The Internal Structural Adjustment due to Tidal Heating of Short - Period Inflated Giant Planets

Several short-period Jupiter-mass planets have been discovered around nearby solar-type stars. During the circularization of their orbits, the dissipation of tidal disturbance by their host stars heats the interior and inflates the sizes of these planets. Based on a series of internal structure calculations for giant planets, we examine the physical processes which determine their luminosity-radius relation. In the gaseous envelope of these planets, efficient convection enforces a nearly adiabatic stratification. During their gravitational contraction, the planets’ radii are determined, through the condition of a quasi-hydrostatic equilibrium, by their central pressure. In interiors of mature, compact, distant planets, such as Jupiter, degeneracy pressure and the non-ideal equation of state determine their structure. But, in order for young or intensely heated gas giant planets to attain quasi-hydrostatic equilibria, with sizes comparable to or larger than two Jupiter radii, their interiors must have sufficiently high temperature and low density such that degeneracy effects are relatively weak. Consequently, the effective polytropic index monotonically increases whereas the central temperature increases and then decreases with the planets’ size. These effects, along with a temperature-sensitive opacity for the radiative surface layers of giant planets, cause the power index of the luminosity’s dependence on radius to decrease with increasing radius. For planets larger than twice Jupiter’s radius, this index is sufficiently small that they become unstable to tidal inflation. We make comparisons between cases of uniform heating and cases in which the heating is concentrated in various locations within the giant planet. Based on these results we suggest that accurate measurement of the sizes of close-in young Jupiters can be used to probe their internal structure under the influence of tidal heating.