Core-nucleated Accretion Research Articles

Helium in the Extended Atmosphere of the Warm Superpuff TOI-1420b

Superpuffs are planets with exceptionally low densities (ρ ≲ 0.1 g cm−3) and core masses (M c ≲ 5M ⊕). Many lower-mass (M p ≲ 10M ⊕) superpuffs are expected to be unstable to catastrophic mass loss via photoevaporation and/or boil-off, whereas the larger gravitational potentials of higher-mass (M p ≳ 10M ⊕) superpuffs should make them more stable to these processes. We test this expectation by studying atmospheric loss in the warm, higher-mass superpuff TOI-1420b (M = 25.1M ⊕, R = 11.9R ⊕, ρ = 0.08 g cm−3, T eq = 960 K). We observed one full transit and one partial transit of this planet using the metastable helium filter on Palomar/WIRC and found that the helium transits were 0.671% ± 0.079% (8.5σ) deeper than the TESS transits, indicating an outflowing atmosphere. We modeled the excess helium absorption using a self-consistent 1D hydrodynamics code to constrain the thermal structure of the outflow given different assumptions for the stellar XUV spectrum. These calculations then informed a 3D simulation, which provided a good match to the observations with a modest planetary mass-loss rate of 1010.82 g s−1 ( Mp/Ṁ≈70 Gyr). Superpuffs with M p ≳ 10M ⊕, like TOI-1420b and WASP-107b, appear perfectly capable of retaining atmospheres over long timescales; therefore, these planets may have formed with the unusually large envelope mass fractions they appear to possess today. Alternatively, tidal circularization could have plausibly heated and inflated these planets, which would bring their envelope mass fractions into better agreement with expectations from core-nucleated accretion.

Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch

The formation of Jupiter is modeled via core-nucleated accretion, and the planet's evolution is simulated up to the present epoch. Throughout the phases when the planet acquires most of its heavy-element content, the calculation of solids' accretion accounts for interactions with an evolving disk of planetesimals. The phase of growth from an embryo of a few hundred kilometers in radius until the time when the accretion of gas overtakes solids' accretion was presented by D'Angelo et al. (2014), and the same numerical methods are applied here. Those calculations followed the formation for about 4 × 105 years, until the epoch when the heavy-element and hydrogen/helium masses wereMZ ≈ 7.3 andMXY ≈ 0.15 Earth's masses (M⊕), respectively, and ṀXY≈ṀZ. Herein, the calculation is continued through the phase when MXYgrows to equalMZ, at which age, about 2.4 × 106 years, the total mass of the planet isMp ≈ 20M⊕. About 9 × 105 years later,Mpis approximately 60M⊕and MZ ≈ 16M⊕, three-quarters of which are delivered by planetesimals larger than 10km in radius. Around this epoch, the contraction of the envelope dictates gas accretion rates a few times 10−3M⊕per year, initiating the regime of disk-limited accretion, whereby the planet can accrete all the gas provided by the disk, and its evolution is therefore tied to disk's evolution. Growth is continued by constructing simplified models of protosolar accretion disks that evolve through viscous diffusion, winds, and accretion on the planet. Jupiter's formation ends after ≈ 3.4–4.2Myr, depending on the applied disk viscosity parameter, when nebula gas disperses. The young Jupiter is 4.5–5.5 times as voluminous as it is presently and thousands of times as luminous, ~10−5L⊙. The heavy-element mass is ≈ 20M⊕. The evolution proceeds through the cooling and contraction phase, in isolation except for solar irradiation. After 4570Myr, the age of the solar system, radius and luminosity of the planet are within 10% of current values, accounting also for uncertainties in the power absorbed from the Sun. During formation, and soon thereafter, the planet exhibits features, e.g., luminosity and effective temperature, that may probe aspects of the latter stages of formation, if observable. These possibly distinctive features, however, seem to disappear within a few tens of Myr

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.

K2-19b and c are in a 3:2 Commensurability but out of Resonance: A Challenge to Planet Assembly by Convergent Migration

