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Photophoretic Strength on Chondrules 1: Modeling

Photophoresis is a physical process that transports particles in optical thin parts of protoplanetary disks, especially at the inner edge and at the optically surface. To model the transport and resulting effects in detail, it is necessary to quantify the strength of photophoresis for different particle classes as a fundamental input. Here, we explore photophoresis for a set of chondrules. The composition and surface morphology of these chondrules was measured by X-ray tomography. Based on the three-dimensional models, heat transfer through illuminated chondrules was calculated. The resulting surface temperature map was then used to calculate the photophoretic strength. We found that irregularities in particle shape and variations in composition induce variations in the photophoretic force. These depend on the orientation of a particle with respect to the light source. The variations of the absolute value of the photophoretic force on average over all chondrules is $4.17\%$. The deviation between the direction of the photophoretic force and illumination is $3.0^\circ \pm 1.5^\circ$. The average photophoretic force can be well approximated and calculated analytically assuming a homogeneous sphere with a volume equivalent mean radius and an effective thermal conductivity. We found an analytic expression for the effective thermal conductivity. The expression depends on the two main phases of a chondrule, and decreases with the amount of fine-grained devitrified, plagioclase-normative mesostasis up to factor of three. For the chondrule sample studied (Bjurböle chondrite), we found a dependence of the photophoretic force on chondrule size.