A non-grey analytical model for irradiated atmospheres. I: Derivation

Context. Semi-grey atmospheric models (with one opacity for the visible and one opacity for the infrared) are useful to understand the global structure of irradiated atmospheres, their dynamics and the interior structure and evolution of planets, brown dwarfs and stars. But when compared to direct numerical radiative transfer calculations for irradiated exoplanets, these models systematically overestimate the temperatures at low optical depth, independently of the opacity parameters. We wish to understand why semi-grey models fail at low optical depths, and provide a more accurate approximation to the atmospheric structure by accounting for the variable opacity in the infrared. Our analytical irradiated non-grey model is found to provide a range of temperatures that is consistent with that obtained by numerical calculations. We find that even for slightly non-grey thermal opacities the temperature structure differs significantly from previous semi-grey models. For small values of beta (expected when lines are dominant), we find that the non-grey effects are confined to low-optical depths. However, for beta larger than 0.5 (appropriate in the presence of bands with a wavelength-dependence smaller or comparable with the width of the Planck function), we find that the temperature structure is affected even down to infrared optical depths unity and deeper as a result of the so-called blanketing effect. The expressions that we derive may be used to provide a proper functional form for algorithms that invert the atmospheric properties from spectral information. Because a full atmospheric structure can be calculated directly, these expressions should be useful for simulations of the dynamics of these atmospheres and of the thermal evolution of the planets. Finally, they should be used to test full radiative transfer models and improve their convergence.Comment: Accepted by A&A, model available at http://www.oca.eu/parmentier/nongre

The Influence of Non-Uniform Cloud Cover on Transit Transmission Spectra

We model the impact of non-uniform cloud cover on transit transmission spectra. Patchy clouds exist in nearly every solar system atmosphere, brown dwarfs, and transiting exoplanets. Our major findings suggest that fractional cloud coverage can exactly mimic high mean molecular weight atmospheres and vice-versa over certain wavelength regions, in particular, over the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) bandpass (1.1-1.7 $\mu$m). We also find that patchy cloud coverage exhibits a signature that is different from uniform global clouds. Furthermore, we explain analytically why the "patchy cloud-high mean molecular weight" degeneracy exists. We also explore the degeneracy of non-uniform cloud coverage in atmospheric retrievals on both synthetic and real planets. We find from retrievals on a synthetic solar composition hot Jupiter with patchy clouds and a cloud free high mean molecular weight warm Neptune, that both cloud free high mean molecular weight atmospheres and partially cloudy atmospheres can explain the data equally well. Another key find is that the HST WFC3 transit transmission spectra of two well observed objects, the hot Jupiter HD189733b and the warm Neptune HAT-P-11b, can be explained well by solar composition atmospheres with patchy clouds without the need to invoke high mean molecular weight or global clouds. The degeneracy between high molecular weight and solar composition partially cloudy atmospheres can be broken by observing the molecular Rayleigh scattering differences between the two. Furthermore, the signature of partially cloudy limbs also appears as a $\sim$100 ppm residual in the ingress and egress of the transit light curves, provided the transit timing is known to seconds.Comment: Accepted to ApJ Feb. 8, 201

3D mixing in hot Jupiter atmospheres. I. application to the day/night cold trap in HD 209458b

Hot Jupiters exhibit atmospheric temperatures ranging from hundreds to thousands of Kelvin. Because of their large day-night temperature differences, condensable species that are stable in the gas phase on the dayside, such as TiO and silicates, may condense and gravitationally settle on the nightside. Atmospheric circulation may counterbalance this tendency to gravitationally settle. This three dimensional (3D) mixing of chemical species has not previously been studied for hot Jupiters, yet it is crucial to assess the existence and distribution of TiO and silicates in the atmospheres of these planets. We perform 3D global circulation models of HD209458b including passive tracers that advect with the 3D flow, including a source/sink on the nightside to represent condensation and gravitational settling of haze particles. We show that global advection patterns produce strong vertical mixing that can keep condensable species lofted as long as they are trapped in particles of sizes of a few microns or less on the night side. We show that vertical mixing results not from small-scale convection but from the large-scale circulation driven by the day-night heating contrast. Although this vertical mixing is not diffusive in any rigorous sense, a comparison of our results with idealized diffusion models allows a rough estimate of the vertical diffusion coefficient. Kzz=5x10**4/Sqrt(Pbar) m2/s can be used in 1D models of HD 209458b. Moreover, our models exhibit strong spatial and temporal variability in the tracer concentration that could result in observable variations during transit or secondary eclipse measurements. Finally, we apply our model to the case of TiO in HD209458b and show that the day-night cold trap would deplete TiO if it condenses into particles bigger than a few microns on the planet's night side, making it unable to create the observed stratosphere of the planet.Comment: Accepted in A&A in August 2013 http://dx.doi.org/10.1051/0004-6361/20132113