Abstract K2-19b and c were among the first planets discovered by NASA’s K2 mission and together stand in stark contrast with the physical and orbital properties of the solar system planets. The planets are between the size of Uranus and Saturn at 7.0 ± 0.2 and 4.1 ± 0.2 , respectively, and reside a mere 0.1% outside the nominal 3:2 mean-motion resonance. They represent a different outcome of the planet formation process than the solar system, as well as the vast majority of known exoplanets. We measured the physical and orbital properties of these planets using photometry from K2, Spitzer, and ground-based telescopes, along with radial velocities from Keck/HIRES. Through a joint photodynamical model, we found that the planets have moderate eccentricities of e ≈ 0.20 and well-aligned apsides Δϖ ≈ 0°. The planets occupy a strictly nonresonant configuration: the resonant angles circulate rather than librate. This defies the predictions of standard formation pathways that invoke convergent or divergent migration, both of which predict Δϖ ≈ 180° and eccentricities of a few percent or less. We measured masses of M p,b = 32.4 ± 1.7 and M p,c = 10.8 ± 0.6 . Our measurements, with 5% fractional uncertainties, are among the most precise of any sub-Jovian exoplanet. Mass and size reflect a planet’s core/envelope structure. Despite having a relatively massive core of ≈ 15 , K2-19b is envelope-rich, with an envelope mass fraction of roughly 50%. This planet poses a challenge to standard models of core-nucleated accretion, which predict that cores ≳10 will quickly accrete gas and trigger runaway accretion when the envelope mass exceeds that of the core.

New Formation Models for the Kepler-36 System

Abstract Formation of the planets in the Kepler-36 system is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. The standard model is updated to include the dissolution of accreting rocky planetesimals in the gaseous envelope of the planet, leading to substantial enrichment of the envelope mass in heavy elements and a non-uniform composition with depth. For Kepler-36 c, models involving in situ formation and models involving orbital migration are considered. The results are compared with standard formation models. The calculations include the formation (accretion) phase as well as the subsequent cooling phase, up to the age of Kepler-36 (7 Gyr). During the latter phase, mass loss induced by stellar XUV radiation is included. In all cases, the results fit the measured mass, 7.84 M ⊕, and radius, 3.68 R ⊕, of Kepler-36 c. Two parameters are varied to obtain these fits: the disk solid surface density at the formation location and the “efficiency” factor in the XUV mass-loss rate. The updated models are hotter and therefore less dense in the silicate portion of the planet and in the overlying layers of H/He, as compared with standard models. The lower densities mean that only about half as much H/He is needed to be accreted to fit the present-day mass and radius constraints. For Kepler-36 b, an updated in situ calculation shows that the entire H/He envelope is lost, early in the cooling phase, in agreement with observation.

Dynamics and Formation of the Near-resonant K2-24 System: Insights from Transit-timing Variations and Radial Velocities

Abstract While planets between the size of Uranus and Saturn are absent within the solar system, the star K2-24 hosts two such planets, K2-24b and c, with radii equal to 5.4 and 7.5 , respectively. The two planets have orbital periods of 20.9 days and 42.4 days, residing only 1% outside the nominal 2:1 mean-motion resonance. In this work, we present results from a coordinated observing campaign to measure planet masses and eccentricities that combines radial velocity measurements from Keck/HIRES and transit-timing measurements from K2 and Spitzer. K2-24b and c have low, but nonzero, eccentricities of . The low observed eccentricities provide clues to the formation and dynamical evolution of K2-24b and K2-24c, suggesting that they could be the result of stochastic gravitational interactions with a turbulent protoplanetary disk, among other mechanisms. K2-24b and c are and , respectively; K2-24c is 20% less massive than K2-24b, despite being 40% larger. Their large sizes and low masses imply large envelope fractions, which we estimate at % and %. In particular, K2-24c’s large envelope presents an intriguing challenge to the standard model of core-nucleated accretion that predicts the onset of runaway accretion when ≈ 50%.

On the Terminal Rotation Rates of Giant Planets

Abstract Within the general framework of the core-nucleated accretion theory of giant planet formation, the conglomeration of massive gaseous envelopes is facilitated by a transient period of rapid accumulation of nebular material. While the concurrent build-up of angular momentum is expected to leave newly formed planets spinning at near-breakup velocities, Jupiter and Saturn, as well as super-Jovian long-period extrasolar planets, are observed to rotate well below criticality. In this work, we demonstrate that the large luminosity of a young giant planet simultaneously leads to the generation of a strong planetary magnetic field, as well as thermal ionization of the circumplanetary disk. The ensuing magnetic coupling between the planetary interior and the quasi-Keplerian motion of the disk results in efficient braking of planetary rotation, with hydrodynamic circulation of gas within the Hill sphere playing the key role of expelling spin angular momentum to the circumstellar nebula. Our results place early-stage giant planet and stellar rotation within the same evolutionary framework, and motivate further exploration of magnetohydrodynamic phenomena in the context of the final stages of giant planet formation.

ACCRETION AND EVOLUTION OF ∼2.5M⊕PLANETS WITH VOLUMINOUS H/He ENVELOPES

Formation of planets in the Neptune size range with low-mass, but voluminous, H_2/He gaseous envelopes is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. Formation locations ranging from 0.5 to 4 AU from a star of 1 solar mass are considered. The final planets have heavy-element cores of 2.2--2.5 Earth masses and envelopes in the range 0.037--0.16 Earth masses. After the formation process, which lasts 2 Myr or less, the planets evolve at constant mass up to an age of several Gyr. For assumed equilibrium temperatures of 250, 500, and 1000 K, their calculated final radii are compared with those observed by the Kepler spacecraft. For the particular case of Kepler-11 f, we address the question whether it could have formed in situ or whether migration from a formation location farther out in the disk is required.

