2007ApJ...659..459S

We present the results of C¹⁸O observations by the 45 m Nobeyama radio telescope toward dense clumps with young clusters in nine massive star-forming regions. We identified 39 clumps whose mass, radius, and line width range from 15 to 1500 M_☉, from 0.14 to 0.76 pc, and from 0.6 to 3.2 km/s, respectively. The clumps associated with massive (proto)stars have a large line width (∼2.5 km/s) and a large mass (∼500 M_☉). Most of the clumps are sufficiently gravitationally bound because they have a virial mass similar to the gas mass, and the average H₂density of the clumps increases with increasing internal kinetic motion. Next, we found two relations, one between the number density of associated 2MASS sources and the average H₂density of the clump and the other between the number density of sources and the star formation efficiency of the clump. From these results, we suggest that a structure, whose size scale is ∼0.3 pc, with a high average H₂density is required in order for cluster formation to occur. In addition, we found that the internal kinetic motion of a clump has to be large in order to form massive stars, because there is a good correlation between the maximum mass of associated stars and the line width of the clump. Such clumps with large internal motion must generally have a high average H₂density in order to be gravitationally bound. Thus, massive stars are formed in a dense cluster.