THE DELTA-V-L DEPENDENCE AND VIRIAL EQUILIBRIUM OF DENSE MOLECULAR-CLOUD CORES

The dependence of the HCO+ and (HCO+)-C-13 linewidths on the size of t he emission region (Delta V approximate to 2.9L((0.5 +/- 0.1))) has be en found for a sample of 12 dense molecular-cloud cores associated wit h Sharpless H II regions. Estimates of the core masses calculated in a n isothermal dust component approximation are low if the dust temperat ure decreases toward the core boundary. If the core density profiles a re described by a power law rho proportional to r(-beta), the exponent beta has an upper limit beta(max), which varies from 0.5 to 1.3 for t he cores in the sample. It is not possible to obtain model spectra tha t agree with the observational data for beta > beta(max). The core mas ses are close to the virial masses for beta = 0.5, indicating that the cores may be close to a critical state at the threshold of gravitatio nal instability. The observed correlation between Delta V and L cannot be explained by the radial dependence of the velocity dispersion that results from the logotropic equation of state, which has recently bee n successfully used to explain similar dependences for both massive an d low-mass cores. This may also testify that the dense cores studied a re close to the critical state, in which the Delta V proportional to P -ext(1/4) L-1/2 relation is independent of the equation of state (wher e P-ext is the external pressure on the core). In this case, the mean external pressure for the sample cores should be P-ext/k approximate t o 5.9 x 10(6) cm(-3) K.