Evidence of surface magnetism is now observed on an increasing number of cool stars. The detailed manner by which dynamo-generated magnetic fields giving rise to starspots traverse the convection zone still remains unclear. Some insight into this flux emergence mechanism has been gained by assuming bundles of magnetic field can be represented by idealized thin flux tubes (TFTs). Weber & Browning (2016) have recently investigated how individual flux tubes might evolve in a 0.3 solar-mass M dwarf by effectively embedding TFTs in time-dependent flows representative of a fully convective star. We expand upon this work by initiating flux tubes at various depths in the upper 50-75% of the star in order to sample the differing convective flow pattern and differential rotation across this region. Specifically, we comment on the role of differential rotation and time-varying flows in both the suppression and promotion of the magnetic flux emergence process.
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