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 \approx 7 days , the planet of mass > 1 Jupiter mass with moderate initial eccentricities ( \gtrsim 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 can not .
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 \approx 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 \sim 0.03 AU from their dwarf stars revealed by transit surveys .