Volume 574, February 2015
|Number of page(s)||22|
|Section||Planets and planetary systems|
|Published online||20 January 2015|
II. Analytical vs. numerical solutions
1 Laboratoire J.-L. Lagrange, Université de Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice, France
2 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA
3 NASA Ames Research Center, MS-245-3, Mofett Field, CA 94035, USA
Received: 25 November 2013
Accepted: 29 October 2014
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.
Key words: radiative transfer / planets and satellites: atmospheres / stars: atmospheres / planet-star interactions
A FORTRAN implementation of the analytical model is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (22.214.171.124) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/574/A35 or at http://www.oca.eu/parmentier/nongrey.
Appendix A is available in electronic form at http://www.aanda.org
© ESO, 2015
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