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Determining the internal structure of Uranus is a key objective for planetary science. Knowledge of Uranus's bulk composition and the distribution of elements is crucial to understanding its origin and evolutionary path. In addition, Uranus represents a poorly understood class of intermediate-mass planets (intermediate in size between the relatively well studied terrestrial and gas giant planets), which appear to be very common in the Galaxy. As a result, a better characterization of Uranus will also help us to better understand exoplanets in this mass and size regime. Recognizing the importance of Uranus, a Keck Institute for Space Studies (KISS) workshop was held in September 2023 to investigate how we can improve our knowledge of Uranus's internal structure in the context of a future Uranus mission that includes an orbiter and a probe. The scientific goals and objectives of the recently released Planetary Science and Astrobiology Decadal Survey were taken as our starting point. We reviewed our current knowledge of Uranus's interior and identified measurement and other mission requirements for a future Uranus spacecraft, providing more detail than was possible in the Decadal Survey's mission study and including new insights into the measurements to be made. We also identified important knowledge gaps to be closed with Earth-based efforts in the near term that will help guide the design of the mission and interpret the data returned., Comment: Study Report prepared for the W. M. Keck Institute for Space Studies (KISS). Study title: Determining the Interior Structure of Uranus: A Case Study for Leveraging Cross-Discipline Science to Answer Tough Questions. Study dates: September 11-15, 2023. Team Leads: Mark Hofstadter, Ravit Helled, and David Stevenson

Demixing properties of planetary major constituents influence the interior structure and evolution of planets. Comparing experimental and computational data on the miscibility of hydrogen and water to adiabatic profiles suggests phase separation between these components occurs in the ice giants Uranus and Neptune. We aim to predict the atmospheric water abundance and transition pressure between the water-poor outer envelope and the water-rich deep interior in Uranus and Neptune. We construct seven H2-H2O phase diagrams from the available experimental and computational data. We compute interior adiabatic structure models and compare these to the phase diagrams to infer whether demixing is occurring. We obtain a strong water depletion in the top layer due to rain-out of water and find upper limits on the atmospheric water mass fraction Z_atm of 0.21 for Uranus and 0.16 for Neptune. The transition from the water-poor to the water-rich layer is sharp and occurs at pressures P_Z between 4 and 11 GPa. Using these constraints on Z_atm and P_Z, we find that the observed gravitational harmonics J2 and J4 can be reproduced if P_Z > 10 GPa in Uranus and > 5 GPa in Neptune, and if the deep interior has a high primordial water mass fraction of 0.8, unless rocks are also present. The agreement with J4 is improved if rocks are confined deeper than P_Z, for instance below a rock cloud level at 2000 K (20-30 GPa). These findings confirm classical few-layer models and suggest that a layered structure may result from a combination of primordial mass accretion and subsequent phase separation. Reduced observational uncertainty in J4 and its dynamic contribution, atmospheric water abundance measurements from an Orbiter with a Probe mission to Uranus (UOP) or Neptune, and better understanding of the mixing behaviour of constituents are needed to constrain the interiors of ice giants., Comment: Accepted for publication in Astronomy and Astrophysics

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Models of Jupiter s interior struggle to agree with measurements of the atmospheric composition. Interior models favour a subsolar or solar abundance of heavy elements Z while atmospheric measurements suggest a supersolar abundance. One potential solution may be the presence of an inverted Z-gradient, namely an inward decrease of Z, which implies a larger heavy element abundance in the atmosphere than in the outer envelope. We investigate two scenarios in which the inverted Z gradient is located either where helium rain occurs (Mbar level) or at upper levels (kbar level) where a radiative region could exist. We aim to assess how plausible these scenarios are. We calculate interior and evolution models of Jupiter with such inverted Z-gradient and use constraints on the stability and the formation of an inverted Z-gradient. We find that an inverted Z-gradient at the location of helium rain cannot work as it requires a late accretion and of too much material. We find interior models with an inverted Z-gradient at upper levels, due to a radiative zone preventing downward mixing, that could satisfy the present gravity field of the planet. However, our evolution models suggest that this second scenario might not be in place. An inverted Z-gradient in Jupiter could be stable. Yet, its presence either at the Mbar level or kbar level is rather unlikely., Comment: Accepted for publication in A&A

