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The recently adopted Ariel ESA mission will measure the atmospheric composition of a large number of exoplanets. This information will then be used to better constrain planetary bulk compositions. While the connection between the composition of a planetary atmosphere and the bulk interior is still being investigated, the combination of the atmospheric composition with the measured mass and radius of exoplanets will push the field of exoplanet characterisation to the next level, and provide new insights of the nature of planets in our galaxy. In this white paper, we outline the ongoing activities of the interior working group of the Ariel mission, and list the desirable theoretical developments as well as the challenges in linking planetary atmospheres, bulk composition and interior structure., Experimental Astronomy, 53, ISSN:0922-6435, ISSN:1572-9508

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made., The goal of the Ariel space mission is to observe a large and diversified population of transiting planets around a range of host star types to collect information on their atmospheric composition. The planetary bulk and atmospheric compositions bear the marks of the way the planets formed: Ariel’s observations will therefore provide an unprecedented wealth of data to advance our understanding of planet formation in our Galaxy. A number of environmental and evolutionary factors, however, can affect the final atmospheric composition. Here we provide a concise overview of which factors and effects of the star and planet formation processes can shape the atmospheric compositions that will be observed by Ariel, and highlight how Ariel’s characteristics make this mission optimally suited to address this very complex problem. © The Author(s) 2021., D.T., S.F., S.M., E.S., and A.N. acknowledge the support of the Italian Space Agency (ASI) through the ASI-INAF contract 2018-22-HH.0. D.T., C.C., D.F., and L.P. acknowledge the support of the PRIN-INAF 2016 “The Cradle of Life - GENESIS-SKA (General Conditions in Early Planetary Systems for the rise of life with SKA”. D.T., S.F., S.M. D.F, J.M., F.O., P.W. acknowledge the support of the Italian National Institute of Astrophysics (INAF) through the INAF Main Stream project “Ariel and the astrochemical link between circumstellar discs and planets” (CUP: C54I19000700005). S.M. acknowledges support from the European Research Council via the Horizon 2020 Framework Programme ERC Synergy “ECOGAL” Project GA-855130. M.K. acknowledges funding by the University of Tartu ASTRA project 2014-2020.4.01.16-0029 KOMEET “Benefits for Estonian Society from Space Research and Application”, financed by the EU European Regional Development Fund. J.M.D.K. gratefully acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through an Emmy Noether Research Group (grant number KR4801/1-1) and the DFG Sachbeihilfe (grant number KR4801/2-1), as well as from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme via the ERC Starting Grant MUSTANG (grant agreement number 714907). The research of O.P. is funded by the Royal Society, through Royal Society Dorothy Hodgkin Fellowship DH140243. M.P. thanks the support to NuGrid from STFC (through the University of Hull’s Consolidated Grant ST/R000840/1), and access to VIPER, the University of Hull High Performance Computing Facility. M.P. acknowledges the support from the ”Lendulet-2014” Program of the Hungarian Academy of Sciences (Hungary), from the ERC Consolidator Grant (Hungary) funding scheme (Project RADIOSTAR, G.A. n. 724560), by the National Science Foundation (NSF, USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the Elements). M.P. also thanks the UK network BRIDGCE and the ChETEC COST Action (CA16117), supported by COST (European Cooperation in Science and Technology). M.I. thanks the support by JSPS KAKENHI 18H05439. C.D. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709), and the Group project Ref. PID2019-110689RB-I00/AEI/10.13039/501100011033.

