Transport of First Rocks of The Solar System by X-winds

TL;DR

This study models the trajectories of early solar system solid bodies entrained in X-winds, revealing how disk gravity and size-dependent gas drag influence their re-entry points and potential for size-sorting, explaining observed chondrule size distributions.

Contribution

It introduces a detailed dynamical model including disk gravity and gas drag effects, showing how these factors influence solid body trajectories and size-sorting in the early solar system.

Findings

Disk gravity affects re-entry radius by up to 30%.

A threshold parameter $ta_t$ determines whether bodies are expelled or re-enter the disk.

Size-sorting explains narrow chondrule size ranges within chondritic classes.

Abstract

It has been suggested that chondrules and calcium-aluminum-rich inclusions (CAIs) were formed at the inner edge of the protoplanetary disk and then entrained in magnetocentrifugal X-winds. We study trajectories of such solid bodies with the consideration of the central star gravity, the protoplanetary disk gravity, and the gas drag of the wind. The efficiency of the gas drag depends on a parameter $\eta$, which is the product of the solid body size and density. We find that the gravity of the protoplanetary disk has a non-negligible effect on the trajectories. If a solid body re-enters the flared disk, the re-entering radius depends on the stellar magnetic dipole moment, the disk's gravity, the parameter $\eta$, and the initial launching angle. The disk's gravity can make the re-entering radius lower by up to 30%. We find a threshold $\eta$, denoted as $\eta_t$, for any particular configuration of the X-wind, below which the solid bodies will be expelled from the planetary system. $\eta_t$ sensitively depends on the initial launching angle, and also depends on the mass of the disk. Only the solid bodies with a $\eta$ larger than but very close to $\eta_t$ can be launched to a re-entering radius larger than 1 AU. This size-sorting effect may explain why chondrules come with a narrow range of sizes within each chondritic class. In general, the size distributions of CAIs and chondrules in chondrites can be determined from the initial size distribution as well as the distribution over the initial launching angle.