TEMPERATURE AND DENSITY DISTRIBUTION IN THE MOLECULAR GAS TOWARD WESTERLUND 2: FURTHER EVIDENCE FOR PHYSICAL ASSOCIATION

Figure 1 shows the integrated intensity distributions of the three CO transitions, overlaid on a three-color IR image from the Spitzer/IRAC GLIMPSE survey. Following Paper I, we show the molecular gas distribution in velocity ranges of −11 to 0 km s⁻¹, 1 to 9 km s⁻¹ and 11 to 21 km s⁻¹ and hereafter refer to emission in these ranges as the −4 km s⁻¹, 4 km s⁻¹, and 16 km s⁻¹ clouds, respectively. However, it should be noted that the 4 km s⁻¹ and −4 km s⁻¹ clouds do not form completely distinct entities in the three-dimensional data cubes, and that spectra in the −11 to 9 km s⁻¹ range are sometimes complex and blended.

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As described in Paper I, the northeastern half of the 16 km s⁻¹ cloud is located toward the central regions of RCW49. Notably, the southeastern edge of the cloud, between (l, b) = (284.33, − 0.28) and (284.27, − 0.40), shows a strong correlation with a bright filamentary ridge of Spitzer emission ∼2' southeast of Wd2. The remainder of the cloud extends 02 to the southwest, extending fully outside the area of influence of the H ii region. The 4 km s⁻¹ cloud shows an excellent morphological correlation with the large-scale shape of the H ii region. Emission at this velocity range is entirely absent within a radius of 3' of Wd2, and at larger distances from the cluster the molecular gas fans out to the north and south, matching well with the IR-bright gas. The −4 km s⁻¹ cloud distribution also matches well with the IR nebula and in particular we note that a prominent CO clump centered on (284.22, −0.29) appears to be associated with a number of IR point sources, one of which has been identified as a YSO of spectral type B2 (Churchwell et al. 2004).

New to the present study is the addition of ¹³CO(J = 2–1) data from NANTEN2, as well as archival ¹²CO(J = 1–0) data from the older NANTEN Galactic Plane Survey. All three lines follow very similar distributions at the present spatial resolution, with ¹³CO(J = 2–1) emission detected toward the brighter regions of the ¹²CO clouds. This can be seen in Figure 1.

We convolve the ¹²CO(J = 2–1) and ¹³CO(J = 2–1) data with a Gaussian of FWHM 26 in order to smooth the cubes to the resolution of the ¹²CO(J = 1–0) beam. We then derive peak main beam temperatures, T_mb (K), and line widths for the relevant emission components at each ¹²CO(J = 1–0) pixel position by fitting either single or double-Gaussian functions to the line profiles. Two ratios, R_{2 − 1/1 − 0} = T_mb[¹²CO(J = 2–1)]/T_mb[¹²CO(J = 1–0)] and R_12/13 = T_mb[¹²CO(J = 2–1)]/T_mb[¹³CO(J = 2–1)], are then calculated. The uncertainties on these ratios are around 15%, as calculated from the propagation of the intensity calibration errors, under the assumption that these errors are uncorrelated.

Of these ratios, the former is of most immediate interest, being a measure of the level of excitation of the molecular gas. We find that in the 4 km s⁻¹ cloud R_{2 − 1/1 − 0} ranges from 0.42 to 1.34, while the 16 km s⁻¹ cloud shows values of between 0.36 and 1.09. In the −4 km s⁻¹ cloud, for which all three lines were significantly detected at only five 2' pixels, ratios of between 0.80 and 1.34 are observed. The spatial distribution of R_{2 − 1/1 − 0} is shown in panels (a) and (b) of Figure 2. It is striking that molecular gas at smaller projected distances from Wd2 generally shows higher ratios. In both the −4 and 4 km s⁻¹ clouds, molecular gas spatially coincident with the H ii region shows markedly enhanced ratios, and in particular the southern part of the 4 km s⁻¹ cloud shows the highest ratios toward the cluster in the north but lower ones in the south. This suggests that gas closer to the cluster is more highly excited, and is quite consistent with the association suggested by Furukawa et al. (2009).

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Panels (c) and (d) of Figure 2 show the spatial distribution of R_12/13. This ratio ranges from 4.1 to 13.0 across the entire molecular gas complex. Smaller values indicate higher optical depths and, as expected, are generally found toward CO emission peaks where column densities are larger.