The small semi-major axes of Hot Jupiters lead to high atmospheric temperatures of up to several thousand Kelvin. Under these conditions, thermally ionised metals provide a rich source of charged particles and thus build up a sizeable electrical conductivity. Subsequent electromagnetic effects, such as the induction of electric currents, Ohmic heating, magnetic drag, or the weakening of zonal winds have thus far been considered mainly in the framework of a linear, steady-state model of induction. For Hot Jupiters with an equilibrium temperature $T_{eq} > 1500$ K, the induction of atmospheric magnetic fields is a runaway process that can only be stopped by non-linear feedback. For example, the back-reaction of the magnetic field onto the flow via the Lorentz force or the occurrence of magnetic instabilities. Moreover, we discuss the possibility of self-excited atmospheric dynamos. Our results suggest that the induced atmospheric magnetic fields and electric currents become independent of the electrical conductivity and the internal field, but instead are limited by the planetary rotation rate and wind speed. As an explicit example, we characterise the induction process for the hottest exoplanet, KELT-9b by calculating the electrical conductivity along atmospheric $P-T$-profiles for the day- and nightside. Despite the temperature varying between 3000 K and 4500 K, the resulting electrical conductivity attains an elevated value of roughly 1 S/m throughout the atmosphere. The induced magnetic fields are predominately horizontal and might reach up to a saturation field strength of 400 mT, exceeding the internal field by two orders of magnitude.

Revealing the true nature of the gas giant planets in our Solar System is challenging. The masses of Jupiter and Saturn are about 318 and 95 Earth masses, respectively. While they mostly consist of hydrogen and helium, the total mass and distribution of the heavier elements, which reveal information on their origin, are still unknown. Recent accurate measurements of the gravitational fields of Jupiter and Saturn together with knowledge of the behavior of planetary materials at high pressures allow us to better constrain their interiors. Updated structure models of Jupiter and Saturn suggest that both planets have complex interiors that include composition inhomogeneities, non-convective regions, and fuzzy cores. In addition, it is clear that there are significant differences between Jupiter and Saturn and that each giant planet is unique. This has direct implications for giant exoplanet characterization and for our understanding of gaseous planets as a class of astronomical objects. In this review we summarize the methods used to model giant planet interiors and recent developments in giant planet structure models., Comment: a review chapter, to appear in "Planetary systems now" edited by Luisa M. Lara and David C. Jewitt

The Juno mission has revolutionized and challenged our understanding of Jupiter. As Juno transitioned to its extended mission, we review the major findings of Jupiter's internal structure relevant to understanding Jupiter's formation and evolution. Results from Juno's investigation of Jupiter's interior structure imply that the planet has compositional gradients and is accordingly non-adiabatic, with a complex internal structure. These new results imply that current models of Jupiter's formation and evolution require a revision. In this paper, we discuss potential formation and evolution paths that can lead to an internal structure model consistent with Juno data, and the constraints they provide. We note that standard core accretion formation models, including the heavy-element enrichment during planetary growth is consistent with an interior that is inhomogeneous with composition gradients in its deep interior. However, such formation models typically predict that this region, which could be interpreted as a primordial dilute core, is confined to about 10% of Jupiter's total mass. In contrast, structure models that fit Juno data imply that this region contains 30% of the mass or more. One way to explain the origin of this extended region is by invoking a relatively long (about 2 Myrs) formation phase where the growing planet accretes gas and planetesimals delaying the runaway gas accretion. Alternatively, Jupiter's fuzzy core could be a result of a giant impact or convection post-formation. These novel scenarios require somewhat special and specific conditions. Clarity on the plausibility of such conditions could come from future high-resolution observations of planet-forming regions around other stars, from the observed and modeled architectures of extrasolar systems with giant planets, and future Juno data obtained during its extended mission., Comment: invited review for Icarus, accepted for publication

