Distorted, non-spherical transiting planets: impact on the transit depth and on the radius determination

We quantify the systematic impact of the non-spherical shape of transiting planets and brown dwarfs, due to tidal forces and rotation, on the observed transit depth. Such a departure from sphericity leads to a bias in the derivation of the transit radius from the light curve and affects the comparison with planet structure and evolution models which assume spherical symmetry. As the tidally deformed planet projects its smallest cross section area during the transit, the measured effective radius is smaller than the one of the unperturbed spherical planet. This effect can be corrected by calculating the theoretical shape of the observed planet. We derive simple analytical expressions for the ellipsoidal shape of a fluid object (star or planet) accounting for both tidal and rotational deformations and calibratre it with fully numerical evolution models in the 0.3Mjup-75Mjup mass range. Our calculations yield a 20% effect on the transit depth, i.e. a 10% decrease of the measured radius, for the extreme case of a 1Mjup planet orbiting a Sun-like star at 0.01AU. For the closest planets detected so far (< 0.05 AU), the effect on the radius is of the order of 1 to 10%, by no means a negligible effect, enhancing the puzzling problem of the anomalously large bloated planets. These corrections must thus be taken into account for a correct determination of the radius from the transit light curve. Our analytical expressions can be easily used to calculate these corrections, due to the non-spherical shape of the planet, on the observed transit depth and thus to derive the planet's real equilibrium radius. They can also be used to model ellipsoidal variations of the stellar flux now detected in the CoRoT and Kepler light curves. We also derive directly usable analytical expressions for the moment of inertia, oblateness and Love number (k_2) of a fluid planet as a function of its mass.Comment: 19 pages, 6 figures, 5 tables. Published in A&A. Correction of minor errors in Appendix B. An electronic version of the grids of planetary models is available at http://perso.ens-lyon.fr/jeremy.leconte/JLSite/JLsite/Exoplanets_Simulations.htm

The mass-radius relationship from solar-type stars to terrestrial planets: a review

In this review, we summarize our present knowledge of the behaviour of the mass-radius relationship from solar-type stars down to terrestrial planets, across the regime of substellar objects, brown dwarfs and giant planets. Particular attention is paid to the identification of the main physical properties or mechanisms responsible for this behaviour. Indeed, understanding the mechanical structure of an object provides valuable information about its internal structure, composition and heat content as well as its formation history. Although the general description of these properties is reasonably well mastered, disagreement between theory and observation in certain cases points to some missing physics in our present modelling of at least some of these objects. The mass-radius relationship in the overlaping domain between giant planets and low-mass brown dwarfs is shown to represent a powerful diagnostic to distinguish between these two different populations and shows once again that the present IAU distinction between these two populations at a given mass has no valid foundation.Comment: Cool Stars, Stellar Systems and the Sun 15, invited revie

3D climate modeling of close-in land planets: Circulation patterns, climate moist bistability and habitability

The inner edge of the classical habitable zone is often defined by the critical flux needed to trigger the runaway greenhouse instability. This 1D notion of a critical flux, however, may not be so relevant for inhomogeneously irradiated planets, or when the water content is limited (land planets). Here, based on results from our 3D global climate model, we find that the circulation pattern can shift from super-rotation to stellar/anti stellar circulation when the equatorial Rossby deformation radius significantly exceeds the planetary radius. Using analytical and numerical arguments, we also demonstrate the presence of systematic biases between mean surface temperatures or temperature profiles predicted from either 1D or 3D simulations. Including a complete modeling of the water cycle, we further demonstrate that for land planets closer than the inner edge of the classical habitable zone, two stable climate regimes can exist. One is the classical runaway state, and the other is a collapsed state where water is captured in permanent cold traps. We identify this "moist" bistability as the result of a competition between the greenhouse effect of water vapor and its condensation. We also present synthetic spectra showing the observable signature of these two states. Taking the example of two prototype planets in this regime, namely Gl581c and HD85512b, we argue that they could accumulate a significant amount of water ice at their surface. If such a thick ice cap is present, gravity driven ice flows and geothermal flux should come into play to produce long-lived liquid water at the edge and/or bottom of the ice cap. Consequently, the habitability of planets at smaller orbital distance than the inner edge of the classical habitable zone cannot be ruled out. Transiting planets in this regime represent promising targets for upcoming observatories like EChO and JWST.Comment: Accepted for publication in Astronomy and Astrophysics, complete abstract in the pdf, 18 pages, 18 figure

