Planetary Envelope Research Articles

Growing planet envelopes in spite of recycling flows

Abstract The hydrodynamic exchange of a protoplanet’s envelope material with the background protoplanetary disk has been proposed as one mechanism to account for the diversity of observed planet envelopes which range in mass fractions of $\sim 1~{{\%}}$ for super-Earths to $\sim 90~{{\%}}$ for giants. Here we present 3D radiation-hydrodynamics models of protoplanet envelopes applicable to gas-giant cores at intermediate distances and a subset of close-in super-Earths in hot or low-density disks. We analyze how hydrodynamic mass and energy exchange impact the formation process. Our protoplanet envelope simulations show an exchange of material bringing the outer ≳ 0.4Rb envelope to steady-state. This exchange provides a continuous source of energy, which acts to increase the observed luminosity beyond that inferred from the binding energy liberated from Kelvin-Helmholtz contraction alone – a finding important for potential protoplanet observations. The inner envelope at ≲ 0.4Rb remains insulated however – growing in accordance with 1D quasi-static theory. We incorporate these 3D hydrodynamic effects into an extensible 1D framework with a physically motivated three-layer recycling parameterization. Specializing to the case of Jupiter, recycling produces minimal changes to the growth rate with the planet still entering runaway accretion and becoming a gas giant in ∼1 Myr. Even in the inner disk (0.1 AU), our 1D models suggest that recycling is not so robust and ubiquitous as to stop all cores from becoming giants. At the same time however, this recycling can delay a runaway phase by an order-of-magnitude depending on the inner disk conditions and core mass.

Chemical Mapping of Temperate Sub-Neptune Atmospheres: Constraining the Deep Interior H2O/H2 Ratio from the Atmospheric CO2/CH4 Ratio

Understanding the planetary envelope composition of sub-Neptune-type exoplanets is challenging due to the inherent degeneracy in their interior composition scenarios. Particularly, the planetary envelope’s H2O/H2 ratio, which can also be expressed as the O/H ratio, provides crucial insights into its original location relative to the ice line during planetary formation. Using self-consistent radiative transfer modeling and a rate-based automatic chemical network generator combined with 1D photochemical kinetic-transport atmospheric modeling, we investigate various atmospheric scenarios of temperate sub-Neptunes, ranging from H2-dominated to H2O-dominated atmospheres with equilibrium temperatures (T eq) of 250—400 K. This study includes examples such as K2-18 b (T eq = 255 K), LP 791-18 c (T eq = 324 K), and TOI-270 d (T eq = 354 K). Our models indicate that the atmospheric CO2/CH4 ratio can be used to infer the deep interior H2O/H2 ratio. Applying this method to recent JWST observations, our findings suggest that K2-18 b likely has an interior that is 50% highly enriched in water, exceeding the water content in a 100 × Z ⊙ scenario and suggesting a planetary formation mechanism involving substantial accretion of ices. In contrast, our model suggests that approximately 25% of TOI-270 d’s interior is composed of H2O, which aligns with the conventional metallicity framework with a metallicity higher than 100 × Z ⊙. Furthermore, our models identify carbonyl sulfide (OCS) and sulfur dioxide (SO2) as strong indicators for temperate sub-Neptunes with at least 10% of their interior composed of water. These results provide a method to delineate the internal composition and formation mechanisms of temperate sub-Neptunes (T eq < ∼ 500 K) via atmospheric characterization through transmission spectroscopy.