The first mass-estimate of an exoplanet around a Sun-like star, 51 Peg b and the first radius measurement of an exoplanet, HD209458b pointed to the challenges of understanding the atmosphere, interior, and evolution of exoplanets including the possibility of mass loss of planets on close-orbits that are exposed to strong irradiation. These discoveries raised the question of heating and inflation mechanisms, and of the nature of these objects in terms of composition compared to the known planets in the Solar system. The field of exoplanet interior modeling was born. Here, we outline and discuss current big science questions: (i) What is the amount of heavy elements in a planet and do all planets possess an iron-rock core? We suggest that a promising and novel approach for exoplanets can be measuring their tidal response in form of the Love numbers h2 and k2. (ii) How much and through what mechanisms are the interiors of planets heated or delayed from cooling? Many strongly irradiated gaseous planets require an additional heat source to explain their large radii. (iii) What is the origin of the observed populations in the radius-period diagram? Objects in and along the radius valley are excellent targets to study planetary formation and evaporation. (iv) What does the composition of rocky planets tell us about their formation? Planets more iron-rich than Mercury are found, as well as planets that if rocky, are depleted in iron with respect to Earth. We do not have yet a reliable formation theory that would explain their existence., Comment: To appear as a book chapter in "ExoFrontiers: Big questions in exoplanetary science", Ed. N Madhusudhan (Bristol: IOP Publishing Ltd) AAS-IOP ebooks https://iopscience.iop.org/bookListInfo/aas-iop-astronomy

Thermal evolution models suggest that the luminosities of both Uranus and Neptune are inconsistent with the classical assumption of an adiabatic interior. Such models commonly predict Uranus to be brighter and, recently, Neptune to be fainter than observed. In this work, we investigate the influence of a thermally conductive boundary layer on the evolution of Uranus- and Neptune-like planets. This thermal boundary layer (TBL) is assumed to be located deep in the planet, and be caused by a steep compositional gradient between a H-He-dominated outer envelope and an ice-rich inner envelope. We investigate the effect of TBL thickness, thermal conductivity, and the time of TBL formation on the planet's cooling behaviour. The calculations were performed with our recently developed tool based on the Henyey method for stellar evolution. We make use of state-of-the-art equations of state for hydrogen, helium, and water, as well as of thermal conductivity data for water calculated via ab initio methods. We find that even a thin conductive layer of a few kilometres has a significant influence on the planetary cooling. In our models, Uranus' measured luminosity can only be reproduced if the planet has been near equilibrium with the solar incident flux for an extended time. For Neptune, we find a range of solutions with a near constant effective temperature at layer thicknesses of 15 km or larger, similar to Uranus. In addition, we find solutions for thin TBLs of few km and strongly enhanced thermal conductivity. A $\sim$ 1$~$Gyr later onset of the TBL reduces the present $\Delta T$ by an order of magnitude to only several 100 K. Our models suggest that a TBL can significantly influence the present planetary luminosity in both directions, making it appear either brighter or fainter than the adiabatic case., Comment: accepted to A&A, Reproduced with permission from Astronomy & Astrophysics, \copyright ESO

Uranus and Neptune are the archetypes of "ice giants", a class of planets that may be among the most common in the Galaxy. They hold the keys to understand the atmospheric dynamics and structure of planets with hydrogen atmospheres inside and outside the solar system; however, they are also the last unexplored planets of the Solar System. Their atmospheres are active and storms are believed to be fueled by methane condensation which is both extremely abundant and occurs at low optical depth. This means that mapping temperature and methane abundance as a function of position and depth will inform us on how convection organizes in an atmosphere with no surface and condensates that are heavier than the surrounding air, a general feature of giant planets. Owing to the spatial and temporal variability of these atmospheres, an orbiter is required. A probe would provide a reference atmospheric profile to lift ambiguities inherent to remote observations. It would also measure the abundances of noble gases which can be used to reconstruct the history of planet formation in the Solar System. Finally, mapping the planets' gravity and magnetic fields will be essential to constrain their global composition, atmospheric dynamics, structure and evolution. An exploration of Uranus or Neptune will be essential to understand these planets and will also be key to constrain and analyze data obtained at Jupiter, Saturn, and for numerous exoplanets with hydrogen atmospheres., Comment: arXiv admin note: substantial text overlap with arXiv:1908.02092

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures., Comment: 14 pages, 7 figures, accepted for publication in ApJ

