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

Viscosity and viscosity anomalies of model silicates and magmas: a numerical investigation

We present results for transport properties (diffusion and viscosity) using computer simulations. Focus is made on a densified binary sodium disilicate 2SiO$_2$-Na$_2$O (NS2) liquid and on multicomponent magmatic liquids (MORB, basalt). In the NS2 liquid, results show that a certain number of anomalies appear when the system is densified: the usual diffusivity maxima/minima is found for the network-forming ions (Si,O) whereas the sodium atom displays three distinct r\'egimes for diffusion. Some of these features can be correlated with the obtained viscosity anomaly under pressure, the latter being be fairly well reproduced from the simulated diffusion constant. In model magmas (MORB liquid), we find a plateau followed by a continuous increase of the viscosity with pressure. Finally, having computed both diffusion and viscosity independently, we can discuss the validity of the Eyring equation for viscosity which relates diffusion and viscosity. It is shown that it can be considered as valid in melts with a high viscosity. On the overall, these results highlight the difficulty of establishing a firm relationship between dynamics, structure and thermodynamics in complex liquids.Comment: 13 pages, 8 figure

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

An analysis of the CoRoT-2 system: A young spotted star and its inflated giant planet

Context: CoRoT-2b is one of the most anomalously large exoplanet known. Given its large mass, its large radius cannot be explained by standard evolution models. Interestingly, the planet's parent star is an active, rapidly rotating solar-like star with a large fraction (7 to 20%) of spots. Aims: We want to provide constraints on the properties of the star-planet system and understand whether the planet's inferred large size may be due to a systematic error on the inferred parameters, and if not, how it may be explained. Methods: We combine stellar and planetary evolution codes based on all available spectroscopic and photometric data to obtain self-consistent constraints on the system parameters. Results: We find no systematic error in the stellar modeling (including spots and stellar activity) that would yield the required ~10% reduction in size for the star and thus the planet. Two classes of solutions are found: the usual main sequence solution for the star yields for the planet a mass of 3.67+/-0.13 Mjup, a radius of 1.55+/-0.03 Rjup for an age that is at least 130Ma, and should be less than 500Ma given the star's fast rotation and significant activity. We identify another class of solutions on the pre-main sequence, in which case the planet's mass is 3.45\pm 0.27 Mjup, its radius is 1.50+/-0.06 Rjup for an age between 30 and 40 Ma. These extremely young solutions provide the simplest explanation for the planet's size which can then be matched by a simple contraction from an initially hot, expanded state, provided the atmospheric opacities are increased by a factor ~3 compared to usual assumptions for solar compositions atmospheres. Other solutions imply in any case that the present inflated radius of CoRoT-2b is transient and the result of an event that occurred less than 20 Ma ago: a giant impact with another Jupiter-mass planet, or interactions with another object in the system which caused a significant rise of the eccentricity followed by the rapid circularization of its orbit. Conclusions: Additional observations of CoRoT-2 that could help understanding this system include searches for infrared excess and the presence of a debris disk and searches for additional companions. The determination of a complete infrared lightcurve including both the primary and secondary transits would also be extremely valuable to constrain the planet's atmospheric properties and to determine the planet-to-star radius ratio in a manner less vulnerable to systematic errors due to stellar activity.Comment: 16 pages, 15 figures, accepted for A&

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this work, we present an extensive analytical, numerical and experimental analysis of confined capillary jets extending previous studies. We propose an extended, accurate analytic model in the limit of low Reynolds flows, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show a remarkable accuracy with results from the extensive experimental exploration provided.Comment: Submitted to the Physical Review E (20-March-2008

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

Can Fregeans have 'I'-thoughts?

We examine how Frege?s contrast between identity judgments of the forms ?a=a? vs. ?a=b? would fare in the special case where ?a? and ?b? are complex mental representations, and ?a? stands for an introspected ?I?-thought. We first argue that the Fregean treatment of I-thoughts entails that they are what we call ?one-shot thoughts?: they can only be thought once. This has the surprising consequence that no instance of the ?a=a? form of judgment in this specific case comes out true, let alone a priori true. This further reinforces Glezakos?s objections against the set-up of Frege?s puzzle, while also raising what we think is an acute problem for Fregeans, insofar as I-thought (and indexical thinking more generally), understood in their way, turns out to be incompatible with some basic features of rationality