Mass-radius relationships for exoplanets

For planets other than Earth, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key materials whose equation of state is reasonably well established, and for differentiated Fe/rock. We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted mass- radius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth- like,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa.Comment: Added more recent exoplanets. Tidied text and references. Added extra "rock" compositions. Responded to referee comment

The MgSiO_3 system at high pressure: Thermodynamic properties of perovskite, postperovskite, and melt from global inversion of shock and static compression data

We present new equation-of-state (EoS) data acquired by shock loading to pressures up to 245 GPa on both low-density samples (MgSiO_3 glass) and high-density, polycrystalline aggregates (MgSiO_3 perovskite + majorite). The latter samples were synthesized using a large-volume press. Modeling indicates that these materials transform to perovskite, postperovskite, and/or melt with increasing pressure on their Hugoniots. We fit our results together with existing P-V-T data from dynamic and static compression experiments to constrain the thermal EoS for the three phases, all of which are of fundamental importance to the dynamics of the lower mantle. The EoS for perovskite and postperovskite are well described with third-order Birch-Murnaghan isentropes, offset with a Mie-Grüneisen-Debye formulation for thermal pressure. The addition of shock data helps to distinguish among discrepant static studies of perovskite, and for postperovskite, constrain a value of K' significantly larger than 4. For the melt, we define for the first time a single EoS that fits experimental data from ambient pressure to 230 GPa; the best fit requires a fourth-order isentrope. We also provide a new EoS for Mg_2SiO_4 liquid, calculated in a similar manner. The Grüneisen parameters of the solid phases decrease with pressure, whereas those of the melts increase, consistent with previous shock wave experiments as well as molecular dynamics simulations. We discuss implications of our modeling for thermal expansion in the lower mantle, stabilization of ultra-low-velocity zones associated with melting at the core-mantle boundary, and crystallization of a terrestrial magma ocean

Microscopic calculations of Hugoniot curves of neat TATB and of its detonation products

We compute the Hugoniot curves of both neat TATB and its detonation products mixture using atomistic simulation tools. To compute the Hugoniot states, we adapted our "Sampling Constraints in Average" (SCA) method (Maillet et al., Applied Math. Research eXpress 2008, 2009) to Monte-Carlo simulations. For neat TATB, we show that the potential proposed by Rai (Rai et al., J. Chem. Phys. 129, 2008) is not accurate enough to predict the Hugoniot curve and requires some optimization of its parameters. Concerning detonation products, thermodynamic properties at chemical equilibrium are computed using a specific RxMC method (Bourasseau et al., Phys. Chem. Chem. Phys. 13, 2011) taking into account the presence of carbon clusters in the fluid mixture. We show that this explicit description of the solid phase immersed in the fluid phase modifies the chemical equilibrium

Planetary internal structures

This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we will discuss the various types of planets appearing in this diagram and describe internal structures for each type. The review will summarize the status of theoretical and experimental works performed in the field of equation of states (EOS) for materials relevant to planetary interiors and will address the main theoretical and experimental uncertainties and challenges. It will discuss the impact of new EOS on interior structures and bulk composition determination. We will discuss important dynamical processes which strongly impact the interior and evolutionary properties of planets (e.g plate tectonics, semiconvection) and describe non standard models recently suggested for our giant planets. We will address the case of short-period, strongly irradiated exoplanets and critically analyse some of the physical mechanisms which have been suggested to explain their anomalously large radius.Comment: 24 pages, 8 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Henning.

Stochastic optimization and worst-case analysis in monetary policy design

In this paper, we examine the cost of insurance against model uncertainty for the Euro area considering four alternative reference models, all of which are used for policy-analysis at the ECB.We find that maximal insurance across this model range in terms of aMinimax policy comes at moderate costs in terms of lower expected performance. We extract priors that would rationalize the Minimax policy from a Bayesian perspective. These priors indicate that full insurance is strongly oriented towards the model with highest baseline losses. Furthermore, this policy is not as tolerant towards small perturbations of policy parameters as the Bayesian policy rule. We propose to strike a compromise and use preferences for policy design that allow for intermediate degrees of ambiguity-aversion.These preferences allow the specification of priors but also give extra weight to the worst uncertain outcomes in a given context. JEL Klassifikation: E52, E58, E6

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport. An approach based on non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected by any number of high-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability of the multifidelity polynomial chaos approach, two model problems were explored. The first was supersonic airfoil with three levels of modeling fidelity, each capturing an additional level of physics. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Both problems illustrate the applicability and significant computational savings of the multifidelity polynomial chaos method

Comparative study of turbulence models in predicting hypersonic inlet flows

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared very well with the experimental data, and performed better than the Thomas model near the walls

A moving cold front in the intergalactic medium of A3667

We present results from a Chandra observation of the central region of the galaxy cluster A3667, with emphasis on the prominent sharp X-ray brightness edge spanning 0.5 Mpc near the cluster core. Our temperature map shows large-scale nonuniformities characteristic of the ongoing merger, in agreement with earlier ASCA results. The brightness edge turns out to be a boundary of a large cool gas cloud moving through the hot ambient gas, very similar to the "cold fronts" discovered by Chandra in A2142. The higher quality of the A3667 data allows the direct determination of the cloud velocity. At the leading edge of the cloud, the gas density abruptly increases by a factor of 3.9+-0.8, while the temperature decreases by a factor of 1.9+-0.2 (from 7.7 keV to 4.1 keV). The ratio of the gas pressures inside and outside the front shows that the cloud moves through the ambient gas at near-sonic velocity, M=1+-0.2 or v=1400+-300 km/s. In front of the cloud, we observe the compression of the ambient gas with an amplitude expected for such a velocity. A smaller surface brightness discontinuity is observed further ahead, ~350 kpc in front of the cloud. We suggest that it corresponds to a weak bow shock, implying that the cloud velocity may be slightly supersonic. Given all the evidence, the cold front appears to delineate the remnant of a cool subcluster that recently has merged with A3667. The cold front is remarkably sharp. The upper limit on its width, 3.5 arcsec or 5 kpc, is several times smaller than the Coulomb mean free path. This is a direct observation of suppression of the transport processes in the intergalactic medium, most likely by magnetic fields.Comment: Submitted to ApJ. 9 pages with embedded color figures, uses emulateapj5. Postscript with higher quality figures is available at http://hea-www.harvard.edu/~alexey/a3667-hydro.ps.g