The Internal Structural Adjustment Due to Tidal Heating of Short‐Period Inflated Giant Planets

Abstract

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 that 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 nonideal equation of state determine their structure. However, in order for young or intensely heated gas giant planets to attain quasihydrostatic equilibria, with sizes comparable to or larger than 2R J , 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. Subject headings: planetary systems -planets and satellites: general On-line material: color figure

Theoretical Radii of Extrasolar Giant Planets: The Cases of TrES‐4, XO‐3b, and HAT‐P‐1b

“…In the past, the semimajor axis had been assumed to be constant when conducting tidal evolution studies (e.g., Bodenheimer et al 2001Bodenheimer et al , 2003Gu et al 2004). Jackson et al (2008b) calculate the evolutionary histories of the tidal dissipation rate for several EGPs, and find that in most cases the tidal heating rate increases as a planet moves inward and then decreases as the orbit circularizes.…”

Interaction of Close‐in Planets with the Magnetosphere of Their Host Stars. I. Diffusion, Ohmic Dissipation of Time‐dependent Field, Planetary Inflation, and Mass Loss

“…In the proximity of its host star, this extra energy source may cause a planet to inflate beyond its Hill's radius and lose mass (Gu et al 2004). …”

“…First, in order for the Roche lobe overflow to provide angular momentum, the actual shape of the Roche lobe should be taken into account. However, for computational simplicity, we adopt in this paper a spherically symmetric approximation (refer to Gu et al 2003, hereafter GBL03, for a detailed study). Second, we have only considered the contribution of ohmic dissipation P to the planetary inflation.…”

Observations of the companion to the pulsar PSR B1718-19

“…One is described in Zahn (1989, indicated with [Z]), the other in Goodman & Oh (1997, indicated with [G&O]). Ray et al 1987;Podsiadlowski 1996;Gu et al 2004;Ivanov & Papaloizou 2004), but none of these studies is directly applicable to our situation. Specifically for PSR B1718−19, Verbunt (1994) showed that the tidal energy is on the order of the potential energy of the star, assuming a ini a c or e ini ∼ 1 (here and below, the labels "ini" and "c" refer to those situations where the pulsar binary has just been formed and where the orbit has been circularised, respectively).…”