The effect of dissipation on the generation of density structure by magnetohydrodynamic waves

Abstract

Observations of absorption lines in diffuse interstellar clouds may indicate that significant fluctuations in physical conditions exist on scales comparable to, or even smaller than, the dissipation length associated with ambipolar diffusion. Here we describe the results of simulations of magnetohydrodynamic (MHD) wave evolution in which ambipolar diffusion plays a major role. We find that ambipolar diffusion affects the evolution of waves with wavelengths up to about a thousand times the dissipation length-scale, which means that these results are relevant to both molecular and atomic interstellar clouds. The initial conditions consist of a uniform background upon which is superposed a non-linear fast-mode ideal MHD wave with a density contrast comparable to unity or less. The ratio, β, of the thermal pressure to the magnetic pressure is assumed to be small. For initial disturbances that have wavelengths that are very large compared to the dissipation length, the generation of structures with high-density contrast is due to the excitation of slow-mode waves by non-linear steepening of the fast-mode wave. In this case, collisions between the resulting structures lead to additional density enhancement for some ranges of the initial wave amplitude. For initial disturbances that have wavelengths such that dissipation is significant, slow-mode waves are also produced by ambipolar diffusion and this can generate higher density contrasts than those found in the corresponding cases in which dissipation is negligible. Large density contrasts on scales comparable to the dissipation length are found only when the wavelength of the initial perturbation is comparatively small. Because such waves do not propagate far before they are dissipated, we suggest that the variations in absorption features with time-scales ≃10 yr can only be generated by waves if they are located at the surfaces of clouds and are excited by external disturbances such as stellar winds, supernovae, etc. In order to produce the highest density contrasts that have been detected, the waves must have even larger amplitudes than those we have examined. This places severe restrictions on the properties of waves that could produce the kind of microstructure that some believe to be responsible for the rapid variations of absorption features.