A formation pathway for terrestrial planets with moderate water content involving atmospheric-volatile recycling

Of the many recently discovered terrestrial exoplanets, some are expected to harbor moderate water mass fractions of a few percent. The formation pathways that can produce planets with these water mass fractions are not fully understood. Here, we use the code chemcomp which consists of a semi-analytical 1D protoplanetary disk model harboring a migrating and accreting planet, to model the growth and composition of planets with moderate water mass fractions by pebble accretion in a protoplanetary disk around a TRAPPIST-1 analog star. This star is accompanied by seven terrestrial planets, of which the outer four planets likely contain water mass fractions of between 1&lt;!PCT!&gt; and 10&lt;!PCT!&gt;. We adopt a published model that considers the evaporation of pebbles in the planetary envelope, from where recycling flows can transport the volatile vapor back into the disk. We find that with this model, the planetary water content depends on the influx rate of pebbles onto the planet. A decreasing pebble influx with time reduces the envelope temperature and consequently allows the formation of planets with moderate water mass fractions as inferred for the outer TRAPPIST-1 planets for a number of different simulation configurations. This is further evidence that the recycling of vapor is an important component of planet formation needed to explain the vast and diverse population of exoplanets.

Planet Formation by Gas-assisted Accretion of Small Solids

We compute the accretion efficiency of small solids, with radii 1 cm ≤ R s ≤ 10 m, on planets embedded in gaseous disks. Planets have masses 3 ≤ M p ≤ 20 Earth masses (M ⊕) and orbit within 10 au of a solar mass star. Disk thermodynamics is modeled via 3D radiation-hydrodynamics calculations that typically resolve the planetary envelopes. Both icy and rocky solids are considered, explicitly modeling their thermodynamic evolution. The maximum efficiencies of 1 ≤ R s ≤ 100 cm particles are generally ≲10%, whereas 10 m solids tend to accrete efficiently or be segregated beyond the planet’s orbit. A simplified approach is applied to compute the accretion efficiency of small cores, with masses M p ≤ 1 M ⊕ and without envelopes, for which efficiencies are approximately proportional to Mp2/3 . The mass flux of solids, estimated from unperturbed drag-induced drift velocities, provides typical accretion rates dM p /dt ≲ 10−5 M ⊕ yr−1. In representative disk models with an initial gas-to-dust mass ratio of 70–100 and total mass of 0.05–0.06 M ⊙, the solids’ accretion falls below 10−6 M ⊕ yr−1 after 1–1.5 Myr. The derived accretion rates, as functions of time and planet mass, are applied to formation calculations that compute dust opacity self-consistently with the delivery of solids to the envelope. Assuming dust-to-solid coagulation times of ≈0.3 Myr and disk lifetimes of ≈3.5 Myr, heavy-element inventories in the range 3–7 M ⊕ require that ≈90–150 M ⊕ of solids cross the planet’s orbit. The formation calculations encompass a variety of outcomes, from planets a few times M ⊕, predominantly composed of heavy elements, to giant planets. The peak luminosities during the epoch of the solids’ accretion range from ≈10−7 to ≈10−6 L ⊙.

Constraints on Lateral Variations of Martian Crustal Thickness From Seismological and Gravity Field Measurements

AbstractUsing body wave arrival times from 31 seismic events recorded on Mars by the InSight mission, combined with topography and gravity field modeling, we constrained lateral variations of crustal thickness through a Bayesian inversion approach. The parameterization of the seismic structure relies on quantities that influence the thermochemical evolution of Mars, enabling the seismic velocities and densities in the different planetary envelopes to be consistently linked through common physical assumptions. Compared to a 1D structure, models with lateral variations of crustal thickness show two possible interpretations of the thermal evolution of Mars, with either a hot or cold scenario at the present‐day. We found the hot scenario to be more compatible with InSight's radiotracking data and the tidal Love number. We relocated the marsquakes and derived maps of seismicity recorded by InSight, which is mostly located along or North of the boundary between the Northern lowlands and the Southern highlands.

