THE ARIZONA RADIO OBSERVATORY CO MAPPING SURVEY OF GALACTIC MOLECULAR CLOUDS. II. THE W3 REGION IN CO J = 2–1, ¹³CO J = 2–1, AND CO J = 3–2 EMISSION

Figure 3 shows an image of the maximum main beam brightness temperature for the CO J = 2–1 line in the LSR velocity range −60 to −25 km s⁻¹, which covers the full range of emission from the Perseus arm clouds (e.g., Heyer & Terebey 1998). (There is weak, diffuse emission at velocities near 0 km s⁻¹ produced by local clouds, but we do not consider that in this paper.) In Figure 3, three areas of very bright CO emission stand out, and these are in the direction of three known regions of massive star formation: W3 Main, W3(OH), and AFGL 333. W3 North is another H ii region, containing a single O6 star (Feigelson & Townsley 2008) apparently associated with the W3 molecular cloud complex. In the south,² KR 140 is a diffuse H ii region (Kallas & Reich 1980) which is probably more distant than W3 but shows evidence of star formation now occurring in a swept-up shell of gas surrounding the H ii region (Kerton et al. 2001). The magenta contours in Figure 3 show the 1420 MHz continuum emission from the CGPS (Taylor et al. 2003), which traces here mainly the emission measure of ionized gas. The brightest continuum is from the W3 Main H ii region complex, with weaker diffuse emission extending out to a distance of a degree around the peak.

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Only ∼50% of the pixels in Figure 3 show CO emission greater than 0.5 K, which is about the 4σ level for the map and is a conservative lower limit to a detection threshold. The majority of the detected gas as seen projected on the plane of the sky has a relatively low CO J = 2–1 brightness temperature. Some 90% of the mapped area has CO peak brightness temperatures <6 K, as shown in the cumulative distribution of pixel values in Figure 4 (top left). The differential brightness temperature distribution (Figure 4, bottom left) shows a peak near 0.2 K due to the relatively large fraction (∼50%) of undetected pixels, with a nearly flat distribution extending from 1 K up to about 5.5 K, then declining toward higher temperatures. Less than 5% of the mapped area shows CO J = 2–1 emission brighter than 10 K.

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Figure 5 shows an image of the maximum brightness temperature in the ¹³CO J = 2–1 line, over the same velocity range as for CO in Figure 3. About 70% of the area shown in Figure 5 has T_mb < 0.5 K (see Figure 4, top right), which is ∼3.5 × the rms noise level per pixel and per velocity channel in the ¹³CO line. Only 10% of the pixels in the ¹³CO map have a peak brightness temperature >1.5 K.

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The integrated line intensities for CO J = 2–1 and ¹³CO J = 2–1 are shown in Figures 6 and 7. The emission spectrum in each pixel was summed over the velocity range −60 to −25 km s⁻¹, which is the range of velocities associated with the Perseus spiral arm material. The images are displayed in units of T_mb × velocity (K km s⁻¹). The integrated intensity images resemble the peak brightness temperature images (Figures 3 and 5). The integrated emission in both CO isotopologues is dominated by the three bright CO emission regions associated with W3 Main, W3(OH), and AFGL 333.

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Histograms of the distributions of integrated intensities for both CO and ¹³CO are shown in Figure 8. The majority of pixels have low integrated line intensities relative to the peak in each image. For CO J = 2–1, about 80% of the image has integrated intensities <50 K km s⁻¹, and for ¹³CO J = 2–1, a similar fraction has integrated intensity <10 K km s⁻¹.

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The gas kinematics are illustrated in Figures 9 and 10, which show the CO and ¹³CO J = 2–1 brightness temperature distributions averaged in 2 km s⁻¹ wide velocity intervals over the range from −54.5 to −31 km s⁻¹. This range covers essentially all the significant emission. Figure 9 shows that the CO emission is produced in very complex spatial structures which change dramatically with velocity across the line. There are areas of extended diffuse emission as well as many compact, barely resolved clumps. At 2.0 kpc, the distance to W3, the resolution of these maps (38'') corresponds to a linear size of 0.4 pc, so the numerous barely resolved features in the velocity channel maps must be subparsec in size.

