Theoretical Radii of Extrasolar Giant Planets: the Cases of TrES-4, XO-3b, and HAT-P-1b

To explain their observed radii, we present theoretical radius-age trajectories for the extrasolar giant planets (EGPs) TrES-4, XO-3b, and HAT-P-1b. We factor in variations in atmospheric opacity, the presence of an inner heavy-element core, and possible heating due to orbital tidal dissipation. A small, yet non-zero, degree of core heating is needed to explain the observed radius of TrES-4, unless its atmospheric opacity is significantly larger than a value equivalent to that at 10$\times$solar metallicity with equilibrium molecular abundances. This heating rate is reasonable, and corresponds for an energy dissipation parameter ($Q_p$) of $\sim10^{3.8}$ to an eccentricity of $\sim$0.01, assuming 3$\times$solar atmospheric opacity and a heavy-element core of $M_c = 30$ $M_{\oplus}$. For XO-3b, which has an observed orbital eccentricity of 0.26, we show that tidal heating needs to be taken into account to explain its observed radius. Furthermore, we reexamine the core mass needed for HAT-P-1b in light of new measurements and find that it now generally follows the correlation between stellar metallicity and core mass suggested recently. Given various core heating rates, theoretical grids and fitting formulae for a giant planet's equilibrium radius and equilibration timescale are provided for planet masses $M_p=$ 0.5, 1.0, and 1.5 $M_J$ with $a =$ 0.02-0.06 AU, orbiting a G2V star. When the equilibration timescale is much shorter than that of tidal heating variation, the ``effective age'' of the planet is shortened, resulting in evolutionary trajectories more like those of younger EGPs. Motivated by the work of \citet{jackson08a,jackson08b}, we suggest that this effect could indeed be important in better explaining some observed transit radii.Comment: 11 pages; references added; ApJ accepted versio

Tidal Heating Models for the Radii of the Inflated Transiting Giant Planets WASP-4b, WASP-6b, WASP-12b, and TrES-4

In order to explain the inflated radii of some transiting extrasolar giant planets, we investigate a tidal heating scenario for the inflated planets WASP-4b, WASP-6b, WASP-12b, WASP-15b, and TrES-4. To do so, we assume that they retain a nonzero eccentricity, possibly by dint of continuing interaction with a third body. We calculate the amount of extra heating in the envelope that is then required to fit the radius of each planet, and we explore how this additional power depends on the planetary atmospheric opacity and on the mass of a heavy-element central core. There is a degeneracy between the core mass $M_{\rm core}$ and the heating $\dot{E}_{\rm heating}$. Therefore, in the case of tidal heating, there is for each planet a range of the couple $\{M_{\rm core},e^2/Q'_p\}$ that can lead to the same radius, where $Q'_p$ is the tidal dissipation factor and $e$ is the eccentricity. With this in mind, we also investigate the case of the non-inflated planet HAT-P-12b, which can admit solutions combining a heavy-element core and tidal heating. A substantial improvement of the measured eccentricities of such planetary systems could simplify this degeneracy by linking the two unknown parameters $\{M_{\rm core},Q'_p\}$. Further independent constraints on either of these parameters would, through our calculations, constrain the other.Comment: Accepted in ApJ; 17 pages, 3 figures, 6 tables (emulateapj format); expanded explanatory tex

Explorations into the Viability of Coupled Radius-Orbit Evolutionary Models for Inflated Planets

The radii of some transiting extrasolar giant planets are larger than would be expected by the standard theory. We address this puzzle with the model of coupled radius-orbit tidal evolution developed by \citet{Ibgui_and_Burrows_2009}. The planetary radius is evolved self-consistently with orbital parameters, under the influence of tidal torques and tidal dissipation in the interior of the planet. A general feature of this model, which we have previously demonstrated in the generic case, is that a possible transient inflation of the planetary radius can temporarily interrupt its standard monotonic shrinking and can lead to the inflated radii that we observe. In particular, a bloated planet with even a circular orbit may still be inflated due to an earlier episode of tidal heating. We have modified our model to include an orbital period dependence of the tidal dissipation factor in the star, $Q'_{\ast} \propto P^{\gamma}$, $-1 \leqslant \gamma \leqslant 1$. With this model, we search, for a tidally heated planet, orbital and radius evolutionary tracks that fall within the observational limits of the radius, the semimajor axis, and the eccentricity of the planet in its current estimated age range. We find that, for some inflated planets (WASP-6b and WASP-15b), there are such tracks; for another (TrES-4), there are none; and for still others (WASP-4b and WASP-12b), there are such tracks, but our model might imply that we are observing the planets at a special time. Finally, we stress that there is a two to three order-of-magnitude timescale uncertainty of the inspiraling phase of the planet into its host star, arising from uncertainties in the tidal dissipation factor in the star $Q'_{\ast}$.Comment: Submitted to ApJ; 13 pages, 3 figures, 2 tables; (emulateapj format

