Jeans collapse in a turbulent medium

According to the classical Jeans criterion, all the observed molecular clouds of mass M greater than 100 solar masses, radius R greater than 1 pc and gas kinetic temperature Tk less than 30 K are gravitationally unstable. However, millimetric and infrared observations show that low mass dense cores (M greater than 3 solar masses) can collapse and form stars within clouds for which there is no evidence for global collapse. It is shown that, if the power spectrum of the turbulent internal motions which support them against gravity is steep enough, the molecular clouds are stable as long as their gas density remains close to the observed low mean densities (a few 100 per cu cm). For larger densities, only a narrow range of scales become gravitationally unstable. In that context, unstable low mass dense cores eventually form only when the density fluctuations within the clouds happen to be large.