A non-grey analytical model for irradiated atmospheres

Abstract

Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims. We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods. We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results. We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ∼5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ∼2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (∼2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper atmosphere to cool down rather than an enhanced absorption of the stellar light as previously thought. Finally, we provide a functional form for the coefficients of our analytical model for solar-composition giant exoplanets and brown dwarfs. This leads to fully analytical pressure-temperature profiles for irradiated atmospheres with a relative accuracy better than 10% for gravities between 2.5 m s −2 and 250 m s −2 and effective temperatures between 100 K and 3000 K. This is a great improvement over the commonly used Eddington boundary condition.

A Comparison of Simulated JWST Observations Derived from Equilibrium and Non-equilibrium Chemistry Models of Giant Exoplanets

“…For HD 189733b, we use the temperature-pressure profile from Moses et al (2011). For WASP-80b, and GJ 436b, we generate a temperature-pressure profile using Parmentier et al (2015) and heat the upper atmosphere according to the process outlined in Moses et al (2011).…”

Transitions in the Cloud Composition of Hot Jupiters

“…The pressure ranges from 200 bar to 2 μbar over 53 levels, so that we have a resolution of almost 3 levels per scale height. We use a horizontal resolution of C32, equivalent to an approximate resolution of 128 cells in longitude and 64 in latitude and a timestep of 25 s. We initialize the model at rest with a temperature profile from the analytical model of Parmentier et al (2015) that uses the analytical expression of Parmentier & Guillot (2014) fitted to represent the global average temperature profile of solar-composition atmospheres without TiO/VO (Fortney et al 2007). The simulations all run for 150 Earth days, a length over which the observable atmosphere hasreached a quasi steadystate (Showman et al 2009).…”

Atmospheric Circulations of Hot Jupiters as Planetary Heat Engines

“…) , where the power-law exponent comes from fitting the analytic model of Parmentier & Guillot (2014) and Parmentier et al (2015) to radiative transfer models with realistic opacities. With these values, the photosphere (where the optical thickness equals unity) for stellar radiation lies at about 0.23 bar and the photosphere for thermal radiation lies at 0.28 bar.…”