Dust Dynamics in Compressible MHD Turbulence

We calculate the relative grain-grain motions arising from interstellar magnetohydrodynamic (MHD) turbulence. The MHD turbulence includes both fluid motions and magnetic fluctuations. While the fluid motions accelerate grains through hydro-drag, the electromagnetic fluctuations accelerate grains through resonant interactions. We consider both incompressive (Alfv\'{e}n) and compressive (fast and slow) MHD modes and use descriptions of MHD turbulence obtained in Cho & Lazarian (2002). Calculations of grain relative motion are made for realistic grain charging and interstellar turbulence that is consistent with the velocity dispersions observed in diffuse gas, including cutoff of the turbulence from various damping processes. We show that fast modes dominate grain acceleration, and can drive grains to supersonic velocities. Grains are also scattered by gyroresonance interactions, but the scattering is less important than acceleration for grains moving with sub-Alfv\'{e}nic velocities. Since the grains are preferentially accelerated with large pitch angles, the supersonic grains will be aligned with long axes perpendicular to the magnetic field. We compare grain velocities arising from MHD turbulence with those arising from photoelectric emission, radiation pressure and H$_{2}$ thrust. We show that for typical interstellar conditions turbulence should prevent these mechanisms from segregating small and large grains. Finally, gyroresonant acceleration is bound to preaccelerate grains that are further accelerated in shocks. Grain-grain collisions in the shock may then contribute to the overabundance of refractory elements in the composition of galactic cosmic rays.