We may explore the issues of temperature and density more robustly by using a LVG analysis (Goldreich & Kwan 1974). LVG analysis is a method of calculating a simplified radiative transfer code based on the approximate escape probability formalism of Castor (1970). We assume a spherically symmetric cloud of constant density and temperature with radial velocity distribution proportional to the radial distance from the cloud center. We then utilize the line ratios measured above to solve the equations of statistical equilibrium for the fractional population of the lowest 40 rotational levels of the ground vibrational level of CO. The velocity gradient, dv/dr, is taken to be 2.6 km s⁻¹ pc⁻¹, as estimated from the typical line width in a single 3.5 pc cell. In order to evaluate the dependence of temperature on the adopted parameters, we tested three values of dv/dr: 1.2, 2.6, and 5.0 km s⁻¹ pc⁻¹, while keeping the other parameters fixed. We find that T_k varies by about a factor of 1.6 for a factor of 2 change in dv/dr, indicating that the results do not depend strongly on dv/dr. The CO fractional abundance X(CO) is taken to be 5 × 10⁻⁵ (Sakamoto 1993), and the ¹²CO/¹³CO abundance ratio is taken to be 75 (Güsten & Philipp 2004).

Figure 3 shows solutions for kinetic temperature, T_k, and number density, n₀, at selected positions, labeled A–F in Figure 2. In Figure 4, we plot the spatial distributions of T_k and n₀ over the entire extent of the clouds, only excluding points for which no ¹³CO(J = 2–1) emission was detected. (In the case of the −4 km s⁻¹ cloud ¹³CO(J = 2–1) is only significantly detected at seven pixels and we therefore exclude it from the following discussion.) It may be seen that for both the 16 km s⁻¹ and 4 km s⁻¹ clouds the kinetic temperature is enhanced toward the Spitzer IR nebula and at smaller projected distances from the cluster. This is especially true in the case of the 4 km s⁻¹ cloud, which shows temperatures as high as 70–150 K on the side facing Wd2. T_k in the 16 km s⁻¹ cloud is generally lower, reaching peak values of 30–70 K toward the IR nebula. However, these values are still significantly enhanced with respect to the typical temperatures of ∼10 K observed in molecular clouds without a local heat source. Moreover, the 16 km s⁻¹ cloud shows a clear decrease in T_k with projected distance from Wd2, decreasing to 10 K beyond the IR nebula at distances of 15–20 pc from the central cluster. The temperature in the southern part of 4 km s⁻¹ cloud also drops slightly to 30–50 K beyond the IR nebula at projected distances of 10–20 pc from the cluster, while the northern part of 4 km s⁻¹ cloud located toward the IR nebula within 10 pc of Wd2 remains high in temperature. This is illustrated in Figure 5, which shows plots of T_k as a function of projected distance from Wd2. This relationship supports the association between the molecular clouds and the stellar cluster suggested in Paper I, while the lower T_k in the 16 km s⁻¹ cloud compared to the 4 km s⁻¹ cloud may suggest that it is located further from the cluster. We also note that the 4 km s⁻¹ cloud follows more closely the shape of the IR nebula as it extends in the north–south direction, whereas the 16 km s⁻¹ cloud is elongated to the southwest, with only its northeastern most portions coincident with the Spitzer emission. The extent of the IR emission in each cloud with increasing distance from Wd2 is indicated in Figure 5 and explains why the high-temperature regions in the 4 km s⁻¹ cloud extend to larger radii than in the 16 km s⁻¹ cloud.

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In general, it is sensible to be cautious about the accuracy of the quantity T_k when the energy levels employed are not as high as the temperatures derived. In the present case, the J = 1 and 2 levels of CO are at 5.5 K and 16 K above ground level, respectively. Nevertheless, the temperature ranges indicated in Figure 3 demonstrate that the analysis is accurate enough to conclude that the kinetic temperatures are significantly higher than 10 K, the typical temperature of molecular gas without an extra heat source other than the general interstellar radiation field and cosmic-ray sea.

Number densities are typically ∼3000 cm⁻³ in both clouds, with the southern part of the 4 km s⁻¹ cloud showing higher densities than the northern part. In particular, the ¹²CO (J = 2–1) integrated intensity peak has an estimated n₀ of ∼8000 cm⁻³. It is also notable that the 16 km s⁻¹ cloud shows a slight density depression close to Wd2, suggesting gas dispersal by the stellar cluster.

In PDR regions, the abundance of ¹³CO may change by a factor up to 2.0 relative to ¹²CO in regions of A_V less than ∼1 mag, where chemistry becomes complicated by partial ionization (Visser et al. 2009). The present clouds have significantly higher A_V, of up to 10 mag, and the fraction of the positions with A_V less than 1.5 mag is only ∼15%, suggesting that the effects of ¹³CO abundance variation may not be important. In order to test the effects of the ¹²CO/¹³CO ratio, we examine cases in which this ratio varies between 40 and 150, instead of the 75 assumed in the original analysis. We find that the derived temperature is still significantly high; for example, T_k = 70 K at (Position A) in the −4 km s⁻¹ cloud falls in the range 45–90 K, significantly higher than 10 K. Considering the large values of A_V noted above, this temperature range gives conservative limits. Thus, we argue that the effect of the PDR on ¹³CO abundances does not alter the key result that temperatures toward the H ii region are high, and the association of the clouds remains valid.

