Coagulation of inertial particles in supersonic turbulence

We study coagulation of inertial particles in compressible turbulence using high resolution direct and shock capturing numerical simulations with a wide range of Mach numbers-from nearly incompressible to moderately supersonic. The particle dynamics is \obsb{simulated} by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). For the sake of computational economy, the simulations are not scaled to match astrophysical conditions, but our results imply that a massive computational effort to target interstellar conditions may be worthwhile. We find that in the transonic regime the average coagulation rate $\langle R_c\rangle$ roughly scales linearly with the average Mach number $\mathcal{M}_{\rm rms}$ multiplied by the combined size of the colliding particles, i.e., $\langle R_c\rangle \sim (a_i + a_j)^3\, \mathcal{M}_{\rm rms}$, which is qualitatively consistent with expectations from analytical estimates. It is shown that the scaling is different in the supersonic regime.