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Coupled evolutions of the stellar obliquity, orbital distance, and planet's radius due to the Ohmic dissipation induced in a diamagnetic hot Jupiter around a magnetic T Tauri star

We revisit the calculation of the Ohmic dissipation in a hot Jupiter presented in Laine et al. (2008) by considering more realistic interior structures, stellar obliquity, and the resulting orbital evolution. In this simplified approach, the young hot Jupiter of one Jupiter mass is modelled as a diamagnetic sphere with a finite resistivity, orbiting across tilted stellar magnetic dipole fields in vacuum. Since the induced Ohmic dissipation occurs mostly near the planet's surface, we find that the dissipation is unable to significantly expand the young hot Jupiter. Nevertheless, the planet inside a small co-rotation orbital radius can undergo orbital decay by the dissipation torque and finally overfill its Roche lobe during the T Tauri star phase. The stellar obliquity can evolve significantly if the magnetic dipole is parallel/anti-parallel to the stellar spin. Our results are validated by the general torque-dissipation relation in the presence of the stellar obliquity. We also run the fiducial model in Laine et al. (2008) and find that the planet's radius is sustained at a nearly constant value by the Ohmic heating, rather than being thermally expanded to the Roche radius as suggested by the authors.