Uncertainties in tidal theory: Implications for bloated hot Jupiters

Abstract

AbstractThanks to the combination of transit photometry and radial velocity doppler measurements, we are now able to constrain theoretical models of the structure and evolution of objects in the whole mass range between icy giants and stars, including the giant planet/brown dwarf overlapping mass regime (Leconte et al. 2009). In the giant planet mass range, the significant fraction of planets showing a larger radius than predicted by the models suggests that a missing physical mechanism which is either injecting energy in the deep convective zone or reducing the net outward thermal flux is taking place in these objects. Several possibilities have been suggested for such a mechanism: •downward transport of kinetic energy originating from strong winds generated at the planet's surface (Showman & Guillot 2002),•enhanced opacity sources in hot-Jupiter atmospheres (Burrows et al. 2007),•ohmic dissipation in the ionized atmosphere (Batygin & Stevenson 2010),•(inefficient) layered or oscillatory convection in the planet's interior (Chabrier & Baraffe 2007),•Tidal heating due to circularization of the orbit, as originally suggested by Bodenheimer, Lin & Mardling (2001). Here we first review the differences between current models of tidal evolution and their uncertainties. We then revisit the viability of the tidal heating hypothesis using a tidal model which treats properly the highly eccentric and misaligned orbits commonly encountered in exoplanetary systems. We stress again that the low order expansions in eccentricity often used in constant phase lag tidal models (i.e. constant Q) necessarily yields incorrect results as soon as the (present or initial) eccentricity exceeds ~ 0.2, as can be rigorously demonstrated from Kepler's equations.