Highly compressible MHD turbulence and gravitational collapse

We investigate the properties of highly compressible turbulence and its ability to produce self-gravitating structures. The compressibility is parameterized by an effective polytropic exponent gamma(e). In the limit of small gamma(e), the density jump at shocks is shown to be of the order of e(M2). In the presence of self-gravity, we suggest that turbulence can produce bound structures for gamma(e) < 2(1 - 1/n), where n is the typical dimensionality of the turbulent compressions. We show, by means of numerical simulations, that, for sufficiently small gamma(e), small-scale turbulent density fluctuations eventually collapse even though the medium is globally stable. This result is preserved in the presence of a magnetic field for supercritical mass-to-flux ratios.