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

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 $η$, 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 $η$, and the initial launching angle. The disk's gravity can make the re-entering radius lower by up to 30%. We find a threshold $η$, denoted as $η_t$, for any particular configuration of the X-wind, below which the solid bodies will be expelled from the planetary system. $η_t$ sensitively depends on the initial launching angle, and also depends on the mass of the disk. Only the solid bodies with a $η$ larger than but very close to $η_t$ 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.