On the radiative equilibrium of irradiated planetary atmospheres

By T. Guillot. 2010

426 citations recorded by the source corpus.

The evolution of stars and planets is mostly controlled by the properties of their atmosphere. This is particularly true in the case of exoplanets close to their stars, for which one has to account both for an (often intense) irradiation flux, and from an intrinsic flux responsible for the progressive loss of the inner planetary heat. The goals of the present work are to help understanding the coupling between radiative transfer and advection in exoplanetary atmospheres and to provide constraints on the temperatures of the deep atmospheres. This is crucial in assessing whether modifying assumed opacity sources and/or heat transport may explain the inflated sizes of a significant number of giant exoplanets found so far. I use a simple analytical approach inspired by Eddington's approximation for stellar atmospheres to derive a relation between temperature and optical depth valid for plane-parallel static grey atmospheres which are both transporting an intrinsic heat flux and receiving an outer radiation flux. The model is parameterized as a function of mean visible and thermal opacities, respectively. The model is shown to reproduce relatively well temperature profiles obtained from more sophisticated radiative transfer calculations of exoplanetary atmospheres. It naturally explains why a temperature inversion (stratosphere) appears when the opacity in the optical becomes significant compared to that in the infrared. I further show that the mean equivalent flux (proportional to T^4) is conserved in the presence of horizontal advection on constant optical depth levels. This implies with these hypotheses that the deep atmospheric temperature used as outer boundary for the evolution models should be calculated from models pertaining to the entire planetary atmosphere, not from ones that are relevant to the day side or to the substellar point. In these conditions, present-day models yield deep temperatures that are ~1000K too cold to explain the present size of planet HD 209458b. An tenfold increase in the infrared to visible opacity ratio would be required to slow the planetary cooling and contraction sufficiently to explain its size. However, the mean equivalent flux is not conserved anymore in the presence of opacity variations, or in the case of non-radiative vertical transport of energy: The presence of clouds on the night side or a downward transport of kinetic energy and its dissipation at deep levels would help making the deep atmosphere hotter and may explain the inflated sizes of giant exoplanets.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b21aab40e8cc6056710a08d1e819dc1518dfc5f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. N. Madhusudhan
2. Jon Fortney
3. C. Mordasini
4. A. Showman
5. M. Marley
6. V. Parmentier
7. M. Line
8. J. Owen

