We report the results of a spectroscopic search for inward motions of the dense gas around 19 young stellar clusters. Single point observations of CS(2-1) and N2H+(1-0) were made using the Haystack 37 m telescope at 21'' resolution, and CS(2-1) and C34S(2-1) maps were made using the FCRAO 14 m telescope at 50'' resolution. Strong, spatially extended CS self-absorption is seen in Mon OB1-D, IRAS 20050+2720, and Cepheus A, which indicates that these sources are good candidates for follow-up observations of kinematic structure. In Cepheus A, in particular, we identify a region that shows inward motions over a region 0.2 pc in extent, which suggests that models of core collapse should take into account the turbulent motions in these sources. We use the normalized velocity difference, δv=[v(thick)-v(thin)]/Δv(thin), between the optically thick (CS) and thin (N2H+ or C34S) lines to quantify the relative motions between the forward and central layers of dense gas. The average value of this velocity difference is not significantly different from zero for either data set, and there is no correlation with the source bolometric temperature as determined from IRAS flux measurements. Thus this cluster sample has no significant excess of sources with inward motions, unlike the samples of individual YSOs recently reported by Gregerson et al. and Mardones et al. The lower incidence of high absolute values of δv in our sample can be attributed to a lower optical depth in the CS line due to the greater distance, and therefore poorer linear resolution, of the sources here, and to the higher kinetic and excitation temperatures in these more massive, cluster forming environments.
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