Turbulent molecular cloud cores: Rotational properties

The rotational properties of numerical models of centrally condensed, turbu lent molecular cloud cores with velocity fields that are characterized by G aussian 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) proportional to k(n) and n = -3 to -4. The line-of-s ight velocity maps of these cores show velocity gradients that can be inter preted as rotation. For n = -4, the deduced values of angular velocity n = 1.6 km s(-1) pc(-1) x(R/0.1 pc)(-0.5), and the scaling relations between Om ega 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 x 10(20) x (R/0.1 pc)(1.5) cm(2) s(-1) with a large spread. Their internal dimension less rotational parameter is beta approximate to 0.03, independent of the s cale radius R. In general, the line-of-sight velocity gradient of an indivi dual turbulent core does not provide a good estimate of its internal specif ic 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 t heir line-of-sight velocity gradients Omega using the simple formula j = p OmegaR(2), 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 centra lly condensed cores the intrinsic angular momentum is overestimated by a fa ctor of 2-3 if p = 0.4 is used.