Infall

Four sources, N62-1, N65-2, N90-2 and N117-3, have a non-Gaussian line profile. In three cases the line profile is stronger on the blue-side (see Fig. \ref{infall}). Of these three sources, N117-3 has the strongest red-shifted emission, with two clear peaks present. The line-profiles of N62-1 and N90-2 are single-peaked but with a plateau on the red-shifted side. We interpret these three profiles as evidence of infall. N62-1 and N90-2 both are located in infrared dark clouds that intersect their nearby bubble (N62 and N90). Thus, infall, if present, could be triggered by an expanding HII region via radiatively driven implosion or collect-and-collapse. N117-3 is located within in the bubble, in projection. There is no obvious interpretation for this infall candidate’s interaction with the associated bubble N117.

\citet{Myers1996} and \citet{Williams1999} present a model of infall that predicts line profiles similar to these observations. They assume two clouds (near and far) falling toward a common center and estimate the resulting line profiles accounting for optical depth effects as well as standard radial-dependencies of velocity and excitation temperature. \citet{Myers1996} show that an optically thick line and a higher excitation temperature in the cloud on the far side can produce a blue-shifted weighted line-shape. With further simplifications they show that by measuring five parameters, the Myers et al. (1996) model allows an estimate of the infall velocity. The measured parameters are: \(\sigma\) (velocity dispersion of an optically thin tracer), T\({}_{BD}\) (the blue-shifted excess emission), T\({}_{RD}\) (the red-shifted emission), T\({}_{D}\) (the plateau emission), v\({}_{red}\) (the red-shifted peak emission velocity) and v\({}_{blue}\) (the blue-shifted peak emission velocity). See Figure 2 in \citet{Myers1996} for a diagram of these different quantities. When all quantities can be measured, the infall velocity is estimated to be:

\begin{equation} v_{in}\approx\frac{\sigma^{2}}{v_{red}-v_{blue}}\ln\left(\frac{1+eT_{BD}/T_{D}}{1+eT_{RD}/T_{D}}\right)\nonumber \\ \end{equation}

When the optical depth and V\({}_{in}\)/\(\sigma\) are sufficient large, the red peak can disappear (see Myers et al. 1996 for discussion of this effect). Thus, we are limited in our numerical analysis to N117-3. We estimated the relevant line parameters by eye. Our line profile measurements and infall velocity calculation are given in Table \ref{infalltable}. Since we do not have an optically thin measurement of this source, we have assumed the value of the velocity dispersion based on the optically thin \({}^{34}\)CS observations by \citet{Williams1999}. They found a typical value to be 1.5 km/s. A smaller value would decrease the infall velocity (see equation above).