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

Abstract

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.

WASP-103 b: a new planet at the edge of tidal disruption

“…In this context, the fact that OGLE-TR-56 b, WASP-12 b, WASP-19 b and WASP-103 b have very similar masses (between 1.1 and 1.5 M Jup , see Fig. 3.2) may be meaningful, possibly suggesting a relatively narrow range of tidal dissipation efficiencies for solar-type stars (Chang et al 2010).…”

“…These transiting hot Jupiters undergo irradiation orders of magnitude larger than any solar system planets (Fortney et al 2007), and are also subject to intense gravitational and magnetic fields (Correia & Laskar 2011;Chang et al 2010). Their eclipsing configuration provides us with a unique opportunity to study their response to such extreme conditions and to improve substantially our knowledge of planetary structure, chemical composition and physical mechanisms.…”

The roles of tidal evolution and evaporative mass loss in the origin of CoRoT-7 b

“…This effect would be especially important during Roche lobe overflow, when a substantial portion of the planet's atmosphere may become unbound from the planet. Exchange of momentum between the escaping gas and the remaining planet can counteract the inwards pull of tides, even causing the planet to recede from the star (Chang, Gu & Bodenheimer 2010). This effect may significantly modify the orbital evolution we have considered here and may be responsible, at least in part, for the clustering of the orbital periods of close‐in exoplanets around 3 d (Cumming et al 2008).…”

Habitable Evaporated Cores: Transforming Mini-Neptunes into Super-Earths in the Habitable Zones of M Dwarfs

“…for a planet on a circular orbit (Gu et al, 2003;Chang et al, 2010). This leads to a corresponding increase in R Roche until it reaches R XUV and the overflow is halted.…”