Atmospheres regulate the planetary heat loss and therefore influence planetary thermal evolution. Uncertainty in a giant planet's thermal state contributes to the uncertainty in the inferred abundance of heavy elements it contains. Within an analytic atmosphere model, we here investigate the influence that different cloud opacities and cloud depths can have on the metallicity of irradiated extrasolar gas giants, which is inferred from interior models. In this work, the link between inferred metallicity and assumed cloud properties is the thermal profile of atmosphere and interior. Therefore, we perform coupled atmosphere, interior, and evolution calculations. The atmosphere model includes clouds in a much simplified manner; it includes long-wave absorption but neglects shortwave scattering. Within that model, we show that optically thick, high clouds have negligible influence, whereas deep-seated, optically very thick clouds can lead to warmer deep tropospheres and therefore higher bulk heavy element mass estimates. For the young hot Jupiter WASP-10b, we find a possible enhancement in inferred metallicity of up to 10% due to possible silicate clouds at $\sim$0.3 bar. For WASP-39b, whose observationally derived metallicity is higher than predicted by cloudless models, we find an enhancement by at most 50%. However, further work on cloud properties and their self-consistent coupling to the atmospheric structure is needed in order to reduce uncertainties in the choice of model parameter values, in particular of cloud opacities., Comment: Published: 30 October 2019 in Atmosphere

The brightness of Neptune is often found to be in accordance with an adiabatic interior, while the low luminosity of Uranus challenges this assumption. Here we apply revised equation of state data of hydrogen, helium, and water and compute the thermal evolution of Uranus and Neptune assuming an adiabatic interior. For this purpose, we have developed a new planetary model and evolution code. We investigate the influence of albedo, solar energy influx, and equations of state of H and He, and water on the cooling time. Our cooling times of about $\tau_\text{U}=5.1\times 10^9\text{ years}$ for Uranus and $\tau_\text{N}=3.7\times 10^9\text{ years}$ for Neptune bracket the known age of the planets of $4.56\times 10^9\text{ years}$ implying that neither planet's present-day luminosity can be explained by adiabatic cooling. We also find that uncertainties on input parameters such as the level of irradiation matter generally more for Uranus than for Neptune. Our results suggest that in contrast to common assumptions, neither planet is fully adiabatic in the deeper interior., Comment: Accepted for publication in A&A. Reproduced with permission from Astronomy & Astrophysics, \copyright ESO

There are still many open questions regarding the nature of Uranus and Neptune, the outermost planets in the Solar System. In this review we summarize the current-knowledge about Uranus and Neptune with a focus on their composition and internal structure, formation including potential subsequent giant impacts, and thermal evolution. We present key open questions and discuss the uncertainty in the internal structures of the planets due to the possibility of non-adiabatic and inhomogeneous interiors. We also provide the reasoning for improved observational constraints on their fundamental physical parameters such as their gravitational and magnetic fields, rotation rates, and deep atmospheric composition and temperature. Only this way will we be able to improve our understating of these planetary objects, and the many similar-sized objects orbiting other stars., Comment: Accepted for publication in Space Science Reviews

The Juno Orbiter is measuring the three-dimensional gravity field perturbation of Jupiter induced by its rapid rotation, zonal flows, and tidal response to its major natural satellites. This paper aims to provide the contributions to the tesseral harmonics coefficients Cnm, Snm, and the Love numbers knm to be expected from static tidal response in the gravity field of rotating Jupiter. For that purpose, we apply the method of Concentric Maclaurin Ellipsoids (CMS). As we are interested in the variation of the tidal potential with the longitudes of the moons, we take into account the simultaneous presence of the satellites Io, Europa, and Ganymede. We assume co-planar, circular orbits with normals parallel to Jupiter's spin axis. The planet-centered longitude of Io in the three-moon case is arbitrarily assumed varphi = 0. Under these assumptions we find maximum amplitudes and fluctuations of 3.5 times 10^-8 +- 15% for C22. For the Love numbers, largest variation of 10% to 20% is seen in k42 and k62, whereas the values k2, k33, and k44 fall into narrow ranges of 0.1% uncertainty or less. In particular, we find k2=k2,Io(1 +- 0.02%) where k2,Io=0.5897 is the static tidal response to lone Io. Our obtained gravity field perturbation leads to a maximum equatorial shape deformation of up to 28m. We suggest that should Juno measurements of the knm deviate from those values, it may be due to dynamic or dissipative effects on Jupiter's tidal response. Finally, an analytic expression is provided to calculate the tesseral harmonics contribution from static tidal response for any configuration of the satellites., Comment: Accepted to ApJ

The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ($\mathrm{T_{core}} \mathtt{\sim}$ 4000 K).

