Coherence in dense cores. II. The transition to coherence

After studying how line width depends on spatial scale in low-mass star-forming regions, we propose that "dense cores" (Myers & Benson 1983) represent an inner scale of a self-similar process that characterizes larger scale molecular clouds. In the process of coming to this conclusion, we define four distinct types of line width-size relation (Delta upsilon proportional to R-ai), which have power-law slopes a(1), a(2), a(3), and a(4), as follows: Type 1-multitracer, multicloud intercomparison; Type 2-single-tracer, multicloud intercomparison; Type 3-multitracer study of a single cloud; and Type 4-single-tracer study of a single cloud. Type 1 studies (of which Larson 1981 is the seminal example) are compendia of Type 3 studies which illustrate the range of variation in the line width-size relation from one region to another. Using new measurements of the OH and (CO)-O-18 emission emanating from the environs of several of the dense cores studied in NH3 by Barranco & Goodman (1998; Paper I), we show that line width increases with size outside the cores with a(4) similar to 0.2. On scales larger than those traced by (CO)-O-18 or OH, (CO)-C-12 and (CO)-C-13 observations indicate that a(4) increases to similar to 0.5 (Heyer & Schloerb 1997). By contrast, within the half-power contour of the NH3 emission from the cores, line width is virtually constant, with a(4) similar to 0. We interpret the correlation between increasing density and decreasing Type 4 power-law slope as a "transition to coherence." Our data indicate that the radius R-coh at which the gas becomes coherent (i.e., a(4) --> 0) is of order 0.1 pc in regions forming primarily low-mass stars. The value of the nonthermal line width at which "coherence" is established is always less than but still of order of the thermal line width of H-2. Thus coherent cores are similar to, but not exactly the same as, isothermal balls of gas. Two other results bolster our proposal that a transition to coherence takes place at similar to 0.1 pc. First, the OH, (CO)-O-18, and NH3 maps show that the dependence of column density on size is much steeper (N proportional to R-0.9) inside R-coh than outside of it (N proportional to R-0.2), Which implies that the volume filling factor of coherent cores is much larger than in their surroundings. Second, Larson (1995) has recently found a break in the power law characterizing the clustering of stars in Taurus at 0.04 pc, just inside of R-coh. Larson and we interpret this break in slope as the point at which stellar clustering properties change from being determined by the (fractal) gas distribution (on scales greater than 0.04 pc) to being determined by fragmentation processes within coherent cores (on scales less than 0.04 pc). We speculate that the transition to coherence takes place when a dissipation threshold for the MHD turbulence that characterizes the larger scale medium is crossed at the critical inner scale R-coh. We suggest that the most likely explanation for this threshold is the marked decline in the coupling of the magnetic field to gas motions due to a decreased ion/neutral ratio in dense, high filling factor gas.