2 Interior structure

Fully self-consistent models including both the atmospheres and interiors of Pegasi planets$\,\,$do not yet exist. To obtain first-cut estimates of the expected temperature profiles, we therefore use the same approach as in Paper I: we choose two extreme evolution models ("hot'' and "cold'') that match the radius of HD 209458b (but at different ages and hence intrinsic luminosities). These evolution calculations only pertain to pressures larger than 3 to 10 bars (depending on the boundary condition), and so we extend the profiles to lower pressure using radiative-transfer calculations for intensely-irradiated planets from Marley (personal communication) and Barman (2001). The calculations are not strictly appropriate to the case of HD 209458b, but provide us with reasonable estimates of the expected structure (and as we will see our qualitative conclusions are not sensitive to the type of profile chosen). The resulting "hot'' and "cold'' models that we will use hereafter are depicted in Fig. 1. Interestingly, Paper I shows that these two models are representative of a relatively wide variety of models of HD 209458b, including those with energy dissipation.

Figure 1: Left: temperature profiles for the "hot'' model (thin line) and "cold'' model (thick grey line) at times (5.37 and 0.18 Ga, respectively) when the models match HD 209458b's measured radius. The diamonds indicate the radiative/convective boundary. The terms ``hot'' and ``cold'' are chosen to indicate the models' relative temperatures in the region from $\sim$1-300 bars, which is the important region of the atmosphere for affecting the evolution. See Paper I for details. The discontinuity in the profiles' slopes is unphysical; it results from the fact that atmospheric models assume a much higher intrinsic luminosity than predicted by evolution models. Right: dimensionless mean specific heat per particle in the atmosphere. The local maxima in $c_{\rm p}$ are due to the dissociation of the H2 molecule.

It should be noted that the high temperatures can trigger the dissociation of the hydrogen molecule, which is indicated in Fig. 1 by a local maximum of the heat capacity $c_{\rm p}$. This effect is important for our purposes because it implies that stellar heat can be stored in hot regions and reclaimed in colder regions by molecular recombination. Other molecules (e.g. H₂O) can undergo dissociation, but this will be neglected due to their small abundances.

Evolution models of Pegasi planets$\,\,$show that two interior regions exist: a radiative zone (including the atmosphere) that extends down to pressures of 100 to 800bar, and a deeper convective core. The intrinsic luminosity of the planet is about 10000 times smaller than the energy absorbed from the star. If energy dissipation in the outer layers is large (see Paper I), another convective zone can appear at the levels where dissipation is the largest. This however requires a very high dissipation of $\sim$10% of the absorbed stellar flux. We therefore chose to only consider the simple radiative/convective scenario, as depicted in Fig. 2.

Figure 2: Conjectured dynamical structure of Pegasi planets: at pressures larger than 100-800bar, the intrinsic heat flux must be transported by convection. The convective core is at or near synchronous rotation with the star and has small latitudinal and longitudinal temperature variations. At lower pressures a radiative envelope is present. The top part of the atmosphere is penetrated by the stellar light on the day side. The spatial variation in insolation should drive winds that transport heat from the day side to the night side (see text).

We split the planet into an "atmosphere'' dominated by stellar heating, with possible horizontal temperature inhomogeneities, and an "interior'' including the convective core, for which inhomogeneities should be much smaller. The crux of the problem is to understand how the heat absorbed on the day side and near the equator is redistributed by winds and/or rotation to the night side and to the poles.