Anthony R. Dobrovolskis

Size-selective Concentration of Chondrules and Other Small Particles in Protoplanetary Nebula Turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive body precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region, both the characteristic size and size distribution of chondrules are explained. Fluffier particles would be concentrated in nebula regions that were at a lower gas density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (>105) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule-sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.

A numerical turbulence model for multiphase flows in the protoplanetary nebula

It is thought that planets form from solid particles in a flattened, rotating, 99% gaseous nebula. These grains gradually coagulate into millimeter‐to‐meter sized aggregates which settle toward the midplane of the nebula. It is widely believed that the resulting dense layer eventually becomes gravitationally unstable and collapses into ‘‘planetesimals.’’ A new numerical model is presented to simulate the predominant processes (gravitation, vertical convection, and shear‐driven turbulence) during the stage while the particulate material is still dispersed about the midplane of the nebula. In our previous work, particles were assumed to be spheres of a single radius; in the present work, particles are spheres of different radii. Results indicate that neither a broad nor a narrow distribution of particle sizes is likely to become gravitationally unstable.

Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits

Abstract We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch. The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L 4 (leading, near Telesto) or L 5 (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10xa0years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period). Still faster debris with azimuthal velocity components ≳10xa0m/s enter horseshoe orbits which enclose both L 4 and L 5 as well as L 3 , but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ≳40xa0m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years.