Compositional turbulence and layering in the gaseous envelopes of forming planets

ABSTRACT Differential settling and growth of dust grains impact the structure of the radiative envelopes of gaseous planets during formation. Sufficiently rapid dust growth can result in envelopes with substantially reduced opacities for radiation transport, thereby facilitating planet formation. We revisit the problem and establish that dust settling and grain growth also lead to outer planetary envelopes that are prone to compositional instabilities, by virtue of their inverted mean-molecular weight gradients. Under a variety of conditions, we find that the radiative envelopes of forming planets experience compositional turbulence driven by a semi-transparent version of the thermohaline instability (’fingering convection’). The standard double-diffusive thermohaline theory does not apply here and is replaced by a simplified first-principle treatment for the semitransparent regime of interest. The compositional turbulence seems efficient at mixing dust in the radiative envelopes of planets forming at super-au distances (say 5 au) from a Sun-like star, but not so at sub-au distances (say 0.2 au). We also address the possibility of compositional layering in this context. Distinct turbulent regimes for planetary envelopes growing at sub-au versus super-au distances could leave an imprint on the final planets formed.

Directly detecting the envelopes of low-mass planets embedded in protoplanetary discs and the case for TW Hydrae

ABSTRACT Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1D models and 3D simulations to calculate the envelopes around low-mass cores (several to tens of M⊕) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is optically thin at radio wavelengths, radio observations can see through the disc and probe the denser envelope within the planet’s Hill sphere. When the optically thin disc is observed with the resolution reaching one disc scale height, the radio thermal flux from the planetary envelope around a 10 M⊕ core is more than 10 per cent higher than the flux from the background disc. The emitting region can be extended and elongated. Finally, our model suggests that the au-scale clump at 52 au in the TW Hydrae disc revealed by ALMA is consistent with the envelope of an embedded 10–20 M⊕ planet, which can explain the detected flux, the spectral index dip, and the tentative spirals. The observation is also consistent with the planet undergoing pebble accretion. Future ALMA and ngVLA observations may directly reveal more such low-mass planets, enabling us to study core growth and even reconstruct the planet formation history using the embedded ‘protoplanet’ population.

Linking Atmospheric Chemistry of the Hot Jupiter HD 209458b to Its Formation Location through Infrared Transmission and Emission Spectra

The elemental ratios of carbon, nitrogen, and oxygen in the atmospheres of hot Jupiters may hold clues to their formation locations in the protostellar disk. In this work, we adopt gas-phase chemical abundances of C, N, and O from several locations in a disk chemical kinetics model as sources for the envelope of the hot Jupiter HD 209458b and evolve the atmospheric composition of the planet using a 1D chemical kinetics model, treating both vertical mixing and photochemistry. We consider two atmospheric pressure-temperature profiles, one with and one without a thermal inversion. From each of the resulting 32 atmospheric composition profiles, we find that the molecules CH4, NH3, HCN, and C2H2 are more prominent in the atmospheres computed using a realistic noninverted P–T profile in comparison to a prior equilibrium chemistry based work, which used an analytical P–T profile. We also compute the synthetic transmission and emission spectra for these atmospheres and find that many spectral features vary with the location in the disk where the planetary envelope was accreted. By comparing with the species detected using the latest high-resolution ground-based observations, our model suggests that HD 209458b could have accreted most of its gas between the CO2 and CH4 ice lines with a supersolar C/O ratio from its protostellar disk, which in turn directly inherited its chemical abundances from the protostellar cloud. Finally, we simulate observing the planet with the James Webb Space Telescope (JWST) and show that differences in spectral signatures of key species can be recognized. Our study demonstrates the enormous importance of JWST in providing new insights into hot-Jupiter formation environments.

Chemical Equilibrium between Cores, Mantles, and Atmospheres of Super-Earths and Sub-Neptunes and Implications for Their Compositions, Interiors, and Evolution