Growth of Jupiter: Enhancement of core accretion by a voluminous low-mass envelope

We present calculations of the early stages of the formation of Jupiter via core nucleated accretion and gas capture. The core begins as a seed body of about 350km in radius and orbits in a swarm of planetesimals whose initial radii range from 15m to 50km. The evolution of the swarm accounts for growth and fragmentation, viscous and gravitational stirring, and for drag-assisted migration and velocity damping. During this evolution, less than 9% of the mass is in planetesimals smaller than 1km in radius; ≲25% is in planetesimals with radii between 1 and 10km; and ≲7% is in bodies with radii larger than 100km. Gas capture by the core substantially enhances the size-dependent cross-section of the planet for accretion of planetesimals. The calculation of dust opacity in the planet’s envelope accounts for coagulation and sedimentation of dust particles released as planetesimals are ablated. The calculation is carried out at an orbital semi-major axis of 5.2AU and the initial solids’ surface density is 10gcm-2 at that distance. The results give a core mass of nearly 7.3 Earth masses (M⊕) and an envelope mass of ≈0.15M⊕ after about 4×105 years, at which point the envelope growth rate surpasses that of the core. The same calculation without the envelope yields a core of only about 4.4M⊕.

THE FORMATION OF URANUS AND NEPTUNE: CHALLENGES AND IMPLICATIONS FOR INTERMEDIATE-MASS EXOPLANETS

In this paper we investigate the formation of Uranus and Neptune, according to the core-nucleated accretion model, considering formation locations ranging from 12 to 30 AU from the Sun, and with various disk solid-surface densities and core accretion rates. It is shown that in order to form Uranus-like and Neptune-like planets in terms of final mass and solid-to-gas ratio, very specific conditions are required. We also show that when recently proposed high solid accretion rates are assumed, along with solid surface densities about 10 times those in the minimum-mass solar nebula, the challenge in forming Uranus and Neptune at large radial distances is no longer the formation timescale, but is rather finding agreement with the final mass and composition of these planets. In fact, these conditions are more likely to lead to gas-giant planets. Scattering of planetesimals by the forming planetary core is found to be an important effect at the larger distances. Our study emphasizes how (even slightly) different conditions in the protoplanetary disk and the birth environment of the planetary embryos can lead to the formation of very different planets in terms of final masses and compositions (solid-to-gas ratios), which naturally explains the large diversity of intermediate-mass exoplanets.

FORMATION AND STRUCTURE OF LOW-DENSITY EXO-NEPTUNES

Kepler has found hundreds of Neptune-size (2-6 R_Earth) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T_eq>=500K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T_eq=500K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R_Earth. For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass--envelope mass--equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R_Earth planet candidates at T_eq=500--1000K could potentially have masses less than ~4 M_Earth. Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.

Formation of Jupiter using opacities based on detailed grain physics

Numerical simulations, based on the core-nucleated accretion model, are presented for the formation of Jupiter at 5.2 AU in three primordial disks with three different assumed values of the surface density of solid particles. The grain opacities in the envelope of the protoplanet are computed using a detailed model that includes settling and coagulation of grains and that incorporates a recalculation of the grain size distribution at each point in time and space. We generally find lower opacities than the 2% of interstellar values used in previous calculations (Hubickyj, O., Bodenheimer, P., Lissauer, J.J. [2005]. Icarus 179, 415–431; Lissauer, J.J., Hubickyj, O., D’Angelo, G., Bodenheimer, P. [2009]. Icarus 199, 338–350). These lower opacities result in more rapid heat loss from and more rapid contraction of the protoplanetary envelope. For a given surface density of solids, the new calculations result in a substantial speedup in formation time as compared with those previous calculations. Formation times are calculated to be 1.0, 1.9, and 4.0 Myr, and solid core masses are found to be 16.8, 8.9, and 4.7 M ⊕, for solid surface densities, σ, of 10, 6, and 4 g cm −2, respectively. For σ = 10 and σ = 6 g cm −2, respectively, these formation times are reduced by more than 50% and more than 80% compared with those in a previously published calculation with the old approximation to the opacity.

Models of Jupiter's growth incorporating thermal and hydrodynamic constraints

We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk–planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, R H . However, 3-D hydrodynamic simulations show that only gas within ∼ 0.25 R H remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ∼5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼ 3 Myr . To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587–611].