  We present a simplified model to study the orbital evolution of a young hot
Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model
takes into account the disk locking of stellar spin as well as the tidal and
magnetic interactions between the star and the planet. We focus on the orbital
evolution starting from the orbit in the 2:1 resonance with the inner edge of
the disk, followed by the inward and then outward orbital migration driven by
the tidal and magnetic torques as well as the Roche-lobe overflow of the
tidally inflated planet. The goal in this paper is to study how the orbital
evolution inside the magnetospheric cavity depends on the cavity size, planet
mass, and orbital eccentricity. In the present work, we only target the mass
range from 0.7 to 2 Jupiter masses. In the case of the large cavity
corresponding to the rotational period ~ 7 days, the planet of mass >1 Jupiter
mass 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 <1
Jupiter mass cannot. We estimate the critical eccentricity beyond which the
planet of a given mass will overflow its Roche radius and finally lose all of
its gas onto the star due to runaway mass loss. In the case of the small cavity
corresponding to the rotational period ~ 3 days, all of the simulated planets
lose all of their gas even in circular orbits. Our results for the orbital
evolution of young hot Jupiters may have the potential to explain the absence
of low-mass giant planets inside ~ 0.03 AU from their dwarf stars revealed by
transit surveys.