Ariel, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, was adopted as the fourth medium-class mission in ESA's Cosmic Vision programme to be launched in 2029. During its 4-year mission, Ariel will study what exoplanets are made of, how they formed and how they evolve, by surveying a diverse sample of about 1000 extrasolar planets, simultaneously in visible and infrared wavelengths. It is the first mission dedicated to measuring the chemical composition and thermal structures of hundreds of transiting exoplanets, enabling planetary science far beyond the boundaries of the Solar System. The payload consists of an off-axis Cassegrain telescope (primary mirror 1100 mm x 730 mm ellipse) and two separate instruments (FGS and AIRS) covering simultaneously 0.5-7.8 micron spectral range. The satellite is best placed into an L2 orbit to maximise the thermal stability and the field of regard. The payload module is passively cooled via a series of V-Groove radiators; the detectors for the AIRS are the only items that require active cooling via an active Ne JT cooler. The Ariel payload is developed by a consortium of more than 50 institutes from 16 ESA countries, which include the UK, France, Italy, Belgium, Poland, Spain, Austria, Denmark, Ireland, Portugal, Czech Republic, Hungary, the Netherlands, Sweden, Norway, Estonia, and a NASA contribution., Comment: Ariel Definition Study Report, 147 pages. Reviewed by ESA Science Advisory Structure in November 2020. Original document available at: https://www.cosmos.esa.int/documents/1783156/3267291/Ariel_RedBook_Nov2020.pdf/

Direct imaging (DI) surveys suggest that gas giants beyond 20 AU are rare around FGK stars. However, it is not clear what this means for the formation frequency of Gravitational Instability (GI) protoplanets due to uncertainties in gap opening and migration efficiency. Here we combine state-of-the-art calculations of homogeneous planet contraction with a population synthesis code. We find DI constraints to be satisfied if protoplanet formation by GI occurs in tens of percent of systems if protoplanets `super migrate' to small separations. In contrast, GI may occur in only a few percent of systems if protoplanets remain stranded at wide orbits because their migration is `quenched' by efficient gap opening. We then use the frequency of massive giants in radial velocity surveys inside 5 AU to break this degeneracy - observations recently showed that this population does not correlate with the host star metallicity and is therefore suspected to have formed via GI followed by inward migration. We find that only the super-migration scenario can sufficiently explain this population whilst simultaneously satisfying the DI constraints and producing the right mass spectrum of planets inside 5 AU. If massive gas-giants inside 5 AU formed via GI, then our models imply that migration must be efficient and that the formation of GI protoplanets occurs in at least a tens of percent of systems., Accepted to MNRAS

The amount of nebular gas that a planet can bind is limited by its cooling rate, which is set by the opacity of its envelope. Accreting dust and pebbles contribute to the envelope opacity and, thus, influence the outcome of planet formation. Our aim is to model the size evolution and opacity contribution of solids inside planetary envelopes. We then use the resultant opacity relations to study emergent trends in planet formation. We design a model for the opacity of solids in planetary envelopes that accounts for the growth, fragmentation and erosion of pebbles during their sedimentation. We formulate analytical expressions for the opacity of pebbles and dust and map out their trends as a function of depth, planet mass, distance and accretion rate. We find that the accretion of pebbles rather than planetesimals can produce fully convective envelopes, but only in lower-mass planets that reside in the outer disk or in those that are accreting pebbles at a high rate. In these conditions, pebble sizes are limited by fragmentation and erosion, allowing them to pile up in the envelope. At higher planetary masses or reduced accretion rates, a different regime applies where the sizes of sedimenting pebbles are only limited by their rate of growth. The opacity in this growth-limited regime is much lower, steeply declines with depth and planet mass but is invariant with the pebble mass flux. Our results imply that the opacity of a forming planetary envelope can not be approximated by a value that is constant with either depth or planet mass. When applied to the Solar System, we argue that Uranus and Neptune could not have maintained a sufficiently high opacity to avoid runaway gas accretion unless they both experienced sufficiently rapid accretion of solids and formed late., Accepted to A&A. Comments are welcome