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There is an overall gradient of the spatial distribution with velocity. The most negative emission, with V_LSR < −46 km s⁻¹, is mainly confined to roughly the southern half of the field. Diffuse emission to the southwest of W3 Main appears at higher velocities with V_LSR > −46 km s⁻¹. The brightest CO emission peaks lie along a line from SE to NW from AFGL 333 through W3(OH) to W3 Main/W3 North, a locus of clouds that was named the high density layer (HDL) by Lada et al. (1978; see also Megeath et al. 2008). The most negative velocities are in the vicinity of AFGL 333 and W3(OH). W3 Main and W3 North have the most redshifted CO of the HDL peaks, as Lada et al. (1978) noted from their low-resolution study. The W3 Main region has significantly broader lines than other positions in the map, consistent with the high level of massive star formation that has recently occurred there.

The corresponding velocity channel maps for ¹³CO J = 2–1, in Figure 10, show the same trends as seen in Figure 9, but there are many more blank pixels because the ¹³CO line is generally weaker and detected in fewer sight lines. The presence of many small, barely resolved features around W3 Main at the highest velocities is notable. These may represent relatively warm, high column density clumps associated with the current active star formation in the gas surrounding the IC 1795 OB association (Oey et al. 2005), which lies between W3 Main and W3(OH).

We calculated first-moment (or centroid) maps,

$$\begin{equation*} V_c(x,y) \equiv {\sum [I(x,y;V) \times V] \over \sum I(x,y;V)}, \end{equation*}$$

summed over the velocity range (− 60, −25) km s⁻¹, where I is the intensity (brightness temperature) at pixel (x, y) and velocity channel V. Figure 11 displays the velocity centroid map for CO J = 2–1, using a different color palette from the one used for the line intensity maps. Pixels with peak T_mb < 1.3 K are blanked.

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The velocity centroid map shows the overall trends in velocity gradient noted in Figures 9 and 10. The gas in the lower left is more blueshifted relative to the upper half of the map. There are notable "islands" of redshifted gas at the positions between W3 Main and W3(OH), and at (l, b) = (1344, +08), (1331, +09), and (1329, +07). The velocity gradient along the HDL from AFGL 333 to W3 North is clearly visible in the centroid map.

The velocity centroid map for ¹³CO is shown in Figure 12. Pixels with peak T_mb < 1.3 K are blanked. The same trends as in Figure 11 are evident but there are fewer pixels bright enough to show the full area of the clouds.

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We also calculated the second moment (or velocity dispersion) of the spectra at each map pixel,

$$\begin{equation*} \Delta V(x,y) \equiv \left\lbrace {\sum [I(x,y;V) \times (V-V_c)^2] \over \sum I(x,y;V)} \right\rbrace ^{1/2}. \end{equation*}$$

The typical second-moment dispersions are 3–4 km s⁻¹, corresponding to a typical Gaussian FWHM line width of ∼7 km s⁻¹ for both CO and ¹³CO. A small fraction of pixels show second-moment values up to ∼12 km s⁻¹, mainly in the direction of W3 Main. There the line profiles are typically not well represented by a single Gaussian component, indicating that the gas is kinematically disturbed by the associated massive stars and H ii regions.

We have constructed maps of the CO/¹³CO J = 2–1 calibrated line intensity ratios from the data sets presented above. Our data are especially well suited for this kind of analysis because both isotopologues are observed simultaneously through the same telescope optics, so the registration of the two images is guaranteed, even if there are telescope pointing errors (which we argue are small in any case). The intrinsic angular resolutions of the observations differ by the ratio of the line frequencies, and we correct for this difference by convolving the raw maps with appropriate kernel functions to put both isotopologues at an effective resolution of 38'' (FWHM), as described in Section 2. The intensity ratio may be a useful diagnostic of the mean CO optical depth within a map resolution element. If, for example, the intrinsic ratio of abundances is f_12/13 = n(CO)/n(¹³CO), where n(X) is the density of molecular species X, and if we can assume that the abundance ratio is constant within a molecular cloud, then the ratio of line optical depths through the cloud will have this same ratio, provided CO and ¹³CO have the same excitation conditions at each point in the cloud. If so, then the ratio, R, of observed line brightness temperatures (neglecting any background continuum) should be

$$R \equiv {T_{{\rm mb}}({\rm CO})\over T_{{\rm mb}}(^{13}{\rm CO})} = {1 - \exp (-\tau _{{\rm CO}})\over 1 - \exp (-\tau _{{\rm CO}}/f_{12/13})}.$$

