Dust grain dynamics in C-Type shock waves in molecular clouds

We investigate the role and behaviour of dust grains in C-type MHD shock waves in weakly ionized, dense molecular clouds. The structure of C-type shocks in molecular clouds are largely determined by the coupling of the charged species and the magnetic fields in the pre-shock gas. In weakly ionized clouds, charged dust grains enhance the energy and momentum transfer between the magnetic field and the neutral fluid, and dominate the neutral collisional heating rate. New shock models are developed here for steady oblique C-type shock structures with shock speed vs = 18km/s, pre-shock number density nH = 10 cm, and a grain population represented by either a single grain species or a MRN grain size distribution. The grain size distribution is calculated using Gauss-Legendre weights and the integrals over the continuous distribution of grain sizes are represented by a number of grain bins. The grain population can then be thought of as a series of separate grain size classes, each with uniquely specified properties, such as the drift velocity with respect to the neutrals (vg − v), and the Hall parameter βg, which measures the degree of grain coupling to the magnetic field. The dynamics of each grain size class is different through the shock front, with the smaller grain classes remaining coupled to the magnetic field and larger grains becoming partially decoupled from the magnetic field due to collisions with the neutrals. The importance of grain charging is also demonstrated. Several other grain size distributions are considered, including a MRN grain size distribution with grain mantles, and a MRN distribution with a separate population of very small PAH particles. The effects of the orientation of the pre-shock magnetic field B0 with the shock normal, specified by the angle θ, are also considered. It is found that there are critical values for θ below which the shock is no longer C-type and the transition becomes C∗ or J-type. It is also shown that the degree of non-coplanarity of the shock solution depends upon the grain model chosen, as well as the angle θ.