Multifluid, magnetohydrodynamic shock waves with grain dynamics. II. Dust and the critical speed for C shocks

This is the second in a series of papers on the effects of dust on multifluid, magnetohydrodynamic shock waves in weakly ionized molecular gas. We investigate the influence of dust on the critical shock speed, v_crit, above which C shocks cease to exist. Chernoff showed that v_crit cannot exceed the grain magnetosound speed, V_gms, if dust grains are dynamically well coupled to the magnetic field. Since V_gms ≃ 5 km s^-1 in a dense cloud or core, the potential implications for models of shock emission are profound. We present numerical simulations of steady shocks where the grains may be well or poorly coupled to the field. We use a time-dependent, multifluid MHD code that models the plasma as a system of interacting fluids: neutral particles, ions, electrons, and various "dust fluids" comprised of grains with different sizes and charges. Our simulations include grain inertia and grain charge fluctuations, but to highlight the essential physics we assume adiabatic flow and single-size grains and neglect the effects of chemistry. We show that the existence of a phase speed v_φ does not necessarily mean that C shocks will form for all shock speeds v_s less than v_φ. When the grains are weakly coupled to the field, steady, adiabatic shocks resemble shocks with no dust: the transition to J-type flow occurs at v_crit ≈ 2.76V _nA, where V_nA is the neutral Alfvén speed, and steady shocks with v_s > 2.76V_nA are J shocks with magnetic precursors in the ion-electron fluid. When the grains are strongly coupled to the field, v_crit = min(2.76V_nA, V _gms). Shocks with v_crit < v_s < V _gms have magnetic precursors in the ion-electron-dust fluid. Shocks with v_s > V_gms have no magnetic precursor in any fluid. We present time-dependent calculations to study the formation of steady, multifluid shocks. The dynamics differ qualitatively, depending on whether or not the grains and field are well coupled.