An estimate of the ¹²C/¹³C isotope ratio in the interstellar gas is 50 ± 10 (Milam et al. 2005). Taking f_12/13 = 50, the observed line intensity ratio can be used to estimate τ_CO and $\tau _{^{13}{\rm CO}}$. For example, a ratio of R = 10 would imply τ_CO(J = 2–1) ≈ 5 for the simple homogeneous cloud model. R = 3 gives τ_CO(J = 2–1) = 20, and R = 1.58 would imply τ_CO(J = 2–1) = 50 and therefore $\tau _{^{13}{\rm CO}} \approx 1$, i.e., the ¹³CO J = 2–1 line is becoming optically thick for R ⩽ 1.6.

In more realistic models, a low line ratio (even R ⩽ 1) may result from self-absorption by cold foreground gas with high CO opacity but low excitation temperature. A fully quantitative interpretation of the J = 2–1 line ratio requires a statistical equilibrium/radiative transfer calculation for a specific molecular cloud model. Line ratio images can nevertheless be useful for identifying positions and velocities with high line optical depths and/or CO self-absorption, and for estimating initial conditions in constructing such detailed cloud models.

Figure 13 shows images of the J = 2–1 line intensity ratio, R, averaged in 2 km s⁻¹ wide velocity bins, for the same set of velocities as are shown in Figures 9 and 10. Pixels where the ¹³CO brightness temperature is <0.75 K, which is ∼5 times the rms noise level, are blanked out. Figure 13 uses a different color palette than Figures 9 and 10. Magenta indicates regions of low R implying large CO line optical depth. Areas shown in gray have R < 1.6, where the ¹³CO line may also be optically thick. Areas shown in white have R < 1, indicating likely cases of self-absorption in the CO J = 2–1 line.

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The relationship between molecular line emission and thermal dust continuum emission is of great importance in understanding the properties of interstellar matter and the processes which lead to star formation from that matter. Ruch et al. (2007) and Polychroni et al. (2010) have presented Spitzer images from the four IRAC bands as well as MIPS 24 μm results. Ruch et al. (2007) focus on the point sources detected by Spitzer and find that the area lying between W3 Main and W3(OH) contains a large concentration of very young stars, mainly of class I and II, which they call the Central Cluster. The cluster lies in a cavity, with low dust/gas content, and is surrounded by a denser shell that includes the currently active star-forming regions W3 Main and W3(OH). Ruch et al. (2007) argue that this disposition of young stars, gas, and dust is consistent with a scenario of triggered star formation which initiated the formation of the Central Cluster and the ongoing massive star formation now creating the H ii regions in the shell. Polychroni et al. (2010) present Spitzer and JCMT CO J = 3–2 data for a larger region complementing Ruch et al. (2007). They derive star formation efficiencies which indicate that the parts of the molecular cloud which appear to be undergoing triggered star formation have much higher star formation efficiencies than the more quiescent parts.

Besides the Spitzer observations, another important new data set showing millimeter-wavelength continuum emission in the W3 region is the recently released BGPS (Aguirre et al. 2011; Rosolowsky et al. 2010). The 1.1 mm continuum is dominated by thermal emission from cold dust, except in the direction of high emission measure H ii regions where free–free bremsstrahlung may also be a significant contribution. In this section, we draw some comparisons between the BGPS results and our molecular line maps.

Figure 14 displays the peak line intensity, T_mb, for the ¹³CO J = 2–1 line, regardless of velocity, as in Figure 5 but with a different color palette to contrast better with the cyan contours which show the 1.1 mm continuum emission from the BGPS. The BGPS data were smoothed slightly from their original 33'' (FWHM) resolution to match the 38'' resolution of the CO maps. The resulting rms noise level of the 1.1 mm continuum map is 0.025 Jy beam⁻¹. It is evident in Figure 14 that only a modest fraction of the molecular gas detected in this field is also detected in the BGPS as 1.1 mm dust continuum emission. The ¹³CO line intensity is determined by the gas column density as well as the ¹³CO excitation temperature. The relatively good correspondence between the ¹³CO peak intensity and the BGPS contours in Figure 14 illustrates how the 1.1 mm continuum generally picks out the highest column density lines of sight.