Models of Neptune-Mass Exoplanets: Emergent Fluxes and Albedos

There are now many known exoplanets with Msin(i) within a factor of two of Neptune's, including the transiting planets GJ436b and HAT-P-11b. Planets in this mass-range are different from their more massive cousins in several ways that are relevant to their radiative properties and thermal structures. By analogy with Neptune and Uranus, they are likely to have metal abundances that are an order of magnitude or more greater than those of larger, more massive planets. This increases their opacity, decreases Rayleigh scattering, and changes their equation of state. Furthermore, their smaller radii mean that fluxes from these planets are roughly an order of magnitude lower than those of otherwise identical gas giant planets. Here, we compute a range of plausible radiative equilibrium models of GJ436b and HAT-P-11b. In addition, we explore the dependence of generic Neptune-mass planets on a range of physical properties, including their distance from their host stars, their metallicity, the spectral type of their stars, the redistribution of heat in their atmospheres, and the possible presence of additional optical opacity in their upper atmospheres.Comment: Accepted and Published in ApJ (2010 ApJ,709,149

Coupled Evolution with Tides of the Radius and Orbit of Transiting Giant Planets: General Results

Some transiting extrasolar giant planets have measured radii larger than predicted by the standard theory. In this paper, we explore the possibility that an earlier episode of tidal heating can explain such radius anomalies and apply the formalism we develop to HD 209458b as an example. We find that for strong enough tides the planet's radius can undergo a transient phase of inflation that temporarily interrupts canonical, monotonic shrinking due to radiative losses. Importantly, an earlier episode of tidal heating can result in a planet with an inflated radius, even though its orbit has nearly circularized. Moreover, we confirm that at late times, and under some circumstances, by raising tides on the star itself a planet can spiral into its host. We note that a 3$\times$ to 10$\times$solar planet atmospheric opacity with no tidal heating is sufficient to explain the observed radius of HD 209458b. However, our model demonstrates that with an earlier phase of episodic tidal heating we can fit the observed radius of HD 209458b even with lower (solar) atmospheric opacities. This work demonstrates that, if a planet is left with an appreciable eccentricity after early inward migration and/or dynamical interaction, coupling radius and orbit evolution in a consistent fashion that includes tidal heating, stellar irradiation, and detailed model atmospheres might offer a generic solution to the inflated radius puzzle for transiting extrasolar giant planets such as WASP-12b, TrES-4, and WASP-6b.Comment: Accepted for publication in ApJ; 16 pages (emulateapj format), 5 figures; expanded explanatory text and further reference

Études de spectres infrarouges pour des applications de télédétection: - développement d'un calcul raie par raie optimisé - mesures en laboratoires, sur des trajets kilométriques ou à haute température