In Instrumentation

1. N. Madhusudhan
2. Jon Fortney
3. M. Line
4. A. Showman
5. V. Parmentier
6. C. Mordasini
7. M. Marley
8. H. Knutson

In Statistical and Nonlinear Physics

1. N. Madhusudhan
2. Jon Fortney
3. M. Line
4. J. Owen
5. C. Mordasini
6. Yanqin Wu
7. V. Parmentier
8. H. Knutson

Citations in the corpus

•  ?> -REx. II. RETRIEVAL OF EMISSION SPECTRA (2015, methodology): “As described above, the Stage 1 retrieval was first performed using the parmetric TP-profile by Guillot (2010) with the additional optical opacity terms proposed by Line et al. (2012).”
• THE MASS–METALLICITY RELATION FOR GIANT PLANETS (2015, background): “However, given uncertainties in the upper boundary condition in strongly irradiated giant planets (see, e.g., Guillot 2010for an analytic analysis, Spiegel & Burrows 2013for a review of the chemical and physical processes at play, and Guillot & Showman 2002for an application of a 2D boundary…”
• A SYSTEMATIC RETRIEVAL ANALYSIS OF SECONDARY ECLIPSE SPECTRA. I. A COMPARISON OF ATMOSPHERIC RETRIEVAL TECHNIQUES (2013, methodology): “For our particular parameterization, we assume the atmosphere to be in radiative equilibrium based upon the analytic radiative equilibrium temperature profile of Guillot 2010 (and others such as Hansen 2008; Heng et al. 2012; Robinson & Catling 2012).”
• FORMATION AND STRUCTURE OF LOW-DENSITY EXO-NEPTUNES (2011, methodology): “Within the thin outer edge of the envelope, we adopt the isotropic average temperature profile from Equation (29) in Guillot (2010), T (τ)= 3T 4int 4 [ 2 3 + τ ] (5) + 3T 4irr 4 f [ 2 3 + 1 γ √ 3 + ( γ√ 3 − 1 γ √ 3 ) e−γτ √ 3 ] , an analytic solution to the “two-stream” gray equations of radiative…”
• The Hubble Space Telescope PanCET Program: Exospheric Mg ii and Fe ii in the Near-ultraviolet Transmission Spectrum of WASP-121b Using Jitter Decorrelation (2019, methodology): “The T-P profile was generated using the analytical model of Guillot (2010), which assumes radiative equilibrium, and is parameterized with the Planck mean thermal infrared opacity, κIR, the ratio of the optical to infrared opacity, γ, an irradiation efficiency factor β, and the interior temperature…”
• GASEOUS MEAN OPACITIES FOR GIANT PLANET AND ULTRACOOL DWARF ATMOSPHERES OVER A RANGE OF METALLICITIES AND TEMPERATURES (2014, background): “However, in a revision of the Guillot (2010) work, Parmentier et al. (2013) (see their §5.1.1) suggest that instead the stellar-Teff weighted RM is much more useful to understand the depth to which incident stellar flux penentrates, since the RM most heavily weights at wavelengths where opacity is…”
• A SYSTEMATIC RETRIEVAL ANALYSIS OF SECONDARY ECLIPSE SPECTRA. II. A UNIFORM ANALYSIS OF NINE PLANETS AND THEIR C TO O RATIOS (2013, methodology): “The parameterization we use is based on analytic radiative equilibrium profiles (see Guillot 2010; Heng et al. 2012; Robinson & Catling 2012) controlled by 5 free parameters.”
• BULK COMPOSITION OF GJ 1214b AND OTHER SUB-NEPTUNE EXOPLANETS (2013, methodology): “Atmospheric Model The upper boundary condition of our interior model is given by the atmospheric model of Guillot (2010).”
• C/O RATIO AS A DIMENSION FOR CHARACTERIZING EXOPLANETARY ATMOSPHERES (2012, background): “T profiles of strongly irradiated atmospheres asymptote to isotherms at high optical depth, for P ∼ 1 − 10 bar (Burrows et al. 2008; Hansen 2009; Guillot 2010).”
• Characterization of exoplanets from their formation - II. The planetary mass-radius relationship (2012, methodology): “We note that our treatment of the effect of stellar irradiation on the envelope structure is very basic at the moment (Paper I) and will be improved in future (Guillot 2010; Heng et al. 2011).”
• A DETECTION OF WATER IN THE TRANSMISSION SPECTRUM OF THE HOT JUPITER WASP-12b AND IMPLICATIONS FOR ITS ATMOSPHERIC COMPOSITION (2015, methodology): “The T/P profile is modeled with a 5-parameter analytic function (Line et al. 2013b) which produces physically realistic thermal profiles consistent with radiative equilibrium (e.g. Guillot 2010; Robinson & Catling 2012; Heng et al. 2012; Parmentier & Guillot 2014).”
• Characterization of exoplanets from their formation - I. Models of combined planet formation and evolution (2012, background): “In future work, we will include boundary conditions that are also accurate for planets close to the parent star undergoing intense irradiation (Guillot 2010; Heng et al. 2012).”
• Retrieving scattering clouds and disequilibrium chemistry in the atmosphere of HR 8799e (2020, methodology): “The analytical solution (or a modification of it) by Guillot (2010); Parmentier & Guillot (2014) is commonly used, for example in Line et al. (2012, 2013a,b, 2014b), Benneke & Seager (2012), Waldmann et al. (2015), Rocchetto et al. (2016), Kreidberg et al. (2018), Brogi & Line (2019), Mollière et…”
• THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS (2016, methodology): “…calculations As described in Section 2.2.2 the atmospheric model used during the evolution of the planets is the analytic double-gray model by Guillot (2010), which takes the planet’s enrichment into account in an approximative fashion, by using scaled solar abundance Rosseland mean…”
• On the Cool Side: Modeling the Atmospheres of Brown Dwarfs and Giant Planets (2014, background): “…of brown dwarfs (Lunine et al. 1986, 1989) and recent analytic models of the thermal structure of irradiated planetary atmospheres (Hansen 2008; Guillot 2010; Robinson & Catling 2012; Parmentier & Guillot 2014) have used opacities averaged over the entire spectral range, or ‘gray’ opacities,…”
• PLANETARY POPULATION SYNTHESIS COUPLED WITH ATMOSPHERIC ESCAPE: A STATISTICAL VIEW OF EVAPORATION (2014, methodology): “…the equilibrium temperature obtained by averaging the stellar radiation over the entire planet surface (T∗ is the stellar temperature, R∗ is the stellar radius, and D is the distance from the planet to the star), γ = κv/κth is the ratio of the visible opacity to the thermal opacity (Guillot 2010).”