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To quantify this correspondence, we have extracted all the sources from the BGPS catalog (Rosolowsky et al. 2010) that lie within the CO map area. There are 66 objects listed though we found one pair (Nos. 7340/7341) which were weak and probably redundant sources (separated by 19'' or one-half the map resolution), leaving 65 independent BGPS sources in our mapping field. The peak positions of these objects are marked with small yellow crosses in Figure 14. Table 2 lists the BGPS sources, including the galactic coordinates of the peak position and S₄₀, the 1.1 mm continuum flux density within a 40'' diameter aperture, which nearly matches the 38'' FWHM resolution of our CO and ¹³CO maps. The S₄₀ values in Table 2 have not been multiplied by the factor of 1.5 suggested in the BGPS catalog description, but are simply the values as given in the catalog. The integrated ¹³CO intensity at each BGPS source position was extracted from the image in Figure 7 and is listed in Column 5 of Table 2.

Since the BGPS sources are from a continuum survey, therefore lacking in kinematic information, we have examined the ¹³CO spectra at each of the 65 source positions to extract emission line velocities, intensities, and line widths associated with the continuum sources. We used a standard Gaussian component fitting algorithm (task gaufit in the MIRIAD software package). Most sources were adequately fit by a single Gaussian component, i.e., the rms of the residual to the fit was <0.2 K, comparable to the overall map rms. In these cases, Column 6 of Table 2 is set to 1, and Columns 7–9 give the amplitude and velocity of the Gaussian peak, and the FWHM. The last column of Table 2 gives the rms of the residual to the fit. In 12 cases, the ¹³CO line was clearly non-Gaussian, so we allowed two independent Gaussian components to obtain an adequate fit. In these cases, Column 6 lists the component number, with the amplitude and velocity of the component peak and the FWHM in Columns 7–9. Column 10 gives the rms of the residuals for the sum of the components.

The Gaussian fit parameters are only an approximate description of the line shapes. Where a single component gives a good fit to the ¹³CO line profile, or where two well-separated components are present, then the center velocities and widths are probably good representations of the cloud kinematics. For BGPS source positions where blended Gaussian components are needed for an adequate fit, the physical interpretation of the fit parameters is not so clear. The individual components may not correspond to physically distinct clouds viewed along the same line of sight but rather to complex cloud kinematics.

The component center velocities (V_peak) in Table 2 are distributed broadly between −53 and −35 km s⁻¹. The distribution of component velocities in galactic coordinates is shown in Figure 15. The large-scale gradient noted in Section 3.3 above, on velocity moments, is evident in the Gaussian component velocities. The more negative velocities are concentrated at lower latitude and higher longitude, with the gradient most noticeable in the right side of Figure 15, which displays velocity versus longitude.

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If molecular gas and dust are well mixed, one would expect that sight lines with relatively strong ¹³CO emission should also exhibit detectable 1.1 mm dust continuum. However, comparison of BGPS map intensities with the ¹³CO line emission must also consider the spatial filtering effect of the BOLOCAM survey method (Rosolowsky et al. 2010; Aguirre et al. 2011). The BGPS catalog description states that 90% of the total source flux is spatially filtered out for structures with sizes > 59, and 50% is lost for sizes > 38. In contrast, the OTF scanning technique we used for the spectral line maps recovers all of the line flux at each pixel. We might also expect that there is a range of physical properties in the clouds associated with the BGPS sources (though spatial filtering may also have an effect). To examine the role of source properties we graphed pixel-by-pixel correlation diagrams of the BGPS intensity (in Jy beam⁻¹) versus the ¹³CO integrated line intensities for spatially limited regions associated with the brightest H ii regions in the field. Pixels with BOLOCAM intensity <3σ (0.075 Jy K⁻¹) are omitted. (Bieging et al. 2010 made similar correlation plots for selected areas in the W51 field and found relatively tight but nonlinear correlations for limited regions around BGPS peaks, and for limited velocity ranges.) In Figure 16, we show four examples of such correlation plots, for the rectangular boxes labeled in Figure 14.

