Formation and loss of hierarchical structure in two-dimensional magnetohydrodynamic simulations of wave-driven turbulence in interstellar clouds

Abstract

Two-dimensional compressible magnetohydrodynamical (MHD) simulations run for ∼20 crossing times on a 800 × 640 grid with two stable thermal states show persistent hierarchical density structures and Kolmogorov turbulent motions in the interaction zone between incoming nonlinear Alfvén waves. These structures and motions are similar to what is commonly observed in weakly self-gravitating interstellar clouds, suggesting that these clouds get their fractal structures from nonlinear magnetic waves generated in the intercloud medium; no internal source of turbulent energy is necessary. The clumps in the simulated clouds are slightly warmer than the interclump medium as a result of magnetic dissipational and compressive heating when the clumps form. Thus, the interclump medium has a lower pressure than the clumps, demonstrating that the clumps owe their existence entirely to transient compressive motions, not pressure confinement by the interclump medium. Clump lifetimes increase with size and are about one sound crossing time. Two experiments with this model illustrate a possible trigger for star formation during spontaneous cloud evolution driven by self-gravity and increased self-shielding. A first test is of the hypothesis that a low ionization fraction and enhanced magnetic diffusion lead to the disappearance of clumps smaller than an Alfvén wavelength. Two identical models are run that differ only in the magnetic diffusion rate. The results show a significant decrease in the magnetic wave amplitude as the diffusion rate increases, in agreement with expectations for wave damping, but there is virtually no change in the density structure or amplitude of the density fluctuations as a result of this increased diffusion. This is because all of the density fluctuations are essentially sonic in nature, driven by the noise from Alfvén wave motions outside and at the surface of the cloud. These sonic disturbances travel throughout the cloud parallel to the mean field orientation and are not affected by the local magnetic wave dissipation rate. This result implies that low ionization fractions in molecular clouds do not necessarily lead to increased cloud smoothing. The second experiment tests the hypothesis that enhanced density alone in a self-gravitating cloud leads to wave self-shielding and loss of incident turbulent energy. Three models with identical conditions except for the presence or lack of an imposed plane-parallel gravitational field confirm that externally generated magnetic waves tend to be excluded from the densest regions of self-gravitating clouds, and as a result these clouds show a significant loss of density substructure. This loss of turbulent energy and density substructure may trigger star formation in the relatively quiescent gas pools that contain a thermal Jeans mass or more. Such a model fits well with the hypothesis that the stellar initial mass function comes from the structure of turbulent hierarchical clouds.