Conditions for Justifying Single-fluid Approximation for Charged and Neutral Dust Fluids and a Smoothed Particle Magnetohydrodynamics Method for Dust–Gas Mixture

Abstract

Abstract We describe a numerical scheme for magnetohydrodynamics simulations of dust–gas mixture by extending smoothed particle magnetohydrodynamics. We employ the single-species particle approach to describe dust–gas mixture with several modifications from the previous studies. We assume that the charged and neutral dust can be treated as single-fluid, that the electromagnetic force acts on the gas, and that that acting on the charged dust is negligible. The validity of these assumptions in the context of protostar formation is not obvious and is extensively evaluated. By investigating the electromagnetic force and electric current with terminal velocity approximation, it is found that as the dust size increases, the contribution of dust to them becomes smaller and negligible. We conclude that our assumption that the electromagnetic force on the dusts is negligible is valid for the dust size with a d ≳ 10 μm. On the other hand, they do not produce the numerical artifact for the dust a d ≲ 10 μm in the envelope and disk, where the perfect coupling between gas and dust is realized. However, we also found that our assumptions may break down in outflow (or under an environment with very strong magnetic field and low density) for the dust a d ≲ 10 μm. We conclude that our assumptions are valid in almost all cases where macroscopic dust dynamics is important in the context of protostar formation. We conduct numerical tests of dusty waves, dusty magnetohydrodynamics shocks, and gravitational collapse of magnetized cloud cores with our simulation code. The results show that our numerical scheme well reproduces the dust dynamics in the magnetized medium.