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AFGL 333. This region was identified with IRAS 02245+6115 by Carpenter et al. (2000) as a compact cluster of ∼120 stars with a far-IR luminosity of 3300 L_☉. (The IRAS source position is marked by a white cross in Figure 14.) Their CO and ¹³CO J = 1–0 maps agree well with our J = 2–1 maps, which show that the stellar cluster lies in a "bay" to the east of a molecular ridge that coincides with a ridge of 1.1 mm continuum. There is a ∼10σ BGPS continuum source (marked by small yellow cross) very close to the cluster center, which is at a local minimum in the ¹³CO intensity (Figure 14). The plot in Figure 16 shows some correlation between the ¹³CO and 1.1 mm continuum, but for the x-axis range from ∼30 to 40 K km s⁻¹, the continuum is essentially uncorrelated with the line emission. Although the line and continuum emission fall along the same ridge to the west of the AFGL 333 cluster, the intensities do not track in detail. This behavior may be related to heating effects on the dust from the cluster stars. The sharp boundary apparent on the lower right in the distribution of points in Figure 16 may be an artifact resulting from the spatial filtering of the BOLOCAM images.

W3 North. The ¹³CO and 1.1 mm continuum are much weaker in this region than in W3 Main or W3(OH), and exhibit only a modest correlation. Figure 14 shows that the H ii region associated with the isolated O6 V exciting star (Oey et al. 2005; Feigelson & Townsley 2008; marked by a white cross) is not a well-defined ¹³CO peak. There is, however, a "spur" of emission extending north from W3 Main that appears to connect with the W3 North H ii region. This part of the rectangular region outlined in Figure 14 is responsible for the greatest part of the correlation seen in Figure 16. The local maxima in the ¹³CO and 1.1 mm continuum, lying between W3 Main and W3 North, may be potential sites of future star formation.

W3 Main. This region contains the brightest radio and mm continuum, associated with the massive forming OB cluster that ionizes the gas, heats the dust, and disrupts the parent molecular cloud. The relatively poor correlation in Figure 16, compared to W3(OH), is therefore not surprising. There is a well-defined lower envelope to the distribution of points, and a locus concentrated just above the lower boundary that is similar to the trend seen for W3(OH), but between 30 and 130 K km s⁻¹ on the x-axis, there are many pixels with 1.1 mm intensities showing little correlation with the ¹³CO intensity. The large scatter probably results from a contribution by free–free emission to the 1.1 mm continuum toward the bright H ii regions.

W3(OH). The best correlation is for the region around W3(OH), an ultracompact (UC) H ii region at the southern end of the molecular shell that extends from W3 Main around the IC 1795 OB association. Comparison of the 1.1 mm continuum contours with the ¹³CO J = 2–1 integrated intensity in Figure 14 shows that the continuum follows the ¹³CO closely, with both having maxima at the position of W3(OH) (white cross in Figure 14). This good correlation suggests that the UC H ii region has not significantly disrupted its parent molecular cloud, and does not contribute significant free–free emission to the 1.1 mm continuum. The distribution of points in Figure 16 intersects the x-axis at ∼30 K km s⁻¹, similar to the examples presented by Bieging et al. (2010) for W51, probably because the BOLOCAM image has filtered out extended low-brightness 1.1 mm continuum emission.

A number of physical effects must influence the correlations seen in Figure 16, making the interpretation of these plots less than straightforward.

• 1.  
  The regions with higher CO J = 2–1 peak temperatures (W3 Main and W3(OH)) show larger extents in both BOLOCAM intensity and ¹³CO integrated intensity, compared to the regions with lower CO peak temperatures (AFGL 333 and W3 North). The CO line peak temperature is likely to be an indicator of the cloud kinetic temperature, so it is reasonable that the colder clouds show smaller spans of ¹³CO intensities, while the warmer regions show a larger range of ¹³CO values. Self-absorption in the CO line may also affect the observed peak temperature leading to an underestimate of the kinetic temperature.
• 2.  
  The slope and linearity of the correlations in Figure 16 vary from region to region. The slope should depend, to first order, on the dust and gas temperatures. If the ¹³CO line is optically thin and the gas and dust are thermally well coupled, a linear relation should result as a function of line-of-sight column density for an isothermal cloud. The trends in Figure 16 should curve upward as the ¹³CO becomes increasingly saturated at higher column density, provided the cloud is isothermal. Another possible source of nonlinear correlations could be gradients in cloud temperature and density. At the BOLOCAM wavelength of 1.1 mm, hc/λk = 13.0 K which is comparable to the grain temperatures of interest, so the dust emission will vary more steeply than linearly with grain temperature, while the ¹³CO excitation temperature should vary no more than linearly with gas kinetic temperature. Therefore, we would expect a warmer cloud to produce greater 1.1 mm continuum relative to ¹³CO line emission for a given column density, compared to a colder cloud. The 1.1 mm continuum emission will be more strongly weighted toward dense, warm inner cores of molecular clouds compared to the ¹³CO line, so a set of sight lines through a range of column densities, as shown in the panels of Figure 16, would also show the upward curving trends seen in some of the example regions even if the ¹³CO line is optically thin throughout the cloud. Our CO/¹³CO line ratio maps (Figure 13) indicate that the ¹³CO line is just becoming optically thick at some of the BGPS source peaks. An inward temperature gradient is probably also present in the clouds, which clearly have internal heat sources. In either case, the correlations in Figure 16 should exhibit nonlinear behavior, as is in fact observed.
• 3.  
  The scatter of points above the general trend for W3 Main is probably a result of free–free emission contributions to the 1.1 mm continuum, in addition to the thermal dust emission. The lack of correlation for AFGL 333 may be related to molecular dissociation or dynamical effects of the ionized gas, suggested by the morphology of the CO maps compared with the BOLOCAM map.

