On the Absorption and Redistribution of Energy in Irradiated Planets

Abstract

We present a sequence of toy models for irradiated planet atmospheres, in which the effects of geometry and energy redistribution are modeled self-consistently. We use separate but coupled gray atmosphere models to treat the ingoing stellar irradiation and outgoing planetary reradiation. We investigate how observed quantities such as full phase secondary eclipses and orbital phase curves depend on various important parameters, such as the depth at which irradiation is absorbed, the depth at which energy is redistributed, and the eccentricity of the orbit. We also compare our results to the more detailed radiative transfer models in the literature in order to understand how those map onto the toy model parameter space. Such an approach can prove complementary to more detailed calculations, in that they demonstrate, in a simple way, how the solutions change depending on where, and how, energy redistribution occurs. As an example of the value of such models, we demonstrate how energy redistribution and temperature equilibration at moderate optical depths can lead to temperature inversions in the planetary atmosphere, which is of some relevance to recent observational findings.

On the radiative equilibrium of irradiated planetary atmospheres

“…This equation is almost identical to the one derived by Hansen (2008). However, a difference arises: the factor (3μ * /γ − γ/μ * ) has replaced Hansen's (3μ * /γ).…”

“…3.4). However, there are noticeable differences with the solutions provided by Hansen (2008) for low μ values. In particular, temperature inversions that should occur either for low μ or high γ values are absent of Hansen's solutions, a direct consequence of neglecting the heating caused by absorption of visible radiation.…”

“…The solution is equivalent to that obtained by Hansen (2008), except for a different boundary closure relation, and the fact that Eq. (27) accounts for atmospheric heating due to visible radiation (see Appendix).…”

The TRAPPIST survey of southern transiting planets

“…Clearly the planet is much warmer than this model. In blue and red are two models where the dayside incident flux is increased by a factor of 4/3 to simulate zero redistribution of absorbed flux (see, e.g., Hansen 2008). The red model features a dayside temperature inversion due to the strong optical opacity of TiO and VO gases (Hubeny et al 2003;Fortney et al 2006).…”

Observed spectral energy distribution of the thermal emission from the dayside of WASP-46b

“…The J, H, and K bands probe deep into the lower layers of the atmosphere because of weaker molecular absorptions at these bands. The isothermal temperature profile is expected to be present at the optical depth τ ∼ 1 (Hansen 2008;Madhusudhan & Seager 2009;Guillot 2010).…”