Vertical Tracer Mixing in Hot Jupiter Atmospheres

Aerosols appear to be ubiquitous in close-in gas giant atmospheres, and disequilibrium chemistry likely impacts the emergent spectra of these planets. Lofted aerosols and disequilibrium chemistry are caused by vigorous vertical transport in these heavily irradiated atmospheres. Here we numerically and analytically investigate how vertical transport should change over the parameter space of spin-synchronized gas giants. In order to understand how tracer transport depends on planetary parameters, we develop an analytic theory to predict vertical velocities and mixing rates ($K_\mathrm{zz}$) and compare the results to our numerical experiments. We find that both our theory and numerical simulations predict that, if the vertical mixing rate is described by an eddy diffusivity, then this eddy diffusivity $K_\mathrm{zz}$ should increase with increasing equilibrium temperature, decreasing frictional drag strength, and increasing chemical loss timescales. We find that the transition in our numerical simulations between circulation dominated by a superrotating jet and that with solely day-to-night flow causes a marked change in the vertical velocity structure and tracer distribution. The mixing ratio of passive tracers is greatest for intermediate drag strengths that corresponds to this transition between a superrotating jet with columnar vertical velocity structure and day-to-night flow with upwelling on the dayside and downwelling on the nightside. Lastly, we present analytic solutions for $K_\mathrm{zz}$ as a function of planetary effective temperature, chemical loss timescales, and other parameters, for use as input to one-dimensional chemistry models of spin-synchronized gas giant atmospheres.Comment: 25 pages, 12 figures, Accepted at Ap

Another look at the dayside spectra of WASP-43b and HD 209458b: are there scattering clouds?

The search for clouds on the dayside of hot Jupiters has been disadvantaged due to hot Jupiters having a limited number of high quality space-based observations. To date, retrieval studies have found no evidence for grey clouds on the dayside, however none of these studies explored the impact of scattering clouds. In this study we reanalyse the dayside emission spectrum of the hot Jupiter WASP-43b considering the different Spitzer data in the literature. We find that, in 2 of the 4 data sets explored, retrieving with a model that contains a scattering cloud is favoured over a cloud free model by a confidence of 3.13 - 3.36 $\sigma$. The other 2 data sets finds no evidence for scattering clouds. We find that the retrieved H$_2$O abundance is consistent regardless of the Spitzer data used and is consistent with literature values. We perform the same analysis for the hot Jupiter HD 209458b and find no evidence for dayside clouds, consistent with previous studies.Comment: 7 pages, 6 figures. Accepted for publication with MNRA

An Observational Diagnostic for Distinguishing Between Clouds and Haze in Hot Exoplanet Atmospheres

The nature of aerosols in hot exoplanet atmospheres is one of the primary vexing questions facing the exoplanet field. The complex chemistry, multiple formation pathways, and lack of easily identifiable spectral features associated with aerosols make it especially challenging to constrain their key properties. We propose a transmission spectroscopy technique to identify the primary aerosol formation mechanism for the most highly irradiated hot Jupiters (HIHJs). The technique is based on the expectation that the two key types of aerosols -- photochemically generated hazes and equilibrium condensate clouds -- are expected to form and persist in different regions of a highly irradiated planet's atmosphere. Haze can only be produced on the permanent daysides of tidally-locked hot Jupiters, and will be carried downwind by atmospheric dynamics to the evening terminator (seen as the trailing limb during transit). Clouds can only form in cooler regions on the night side and morning terminator of HIHJs (seen as the leading limb during transit). Because opposite limbs are expected to be impacted by different types of aerosols, ingress and egress spectra, which primarily probe opposing sides of the planet, will reveal the dominant aerosol formation mechanism. We show that the benchmark HIHJ, WASP-121b, has a transmission spectrum consistent with partial aerosol coverage and that ingress-egress spectroscopy would constrain the location and formation mechanism of those aerosols. In general, using this diagnostic we find that observations with JWST and potentially with HST should be able to distinguish between clouds and haze for currently known HIHJs.Comment: 10 pages, 4 figures, accepted to ApJ Letter