The trends in the correlations of the line and continuum data suggest that they could usefully constrain detailed cloud models in terms of gas and dust temperature distributions as well as density gradients and H ii regions, in determining molecular excitation and line profiles. Such detailed models are beyond the scope of this paper but will be undertaken in future work.

3.6.1. Image Data

The CO J = 3–2 map of the 30' × 20'(l × b) region encompassing W3 Main and W3(OH) is shown in Figure 17, which presents the peak CO J = 3–2 line intensity within the velocity range −60 to −25 km s⁻¹. The positions of the H ii regions are marked by the white crosses. The circle of radius 5' shows the location of the OB association IC 1795, from the photometric study of Oey et al. (2005). The yellow cross marks the dominant O star in the cluster, BD+61°411, which lies nearly centered between W3(OH) and W3 Main. Radio continuum emission at 1420 MHz from the CGPS is shown in contours as in Figure 3.

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Figure 17 shows that CO J = 3–2 emission is present at almost every pixel, above the 3σ level (6 K). The brightest CO is at the W3 Main H ii region complex, as in the CO J = 2–1 maps. In contrast, the position of the UC H ii region W3(OH) does not stand out in the CO cloud surrounding it. There is an arc of CO around the southwest half of the IC 1795 cluster and extending from W3 Main to W3(OH). A similar but clumpier arc of CO emission extends around the northeast side of IC 1795 from W3(OH) to W3 Main. These structures have the appearance of a shell of molecular gas surrounding the OB cluster.

The integrated CO J = 3–2 line intensity is shown in Figure 18. The general appearance of the emission is similar to that in Figure 17 but with greater contrast. The CO associated with W3 Main dominates the map, while the cloud around W3(OH) is a relatively minor peak. There is also at least a partial arc of CO evident on the southwest perimeter of IC 1795, but is less obvious on the northeast side.

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The CO J = 3–2 images closely resemble the corresponding CO J = 2–1 maps for the same region encompassing W3 Main and W3(OH). If the CO excitation were uniform at all locations, the 3–2 and 2–1 images should be identical in appearance except for optical depth effects. Where the CO is optically thick, presumably at the peak of the emission lines, we would expect the peak brightness temperatures to be identical within a scale factor of order unity, due to the different velocity resolutions giving slightly different channel dilutions at the line peaks. In fact, we find significant variations in the ratio of peak line intensities,

$$\begin{equation*} {T_{{\rm peak}} {\rm (CO\, 3\hbox{--}2)}} \over {T_{{\rm peak}}{\rm (CO\, 2\hbox{--}1)}} \end{equation*}$$