We investigate the equilibrium chemistry between molten metal and silicate and a hydrogen-rich envelope using 18 independent reactions among 25 phase components for sub-Neptune-like exoplanets. Both reactive and unreactive metal sequestered in an isolated core are modeled. The overarching effects of equilibration are oxidation of the envelope and reduction of the mantle and core. Hydrogen and oxygen typically comprise significant fractions of metal cores at chemical equilibrium, leading to density deficits that offer a possible alternative explanation for the low densities of the Trappist-1 planets. Reactions with the magma ocean produce significant amounts of SiO and H2O in the envelopes directly above the magma ocean. Molar concentrations in the envelopes of planets with reactive metal are H2 > SiO > CO ∼ Na ∼ Mg > H2O ≫ CO2 ∼ CH4 ≫ O2, while for the unreactive metal case, H2O becomes the second most abundant species, after H2, providing an arbiter for the two scenarios amenable to observation. The water abundances in the atmospheres exceed those in the mantles by at least an order of magnitude in both scenarios. The water concentrations in the silicate mantles are ∼0.01 and ∼0.1 wt% in the reactive and unreactive metal core cases, respectively, limiting the H2O that might be outgassed in a future super-Earth. Less dissolved water in the reactive core case is due to sequestration of H and O in the Fe-rich metal. The total hydrogen budget of most sub-Neptunes can, to first order, be estimated from their atmospheres alone, as the atmospheres typically contain more than 90% of all H.

Enrichment of Jupiter’s Atmosphere by Late Planetesimal Bombardment

Abstract Jupiter’s atmosphere is enriched with heavy elements by a factor of about 3 compared to a protosolar composition. The origin of this enrichment and whether it represents the bulk composition of the planetary envelope remain unknown. Internal structure models of Jupiter suggest that its envelope is separated from the deep interior and that the planet is not fully mixed. This implies that Jupiter’s atmosphere was enriched with heavy elements just before the end of its formation. Such enrichment can be a result of late planetesimal accretion. However, in situ Jupiter formation models suggest a decreasing accretion rate with increasing planetary mass, which cannot explain Jupiter’s atmospheric enrichment. In this study, we model Jupiter’s formation and show that the migration of proto-Jupiter from ∼20 au to its current location can lead to late planetesimal accretion and atmospheric enrichment. Late planetesimal accretion does not occur if proto-Jupiter migrates only a few astronomical units. We suggest that if Jupiter’s outermost layer is fully mixed and is relatively thin (up to ∼20% of its mass), such late accretion can explain its measured atmospheric composition. It is therefore possible that Jupiter underwent significant orbital migration followed by late planetesimal accretion.

Global 3D radiation hydrodynamic simulations of proto-Jupiter’s convective envelope

ABSTRACT The core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with an updated opacity compilation to model the proto-Jupiter’s envelope. To isolate the 3D effects of convection and recycling, we simulate both isolated spherical envelopes and envelopes embedded in discs. The envelopes are heated at given rates to achieve steady states, enabling comparisons with 1D models. We vary envelope properties to obtain both radiative and convective solutions. Using a passive scalar, we observe significant mass recycling on the orbital time-scale. For a radiative envelope, recycling can only penetrate from the disc surface until ∼0.1–0.2 planetary Hill radii, while for a convective envelope, the convective motion can ‘dredge up’ the deeper part of the envelope so that the entire convective envelope is recycled efficiently. This recycling, however, has only limited effects on the envelopes’ thermal structure. The radiative envelope embedded in the disc has identical structure as the isolated envelope. The convective envelope has a slightly higher density when it is embedded in the disc. We introduce a modified 1D approach which can fully reproduce our 3D simulations. With our updated opacity and 1D model, we recompute Jupiter’s envelope accretion with a 10 M⊕ core, and the time-scale to runaway accretion is shorter than the disc lifetime as in prior studies. Finally, we discuss the implications of the efficient recycling on the observed chemical abundances of the planetary atmosphere (especially for super-Earths and mini-Neptunes).

How planets grow by pebble accretion

Context. In the theory of pebble accretion, planets form by the subsequent accretion of solids (micron-sized dust and larger pebbles) and gas. 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. Aims. 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. Methods. 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. It also includes a separate dust component, which can be both replenished and swept up by encounters with pebbles, depending on the relative velocities. 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. Results. 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 and declines steeply with depth and planet mass but is invariant with the pebble mass flux. Our results imply that the opacity of a forming planet’s envelope cannot be approximated by a value that is constant with either depth or planet mass. Applying these results 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.

