Transient evolution of C-type shocks in dusty regions of varying density

Context. Outflows of young stars drive shocks into dusty, molecular regions. Most models of such shocks are restricted by the assumptions that they are steady and propagating in directions perpendicular to the magnetic fields. However, the media through which shocks propagate are inhomogeneous and shocks are not steady. Furthermore, only a small fraction of shocks are nearly perpendicular. Aims. We identify features that develop when a shock encounters a density inhomogeneity and ascertain if any part of the precursor region of a non-steady multifluid shock ever behaves in a quasi-steady fashion. If it does, some time-dependent shocks may be modelled approximately without solving the time-dependent hydromagnetic equations. Methods. We use the code employed previously to produce the first time-dependent simulations of fast-mode oblique C-type shocks including a self-consistent calculation of the thermal and ionisation balances and a fluid treatment of grains. Results. Simulations were made for initially steady oblique C-type shocks, each of which encounters one of three types of density inhomogeneities. For a semi-finite inhomogeneity with a density larger than the surrounding medium's, a transmitted shock evolves from being of J-type to a steady C-type shock on a timescale comparable to the ion-flow time through it. A sufficiently upstream part of the precursor of an evolving J-type shock is quasi-steady. The ion-flow timescale is also relevant for the evolution of a shock moving into a region of decreasing density. The models for shocks propagating into regions in which the density increases and then decreases to its initial value cannot be entirely described in terms of the results obtained for monotonically increasing and decreasing densities. Conclusions. We present the first time-dependent simulations of dusty C-type shocks interacting with density perturbations. We studied the transient evolution of the shock structure and find that the initial interaction always produces a transition to a J-type shock. Furthermore, the long-term evolution back to a C-type shock cannot always be approximated by quasi-steady models.