The Juno Orbiter has provided improved estimates of the even gravitational harmonics J2 to J8 of Jupiter. To compute higher-order moments, new methods such as the Concentric Maclaurin Spheroids (CMS) method have been developed which surpass the so far commonly used Theory of Figures (ToF) method in accuracy. This progress rises the question whether ToF can still provide a useful service for deriving the internal structure of giant planets in the Solar system. In this paper, I apply both the ToF and the CMS method to compare results for polytropic Jupiter and for the physical equation of state H/He-REOS.3 based models. An accuracy in the computed values of J2 and J4 of 0.1% is found to be sufficient in order to obtain the core mass safely within 0.5 Mearth numerical accuracy and the atmospheric metallicity within about 0.0004. ToF to 4th order provides that accuracy, while ToF to 3rd order does not for J4. Furthermore, I find that the assumption of rigid rotation yields J6 and J8 values in agreement with the current Juno estimates, and that higher order terms (J10 to J18) deviate by about 10% from predictions by polytropic models. This work suggests that ToF4 can still be applied to infer the deep internal structure, and that the zonal winds on Jupiter reach less deep than 0.9 RJup., Comment: 8 pages, accepted to A&A

We review our current understanding of the interior structure and thermal evolution of Saturn, with a focus on recent results in the Cassini era. There has been important progress in understanding physical inputs, including equations of state of planetary materials and their mixtures, physical parameters like the gravity field and rotation rate, and constraints on Saturnian free oscillations. At the same time, new methods of calculation, including work on the gravity field of rotating fluid bodies, and the role of interior composition gradients, should help to better constrain the state of Saturn's interior, now and earlier in its history. However, a better appreciation of modeling uncertainties and degeneracies, along with a greater exploration of modeling phase space, still leave great uncertainties in our understanding of Saturn's interior. Further analysis of Cassini data sets, as well as precise gravity field measurements from the Cassini Grand Finale orbits, will further revolutionize our understanding of Saturn's interior over the next few years., Comment: Invited review for the forthcoming volume "Saturn in the 21st Century." If you want a nice version with figures in the right places, go here: http://www.ucolick.org/~jfortney/Saturn21st.pdf

We investigate the physical characteristics of the Solar System's proposed Planet Nine using modeling tools with a heritage in studying Uranus and Neptune. For a range of plausible masses and interior structures, we find upper limits on the intrinsic Teff, from ~35-50 K for masses of 5-20 M_Earth, and we also explore lower Teff values. Possible planetary radii could readily span from 3 to 6 R_Earth depending on the mass fraction of any H/He envelope. Given its cold temperature, the planet encounters significant methane condensation, which dramatically alters the atmosphere away from simple Neptune-like expectations. We find the atmosphere is strongly depleted in molecular absorption at visible wavelengths, suggesting a Rayleigh scattering atmosphere with a high geometric albedo approaching 0.75. We highlight two diagnostics for the atmosphere's temperature structure, the first being the value of the methane mixing ratio above the methane cloud. The second is the wavelength at which cloud scattering can be seen, which yields the cloud-top pressure. Surface reflection may be seen if the atmosphere is thin. Due to collision-induced opacity of H2 in the infrared, the planet would be extremely blue (instead of red) in the shortest wavelength WISE colors if methane is depleted, and would, in some cases, exist on the verge of detectability by WISE. For a range of models, thermal fluxes from ~3-5 microns are ~20 orders of magnitude larger than blackbody expectations. We report a search of the AllWISE Source Catalog for Planet Nine, but find no detection., Comment: Accepted to ApJ Letters, with minor changes from the submitted version

We present new equations of state (EOS) for hydrogen and helium covering a wide range of temperatures from 60 K to 10$^7$ K and densities from $10^{-10}$ g/cm$^3$ to $10^3$ g/cm$^3$. They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear-mixing isotherms based on our EOS tables with available real-mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models for Jupiter and the comparison with recent results. Secondly, mass-radius relations are calculated for Brown Dwarfs which we compare with predictions derived from the widely used EOS of Saumon, Chabrier and van Horn. Furthermore, we calculate interior models for typical Brown Dwarfs with different masses, namely Corot-3b, Gliese-229b and Corot-15b, and the Giant Planet KOI-889b. The predictions for the central pressures and densities differ by up to 10$\%$ dependent on the EOS used. Our EOS tables are made available in the supplemental material of this paper., Comment: 14 pages, 19 Figures, accepted at ApJS

