Critical core mass for enriched envelopes: the role of H2O condensation

Context. Within the core accretion scenario of planetary formation, most simulations performed so far always assume the accreting envelope to have a solar composition. From the study of meteorite showers on Earth and numerical simulations, we know that planetesimals must undergo thermal ablation and disruption when crossing a protoplanetary envelope. Once the protoplanet has acquired an atmosphere, the primordial envelope gets enriched in volatiles and silicates from the planetesimals. This change of envelope composition during the formation can have a significant effect in the final atmospheric composition and on the formation timescale of giant planets. Aims. To investigate the physical implications of considering the envelope enrichment of protoplanets due to the disruption of icy planetesimals during their way to the core. Particular focus is placed on the effect on the critical core mass for envelopes where condensation of water can occur. Methods. Internal structure models are numerically solved with the implementation of updated opacities for all ranges of metallicities and the software CEA to compute the equation of state. CEA computes the chemical equilibrium for an arbitrary mixture of gases and allows the condensation of some species, including water. This means that the latent heat of phase transitions is consistently incorporated in the total energy budget. Results. The critical core mass is found to decrease significantly when an enriched envelope composition is considered in the internal structure equations. A particular strong reduction of the critical core mass is obtained for planets whose envelope metallicity is larger than Z=0.45 when the outer boundary conditions are suitable for condensation of water to occur in the top layers of the atmosphere. We show that this effect is qualitatively preserved when the atmosphere is out of chemical equilibrium.Comment: Accepted for publication in A&

Elemental abundances and minimum mass of heavy elements in the envelope of HD 189733b

Oxygen (O) and carbon (C) have been inferred recently to be subsolar in abundance from spectra of the atmosphere of the transiting hot Jupiter HD 189733b. Yet, the mass and radius of the planet coupled with structure models indicate a strongly supersolar abundance of heavy elements in the interior of this object. Here we explore the discrepancy between the large amount of heavy elements suspected in the planet's interior and the paucity of volatiles measured in its atmosphere. We describe the formation sequence of the icy planetesimals formed beyond the snow line of the protoplanetary disk and calculate the composition of ices ultimately accreted in the envelope of HD 189733b on its migration pathway. This allows us to reproduce the observed volatile abundances by adjusting the mass of ices vaporized in the envelope. The predicted elemental mixing ratios should be 0.15--0.3 times solar in the envelope of HD 189733b if they are fitted to the recent O and C determinations. However, our fit to the minimum mass of heavy elements predicted by internal structure models gives elemental abundances that are 1.2--2.4 times oversolar in the envelope of HD189733b. We propose that the most likely cause of this discrepancy is irradiation from the central star leading to development of a radiative zone in the planet's outer envelope which would induce gravitational settling of elements. Hence, all strongly irradiated extrasolar planets should present subsolar abundances of volatiles. We finally predict that the abundances of nitrogen (N), sulfur (S) and phosphorus (P) are of $\sim$ $2.8 \times 10^{-5}$, $5.3 \times 10^{-6}$ and $1.8 \times 10^{-7}$ relative to H$_2$, respectively in the atmosphere of HD 189733b.Comment: Accepted for publication in Astronomy & Astrophysic

A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied. Our main conclusions are: [...]Comment: Astronomy & Astrophysics, 597, A37, 17 pages, 11 figure

Planetary mass-radius relations across the galaxy

Planet formation theory suggests that planet bulk compositions are likely to reflect the chemical abundance ratios of their host star's photosphere. Variations in the abundance of particular chemical species in stellar photospheres between different galactic stellar populations demonstrate that there are differences among the expected solid planet bulk compositions. We aim to present planetary mass-radius relations of solid planets for kinematically differentiated stellar populations, namely, the thin disc, thick disc, and halo. Using two separate internal structure models, we generated synthetic planets using bulk composition inputs derived from stellar abundances. We explored two scenarios, specifically iron-silicate planets at 0.1 AU and silicate-iron-water planets at 4 AU. We show that there is a persistent statistical difference in the expected mass-radius relations of solid planets among the different galactic stellar populations. At 0.1 AU for silicate-iron planets, there is a 1.51 to 2.04\% mean planetary radius difference between the thick and thin disc stellar populations, whilst for silicate-iron-water planets past the ice line at 4 AU, we calculate a 2.93 to 3.26\% difference depending on the models. Between the halo and thick disc, we retrieve at 0.1 AU a 0.53 to 0.69\% mean planetary radius difference, and at 4 AU we find a 1.24 to 1.49\% difference depending on the model. Future telescopes (such as PLATO) will be able to precisely characterize solid exoplanets and demonstrate the possible existence of planetary mass-radius relationship variability between galactic stellar populations.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Origin of volatiles in the Main Belt

