deletions | additions       diff --git a/subsection_Infall_Four_sources_N62__.tex b/subsection_Infall_Four_sources_N62__.tex  index ff192f5..8630b9c 100644  --- a/subsection_Infall_Four_sources_N62__.tex  +++ b/subsection_Infall_Four_sources_N62__.tex 
...
\subsection{Infall}  Four sources, N62-1, N65-2, N90-2 and N117-3, have a non-Gaussian line profile (see Fig. \ref{infall}). In three cases the line profile is stronger on the blue-side. blue side.  The line-profile of N117-3 is double-peaked with the blue-shifted peak stronger than the red-shifted peak. 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{Myers_1996} and \citet{Williams_1999} 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{Myers_1996} show that an optically thick line and a higher excitation temperature on the cloud on the fars far  side can produce a blue-shifted weighted line-shape. line shape.  With further simplifications they \citet{Myers_1996}  show that by measuring five parameters, the Myers et al. (1996) their  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{Myers_1996} 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+e T_{BD}/T_D}{1+e T_{RD}/T_D}\right)  \end{equation} 
...
If we use the GBT beamsize, adjusted for the near kinematic distance, for R, then we calculate a mass infall rate of 7 $\times$ 10$^{-5}$ M$_\odot$/yr. The dominant source of error in this calculation is likely due to the infall velocity. We estimate the uncertainty to be about a factor of 2. However, if we used a smaller value for R, as suggested by the small source size visible in the 8 $\mu$m GLIMPSE image, the mass infall rate would be proportionally smaller (by a factor of about 3). This result is consistent with massive or intermediate-mass star formation.   For the infall analysis, we have assumed an optically thick line. An alternative interpretation of these three line-profiles is that they are caused by alignment of two clouds along the line-of-sight. Observing an optically-thin tracer, such as $^{34}$CS $^{34}$CS,  would distinguish between these interpretations since the infall-model infall model  would predict a single-peak single peak in the optically thin line,  whereas the two cloud model predicts a double-peak. double peak.    N65-2, the fourth source which shows a non-gaussian line shape, is stronger on the red-shifted side. This shape is not consistent with the infall model of Myers et al. (1996). This shape could be caused by two unrelated clouds along the line of the sight. There is further evidence of this interpretation in the map of N65 (see discussion below).    N65-2, the other source which shows a non-gaussian line shape, is stronger on the red-shifted side. This shape is not consistent with the infall model of Myers et al. (1996). This shape could be caused by two unrelated clouds along the line of the sight. There is further evidence of this interpretation in the map of N65 (see discussion below).