitivity of the 2MASS and WISE data. We investigated the limiting magnitudes in the 2MASS J, H, K_s and WISE W1, W2, W3 and W4 bands for the SVM selection method in the entire Sh2-235 complex mapped in CO. Based on the grid of 200,000 YSO models of Robitaille et al. (2006) we estimated the minimum luminosity and mass of a YSO at a distance of 2 kpc that would be classifiable by the SVM method (Marton et al. 2016). The infrared fluxes depend on various other YSO parameters as well, such as the inclination and mass of the protostellar disk and the mass of the envelope around the YSOs. Depending on these parameters, we would be able to identify YSOs with a range of masses and luminosities for a given set of limiting magnitudes. In Table 2 we list the limiting magnitudes for the bands used in our statistical selection of Class I/II and Class III YSOs, and also the masses and luminosities for the faintest YSOs we could reliably classify in the Sh2-235 region. The observations are likely to be biased toward the earlier stages, because the infrared luminosity of the sources decreases with age.

Recent work with JHK band imaging that goes deeper than 2MASS has been published for subsets of the area we mapped in CO, thereby allowing the identification of a more complete list of YSOs, though it was over a more limited spatial extent. A study by Dewangan & Anandarao (2011) of a region ∼20' in size and centered on the Sh2-235 H ii region, combined Spitzer IRAC images together with point-source photometry from ground-based JHK photometric imaging to classify YSOs into class 0/I and class II. Chavarria et al. (2014) analyzed essentially this same region centered on Sh2-235 with the same Spitzer IRAC images but with deeper JHK imaging photometry. Given the deeper near-IR images, they were able to identify about three times as many YSO candidates as Dewangan & Anandarao (2011).

In Figure 20 we show a detail of the ¹³CO J = 2 − 1 integrated intensity map (from Figure 7, right panel) with the class I YSOs identified by Chavarria et al. (2014) plotted in the left panel and the class II objects in the right panel. The younger class I objects are strongly clustered on the brightest ¹³CO integrated intensity regions, which also coincide with the Sh2-235 main H ii region and with the group of three compact H ii regions and IR sources, called A, B, and C, that lie ∼8' south of Sh2-235 (see Table 1). The class II objects (right panel of Figure 20), in contrast, are more widely distributed over the region. This greater concentration of the younger class I YSOs on ¹³CO peaks has been found in many dense young YSO clusters, e.g., in the Serpens cloud (Burleigh et al. 2013).

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Chavarria et al. (2014) constructed maps of YSO surface density using a variety of spatial-relationship algorithms. In Figure 21 we show their contours of YSO density (in stars pc⁻²) plotted over the CO J = 2 − 1 peak brightness temperature in the left panel, and over the LTE model-derived total gas column density (in M_⊙ pc⁻²) in the right panel. The highest YSO surface densities generally coincide with the regions of greatest CO J = 2 − 1 brightness temperature and presumably, also the highest gas kinetic temperature. The highest YSO surface densities are also concentrated mainly on the areas with the greatest total gas surface densities.

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