We propose a scenario for the formation of the Main Belt in which asteroids incorporated icy particles formed in the outer Solar Nebula. We calculate the composition of icy planetesimals formed beyond a heliocentric distance of 5 AU in the nebula by assuming that the abundances of all elements, in particular that of oxygen, are solar. As a result, we show that ices formed in the outer Solar Nebula are composed of a mix of clathrate hydrates, hydrates formed above 50 K and pure condensates produced at lower temperatures. We then consider the inward migration of solids initially produced in the outer Solar Nebula and show that a significant fraction may have drifted to the current position of the Main Belt without encountering temperature and pressure conditions high enough to vaporize the ices they contain. We propose that, through the detection and identification of initially buried ices revealed by recent impacts on the surfaces of asteroids, it could be possible to infer the thermodynamic conditions that were present within the Solar Nebula during the accretion of these bodies, and during the inward migration of icy planetesimals. We also investigate the potential influence that the incorporation of ices in asteroids may have on their porosities and densities. In particular, we show how the presence of ices reduces the value of the bulk density of a given body, and consequently modifies its macro-porosity from that which would be expected from a given taxonomic type.Comment: Accepted for publication in MNRA

Giant Planet Formation, Evolution, and Internal Structure

The large number of detected giant exoplanets offers the opportunity to improve our understanding of the formation mechanism, evolution, and interior structure of gas giant planets. The two main models for giant planet formation are core accretion and disk instability. There are substantial differences between these formation models, including formation timescale, favorable formation location, ideal disk properties for planetary formation, early evolution, planetary composition, etc. First, we summarize the two models including their substantial differences, advantages, and disadvantages, and suggest how theoretical models should be connected to available (and future) data. We next summarize current knowledge of the internal structures of solar- and extrasolar- giant planets. Finally, we suggest the next steps to be taken in giant planet exploration.Comment: Accepted for publication as a chapter in Protostars and Planets VI, to be published in 2014 by University of Arizona Pres

Beat Cepheids as Probes of Stellar and Galactic Metallicity

The mere location of a Beat Cepheid model in a Period Ratio vs. Period diagram (Petersen diagram) puts very tight constraints on its metallicity Z. The Beat Cepheid Peterson diagrams are revisited with linear nonadiabatic turbulent convective models, and their accuracy as a probe for stellar metallicity is evaluated. They are shown to be largely independent of the helium content Y, and they are also only weakly dependent on the mass-luminosity relation that is used in their construction. However, they are found to show sensitivity to the relative abundances of the elements that are lumped into the metallicity parameter Z. Rotation is estimated to have but a small effect on the 'pulsation metallicities'. A composite Petersen diagram is presented that allows one to read off upper and lower limits on the metallicity Z from the measured period P0 and period ratio P1/P0.Comment: 9 pages, 12 color figures (black and white version available from 1st author's website). With minor revisions. to appear in Ap

Non-uniform integrability and generalized Young measures,

Given a bounded sequence (u n ) in L 1 (Ω, µ; IR d ), we describe the weak limits in the sense of measures of f (x, u n ) µ for a class of continuous integrands with linear growth at infinity. The defect of uniform integrability of the sequence f (x, u n ) is described by a measure m and a family of probability measures on S d−1 whereas the classical Young measure is associated with the biting limits in the sense of Chacon's lemma. Some consequences of this new approach are given in Calculus of Variations

Impact of the measured parameters of exoplanets on the inferred internal structure

Exoplanet characterization is one of the main foci of current exoplanetary science. For super-Earths and sub-Neptunes, we mostly rely on mass and radius measurements, which allow to derive the body's mean density and give a rough estimate of the planet's bulk composition. However, the determination of planetary interiors is a very challenging task. In addition to the uncertainty in the observed fundamental parameters, theoretical models are limited due to the degeneracy in determining the planetary composition. We aim to study several aspects that affect internal characterization of super-Earths and sub-Neptunes: observational uncertainties, location on the M-R diagram, impact of additional constraints as bulk abundances or irradiation, and model assumptions. We use a full probabilistic Bayesian inference analysis that accounts for observational and model uncertainties. We employ a Nested Sampling scheme to efficiently produce the posterior probability distributions for all the planetary structural parameter of interest. We include a structural model based on self-consistent thermodynamics of core, mantle, high-pressure ice, liquid water, and H-He envelope. Regarding the effect of mass and radius uncertainties on the determination of the internal structure, we find three different regimes: below the Earth-like composition line and above the pure-water composition line smaller observational uncertainties lead to better determination of the core and atmosphere mass respectively, and between them structure characterization only weakly depends on the observational uncertainties. We show that small variations in the temperature or entropy profiles lead to radius variations that are comparable to the observational uncertainty, suggesting that uncertainties linked to model assumptions can become more relevant to determine the internal structure than observational uncertainties.Comment: 12 pages, 12 figure