Dense cores in dark clouds. VII - Line width-size relations

Abstract

Observations of 14 dense cores in lines of CS, C(O-18) and NH3 are combined to examine the relations between the Doppler width of a line and the spatial extent of the map of line intensity. The line width increases with map size R as R exp p. The deduced width of the velocity distribution of the molecule of mean mass has p = 0.20 +/- 0.04, and the deduced width of the nonthermal velocity distribution has p = 0.7 +/- 0.1. The values of p for eight cores with embedded stars and for six cores without embedded stars are statistically indistinguishable, but p is better determined for cores without stars. Thus the physical basis of the line width-size relations is part of the initial conditions for star formation, rather than a consequence of the star-core interaction. The cores appear close to virial equilibrium, consequently the variation of number density with distance from the core density maximum is deduced.