CO cooling rates for clumpy and turbulent molecular clouds

Aims.Based on a stochastic radiative transfer model (SRTM), which accounts for density and velocity fluctuations with a finite correlation length, we have calculated CO cooling rates for a molecular gas at temperatures $T_{{\rm gas}}$ = (10-100) K and densities $n_{{\rm H}_{2}}$ = (102-106) cm-3. In particular, we are interested in how the cooling rates are modified by inhomogeneities of the density distribution and a finite correlation length of the turbulent velocity field. Methods.Assuming spherical symmetry, we solved the generalized radiative transfer equation simultaneously with the rate equations (full NLTE problem). Depending on the temperature assumed, we took up to 18 rotational levels of the CO molecule into account. Results.Our results show that the finite correlation length of the turbulent velocity field has a great influence on the CO cooling rates. In general, the volume averaged cooling rates are noticeably decreasing with an increasing correlation length of the velocity field except for very high CO cloumn densities. The stochastic density fluctuations, on the other side, tend to increase the CO cooling efficiency. For an inhomogeneous stochastic density distribution, cooling by the high rotational lines of CO is substantially enhanced. Most of the radiation is emitted from cloud regions with higher density than the average. In addition, an inhomogeneous density field reduces the effect of photon trapping, which leads to a further increase of the cooling rate. A comparison of the SRTM results with earlier work of Neufeld et al. (1995, ApJS, 100, 132) and Juvela et al. (2001, ApJ, 563, 853) is given. It turns out that their predictions and findings can be reproduced rather well by choosing the parameters describing the stochastic density and velocity field appropriately