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We present a simplified model to study the orbital evolution of a young hotJupiter inside the magnetospheric cavity of a proto-planetary disk. The modeltakes into account the disk locking of stellar spin as well as the tidal andmagnetic interactions between the star and the planet. We focus on the orbitalevolution starting from the orbit in the 2:1 resonance with the inner edge ofthe disk, followed by the inward and then outward orbital migration driven bythe tidal and magnetic torques as well as the Roche-lobe overflow of thetidally inflated planet. The goal in this paper is to study how the orbitalevolution inside the magnetospheric cavity depends on the cavity size, planetmass, and orbital eccentricity. In the present work, we only target the massrange from 0.7 to 2 Jupiter masses. In the case of the large cavitycorresponding to the rotational period ~ 7 days, the planet of mass >1 Jupitermass with moderate initial eccentricities (>~ 0.3) can move to the region <0.03 AU from its central star in 10^7 years, while the planet of mass <1Jupiter mass cannot. We estimate the critical eccentricity beyond which theplanet of a given mass will overflow its Roche radius and finally lose all ofits gas onto the star due to runaway mass loss. In the case of the small cavitycorresponding to the rotational period ~ 3 days, all of the simulated planetslose all of their gas even in circular orbits. Our results for the orbitalevolution of young hot Jupiters may have the potential to explain the absenceof low-mass giant planets inside ~ 0.03 AU from their dwarf stars revealed bytransit surveys.

Tidal and Magnetic Interactions between a Hot Jupiter and its Host Star in the Magnetospheric Cavity of a Protoplanetary Disk