1. Introduction:In the traditional core accretion scenario, a planet grows by the subsequent accretion of a solid core and a gaseous envelope [3]. However, the accretion of these solids generates a large amount of heat, which can easily vaporize incoming pebbles and fractured planetesimals before the core has grown massive [1,4,5]. This naturally leads to the formation of planets with polluted envelopes that are characterized by different interior conditions and that follow an altered evolutionary pathway. In this series of papers [1,2+forthcoming], we develop new analytical and numerical models to describe the formation and evolution of polluted planets and link emerging trends in their formation to observations of planetary systems. 2. Formation of polluted planets: Fig. 1. A sketch of the four potential evolutionary phases of a polluted planet. We find that envelope pollution substantially alters the structure of proto-planets in a number of ways and we suggest that their evolution can be described by four distinct phases, sketched in Fig. 1. (I). In the first phase of direct core growth, the envelope is still cold enough for solids to reach the central core. As the planet's internal temperatures rise, an increasing fraction of the accreting solids sublimates and is absorbed in the envelope. This slows down the growth of the core until it halts completely when all incoming solids become vaporized and remain in the envelope. We find that in the case of pebble accretion, this limits the size of the central cores to ‹ 1-2 M⊕, depending on conditions. (II). We refer to the second phase as that of envelope growth, as this is where all the accreted solids end up after direct core growth ends. In our analytical model, we assume that it mixes efficiently with the nebular gas but we relax this assumption in a forthcoming numerical work. Regardless, we find that polluted interiors become very hot and dense due to a higher mean molecular weight, lower adiabatic index and smaller core. Interior temperatures can already reach values in excess of 104 K at only a few Earth masses. Traditional models use the critical core mass as a criterion to identify the transition to runaway gas accretion but this term becomes a meaningless in planets that do not grow their cores beyond a certain size. We therefore suggest the critical metal mass (Mz,crit) as an equivalent criterion to supercede it. It is defined as the total mass in solids (core + vapor) that a planet needs to accrete in order to reach runaway growth. We derive the first expression for this mass: where κrcb is the opacity at the radiative-convective boundary, d is the planet's semi-major axis, Tvap is the vaporization temperature of the solids, is their accretion rate and Mc is the mass of the central core. Planets that form beyond the ice-line accrete a larger fraction of volatile materials and therefore form smaller cores with material that is characterized by lower vaporization temperatures. Both these effects reduce the critical metal mass compared to the inner disk where super-Earths and mini-Neptunes are more resistant to runaway gas accretion. (III). If a planet stops accreting solids before it reaches runaway accretion and while the disk is still present, it enters a phase of embedded cooling. This naturally happens in pebble accretion when a planet reaches the pebble isolation mass and begins to perturb the surrounding disk. The continued inward drift of tiny dust allows the planet to maintain a high opacity, limiting the pace of cooling. Besides this, the dilution of the interior can counteract the contraction of the envelope and further limit nebular accretion, although this requires the interior to remain compositionally mixed. We suggest that a combination of these effects can help explain why Uranus and Neptune did not reach runaway gas accretion, even if their solids flux dried up while the disk was still present. (IV). Finally, the proto-planetary disk will dissipate and the planets eventually enter phase IV of isolated cooling. In traditional models, this is mainly associated with contraction and potential mass loss. We suggest that in the case of a polluted planet, the cooling will eventually lead to the rainout of the vapor interior and generate a second phase of (indirect) core growth after several Gyr. While the process of photo-evaporation should not be altered by this, we find that it makes internal energy release an ineffective mass-loss mechanism. This is because most of the energy is only liberated late in the planet's evolution after substantial contraction, when mass loss from winds is far less efficient. 2.1 Opacity in pebble accretion Fig. 2. Trends in the critical metal mass from the opacity of gas, dust and pebbles. We model the opacity during pebble accretion in a forthcoming work with a combination of molecular, dust and pebble contributions. We find that pebbles can effectively reduce the dust abundance through sweep-up, but only in the early stages when nebular gas accretion is outpaced by the pebble flux. Near the onset of runaway accretion, the opacity displays a dichotomy between the hot inner disk where molecular opacity dominates and the outer disk where dust obscures the envelopes. The result is an opacity valley around 1-3 AU that translates to an equivalent minimum in the critical metal mass at the same location (see Fig. 2), which can help explain the abundance of warm Jupiters in this region. Acknowledgements:This work has benefited from discussions at the ISSI Ice Giants Meetings in Bern 2019 & 2020. Marc Brouwers acknowledges the support of a Royal Society Studentship, RG 160509. References: [1] Brouwers, M. G., Vazan, A., & Ormel, C. W. 2018, A&A, 611, A65 [2] Brouwers, M. G. & Ormel, C. W. 2020, A&A, 634, A15 [3] Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62 [4] Mordasini, C., Mollière, P., Dittkrist, K.-M., Jin, S., & Alibert, Y. 2015, International Journal of Astrobiology, 14, 201 [5] Valletta, C. & Helled, R. 2019, ApJ, 871, 127

