The multiple planets transiting Kepler-9 I. Inferring stellar properties and planetary compositions

The discovery of multiple transiting planetary systems offers new possibilities for characterising exoplanets and understanding their formation. The Kepler-9 system contains two Saturn-mass planets, Kepler-9b and 9c. Using evolution models of gas giants that reproduce the sizes of known transiting planets and accounting for all sources of uncertainties, we show that Kepler-9b (respectively 9c) contains $45^{+17}_{-12}$\,\mearth\ (resp. $31^{+13}_{-10}$\,\mearth) of hydrogen and helium and $35^{+10}_{-15}$\,\mearth (resp. $24^{+10}_{-12}$\,\mearth) of heavy elements. More accurate constraints are obtained when comparing planets 9b and 9c: the ratio of the total mass fractions of heavy elements are $Z_{\rm b}/Z_{\rm c}=1.02\pm 0.14$, indicating that, although the masses of the planets differ, their global composition is very similar, an unexpected result for formation models. Using evolution models for super-Earths, we find that Kepler-9d must contain less than 0.1% of its mass in hydrogen and helium and predict a mostly rocky structure with a total mass between 4 and 16\,\mearth.Comment: 5 pages + 7 pages of online material ; revised article submitted to A\&A and accepted on March 3

The Interiors of Giant Planets: Models and Outstanding Questions

We know that giant planets played a crucial role in the making of our Solar System. The discovery of giant planets orbiting other stars is a formidable opportunity to learn more about these objects, what is their composition, how various processes influence their structure and evolution, and most importantly how they form. Jupiter, Saturn, Uranus and Neptune can be studied in detail, mostly from close spacecraft flybys. We can infer that they are all enriched in heavy elements compared to the Sun, with the relative global enrichments increasing with distance to the Sun. We can also infer that they possess dense cores of varied masses. The intercomparison of presently caracterised extrasolar giant planets show that they are also mainly made of hydrogen and helium, but that they either have significantly different amounts of heavy elements, or have had different orbital evolutions, or both. Hence, many questions remain and are to be answered for significant progresses on the origins of planets.Comment: 43 pages, 11 figures, 3 tables. To appear in Annual Review of Earth and Planetary Sciences, vol 33, (2005

On the Radii of Close-in Giant Planets

The recent discovery that the close-in extrasolar giant planet, HD209458b, transits its star has provided a first-of-its-kind measurement of the planet's radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet, $\tau$ Boo b. Including the effects of stellar irradiation, we estimate the general behavior of radius/age trajectories for such planets and interpret the large measured radii of HD209458b and $\tau$ Boo b in that context. We find that HD209458b must be a hydrogen-rich gas giant. Furthermore, the large radius of close-in gas giant is not due to the thermal expansion of its atmosphere, but to the high residual entropy that remains throughout its bulk by dint of its early proximity to a luminous primary. The large stellar flux does not inflate the planet, but retards its otherwise inexorable contraction from a more extended configuration at birth. This implies either that such a planet was formed near its current orbital distance or that it migrated in from larger distances ($\geq$0.5 A.U.), no later than a few times $10^7$ years of birth.Comment: aasms4 LaTeX, 1 figure, accepted to Ap.J. Letter

Modeling Pressure-Ionization of Hydrogen in the Context of Astrophysics

The recent development of techniques for laser-driven shock compression of hydrogen has opened the door to the experimental determination of its behavior under conditions characteristic of stellar and planetary interiors. The new data probe the equation of state (EOS) of dense hydrogen in the complex regime of pressure ionization. The structure and evolution of dense astrophysical bodies depend on whether the pressure ionization of hydrogen occurs continuously or through a ``plasma phase transition'' (PPT) between a molecular state and a plasma state. For the first time, the new experiments constrain predictions for the PPT. We show here that the EOS model developed by Saumon and Chabrier can successfully account for the data, and we propose an experiment that should provide a definitive test of the predicted PPT of hydrogen. The usefulness of the chemical picture for computing astrophysical EOS and in modeling pressure ionization is discussed.Comment: 16 pages + 4 figures, to appear in High Pressure Researc

Toward a Deterministic Model of Planetary Formation IV: Effects of Type-I Migration

In a further development of a deterministic planet-formation model (Ida & Lin 2004), we consider the effect of type-I migration of protoplanetary embryos due to their tidal interaction with their nascent disks. During the early embedded phase of protostellar disks, although embryos rapidly emerge in regions interior to the ice line, uninhibited type-I migration leads to their efficient self-clearing. But, embryos continue to form from residual planetesimals at increasingly large radii, repeatedly migrate inward, and provide a main channel of heavy element accretion onto their host stars. During the advanced stages of disk evolution (a few Myr), the gas surface density declines to values comparable to or smaller than that of the minimum mass nebula model and type-I migration is no longer an effective disruption mechanism for mars-mass embryos. Over wide ranges of initial disk surface densities and type-I migration efficiency, the surviving population of embryos interior to the ice line has a total mass several times that of the Earth. With this reservoir, there is an adequate inventory of residual embryos to subsequently assemble into rocky planets similar to those around the Sun. But, the onset of efficient gas accretion requires the emergence and retention of cores, more massive than a few M_earth, prior to the severe depletion of the disk gas. The formation probability of gas giant planets and hence the predicted mass and semimajor axis distributions of extrasolar gas giants are sensitively determined by the strength of type-I migration. We suggest that the observed fraction of solar-type stars with gas giant planets can be reproduced only if the actual type-I migration time scale is an order of magnitude longer than that deduced from linear theories.Comment: 32 pages, 8 figures, 1 table, accepted for publication in Ap

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

Ion structure in warm dense matter: benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential