Deformation and internal flow of a chondrule-precursor molten sphere in a shocked nebular gas

Abstract

Chondrule formation due to a nebular shock wave heating is considered. We calculate the apparent gravitational acceleration, internal flow, and deformation of a chondrule precursor molten sphere in the shocked nebular gas. The gravitational acceleration and the internal flow are caused by momentum flux of gas molecules incident on the surface of the sphere. The gravitational acceleration just behind the shock wave is 1.1 to 330 times the terrestrial one. The velocity of the internal flow reaches around 0.1 m s⁻¹ for the pre-shock nebular gas density and the shock wave velocity are 10⁻⁶ kg m⁻³ and 8.7 km s⁻¹, respectively, and then chondrule melt is stirred well by the flow. As a consequence, if there is oxygen heterogeneity in the precursor particle, it must be homogenized by the high speed circulative flow in the molten sphere within a few seconds. The momentum flux also deforms the sphere. The variation of the radius of the molten sphere due to the deformation is less than 1% of the original radius for mm-sized sphere when the sphere re-solidifies. Because we used the hydrodynamic solution with the linear approximation, the applicability of our result of the internal flow is restricted to some region of the parameter space of the shock velocity, the nebular gas density, radius and viscosity of chondrule melt sphere. For larger values of those parameters than typical ones, nonlinear calculations are needed, which is left for future works.