Dark rings with bright rims are the indirect signposts of planets embedded in protoplanetary discs. In a recent first, an azimuthally elongated AU-scale blob, possibly a planet, was resolved with ALMA in TW Hya. The blob is at the edge of a cliff-like rollover in the dust disc rather than inside a dark ring. Here we build time-dependent models of TW Hya disc. We find that the classical paradigm cannot account for the morphology of the disc and the blob. We propose that ALMA-discovered blob hides a Neptune mass planet losing gas and dust. We show that radial drift of mm-sized dust particles naturally explains why the blob is located on the edge of the dust disc. Dust particles leaving the planet perform a characteristic U-turn relative to it, producing an azimuthally elongated blob-like emission feature. This scenario also explains why a 10 Myr old disc is so bright in dust continuum. Two scenarios for the dust-losing planet are presented. In the first, a dusty pre-runaway gas envelope of about 40 Earth mass Core Accretion planet is disrupted, e.g., as a result of a catastrophic encounter. In the second, a massive dusty pre-collapse gas giant planet formed by Gravitational Instability is disrupted by the energy released in its massive core. Future modelling may discriminate between these scenarios and allow us to study planet formation in an entirely new way -- by analysing the flows of dust and gas recently belonging to planets, informing us about the structure of pre-disruption planetary envelopes., Comment: Typos fixed, references and author list updated

We present WASP-43b climate simulations with deep wind jets (down to 700 bar) that are linked to retrograde (westward) flow at the equatorial day side for p < 0.1 bar. Retrograde flow inhibits efficient eastward heat transport and naturally explains the small hotspot shift and large day-night-side gradient of WASP-43b (Porb = Prot = 0.8135 d) observed with Spitzer. We find that deep wind jets are mainly associated with very fast rotations (Prot = Porb ≤ 1.5 d) which correspond to the Rhines length smaller than 2 planetary radii. We also diagnose wave activity that likely gives rise to deviations from superrotation. Further, we show that we can achieve full steady state in our climate simulations by imposing a deep forcing regime for p > 10 bar: convergence time-scale τconv = 106–108 s to a common adiabat, as well as linear drag at depth (p ≥ 200 bar), which mimics to first-order magnetic drag. Lower boundary stability and the deep forcing assumptions were also tested with climate simulations for HD 209458b (Porb = Prot = 3.5 d). HD 209458b simulations always show shallow wind jets (never deeper than 100 bar) and unperturbed superrotation. If we impose a fast rotation (Porb = Prot = 0.8135 d), also the HD 209458b-like simulation shows equatorial retrograde flow at the day side. We conclude that the placement of the lower boundary at p = 200 bar is justified for slow rotators like HD 209458b, but we suggest that it has to be placed deeper for fast-rotating, dense hot Jupiters (Porb ≤ 1.5 d) like WASP-43b. Our study highlights that the deep atmosphere may have a strong influence on the observable atmospheric flow in some hot Jupiters.

The large brightness variation in the observed lightcurve of Oumuamua is probably related to its shape, i.e., to the ratio between its longest axis and its shortest axis (aspect ratio). Several approaches found the aspect ratio of Oumuamua to be unusually elongated. Moreover, the spin axis orientation has to be almost perpendicular to the observer in order to obtain such an extreme lightcurve, a configuration which is unlikely. However, interstellar Oumuamua may have different surface properties than we know in our solar system. Therefore, in this work we widen the parameter space for surface properties beyond the asteroid-like models and study its effect on the lightcurve of Oumuamua. We calculate reflection from a rotating ellipsoidal object for four models: Lambertian reflection, specular reflection, single scattering diffusive and backscatter. We then calculate the probability to obtain a lightcurve ratio larger than the observed, as a function of the object aspect ratio, assuming an isotopic spin orientation distribution. We find the elongation of Oumuamua to be less extreme for the Lambertian and specular reflection models. Consequently, the probability to observe the lightcurve ratio of Oumuamua given its unknown spin axis orientation is larger for those models. We conclude that different surface reflection properties may suggest alternatives to the extreme shape of Oumuamua, relieving the need for complicated formation scenario, extreme albedo variation, or unnatural origin. Although the models suggested here are for ideal ellipsoidal shape and ideal reflection method, the results emphasize the importance of surface properties for the derived aspect ratio., Comment: 7 pages, accepted for publication in MNRAS

Ice-rich planets are formed exterior to the water ice-line and thus are expected to contain a substantial amount of ices. The high ice content leads to unique conditions in the interior, under which the structure of a planet is affected by ice interaction with other metals. We apply experimental data of ice-rock interaction at high pressure, and calculate detailed thermal evolution for possible interior configurations of ice-rich planets, in the mass range of super-Earth to Neptunes (5-15 Earth masses). We model the effect of migration inward on the ice-rich interior by including the influences of stellar flux and envelope mass loss. We find that ice and rock are expected to remain mixed, due to miscibility at high pressure, in substantial parts of the planetary interior for billions of years. We also find that the deep interior of planetary twins that have migrated to different distances from the star are usually similar, if no mass loss occurs. Significant mass loss results in separation of the water from the rock on the surface and emergence of a volatile atmosphere of less than 1 percent of the planet's mass. The mass of the atmosphere of water/steam is limited by the ice-rock interaction. We conclude that when ice is abundant in planetary interiors the planet structure may differ significantly from the standard layered structure of a water shell on top of a rocky core. Similar structure is expected in both close-in and further-out planets., Comment: Accepted for publication in ApJ. Updated with extensive appendices on ice-rock interaction. Results and conclusions are unchanged

During their formation, planets form large, hot atmospheres due to the ongoing accretion of solids. It has been customary to assume that all solids end up at the center constituting a "core" of refractory materials, whereas the envelope remains metal-free. Recent work, as well as observations by the JUNO mission, indicate however that the distinction may not be so clear cut. Indeed, small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ~ 2,000 K). In this paper we extend previous analytical work to compute the properties of planets under such a pebble accretion scenario. We conduct 1D numerical calculations of the atmosphere of an accreting planet, solving the stellar structure equations, augmented by a non-ideal equation of state that describes a hydrogen/helium-silicate vapor mixture. Calculations terminate at the point where the total mass in metal equals that of the H/He gas, which we numerically confirm as the onset of runaway gas accretion. When pebbles sublimate before reaching the core, insufficient (accretion) energy is available to mix dense, vapor-rich lower layers with the higher layers of lower metallicity. A gradual structure in which Z decreases with radius is therefore a natural outcome of planet formation by pebble accretion. We highlight, furthermore, that (small) pebbles can act as the dominant source of opacity, preventing rapid cooling and presenting a channel for (mini-)Neptunes to survive in gas-rich disks. Nevertheless, once pebble accretion subsides, the atmosphere rapidly clears followed by runaway gas accretion. We consider atmospheric recycling to be the more probable mechanisms that have stalled the growth of these planets' envelopes., Comment: Accepted for publication in A&A

The low luminosity of Uranus is a long-standing challenge in planetary science. Simple adiabatic models are inconsistent with the measured luminosity, which indicates that Uranus is non-adiabatic because it has thermal boundary layers and/or conductive regions. A gradual composition distribution acts as a thermal boundary to suppress convection and slow down the internal cooling. Here we investigate whether composition gradients in the deep interior of Uranus can explain its low luminosity, the required composition gradient, and whether it is stable for convective mixing on a timescale of some billion years. We varied the primordial composition distribution and the initial energy budget of the planet, and chose the models that fit the currently measured properties (radius, luminosity, and moment of inertia) of Uranus. We present several alternative non-adiabatic internal structures that fit the Uranus measurements. We found that convective mixing is limited to the interior of Uranus, and a composition gradient is stable and sufficient to explain its current luminosity. As a result, the interior of Uranus might still be very hot, in spite of its low luminosity. The stable composition gradient also indicates that the current internal structure of Uranus is similar to its primordial structure. Moreover, we suggest that the initial energy content of Uranus cannot be greater than 20% of its formation (accretion) energy. We also find that an interior with a mixture of ice and rock, rather than separated ice and rock shells, is consistent with measurements, suggesting that Uranus might not be "differentiated". Our models can explain the luminosity of Uranus, and they are also consistent with its metal-rich atmosphere and with the predictions for the location where its magnetic field is generated., Comment: 10 pages, 7 figures, accepted for publication in A&A

Sub-Neptune planets are a very common type of planets. They are inferred to harbour a primordial (H/He) envelope, on top of a (rocky) core, which dominates the mass. Here, we investigate the long-term consequences of the core properties on the planet mass-radius relation. We consider the role of various core energy sources resulting from core formation, its differentiation, its solidification (latent heat), core contraction and radioactive decay. We divide the evolution of the rocky core into three phases: the formation phase, which sets the initial conditions, the magma ocean phase, characterized by rapid heat transport, and the solid state phase, where cooling is inefficient. We find that for typical sub-Neptune planets of ~2-10 Earth masses and envelope mass fractions of 0.5-10% the magma ocean phase lasts several Gyrs, much longer than for terrestrial planets. The magma ocean phase effectively erases any signs of the initial core thermodynamic state. After solidification, the reduced heat flux from the rocky core causes a significant drop in the rocky core surface temperature, but its effect on the planet radius is limited. In the long run, radioactive heating is the most significant core energy source in our model. Overall, the long term radius uncertainty by core thermal effects is up to 15%., ApJ Published

The study of extrasolar planets and of the Solar System provides complementary pieces of the mosaic represented by the process of planetary formation. Exoplanets are essential to fully grasp the huge diversity of outcomes that planetary formation and the subsequent evolution of the planetary systems can produce. The orbital and basic physical data we currently possess for the bulk of the exoplanetary population, however, do not provide enough information to break the intrinsic degeneracy of their histories, as different evolutionary tracks can result in the same final configurations. The lessons learned from the Solar System indicate us that the solution to this problem lies in the information contained in the composition of planets. The goal of the Atmospheric Remote-Sensing Infrared Exoplanet Large-survey (ARIEL), one of the three candidates as ESA M4 space mission, is to observe a large and diversified population of transiting planets around a range of host star types to collect information on their atmospheric composition. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres, which should show minimal condensation and sequestration of high-Z materials and thus reveal their bulk composition across all main cosmochemical elements. In this work we will review the most outstanding open questions concerning the way planets form and the mechanisms that contribute to create habitable environments that the compositional information gathered by ARIEL will allow to tackle, Comment: 20 pages, 6 figures, accepted for publication on Experimental Astronomy, to appear in the special issue on the ESA space mission ARIEL

Sub-Neptune planets are very common in our galaxy and show a large diversity in their mass-radius relation. In sub-Neptunes most of the planet mass is in the rocky part (hereafter core) which is surrounded by a modest hydrogen-helium envelope. As a result, the total initial heat content of such a planet is dominated by that of the core. Nonetheless, most studies contend that the core cooling will only have a minor effect on the radius evolution of the gaseous envelope, because the core's cooling is in sync with the envelope, i.e., most of the initial heat is released early on timescales of about 10-100 Myr. In this Letter we examine the importance of the core cooling rate for the thermal evolution of the envelope. Thus, we relax the early core cooling assumption and present a model where the core is characterized by two parameters: the initial temperature and the cooling time. We find that core cooling can significantly enhance the radius of the planet when it operates on a timescale similar to the observed age, i.e. several Gyr. Consequently, the interpretation of sub-Neptunes' mass-radius observations depends on the assumed core thermal properties and the uncertainty therein. The degeneracy of composition and core thermal properties can be reduced by obtaining better estimates of the planet ages (in addition to their radii and masses) as envisioned by future observations., Accepted for publication in A&A Letters

Context: Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by accreting cm-to-m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This provides early enrichment to the planet's envelope, which changes the process of core growth. Aims: We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Methods: We model the early growth of a proto-planet by calculating the structure of its envelope, taking into account the fate of impacting pebbles or planetesimals. The region where high-Z material can exist in vapor form is determined by the vapor pressure. We include enrichment effects by locally modifying the mean molecular weight. Results: In the pebble case, three phases of core growth can be identified. In the first phase, pebbles impact the core without significant ablation. During the second phase, ablation becomes increasingly severe. A layer of high-Z vapor starts to form around the core that absorbs a small fraction of the ablated mass. The rest either rains out to the core or mixes outwards instead, slowing core growth. In the third phase, the vapor inner region expands outwards, absorbing an increasing fraction of the ablated material as vapor. Rainout ends before the core mass reaches 0.6 M_Earth, terminating direct core growth. In the case of icy H2O pebbles, this happens before 0.1 M_Earth. Conclusions: Our results indicate that pebble accretion can directly form rocky cores up to only 0.6 M_Earth, and is unable to form similarly sized icy cores. Subsequent core growth can proceed indirectly when the planet cools, provided it is able to retain its high-Z material., Comment: 12 pages, 6 figures. Published in A&A. Includes corrigendum to Sect. 4.2

The presence of rocky exoplanets with a large refractory carbon inventory is predicted by chemical evolution models of protoplanetary disks of stars with photospheric C/O >0.65, and by models studying the radial transport of refractory carbon. High-pressure high-temperature laboratory experiments show that most of the carbon in these exoplanets differentiates into a graphite outer shell. Our aim is to evaluate the effects of a graphite outer shell on the thermal evolution of rocky exoplanets containing a metallic core and a silicate mantle. We implement a parameterized model of mantle convection to determine the thermal evolution of rocky exoplanets with graphite layer thicknesses up to 1000 km. We find that, due to the high thermal conductivity of graphite, conduction is the dominant heat transport mechanism in a graphite layer for the long-term evolution (>200 Myr). The conductive graphite shell essentially behaves like a stagnant lid with a fixed thickness. Models of Kepler-37b (Mercury-size) and a Mars-sized exoplanet show that a planet with a graphite lid cools faster than a planet with a silicate lid, and a planet without a stagnant lid cools the fastest. A graphite lid needs to be approximately ten times thicker than a corresponding silicate lid in order to produce similar thermal evolution., 13 pages, 6 figures

The internal structure of gas giant planets may be more complex than the commonly assumed core-envelope structure with an adiabatic temperature profile. Different primordial internal structures as well as various physical processes can lead to non-homogenous compositional distributions. A non-homogenous internal structure has a significant impact on the thermal evolution and final structure of the planets. In this paper, we present alternative structure and evolution models for Jupiter and Saturn allowing for non-adiabatic primordial structures and the mixing of heavy elements by convection as these planets evolve. We present the evolution of the planets accounting for various initial composition gradients, and in the case of Saturn, include the formation of a helium-rich region as a result of helium rain. We investigate the stability of regions with composition gradients against convection, and find that the helium shell in Saturn remains stable and does not mix with the rest of the envelope. In other cases, convection mixes the planetary interior despite the existence of compositional gradients, leading to the enrichment of the envelope with heavy elements. We show that non-adiabatic structures (and cooling histories) for both Jupiter and Saturn are feasible. The interior temperatures in that case are much higher that for standard adiabatic models. We conclude that the internal structure is directly linked to the formation and evolution history of the planet. These alternative internal structures of Jupiter and Saturn should be considered when interpreting the upcoming Juno and Cassini data., Comment: accepted for publication in ApJ

Recent formation and structure models of Jupiter suggest that the planet can have composition gradients and not be fully convective (adiabatic). This possibility directly affects our understanding of Jupiter's bulk composition and origin. In this Letter we present Jupiter's evolution with a primordial structure consisting of a relatively steep heavy-element gradient of 40 Earth masses. We show that for a primordial structure with composition gradients, most of the mixing occurs in the outer part of the gradient during the early evolution (several 10^7 years), leading to an adiabatic outer envelope (60% of Jupiter's mass). We find that the composition gradient in the deep interior persists, suggesting that about 40% of Jupiter's mass can be non-adiabatic with a higher temperature than the one derived from Jupiter's atmospheric properties. The region that can potentially develop layered-convection in Jupiter today is estimated to be limited to about 10% of the mass., Comment: accepted for publication in A&A Letters

The primordial internal structures of gas giant planets are unknown. Often giant planets are modeled under the assumption that they are adiabatic, convective, and homogeneously mixed, but this is not necessarily correct. In this work, we present the first self-consistent calculation of convective transport of both heat and material as the planets evolve. We examine how planetary evolution depends on the initial composition and its distribution, whether the internal structure changes with time, and if so, how it affects the evolution. We consider various primordial distributions, different compositions, and different mixing efficiencies and follow the distribution of heavy elements in a Jupiter-mass planet as it evolves. We show that a heavy-element core cannot be eroded by convection if there is a sharp compositional change at the core-envelope boundary. If the heavy elements are initially distributed within the planet according to some compositional gradient, mixing occurs in the outer regions resulting in a compositionally homogeneous outer envelope. Mixing of heavy materials that are injected in a convective gaseous envelope are found to mix efficiently. Our work demonstrates that the primordial internal structure of a giant planet plays a substantial role in determining its long-term evolution and that giant planets can have non-adiabatic interiors. These results emphasize the importance of coupling formation, evolution, and internal structure models of giant planets self-consistently., accepted to ApJ

We model the evolution of a Jupiter-mass protoplanet formed by the disk instability mechanism at various radial distances accounting for the presence of the disk. Using three different disk models, it is found that a newly-formed Jupiter-mass protoplanet at radial distance of $\lesssim$ 5-10 AU cannot undergo a dynamical collapse and evolve further to become a gravitational bound planet. We therefore conclude that {\it giant planets, if formed by the gravitational instability mechanism, must form and remain at large radial distances during the first $\sim$ 10$^5-10^6$ years of their evolution}. The minimum radial distances in which protoplanets of 1 Saturn-mass, 3 and 5 Jupiter-mass protoplanets can evolve using a disk model with $\dot{M}=10^{-6} M_{Sun}/yr$ and $\alpha=10^{-2}$ are found to be 12, 9, and 7 AU, respectively. The effect of gas accretion on the planetary evolution of a Jupiter-mass protoplanet is also investigated. It is shown that gas accretion can shorten the pre-collapse timescale substantially. Our study suggests that the timescale of the pre-collapse stage does not only depend on the planetary mass, but is greatly affected by the presence of the disk and efficient gas accretion., Comment: 26 pages, 2 tables, 10 figures. Accepted for publication in ApJ

We use an improved version of the planetary evolution code described in Helled et al. (2006) to model the effect of opacity on the evolution of giant planets in the disk instability scenario. We find that changing the opacity law can cause significant changes in the evolutionary path of a protoplanet. Sufficiently high opacities cause oscillatory behavior that delays the final collapse. Peak luminosities just before collapse can exceed 10−5L⊙.