Local support against gravity in magneto-turbulent fluids
Comparisons of the integrated thermal pressure support of gas against its gravitational potential energy lead to critical mass scales for gravitational instability such as the Jeans and the Bonnor-Ebert masses, which play an important role in analysis of many physical systems, including the heuristics of numerical simulations. In a strict theoretical sense, however, neither the Jeans nor the Bonnor-Ebert mass are meaningful when applied locally to substructure in a self-gravitating turbulent medium. For this reason, we investigate the local support by thermal pressure, turbulence, and magnetic fields against gravitational compression through an approach that is independent of these concepts. At the centre of our approach is the dynamical equation for the divergence of the velocity field. We carry out a statistical analysis of the source terms of the local compression rate (the negative time derivative of the divergence) for simulations of forced self-gravitating turbulence in periodic boxes with zero, weak, and moderately strong mean magnetic fields (measured by the averages of the magnetic and thermal pressures). We also consider the amplification of the magnetic field energy by shear and by compression. Thereby, we are able to demonstrate that the support against gravity is dominated by thermal pressure fluctuations, although magnetic pressure also yields a significant contribution. The net effect of turbulence, however, is to enhance compression rather than supporting overdense gas even if the vorticity is very high. This is incommensurate with the support of the highly dynamical substructures in magneto-turbulent fluids being determined by local virial equilibria of volume energies without surface stresses.