Turbulent Molecular Cloud Cores: Rotational Properties^*

The rotational properties of numerical models of centrally condensed, turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated. It is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power law with P(k) ∝ kⁿ and n = -3 to -4. The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation. For n = -4, the deduced values of angular velocity Ω = 1.6 km s^-1 pc^-1×(R/0.1 pc)^-0.5, and the scaling relations between Ω and the core radius R are in very good agreement with the observations. As a result of the dominance of long-wavelength modes, the cores also have a net specific angular momentum with an average value of J/M = 7 × 10²⁰ × (R/0.1 pc)^1.5 cm² s^-1 with a large spread. Their internal dimensionless rotational parameter is β ≈ 0.03, independent of the scale radius R. In general, the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum. We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients Ω using the simple formula j = pΩR², where p depends on the density distribution of the core and has to be determined from a Monte Carlo study. Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p = 0.4 is used.