Shock-wave Heating Model for Chondrule Formation: Hydrodynamics of Rotating Droplets Exposed to High-velocity Gas Flows

Introduction: The data of chondrule shapes is a strong clue for elucidating the chondrule formation mechanism. Recently, the three-dimensional data of chondrule shapes has been measured by the X-ray microtomography [1]. The external shapes were approximated as three-axial ellipsoids with a-, band nd c-axes (axial radii are A, B, and C (A≥B≥C), respectively). The plot of C/B vs. B/A shows that two groups can be recognized: oblate to prolate chondrules with large C/B and B/A of 0.9-1.0 (group-A) and prolate chondrules with relatively small B/A of 0.74-0.78 (group-B). The oblate chondrules are naturally explained by the rapid rotation of molten droplets [1, 2]. However, the origin of the prolate shapes is not clear. On the other hand, in the shock-wave heating model, which is one of the most plausible models for chondrule formation [e.g., 3], it is naturally expected that the molten droplet is exposed to the high-velocity rarefied gas flow. The magnitude of the deformation of the molten droplet has been analytically investigated [4]. Although the analysis by [4] did not consider the effect of the rotation, the rotation would play an important role in the droplet deformation. It is thought that the droplet deformation would affect the shapes of chondrules formed after re-solidification. In this study, we perform hydrodynamic simulations of molten silicate dust particles in the framework of the shock-wave heating. We numerically solve the hydrodynamical equations of rapidly rotating molten droplets exposed to the high-velocity rarefied gas and investigate the hydrodynamics of the droplet. Model: In the shock-wave heating model, the rotation of the precursor dust particle is naturally expected if the dust shape is irregular. Before the dust particles melt, it is thought that the precursor dust particles are not perfect spheres and have many bumps on its surface. The asymmetrical structures would cause the net torque in the gas flow and the precursor dust particles should begin to rotate. Therefore, it is expected that the dust particle has already obtained some angular velocity when it melts. We can roughly estimate the angular velocity Ω of the precursor dust particle and use it as the initial angular velocity of the molten droplet. We numerically solve the hydrodynamical equations