The “bubble” model (Silk 1985) of an embedded stellar wind predicts that we should observe a hot and relatively diffuse interior and a warm dense shell. In the case of the embedded stellar wind, the “thickness” of the shell is often much smaller than the radius of the shell (\citet{Churchwell_2007}; \citet{Arce_2011}), thus making the opacity of the shell smaller along lines of sight through the center of the shell. As a result, the projection of the shell on the sky often looks like a “ring.” Due to the variation of the density and the irregularity of the shape of the cloud, the ring is likely incomplete and asymmetric. Estimating mass from the column density within a projected area is thus a lower bound, and serves as a good proxy for the total mass of the shell when the shell is optically thin and symmetric. To estimate the mass of the shell, we first overlay the temperature and density maps to determine an elliptical region with a finite width in the warm and dense part of the map. Notice that we completely exclude the cluster region to avoid confusion between the gas in the shell and within the cluster (Fig. 14, on the 2MASS extinction map). After this projected region of the shell is determined, we use the 2MASS extinction map and convert the extinction magnitude into the mass column density using Eq. 11. Summing up the mass column density within the shell mass region then gives us the shell mass, estimated to be 462 \(M_{\sun}\). This is a lower bound, since the cluster region we exclude when choosing the shell mass region likely contains gas within the shell.
The expanding velocity of the shell is determined from the average spectrum of the shell. The symmetry of the shell predicts that the velocity we observe with the molecular line emission within the “ring” is symmetric around some system velocity. That is, for each “particle” in the shell, the velocity is determined by (\(v_{system}\) + \(v_{expansion}\,\sin{\left(\cos^{-1}{\left(R/R_0\right)}\right)}\) + \(v_{intrinsic}\)), where \(v_{intrinsic}\) is drawn from a velocity distribution characteristic of the molecule’s intrinsic (microscopic) motion. Assuming that the line emission from \(^{12}\)CO (1-0) traces the gas component of the shell and that the intrinsic velocity distribution can be approximated by a normal distribution, we find \(v_{expansion}\) from the residual of fitting the \(^{12}\)CO line with \(N(v_{system}, \sigma)\). Fig. 15 shows the residual as well as the fitted Gaussian line profile, with an asymmetry of the residual due the opacity. \(v_{residual}\) is \(\sim\) 1.2 km/s, which is \(v_{expansion}\,\sin{\left(\cos^{-1}{\left(R/R_0\right)}\right)}\) in the equation above. With the shell mass region selected to have an inner radius \(\sim\) 0.98 pc and an outer radius \(\sim\) 1.61 pc, we find \(v_{expansion}\) to be \(\sim\) 1.52 km/s. Notice that \(v_{residual}\) is a lower bound since the residual calculated from the \(^{12}\)CO (1-0) line profile is likely probing the gas component at a larger radius than the inner radius due to the opacity effect.
From these estimates, we obtain the momentum and the kinetic energy of the shell. These are given by \(P_{shell} = M_{shell}\,v_{expansion}\) and \(E_{shell} = 0.5\,M_{shell}\,v^2_{expansion}\), respectively. For this shell, the momentum is \(\sim\) 702 \(M_{\sun}\,km/s\), and the energy is \(\sim\) \(1.06\times10^{46}\,erg\). This is \(\sim\) 12 % of the total turbulent energy of the cloud (compared to \(\sim\) 15 % for the largest shell in Perseus; Fig. 16). Notice again that since the estimates for the mass and the expansion velocity are both the lower limits of possible values, the momentum and energy of the shell presented here are likely smaller than the real values as well.