Elliptical instability in hot Jupiter systems

Several studies have already considered the influence of tides on the evolution of systems composed of a star and a close-in companion to tentatively explain different observations such as the spin-up of some stars with hot Jupiters, the radius anomaly of short orbital period planets and the synchronization or quasi-synchronization of the stellar spin in some extreme cases. However, the nature of the mechanism responsible for the tidal dissipation in such systems remains uncertain. In this paper, we claim that the so-called elliptical instability may play a major role in these systems, explaining some systematic features present in the observations. This hydrodynamic instability, arising in rotating flows with elliptical streamlines, is suspected to be present in both planet and star of such systems, which are elliptically deformed by tides. The presence and the influence of the elliptical instability in gaseous bodies, such as stars or hot Jupiters, are most of the time neglected. In this paper, using numerical simulations and theoretical arguments, we consider several features associated to the elliptical instability in hot-Jupiter systems. In particular, the use of ad hoc boundary conditions makes it possible to estimate the amplitude of the elliptical instability in gaseous bodies. We also consider the influence of compressibility on the elliptical instability, and compare the results to the incompressible case. We demonstrate the ability for the elliptical instability to grow in the presence of differential rotation, with a possible synchronized latitude, provided that the tidal deformation and/or the rotation rate of the fluid are large enough. Moreover, the amplitude of the instability for a centrally-condensed mass of fluid is of the same order of magnitude as for an incompressible fluid for a given distance to the threshold of the instability. Finally, we show that the assumption of the elliptical instability being the main tidal dissipation process in eccentric inflated hot Jupiters and misaligned stars is consistent with current data.Comment: Icarus (2013) http://dx.doi.org/10.1016/j.icarus.2012.12.01

The effect of rotation and tidal heating on the thermal lightcurves of Super Mercuries

Short period (<50 days) low-mass (<10Mearth) exoplanets are abundant and the few of them whose radius and mass have been measured already reveal a diversity in composition. Some of these exoplanets are found on eccentric orbits and are subjected to strong tides affecting their rotation and resulting in significant tidal heating. Within this population, some planets are likely to be depleted in volatiles and have no atmosphere. We model the thermal emission of these "Super Mercuries" to study the signatures of rotation and tidal dissipation on their infrared light curve. We compute the time-dependent temperature map at the surface and in the subsurface of the planet and the resulting disk-integrated emission spectrum received by a distant observer for any observation geometry. We calculate the illumination of the planetary surface for any Keplerian orbit and rotation. We include the internal tidal heat flow, vertical heat diffusion in the subsurface and generate synthetic light curves. We show that the different rotation periods predicted by tidal models (spin-orbit resonances, pseudo-synchronization) produce different photometric signatures, which are observable provided that the thermal inertia of the surface is high, like that of solid or melted rocks (but not regolith). Tidal dissipation can also directly affect the light curves and make the inference of the rotation more difficult or easier depending on the existence of hot spots on the surface. Infrared light curve measurement with the James Webb Space Telescope and EChO can be used to infer exoplanets' rotation periods and dissipation rates and thus to test tidal models. This data will also constrain the nature of the (sub)surface by constraining the thermal inertia.Comment: 15 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

Fast-thermal coupled cores in ZPR revisited physical specificities and potentialities for ZEPHYR

International audienceThe development of fast reactor GEN-IV technology at an industrial scale would need asignificant improvement of nuclear data and related uncertainties. For this purpose,fast/thermal coupled configurations performed in MINERVE during the 1970’s have beenrecently revisited. The encouraging results obtained have led to further optimizations in orderto prepare experimental programs in the future ZEPHYR facility to be built in Cadarache.This paper describes the concept of fast/thermal coupled core and its use in the improvementof fast-spectrum nuclear data thanks to integral experiments. An optimized configuration ispresented with several variations in order to widen the possibilities of measurement so as toseparate reactivity effects due to absorption and scattering reactions