Influence of grain size and composition on the contraction rates of planetary envelopes and on planetary migration

A crucial phase during planetary growth is the migration, when the planetary core has been assembled but has not yet opened a deep gap. During this phase, the planet is subject to fast type-I migration, which is mostly directed inwards, and the planet can lose a significant fraction of its semi-major axis. The duration of this phase is set by the time required for the planetary envelope to contract before it reaches a mass similar to that of the planetary core, which is when runaway gas accretion can set in and the planet can open a deeper gap in the disc, transitioning into the slower type-II migration. This envelope contraction phase depends crucially on the planetary mass and on the opacity inside the planetary envelope. Here we study how different opacity prescriptions influence the envelope contraction time and how this in turn influences how far the planet migrates through the disc. We find within our simulations that the size distribution of the grains as well as the chemical composition of the grains crucially influences how far the planet migrates before reaches the runaway gas accretion phase. Grain size distributions with larger grain sizes result in less inward migration of the growing planet because of faster gas accretion enabled by more efficient cooling. In addition, we find that planets forming in water-poor environments can contract their envelope faster and therefore migrate less, implying that gas giants forming in water-poor environments might be located further away from their central star compared to gas giants forming in water-rich environments. Future studies of planet formation that aim to investigate the chemical composition of formed gas giants need to take these effects into account self-consistently.

Revealing peculiar exoplanetary shadows from transit light curves

Context. Until now the search of peculiar exoplanetary shadows, particularly those caused by exorings, was focused on the detection of a second-order photometric difference between the ringed and ringless (circular) transiting shadows. Both scenarios involved the parameter fitting to approximate the corresponding transit light curves (TLCs). As a result, the searched difference was extremely difficult to detect in the noise of the real transit photometry signals. Aims. In this work, we look for photometric manifestations of a non-spherical obscuring matter (e.g., exorings) around different exoplanets, mainly hot Jupiters, using a principally new approach. Methods. We used the transit parameters provided in Kepler database from the NASA Exoplanet Archive, where the fitting of the TLCs gives consistent sets of parameters for the transiting objects, assuming their spherical shape. At the same time, the semimajor axes, expressed in units of the stellar radii (initially, also a subject of the fitting), finally appear to be replaced by the calculated values according the Kepler’s third law and known stellar radii and surface gravity that have been determined through other methods. In the most typical case of a spherical transiting planet, such a replacement does not break the consistency of the whole parameter set. However, in the case of a non-spherical transiter and its non-circular shadow, the real (i.e., calculated according physics) value of the orbital semimajor axis could become inconsistent with the rest of the transit parameter set defined with the standard fitting procedure. The search for such inconsistencies, manifested as the difference between the simulated and observed transit duration, constitutes one of the main goals of this work. Moreover, we elaborate on a particular technique to gain information about the shape of planetary shadow, using the derivatives of the TLC during the ingress and egress phases. Results. We checked the TLCs of 21 hot Jupiters and 2 hot Neptunes. The consistent transit parameters and quasi-circular shadows were found for 11 objects. The analysis of the TLCs of five of the objects is complicated due to the noise problems, leading to the instability of solutions and deformation of shadows due to the low resolution of the derivatives. The remaining seven objects were formally qualified as peculiar outliers and among them, the planets Kepler-45b and Kepler-840b appear to be the most intriguing targets, with the most significant inconsistency of the parameter sets and the shadows elongated along their orbital path. Conclusions. We propose a new method for probing of planetary shape that confirms the circular transiting shadows for the majority of objects on the considered list. However, several objects exhibiting peculiar shadows have been discovered. These finds could be interpreted in terms of planetary dusty envelopes or exorings. The obtained results and elaborated methodology are relevant in the context of today’s photometry space missions, such as TESS, CHEOPS, and others.

Planetary Refractory Composition and Volatile Accretion into Gas Giants in the Protoplanetary Disks of the Sun and WASP-12

Abstract We present a detailed theoretical exploration of the refractory compositions and volatile enrichments of planets forming in protoplanetary disks with solar-like conditions. The two cases of the Sun and WASP-12 are studied due to the availability of spectral measurements and their known planets. The distribution throughout their disks of solid compounds with a wide range of volatilities is computed by a comprehensive chemical thermodynamics code. After the calculation of refractory compounds down to the water snowline, the compositional distributions are documented for planets generated in certain locations of protoplanetary disks depending on thermodynamic conditions. These results are referred to proposed bulk compositions for solar terrestrial planets, and for the core of the hot Jupiter WASP-12b. The material left over after the formation of rocky components is collected and treated in calculations to determine the abundances of fundamental volatile molecules in the outer regions of the disks. The distributions of planetesimal volatile composition are then altered for four different cases of the carbon-to-oxygen ratios, and for oxidizing and reducing conditions, in order to adjust the best fit for the accretion zone of Jupiter and WASP-12b. We compare the Jovian results to in situ atmospheric measurements from Jupiter’s atmosphere. Overall, this study proposes a holistic approach to estimate possible planetary interior and envelope compositions from hot toward cold disk zones, along with the mass of planetesimals accreted into the envelopes of gas giants.

Deep model simulation of polar vortices in gas giant atmospheres

ABSTRACTThe Cassini and Juno probes have revealed large coherent cyclonic vortices in the polar regions of Saturn and Jupiter, a dramatic contrast from the east–west banded jet structure seen at lower latitudes. Debate has centred on whether the jets are shallow, or extend to greater depths in the planetary envelope. Recent experiments and observations have demonstrated the relevance of deep convection models to a successful explanation of jet structure, and cyclonic coherent vortices away from the polar regions have been simulated recently including an additional stratified shallow layer. Here we present new convective models able to produce long-lived polar vortices. Using simulation parameters relevant for giant planet atmospheres we find flow regimes of geostrophic turbulence (GT) in agreement with rotating convection theory. The formation of large-scale coherent structures occurs via 3D upscale energy transfers. Our simulations generate polar characteristics qualitatively similar to those seen by Juno and Cassini: They match the structure of cyclonic vortices seen on Jupiter; or can account for the existence of a strong polar vortex extending downwards to lower latitudes with a marked spiral morphology, and the hexagonal pattern seen on Saturn. Our findings indicate that these vortices can be generated deep in the planetary interior. A transition differentiating these two polar flows regimes is described, interpreted in terms of force balances and compared with shallow atmospheric models characterizing polar vortex dynamics in giant planets. In addition, heat transport properties are investigated, confirming recent scaling laws obtained with reduced models of GT.

Accretion of eroding pebbles and planetesimals in planetary envelopes

Wind erosion is a destructive mechanism that completely dissolves a weakly bound object like a planetesimal into its constituent particles, if the velocity relative to the ambient gas and the local gas pressure are sufficiently high. In numerical simulations we study the influence of such wind erosion on pebble and planetesimal accretion by a planetary body up to 10 REarth. Due to the rapid size reduction of an in-falling small body, the accretion outcome changes significantly. Erosion leads to a strong decrease in the accretion efficiency below a threshold size of the small body on the order of 10 m. This slows down pebble accretion significantly for a given size distribution of small bodies. The threshold radius of the small body increases with increasing planet radius and decreases with increasing semi-major axis. Within the parameters studied, an additional planetary atmosphere (up to 1 bar) is of minor importance.

Giant Planet Formation Models with a Self-consistent Treatment of the Heavy Elements

Abstract We present a new numerical framework to model the formation and evolution of giant planets. The code is based on the further development of the stellar evolution toolkit Modules for Experiments in Stellar Astrophysics. The model includes the dissolution of the accreted planetesimals/pebbles, which are assumed to be made of water ice, in the planetary gaseous envelope, and the effect of envelope enrichment on the planetary growth and internal structure is computed self-consistently. We apply our simulations to Jupiter and investigate the impact of different heavy-element and gas accretion rates on its formation history. We show that the assumed runaway gas accretion rate significantly affects the planetary radius and luminosity. It is confirmed that heavy-element enrichment leads to shorter formation timescales due to more efficient gas accretion. We find that with heavy-element enrichment Jupiter’s formation timescale is compatible with typical disks’ lifetimes even when assuming a low heavy-element accretion rate (oligarchic regime). Finally, we provide an approximation for the heavy-element profile in the innermost part of the planet, providing a link between the internal structure and the planetary growth history.

Tidal Inflation Reconciles Low-density Sub-Saturns with Core Accretion

Abstract While the solar system contains no planets between the sizes of Uranus and Saturn, our current exoplanet census includes several dozen such planets with well-measured masses and radii. These sub-Saturns exhibit a diversity of bulk densities, ranging from ∼0.1 to 3 g cm−3. When modeled simply as hydrogen/helium envelopes atop rocky cores, this diversity in densities translates to a diversity in planetary envelope fractions, f env = M env/M p , ranging from ∼10% to ∼50%. Planets with f env ≈ 50% pose a challenge to traditional models of giant planet formation by core-nucleated accretion, which predict the onset of runaway gas accretion when M env ∼ M core. Here, we show that many of these apparent f env ≈ 50% planets are less envelope-rich than they seem, after accounting for tidal heating. We present a new framework for modeling sub-Saturn interiors that incorporates envelope inflation due to tides, which are driven by the observed nonzero eccentricities, as well as potential obliquities. Consequently, when we apply our models to known sub-Saturns, we infer lower f env than tides-free estimates. We present a case study of K2-19 b, a moderately eccentric sub-Saturn. Neglecting tides, K2-19 b appears to have f env ≈ 50%, poised precariously near the runaway threshold; by including tides, however, we find f env ≈ 10%, resolving the tension. Through a systematic analysis of 4–8 R ⊕ planets, we find that most (but not all) of the similarly envelope-rich planets have more modest envelopes of f env ≈ 10%–20%. Thus, many sub-Saturns may be understood as sub-Neptunes that have undergone significant radius inflation, rather than a separate class of objects. Tidally induced radius inflation likely plays an important role in other size classes of planets including ultra-low-density Jupiter-size planets like WASP-107 b.

Coupled Thermal and Compositional Evolution of Photoevaporating Planet Envelopes

Abstract Photoevaporative mass loss sculpts the atmospheric evolution of tightly orbiting sub-Neptune-mass exoplanets. To date, models of the mass loss from warm Neptunes have assumed that the atmospheric abundances remain constant throughout the planet’s evolution. However, the cumulative effects of billions of years of escape modulated by diffusive separation and preferential loss of hydrogen can lead to planetary envelopes that are enhanced in helium and metals relative to hydrogen. We have performed the first self-consistent calculations of the coupled thermal, mass-loss, and compositional evolution of hydrogen–helium envelopes surrounding sub-Neptune-mass planets. We extended the Modules for Experiments in Stellar Astrophysics stellar evolution code to model the evolving envelope abundances of photoevaporating planets. We demonstrate that H–He fractionation can lead to planetary envelopes that are significantly enriched in helium and metals compared to their initial primordial compositions. A subset of our model planets—having R p ≲ 3.00 R ⊕, initial f env &lt; 0.5%, and irradiation flux ∼101–103 times that of Earth—obtain final helium mass fractions in excess of Y = 0.40 after several billion years of mass loss. GJ 436b, the planet that originally inspired Hu et al. to propose the formation of helium-enhanced planetary atmospheres, requires a primordial envelope that is too massive to become helium enhanced. Planets with envelope helium fractions of Y = 0.40 have radii that are between 0.5% and 10% smaller (depending on their mass, irradiation flux, and envelope mass fraction) than similar planets with solar composition (Y = 0.24) envelopes. The results of preferential loss of hydrogen may have observable consequences for the M p − R p relations and atmospheric spectra of sub-Neptune populations.