Neptune-sized extrasolar planets that orbit relatively close to their host stars -- often called "hot Neptunes" -- are common within the known population of exoplanets and planetary candidates. Similar to our own Uranus and Neptune, inefficient accretion of nebular gas is expected produce hot Neptunes whose masses are dominated by elements heavier than hydrogen and helium. At high atmospheric metallicities of 10-10,000x solar, hot Neptunes will exhibit an interesting continuum of atmospheric compositions, ranging from more Neptune-like, H2-dominated atmospheres to more Venus-like, CO2-dominated atmospheres. We explore the predicted equilibrium and disequilibrium chemistry of generic hot Neptunes and find that the atmospheric composition varies strongly as a function of temperature and bulk atmospheric properties such as metallicity and the C/O ratio. Relatively exotic H2O, CO, CO2, and even O2-dominated atmospheres are possible for hot Neptunes. We apply our models to the case of GJ 436b, where we find that a CO-rich, CH4-poor atmosphere can be a natural consequence of a very high atmospheric metallicity. From comparisons of our results with Spitzer eclipse data for GJ 436b, we conclude that although the spectral fit from the high-metallicity forward models is not quite as good as the fit obtained from pure retrieval methods, the atmospheric composition predicted by these forward models is more physically and chemically plausible. High-metallicity atmospheres (orders of magnitude in excess of solar) should therefore be considered as a possibility for GJ 436b and other hot Neptunes., Comment: submitted to Astrophys. J. on 21 June 2013

We perform modeling investigations to aid in understanding the atmospheres and composition of small planets of ~2-4 Earth radii, which are now known to be common in our galaxy. GJ 1214b is a well studied example whose atmospheric transmission spectrum has been observed by many investigators. Here we take a step back from GJ 1214b to investigate the role that planetary mass, composition, and temperature play in impacting the transmission spectra of these low-mass low-density (LMLD) planets. Under the assumption that these planets accrete modest hydrogen-dominated atmospheres and planetesimals, we use population synthesis models to show that predicted metal enrichments of the H/He envelope are high, with metal mass fraction Z_env values commonly 0.6 to 0.9, or ~100 to 400+ times solar. The high mean molecular weight of such atmospheres (\mu ~ 5-12) would naturally help to flatten the transmission spectrum of most LMLD planets. The high metal abundance would also provide significant condensible material for cloud formation. It is known that the H/He abundance in Uranus and Neptune decreases with depth, and we show that atmospheric evaporation of LMLD planets could expose atmospheric layers with gradually higher Z_env. However, values of Z_env close to solar composition can also arise, so diversity should be expected. Photochemically produced hazes, potentially due to methane photolysis, are another possibility for obscuring transmission spectra. Such hazes may not form above T_eq of ~800-1100 K, which is testable if such warm, otherwise low mean molecular weight atmospheres are stable against atmospheric evaporation. We find that available transmission data are consistent with relatively high mean molecular weight atmospheres for GJ 1214b and "warm Neptune" GJ 436b. We examine future prospects for characterizing GJ 1214b with Hubble and the James Webb Space Telescope., Comment: Accepted to The Astrophysical Journal on August 12, 2013. Minor changes, including new-subsection on mass-radius of LMLD planets

The amount and distribution of heavy elements in Jupiter gives indications on the process of its formation and evolution. Core mass and metallicity predictions however depend on the equations of state used, and on model assumptions. We present an improved ab initio hydrogen equation of state, H-REOS.2 and compute the internal structure and thermal evolution of Jupiter within the standard three-layer approach. The advance over our previous Jupiter models with H-REOS.1 by Nettelmann et al.(2008) is that the new models are also consistent with the observed 2 or more times solar heavy element abundances in Jupiter's atmosphere. Such models have a rock core mass Mcore=0-8 ME, total mass of heavy elements MZ=28-32 ME, a deep internal layer boundary at 4 or more Mbar, and a cooling time of 4.4-5.0 Gyrs when assuming homogeneous evolution. We also calculate two-layer models in the manner of Militzer et al.(2008) and find a comparable large core of 16-21 ME, out of which ~11 ME is helium, but a significantly higher envelope metallicity of 4.5 times solar. According to our preferred three-layer models, neither the characteristic frequency (nu0 ~156 microHz) nor the normalized moment of inertia (~0.276) are sensitive to the core mass but accurate measurements could well help to rule out some classes of models., Comment: 7 figures, 1 table, accepted to ApJ