across the map. Figure 19 (top) shows T_peak(CO 3–2) after convolving Figure 17 spatially to match the 38'' (FWHM) resolution of the CO 2–1 map (Figure 3). Figure 19 (bottom) shows the above ratio for the convolved image in Figure 19 (top) divided by the CO 2–1 peak intensity from Figure 3. Pixels where the CO 2–1 peak intensity is <1 K (∼8σ) are blanked. The black contours are the same as the contours in Figure 19 (top) to show how the line ratio varies with respect to the 3–2 peak intensity. Over most of the mapped area, the peak intensity ratio is relatively uniform at around 1.4 ± 0.3. At positions on the edges of the bright CO 3–2 emission, however, the 3–2 line appears to be significantly enhanced relative to the 2–1 line, as indicated by the orange, red, and white colors. Even at these positions the emission is at least several times the rms noise level in both 2–1 and 3–2 maps. The telescope pointing is certainly better than one-half of the 10'' pixel, so we are confident that the areas with high [T_peak(CO  3–2)]/[T_peak(CO  2–1)] are real, not artifacts, e.g., of inaccurate registration of the two maps. Note also the relatively higher 3–2 intensity in the vicinity of the W3 Main complex of H ii regions, where both lines are strong. The areas showing up in red or white in Figure 19 (bottom) are probably locations where the molecular gas is being influenced by UV radiation from nearby OB stars or also by the more general interstellar radiation field with contributions from the various OB clusters in the W3 and W4 H ii region complex, i.e., "photon-dominated regions" or PDRs. We note that the quantitative values for intensity ratios indicated in Figure 19 (bottom) should be taken with some caution, as there may be unrecognized systematics in the overall calibration of the brightness temperature scale of the CO 3–2 data in particular. Despite possible scaling uncertainties, the patterns in Figure 19 (bottom) are suggestive of PDRs located in the interface between the dense, cold molecular gas and the hot, diffuse, UV-illuminated H ii regions which surround the molecular clouds. A detailed excitation/radiative transfer analysis of the CO lines including both the CO and ¹³CO 2–1 and the CO 3–2 lines could better constrain the temperature and excitation conditions in the bulk of molecular clouds as well as in these PDRs. Such an analysis will be the subject of a future study.

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3.6.2. Velocity Channel Maps

There is significant velocity structure in the CO J = 3–2 emission, as seen in the channel maps of Figure 20, which show T_B averaged in 2 km s⁻¹ wide increments from −54 to −30 km s⁻¹ for the same 12 velocities as the CO and ¹³CO J = 2–1 channel maps in Figures 9 and 10. The 3–2 channel maps are very similar to the 2–1 maps, but show some structures more clearly because of the higher angular resolution. The same large-scale gradient from W3(OH) to W3 Main is apparent. The arc of emission around IC 1795 shows up in segments over a range of velocities, encircling the OB cluster and, on opposite ends of the elliptical arcs exhibiting strong CO emission at W3 Main and W3(OH) in distinctly separate velocity channels. The small clumps of CO projected on the center of IC 1795 (yellow circle in Figure 20) show up at the most redshifted velocities, consistent with being portions of a shell on the far side of the OB association and expanding outward and away from us. There are elongated structures in some of the clumps that appear to extend radially away from the O6.5 star BD+61°411 (yellow cross) at velocities from −35.75, −33.75, and −31.75. This morphology is suggestive of some kind of interaction between the O star and the dense molecular gas in the clumps, possibly via radiation or a stellar wind, though it is not possible to determine the location of these clumps along the line of sight relative to the O star. Their proximity as seen in the plane of the sky may suggest a spatial association but that cannot be proven from these data alone.

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3.6.3. Velocity Moment Maps

The first moment or velocity centroid for the CO J = 3–2 map is in Figure 21. The low-level horizontal striping is an artifact of residuals to the fitted spectroscopic baselines, probably due to weather-caused fluctuations in the sky brightness during the OTF scanning. Such residual errors in the spectroscopic baselines are accentuated in the velocity moments. Nevertheless, the overall structure and velocity values agree well with the corresponding region in the CO J = 2–1 first-moment map (Figure 11). The trend from W3(OH) to W3 Main is identical and the sharp local gradient across the position of W3 Main is seen in both transitions, suggestive of a large-scale bipolar outflow or asymmetric expansion centered on the main H ii region complex. We also see the clumpy gas projected near BD+61°411 in the most redshifted centroid velocities, consistent with the channel maps of Figure 20. Our centroid map appears to be consistent with the data of Polychroni et al. (2010) who present a three-color-coded intensity map of CO J = 3–2 emission made with the JCMT. Their map is not a true velocity centroid map but shows the same trends in velocity over the region displayed in Figure 21.

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We also calculated the second-moment map for the CO 3–2 spectra, which is a measure of the line width at each position in the field. The distribution of second moments is comparable to that found for the CO 2–1 line (see Section 3.3). The mean value is 4.2 km s⁻¹ with a long tail to higher values, where the larger line widths are associated with the molecular gas near the W3 Main H ii region complex. Thus, the kinematics inferred from the CO 3–2 line are similar to those for the 2–1 line, as expected.