RCW49 is a classic example of a PDR, in which the dense molecular ISM and dust are being heated by a strong far-ultraviolet (FUV) field. It is therefore instructive to make a simple comparison of the PDR surface temperatures and the molecular gas temperatures obtained above.

We make use of the standard model of Kaufman et al. (1999), which parameterizes the PDR surface temperature of a constant density cloud in terms of the number density of hydrogen nuclei, n₀, and the FUV (6 eV ⩽ E ⩽ 13.6 eV) field at the cloud surface, G₀. We take n₀ as ∼6 × 10³ cm⁻³, based on the LVG analysis above, and estimate G₀ from the far-infrared (FIR) luminosity of the nebula. Here we utilize high-resolution IRAS 60 μm and 100 μm data from the Infrared Processing and Analysis Center (IPAC). The filter properties of IRAS allow us to combine these data sets to obtain the FIR intensity, I_FIR, between 42.5 μm and 122.5 μm, via the following relation (Helou et al. 1988; Nakagawa et al. 1998):

$$\begin{equation} I_{{\rm FIR}} = 3.25 \times 10^{-5}\times F(60\ \mu {\rm m})+1.26 \times 10^{-5} \times F(100\ \mu {\rm m}), \end{equation} \tag{ 1 }$$

where F(60 μm) and F(100 μm) are the 60 μm and 100 μm fluxes in MJy sr⁻¹. Assuming that the FUV energy absorbed by the grains is reradiated in the FIR, we then estimate the FUV flux G₀ impinging onto the cloud surface from

$$\begin{equation} G_0 = 4 \pi \times I_{{\rm FIR}} /1.6 \times 10^{-3}, \end{equation} \tag{ 2 }$$

where G₀ is in units of the Habing field, 1.6 × 10⁻³ erg cm⁻² s⁻¹. Following Kramer et al. (2008), this formula assumes that photons with E ⩽ 6 eV contribute about half of the total heating (Tielens & Hollenbach 1985), but also that the total re-radiated bolometric IR luminosity is a factor of 2 larger than I_FIR (Dale et al. 2001). These factors approximately cancel.

At the hottest location in the 4 km s⁻¹ molecular cloud (l, b) = (284.33, − 0.366), F(60 μm) and F(100 μm) are 2.3 × 10⁴ and 1.7 × 10⁴ MJy sr⁻¹, respectively. G₀ is therefore estimated to be 7.5 × 10³ erg cm⁻² s⁻¹ sr⁻¹. Comparing with Figure 1 of Kaufman et al. (1999), the PDR surface temperature is thus estimated to be several hundred K.

This result, although slightly higher than the derived LVG temperatures in the molecular gas, is nonetheless highly consistent when we consider the fact that the observed CO emission will not originate from the active cloud surface. Instead it is likely to originate from deeper, and therefore presumably colder, regions of the cloud, which have not yet been penetrated by the dissociating radiation.

The above comparison is necessarily crude. Future high-resolution studies with instruments such as ALMA may resolve molecular gas emission down to the size scales as the structures observed by GLIMPSE, and pave the way to more detailed model comparisons.

Finally, we shall also briefly mention the prominent clump in the −4 km s⁻¹ cloud located at (l, b) = (284.23, − 0.36). This clump shows hints of higher values of R_{2 − 1/1 − 0} and T_k in its periphery than in its center (see Figures 2(a) and 4(a)), suggesting that its outer regions are heated by the UV photons of Wd2. The clump itself also appears to be associated with several internal YSOs, with a maximum spectral type of around B2 (Churchwell & Glimpse Team 2005; Whitney et al. 2004). The total luminosity of a single zero-age main sequence (ZAMS) B2 star may be estimated from the evolutionary tracks of Iben (1965) to be around 2.1 × 10³⁷ erg s⁻¹. For comparison, the cooling rate of the molecular clump is estimated to be 1 × 10^{34 ±  0.7} erg s⁻¹, where we follow the cooling rate equation of Goldsmith & Langer (1978) and assume a kinetic temperature of 20 K, a density of 4 × 10³ cm⁻³, and approximate the clump as a sphere of radius 2.5 pc. This figure is of the order of 1% of the estimated B2 star luminosity. Considering that the molecular feature is not bright in the Spitzer PAH bands, we suggest that the interior of the clump is unlikely to be primarily heated by the UV radiation from the central cluster, and that the embedded YSOs are more than sufficient to heat the gas to its present temperature. It is both desirable and important to obtain future detailed molecular observations at higher resolution to explore its detailed properties in order to better understand the star formation occurring within it.