Bulk Composition of GJ 1214b and other sub-Neptune exoplanets

GJ1214b stands out among the detected low-mass exoplanets, because it is, so far, the only one amenable to transmission spectroscopy. Up to date there is no consensus about the composition of its envelope although most studies suggest a high molecular weight atmosphere. In particular, it is unclear if hydrogen and helium are present or if the atmosphere is water dominated. Here, we present results on the composition of the envelope obtained by using an internal structure and evolutionary model to fit the mass and radius data. By examining all possible mixtures of water and H/He, with the corresponding opacities, we find that the bulk amount of H/He of GJ1214b is at most 7% by mass. In general, we find the radius of warm sub-Neptunes to be most sensitive to the amount of H/He. We note that all (Kepler-11b,c,d,f, Kepler-18b, Kepler-20b, 55Cnc-e, Kepler-36c and Kepler-68b) but two (Kepler-11e and Kepler-30b) of the discovered low-mass planets so far have less than 10% H/He. In fact, Kepler-11e and Kepler-30b have 10-18% and 5-15% bulk H/He. Conversely, little can be determined about the H2O or rocky content of sub-Neptune planets. We find that although a 100% water composition fits the data for GJ1214b, based on formation constraints the presence of heavier refractory material on this planet is expected, and hence, so is a component lighter than water required. A robust determination by transmission spectroscopy of the composition of the upper atmosphere of GJ1214b will help determine the extent of compositional segregation between the atmosphere and envelope.Comment: Updated the masses and radii of the Kepler-11 system, added Kepler-30b as well in the analysis. Accepted in ApJ, 39 pages, 9 figure

A non-grey analytical model for irradiated atmospheres. II: Analytical vs. numerical solutions

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. 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. 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. We show that 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 smaller. 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 2.5m/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.Comment: Accepted in A&A, models are available at http://www.oca.eu/parmentier/nongrey or in CD

Evolution of Exoplanets and their Parent Stars

Studying exoplanets with their parent stars is crucial to understand their population, formation and history. We review some of the key questions regarding their evolution with particular emphasis on giant gaseous exoplanets orbiting close to solar-type stars. For masses above that of Saturn, transiting exoplanets have large radii indicative of the presence of a massive hydrogen-helium envelope. Theoretical models show that this envelope progressively cools and contracts with a rate of energy loss inversely proportional to the planetary age. The combined measurement of planetary mass, radius and a constraint on the (stellar) age enables a global determination of the amount of heavy elements present in the planet interior. The comparison with stellar metallicity shows a correlation between the two, indicating that accretion played a crucial role in the formation of planets. The dynamical evolution of exoplanets also depends on the properties of the central star. We show that the lack of massive giant planets and brown dwarfs in close orbit around G-dwarfs and their presence around F-dwarfs are probably tied to the different properties of dissipation in the stellar interiors. Both the evolution and the composition of stars and planets are intimately linked.Comment: appears in The age of stars - 23rd Evry Schatzman School on Stellar Astrophysics, Roscoff : France (2013

Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation

We apply hydrodynamic evaporation models to different synthetic planet populations that were obtained from a planet formation code based on a core-accretion paradigm. We investigated the evolution of the planet populations using several evaporation models, which are distinguished by the driving force of the escape flow (X-ray or EUV), the heating efficiency in energy-limited evaporation regimes, or both. Although the mass distribution of the planet populations is barely affected by evaporation, the radius distribution clearly shows a break at approximately 2 $R_{\oplus}$. We find that evaporation can lead to a bimodal distribution of planetary sizes (Owen & Wu 2013) and to an "evaporation valley" running diagonally downwards in the orbital distance - planetary radius plane, separating bare cores from low-mass planet that have kept some primordial H/He. Furthermore, this bimodal distribution is related to the initial characteristics of the planetary populations because low-mass planetary cores can only accrete small primordial H/He envelopes and their envelope masses are proportional to their core masses. We also find that the population-wide effect of evaporation is not sensitive to the heating efficiency of energy-limited description. However, in two extreme cases, namely without evaporation or with a 100\% heating efficiency in an evaporation model, the final size distributions show significant differences; these two scenarios can be ruled out from the size distribution of $Kepler$ candidates.Comment: Accepted for publication in ApJ; 24 pages, 16 figure