More than 80 giant planets are known by mass and radius. Their interior structure in terms of core mass, number of layers, and composition however is still poorly known. An overview is presented about the core mass Mcore and envelope mass of metals MZ in Jupiter as predicted by various equations of state. It is argued that the uncertainty about the true H/He EOS in a pressure regime where the gravitational moments J2 and J4 are most sensitive, i.e. between 0.5 and 4 Mbar, is in part responsible for the broad range Mcore=0-18 Mearth, MZ=0-38 Mearth, and Mcore+MZ=14-38 Mearth currently offered for Jupiter. We then compare the Jupiter models obtained when we only match J2 with the range of solutions for the exoplanet GJ436b, when we match an assumed tidal Love number k2 value., Comment: Accepted for publication in Astrophyics and Space Science

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 comments

We discuss our current understanding of the interior structure and thermal evolution of giant planets. This includes the gas giants, such as Jupiter and Saturn, that are primarily composed of hydrogen and helium, as well as the "ice giants," such as Uranus and Neptune, which are primarily composed of elements heavier than H/He. The effect of different hydrogen equations of state (including new first-principles computations) on Jupiter's core mass and heavy element distribution is detailed. This variety of the hydrogen equations of state translate into an uncertainty in Jupiter's core mass of 18 M_Earth. For Uranus and Neptune we find deep envelope metallicities up to 0.95, perhaps indicating the existence of an eroded core, as also supported by their low luminosity. We discuss the results of simple cooling models of our solar system's planets, and show that more complex thermal evolution models may be necessary to understand their cooling history. We review how measurements of the masses and radii of the ~50 transiting extrasolar giant planets are changing our understanding of giant planets. In particular a fraction of these planets appear to be larger than can be accommodated by standard models of planetary contraction. We review the proposed explanations for the radii of these planets. We also discuss very young giant planets, which are being directly imaged with ground- and space-based telescopes., Comment: Space Science Reviews, in press. Review based on work presented at the ISSI Workshop "Planetary Magnetism," in Bern, Switzerland, 1-5 September 2008

The discovery of CoRoT-7b, a planet of radius 1.68 +/- 0.09 R_E, mass 4.8 +/- 0.8 M_E and orbital period of 0.854 days demonstrates that small planets can orbit extremely close to their star. We use knowledge of hot Jupiters, mass loss estimates and models for the interior structure and evolution of planets to understand its composition, structure and evolution. The inferred mass and radius of CoRoT-7b are consistent with a rocky planet that would be depleted in iron relative to Earth. However, a one sigma increase in mass (5.6 M_E) and decrease in size (1.59 R_E) are compatible with an Earth-like composition (33% iron, 67% silicates). Alternatively, it is possible that CoRoT-7b contains a significant amount of volatiles. An equally good fit to the data is found for a vapor envelope equal to 3% (and up to 10%) by mass above an Earth-like nucleus. Because of its intense irradiation and small size, the planet cannot possess an envelope of H and He of more than 1/10,000 of its total mass. We show that the mass loss is significant (~ 10^11 g/s) and independent of planetary composition. This is because the hydrodynamical escape rate is independent of the atmosphere's mean molecular mass, and owing to the intense irradiation, even a bare rocky planet would possess an equilibrium vapor atmosphere thick enough to capture stellar UV photons. This escape rate rules out the possibility of a H-He envelope as it would escape in only ~1 Ma. A water vapor atmosphere would escape in ~ 1 Ga, and thus it is a plausible scenario. The origin of CoRoT-7b cannot be inferred from present observations: It may have formed rocky; or be the remnant of a Uranus-like ice giant, or a gas giant with a small core that was stripped of its gaseous envelope., Comment: This is a revised version of the paper submitted to astroph in July 17th 2009. It has been modified to include the measurement for CoRoT-7b's mass which was not determined until after the first version of this paper. 12 pages, 10 figures, accepted in A&A

We calculate the equation of state of dense hydrogen within the chemical picture. Fluid variational theory is generalized for a multi-component system of molecules, atoms, electrons, and protons. Chemical equilibrium is supposed for the reactions dissociation and ionization. We identify the region of thermodynamic instability which is related to the plasma phase transition. The reflectivity is calculated along the Hugoniot curve and compared with experimental results. The equation-of-state data is used to calculate the pressure and temperature profiles for the interior of Jupiter., Comment: 7 pages, 7 figures, contibution to the 12th International Workshop on the Physics of Non-Ideal Plasmas, Darmstadt, Germany