This work deals with infrared radiation by molecular gases, addressing the aerospace community 's requirements for the modeling of plume signature and remote-sensing. The aim is to develop a theoretical and numerical method for the prediction of absorption/emission spectra (transmission and specific intensity). Typical paths consist of a long cold one (atmosphere) and a juxtaposed short hot one (combustion gases). The fine spatial meshes, due to high variability of thermophysical conditions, and wide spectral ranges involved, require so many calculations that a fast, error controlled, computation is necessary. The computational approach was built on a line-by-line radiative transfer model. In this model, the absorption coefficient results from the contributions of allowed (dipole, quadrupole, ...) and of collision induced transitions. This method is globally very precise, but time expensive because of the high number of lines we have to take into account (let us consider the Hitran spectroscopic Data Base : ~ 10^6 lines, Hitemp + Hitran : ~ 3.3x10^6 lines). After a discussion about the precise model of emission - absorption adopted, alI the optimizations studied and included in the new code written with Fortran 90 language are presented. They comprise : a new fast computation of Voigt profile; a method generating different spectral mesh grids, minimizing the number of calculated points; an efficient method to reject weak lines; a line wings cutting technique and use of continuum; calculation stopped where emissivity saturates. Local Thermodynamic Equilibrium is assumed; however, it can easily be upgraded to include Non-LTE. Furthermore, it was conceived in order to make easier its handling, especially for the purpose of further improvements or for easy integration in larger computational structures. The calculation has been parallelized (using MPI), by distributing gas columns on different processors. The new code is thirty times as quick as the previous one used by SNECMA (French Aeronautics and Space Propulsion Group) which could calculate, for the first time, a whole infrared signature of an aircraft with a line-by-line method. Experimental validations of the code are based on two apparatuses. The first one is intended to simulate long atmospheric paths. We developed and exploited it in GSMA laboratory (Group of Molecular and Atmospheric Spectrometry, Reims). It uses a 50 m White cell which allowed, for the first time, transmission spectra measurements between 2 and 14 μm for kilometric paths. The second one, developed in LPALMS laboratory (Laboratory of Atoms, Lasers, Molecules and Surfaces Physics, Rennes, 250 km), is intended to simulate plume signature configurations. It juxtaposes a short hot cell and a long cold cell. CO2 spectra were recorded with high spectral resolution near 10 and 4 μm, till 1000 K. The two campaigns validate the calculations, provided that we use "hot" spectroscopic data bases for the second one (i.e. Hitemp instead of Hitran).Les travaux dont les résultats font l'objet de ce mémoire de doctorat s'inscrivent dans le cadre de l'étude expérimentale et théorique des processus d'absorption/émission de rayonnement infrarouge par des milieux moléculaires gazeux. Il a été motivé par des besoins de modélisation de la signature infrarouge d'aéronefs et de télédétection. Le problème posé est celui de l'élaboration, puis de la validation, d'une approche théorique et numérique permettant de prédire les spectres infrarouges des milieux gazeux rencontrés dans les applications de télédétection. Ces derniers ont la caractéristique de mettre en jeu des trajets optiques comprenant un long parcours froid (l'atmosphère) juxtaposé à une partie plus courte et chaude (gaz de combustion). En raison de la forte variabilité des conditions thermophysiques le long des rayons, du nombre considérable de ces rayons à prendre en compte pour l'intégration sur l'angle solide de visée, et de l'étendue du domaine spectral d'intérêt, le volume de calculs associés à la prédiction de la signature infrarouge est considérable. L'approche théorique se doit donc d'être très efficace et rapide tout en restant la plus précise possible. Ce problème a été abordé ici sur le plan théorique et expérimental. L'approche prédictive développée repose sur un modèle "raie par raie" dans lequel le spectre résulte de l'addition des contributions individuelles des transitions infrarouges des espèces moléculaires présentes. Cette approche est dans l'ensemble très précise mais aussi très coûteuse en temps de calcul en raison du nombre de raies à prendre en compte et de la forte dynamique spectrale aux pressions modérées des milieux considérés. Une fois posées les bases du modèle, un effort important a été consacré à l'optimisation des calculs qui a été faite à plusieurs niveaux en autorisant des erreurs contrôlées sur le résultat final. Nous avons ainsi développé : - une technique (la plus) rapide d'évaluation du profil (Voigt) des raies ; - un système de grilles spectrales de pas différents minimisant le nombre de points de calcul ; - une méthode efficace d'élimination des raies de contribution négligeable ; - une technique de coupure des ailes de raies associée à l'utilisation de continua. Ces concepts ont servi de base pour la construction d'un code informatique profitant des fonctionnalités (notamment la gestion dynamique de la mémoire) du langage Fortran 90. Ce code a été implanté à la SNECMA et à l'ONERA, avec une version parallélisée sous MPI. Ce travail a été un succès puisque l'outil développé a réduit le temps de calcul d'un facteur trente par rapport au code raie par raie déjà optimisé dont disposait la SNECMA. Ceci a permis de mener, pour la première fois, un calcul complet de signature infrarouge avec une approche raie par raie. En parallèle, des études expérimentales ont été menées afin de tester la qualité des prédictions obtenues avec le code développé. Deux dispositifs différents et complémentaires ont été utilisés afin de reproduire, en laboratoire, des milieux "représentatifs" de ceux mis en jeu par les applications de signature. Le premier, que nous avons conçu, construit, et exploité a été développé autour d'un spectromètre à réseau et d'une cuve multi-passages pré-existante de 50 m de base au GSMA (Groupe de Spectrométrie Moléculaire et Atmosphérique, Reims). Ce travail a permis (pour la première fois) la mesure de spectres de transmission dans le domaine 2-14 μm, à température ambiante mais pression variable, pour des trajets optiques supérieurs au kilomètre, schématisant ainsi les longs parcours atmosphériques rencontrés dans les applications pratiques considérées. Les résultats obtenus ont permis de valider les calculs, à quelques exceptions mineures et locales près. Le second dispositif a été développé, à notre suggestion, par une équipe du LPALMS (Laboratoire de Physique des Atomes, Lasers, Molécules et Surfaces, Rennes). Le montage repose sur la juxtaposition d'une courte cuve chaude et d'une longue cuve froide, schématisant ainsi l'aspect gaz chauds + gaz froids des milieux mis en jeu par les applications pratiques. Des spectres du CO2 ont été enregistrés à haute résolution spectrale, à l'aide d'un spectromètre à transformée de Fourier, dans les régions de 10 et 4 μm pour des températures allant jusqu'à 1000 K. Ces données ont confirmé la qualité des calculs prédictifs sous réserve que des bases de données spectroscopiques "chaudes" soient utilisées

ETUDES DE SPECTRES INFRAROUGES POUR DES APPLICATIONS DE TELEDETECTION (- DEVELOPPEMENT D'UN CALCUL RAIE PAR RAIE OPTIMISE - MESURES EN LABORATOIRES, SUR DES TRAJETS KILOMETRIQUES OU A HAUTE TEMPERATURE)

ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF