Cores Of Gas Giants Research Articles

Planetary core formation via multispecies pebble accretion

ABSTRACT In the general classical picture of pebble-based core growth, planetary cores grow by accretion of single pebble species. The growing planet may reach the so-called pebble isolation mass, at which it induces a pressure bump that blocks inward drifting pebbles exterior to its orbit, thereby stalling core growth by pebble accretion. In recent hydrodynamic simulations, pebble filtration by the pressure bump depends on several parameters including core mass, disc structure, turbulent viscosity and pebble size. We have investigated how accretion of multiple, instead of single, pebble species affects core growth rates, and how the dependence of pebble isolation mass on turbulent viscosity and pebble size sets the final core masses. We performed numerical simulations in a viscous one-dimensional disc, where maximal grain sizes were regulated by grain growth, fragmentation and drift limits. We confirm that core growth rates and final core masses are sensitive to three key parameters: the threshold velocity at which pebbles fragment on collision, the turbulent viscosity and the distribution of pebble species, which yield a diversity of planetary cores. With accretion of multiple pebble species, planetary cores can grow very fast, reaching over 30–40 ME in mass. Potential cores of cold gas giants were able to form from embryos initially implanted as far as 50 au. Our results suggest that accretion of multispecies pebbles could explain: the estimated 25–45 ME heavy element abundance inside Jupiter’s core; the massive cores of extrasolar planets; the disc rings and gaps at wider orbits; and the early and rapid formation of planetary bodies.

Merging Criteria for Planetesimal Collisions

Abstract In the standard scenario of planet formation, terrestrial planets, ice giants, and cores of gas giants are formed by the accumulation of planetesimals. However, there are few N-body simulation studies of planetesimal accretion that correctly take into account the merging condition of planetesimals. In order to investigate a realistic accretion process of planetesimals, it is necessary to clarify the merging criteria of planetesimals at collision. We perform numerical collision experiments using smoothed particle hydrodynamics and obtain the merging criteria as a function of planetesimal mass and impact parameters for undifferentiated rocky and icy planetesimals and differentiated icy planetesimals. We vary the total mass of colliding planetesimals, their mass ratios, and the impact angle and obtain the critical impact velocity as the merging criteria distinguishing merging from hit-and-run collision. We find that the critical impact velocity normalized by the two-body surface escape velocity decreases with increasing impact angle. The critical impact velocity does not depend on the total mass, while it has a weak positive dependence on the mass ratio. These results barely depend on the composition and internal structure of the planetesimals.

Radius and Mass Distribution of Ultra-short-period Planets

Abstract Ultra-short-period (USP) planets are an enigmatic subset of exoplanets defined by having orbital periods <1 day. It is still not understood how USP planets form, or to what degree they differ from planets with longer orbital periods. Most USP planets have radii <2 R ⊕, while planets that orbit further from their star extend to Jupiter size (>10 R ⊕). Several theories attempt to explain the formation and composition of USP planets: they could be remnant cores of larger gas giants that lost their atmospheres due to photoevaporation or Roche-lobe overflow, or they could have developed through mass accretion in the innermost part of the protoplanetary disk. The radius and mass distribution of USP planets could provide important clues to distinguish between potential formation mechanisms. In this study, we first verify and update the Kepler catalog of USP planet host star properties, incorporating new data collected by the Gaia mission where applicable. We then use the transit depths measured by Kepler to derive a radius distribution and present occurrence rates for USP planets. Using spherical and tidally distorted planet models, we then derive a mass distribution for USP planets. Comparisons between the updated USP planet mass distribution and simulated planetary systems offer further insights into the formation and evolutionary processes shaping USP planet populations.

Particle–particle particle–tree code for planetary system formation with individual cut-off method: GPLUM

Abstract In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational N-body simulations of a disk system made up of numerous planetesimals are the most direct way to study the accretion process. However, the use of N-body simulations has been limited to idealized models (e.g., perfect accretion) and/or narrow spatial ranges in the radial direction, due to the limited number of simulation runs and particles available. We have developed new N-body simulation code equipped with a particle–particle particle–tree (P3T) scheme for studying the planetary system formation process: GPLUM. For each particle, GPLUM uses the fourth-order Hermite scheme to calculate gravitational interactions with particles within cut-off radii and the Barnes–Hut tree scheme for particles outside the cut-off radii. In existing implementations, P3T schemes use the same cut-off radius for all particles, making a simulation become slower when the mass range of the planetesimal population becomes wider. We have solved this problem by allowing each particle to have an appropriate cut-off radius depending on its mass, its distance from the central star, and the local velocity dispersion of planetesimals. In addition to achieving a significant speed-up, we have also improved the scalability of the code to reach a good strong-scaling performance up to 1024 cores in the case of N = 106.

Solid accretion onto planetary cores in radiative disks

The solid accretion rate, which is necessary to grow gas giant planetary cores within the disk lifetime, has been a major constraint for theories of planet formation. We tested the solid accretion rate efficiency on planetary cores of different masses embedded in their birth disk by means of 3D radiation-hydrodynamics, where we followed the evolution of a swarm of embedded solids of different sizes. We found that by using a realistic equation of state and radiative cooling, the disk at 5 au is able to efficiently cool and reduce its aspect ratio. As a result, the pebble isolation mass is reached before the core grows to 10 M⊕, thus fully stopping the pebble flux and creating a transition disk. Moreover, the reduced isolation mass halts the solid accretion before the core reaches the critical mass, leading to a barrier to giant planet formation, and this explains the large abundance of super-Earth planets in the observed population.

Jupiter formed as a pebble pile around the N2 ice line

Context. The region around the H2O ice line, due to its higher surface density, seems to be the ideal location to form planets. The core of Jupiter, as well as the cores of close-in gas giants are therefore thought to form in this region of the disk. Nevertheless, constraining the formation location of individual planets has proven to be difficult. Aims. We aim to use the nitrogen abundance in Jupiter, which is around four times solar, in combination with Juno constraints on the total mass of heavy elements in Jupiter to narrow down its formation scenario. Methods. Different pathways of enrichment of the atmosphere of Jupiter are considered, such as the accretion of enriched gas, pebbles, and planetesimals, and their implications for the oxygen abundance of Jupiter are discussed. Results. The super-solar nitrogen abundance in Jupiter necessitates the accretion of extra N2 from the proto-solar nebula. The only location of the disk where this can happen is outside or just inside the N2 ice line. These constraints favor a pebble accretion origin of Jupiter, from the perspective of composition and planet formation. We predict that Jupiter’s oxygen abundance is between 3.6 and 4.5 times solar.

Pebble accretion in Class 0/I YSOs as a possible pathway for early planet formation

Recent theoretical works suggest that the pebble accretion process is important for planet formation in protoplanetary disks, because it accelerates the growth of planetary cores. While several observations reveal axisymmetric sharp gaps in very young disks, which may be indicative of the existence of planets. We investigate the possibility of planet formation via pebble accretion in much earlier phases, the gravitationally unstable disks of class 0/I young stellar objects. We find that under the conditions of the class 0/I disks, the pebble accretion timescales can be shorter compared to the typical protoplanetary disks due to larger gas and dust accretion rate, but also find that the accretion timescale is not always a decreasing function of the gas accretion rate. By using estimated accretion timescales, we give a required initial mass to form cores of gas giants within the lifetime of class 0/I phases under several parameters, such as radial distances from the host star, gas accretion rates, and dust-to-gas mass ratio. In the most optimistic case, for example the dust-to-gas mass ratio is $f=3f_{\rm solar}$, $\sim10^{-4}M_{\oplus}$ objects at 10 au can grow to $10M_{\oplus}$ cores during the typical lifetime of the class 0/I phases, 0.5 Myr.

Restrictions on the Growth of Gas Giant Cores via Pebble Accretion

We apply an order-of-magnitude model of gas-assisted growth, known as pebble accretion, in a turbulent medium to suggest a reason why some systems form wide orbital separation gas giants while others do not. In contrast to traditional growth by ballistic collisions with planetesimals, growth by pebble accretion is not necessarily limited by doubling times at the highest core mass. Turbulence, in particular, can cause growth to bottleneck at lower core masses. We demonstrate how a combination of growth by planetesimal and pebble accretion limits the maximum semi-major axis where gas giants can form. We find that, for fiducial disk parameters, strong turbulence ($\alpha \gtrsim 10^{-2}$) restricts gas giant cores to form interior to $a \lesssim 40 \, \text{AU}$, while for weak turbulence gas giants can form out to $a \lesssim 70 \, \text{AU}$. The correspondence between $\alpha$ and semi-major axis depends on the sizes of small bodies available for growth. This dependence on turbulence and small-body size distribution may explain the paucity of wide orbital separation gas giants. We also show that while lower levels of turbulence ($\alpha \lesssim 10^{-4}$) can produce gas giants far out in the disk, we expect these gas giants to be low-mass ($M \lesssim \, 1 M_J$). These planets are not luminous enough to have been observed with the current generation of direct-imaging surveys, which could explain why wide orbital separation gas giants are currently observed only around A stars.

Age of Jupiter inferred from the distinct genetics and formation times of meteorites

The age of Jupiter, the largest planet in our Solar System, is still unknown. Gas-giant planet formation likely involved the growth of large solid cores, followed by the accumulation of gas onto these cores. Thus, the gas-giant cores must have formed before dissipation of the solar nebula, which likely occurred within less than 10 My after Solar System formation. Although such rapid accretion of the gas-giant cores has successfully been modeled, until now it has not been possible to date their formation. Here, using molybdenum and tungsten isotope measurements on iron meteorites, we demonstrate that meteorites derive from two genetically distinct nebular reservoirs that coexisted and remained spatially separated between ∼1 My and ∼3-4 My after Solar System formation. The most plausible mechanism for this efficient separation is the formation of Jupiter, opening a gap in the disk and preventing the exchange of material between the two reservoirs. As such, our results indicate that Jupiter's core grew to ∼20 Earth masses within <1 My, followed by a more protracted growth to ∼50 Earth masses until at least ∼3-4 My after Solar System formation. Thus, Jupiter is the oldest planet of the Solar System, and its solid core formed well before the solar nebula gas dissipated, consistent with the core accretion model for giant planet formation.

SUPER-EARTHS AS FAILED CORES IN ORBITAL MIGRATION TRAPS

ABSTRACT I explore whether close-in super-Earths were formed as rocky bodies that failed to grow fast enough to become the cores of gas giants before the natal protostellar disk dispersed. I model the failed cores’ inward orbital migration in the low-mass or type I regime to stopping points at distances where the tidal interaction with the protostellar disk applies zero net torque. The three kinds of migration traps considered are those due to the dead zone's outer edge, the ice line, and the transition from accretion to starlight as the disk's main heat source. As the disk disperses, the traps move toward final positions near or just outside 1 au. Planets at this location exceeding about 3 M ⊕ open a gap, decouple from their host traps, and migrate inward in the high-mass or type II regime to reach the vicinity of the star. I synthesize the population of planets that formed in this scenario, finding that a fraction of the observed super-Earths could have been failed cores. Most super-Earths that formed this way have more than 4 M ⊕, so their orbits when the disks dispersed were governed by type II migration. These planets have solid cores surrounded by gaseous envelopes. Their subsequent photoevaporative mass loss is most effective for masses originally below about 6 M ⊕. The failed core scenario suggests a division of the observed super-Earth mass–radius diagram into five zones according to the inferred formation history.

Imaging the water snow-line during a protostellar outburst.

A snow-line is the region of a protoplanetary disk at which a major volatile, such as water or carbon monoxide, reaches its condensation temperature. Snow-lines play a crucial role in disk evolution by promoting the rapid growth of ice-covered grains. Signatures of the carbon monoxide snow-line (at temperatures of around 20 kelvin) have recently been imaged in the disks surrounding the pre-main-sequence stars TW Hydra and HD163296 (refs 3, 10), at distances of about 30 astronomical units (au) from the star. But the water snow-line of a protoplanetary disk (at temperatures of more than 100 kelvin) has not hitherto been seen, as it generally lies very close to the star (less than 5 au away for solar-type stars). Water-ice is important because it regulates the efficiency of dust and planetesimal coagulation, and the formation of comets, ice giants and the cores of gas giants. Here we report images at 0.03-arcsec resolution (12 au) of the protoplanetary disk around V883 Ori, a protostar of 1.3 solar masses that is undergoing an outburst in luminosity arising from a temporary increase in the accretion rate. We find an intensity break corresponding to an abrupt change in the optical depth at about 42 au, where the elevated disk temperature approaches the condensation point of water, from which we conclude that the outburst has moved the water snow-line. The spectral behaviour across the snow-line confirms recent model predictions: dust fragmentation and the inhibition of grain growth at higher temperatures results in soaring grain number densities and optical depths. As most planetary systems are expected to experience outbursts caused by accretion during their formation, our results imply that highly dynamical water snow-lines must be considered when developing models of disk evolution and planet formation.

Tidal decay and stable Roche-lobe overflow of short-period gaseous exoplanets

Many gaseous exoplanets in short-period orbits are on the verge or are in the process of Roche-lobe overflow (RLO). Moreover, orbital stability analysis shows tides can drive many hot Jupiters to spiral inevitably toward their host stars. Thus, the coupled processes of orbital evolution and RLO likely shape the observed distribution of close-in exoplanets and may even be responsible for producing some of the short-period rocky planets. However, the exact outcome for an overflowing planet depends on its internal response to mass loss, and the accompanying orbital evolution can act to enhance or inhibit RLO. In this study, we apply the fully-featured and robust Modules for Experiments in Stellar Astrophysics (MESA) suite to model RLO of short-period gaseous planets. We show that, although the detailed evolution may depend on several properties of the planetary system, it is largely determined by the core mass of the overflowing gas giant. In particular, we find that the orbital expansion that accompanies RLO often stops and reverses at a specific maximum period that depends on the core mass. We suggest that RLO may often strand the remnant of a gas giant near this orbital period, which provides an observational prediction that can corroborate the hypothesis that short-period gas giants undergo RLO. We conduct a preliminary comparison of this prediction to the observed population of small, short-period planets and find some planets in orbits that may be consistent with this picture. To the extent that we can establish some short-period planets are indeed the remnants of gas giants, that population can elucidate the properties of gas giant cores, the properties of which remain largely unconstrained.

MIGRATION AND GROWTH OF PROTOPLANETARY EMBRYOS. III. MASS AND METALLICITY DEPENDENCE FOR FGKM MAIN-SEQUENCE STARS

ABSTRACT Radial velocity and transit surveys have found that the fraction of FGKM stars with close-in super-Earth(s) (η ⊕) is around 30%–50%, independent of the stellar mass M * and metallicity Z *. In contrast, the fraction of solar-type stars harboring one or more gas giants (η J) with masses M p &gt; 100 M ⊕ is nearly 10%–15%, and it appears to increase with both M * and Z *. Regardless of the properties of their host stars, the total mass of some multiple super-Earths systems exceeds the core mass of Jupiter and Saturn. We suggest that both super-Earths and supercritical cores of gas giants were assembled from a population of embryos that underwent convergent type I migration from their birthplaces to a transition location between viscously heated and irradiation-heated disk regions. We attribute the cause for the η ⊕–η J dichotomy to conditions required for embryos to merge and to acquire supercritical core mass ( ) for the onset of efficient gaseous envelope accretion. We translate this condition into a critical disk accretion rate, and our analysis and simulation results show that it weakly depends on M * and decreases with metallicity of disk gas Z d. We find that embryos are more likely to merge into supercritical cores around relatively massive and metal-rich stars. This dependence accounts for the observed η J–M *. We also consider the dispersed relationship and reproduce the observed η J–Z * correlation.

Melting curve of SiO2 at multimegabar pressures: implications for gas giants and super-Earths.

Ultrahigh-pressure phase boundary between solid and liquid SiO2 is still quite unclear. Here we present predictions of silica melting curve for the multimegabar pressure regime, as obtained from first principles molecular dynamics simulations. We calculate the melting temperatures from three high pressure phases of silica (pyrite-, cotunnite-, and Fe2P-type SiO2) at different pressures using the Z method. The computed melting curve is found to rise abruptly around 330 GPa, an increase not previously reported by any melting simulations. This is in close agreement with recent experiments reporting the α-PbO2–pyrite transition around this pressure. The predicted phase diagram indicates that silica could be one of the dominant components of the rocky cores of gas giants, as it remains solid at the core of our Solar System’s gas giants. These results are also relevant to model the interior structure and evolution of massive super-Earths.

CHONDRULE FORMATION VIA IMPACT JETTING TRIGGERED BY PLANETARY ACCRETION

ABSTRACT Chondrules are one of the most primitive elements that can serve as a fundamental clue to the origin of our solar system. We investigate a formation scenario of chondrules that involves planetesimal collisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate planetary accretion that leads to the formation of terrestrial planets and cores of gas giants. The key component of this scenario is that ejected materials can melt when the impact velocity between colliding planetesimals exceeds about 2.5 km s−1. Previous simulations have shown that the process is efficient enough to reproduce the primordial abundance of chondrules. We examine this scenario carefully by performing semi-analytical calculations that are developed based on the results of direct N-body simulations. As found in the previous work, we confirm that planetesimal collisions that occur during planetary accretion can play an important role in forming chondrules. This arises because protoplanet–planetesimal collisions can achieve an impact velocity of about 2.5 km s−1 or higher, as protoplanets approach the isolation mass (M p,iso). Assuming that the ejected mass is a fraction (F ch) of the colliding planetesimals’ mass, we show that the resultant abundance of chondrules is expressed well by F ch M p,iso, as long as the formation of protoplanets is completed within a given disk lifetime. We perform a parameter study and examine how the abundance of chondrules and the timing of their formation change. We find that the impact jetting scenario generally works reasonably well for a certain range of parameters, while more dedicated work would be needed to include other physical processes that are neglected in this work and to examine their effects on chondrule formation.

Melting and metallization of silica in the cores of gas giants, ice giants, and super Earths

The physical state and properties of silicates at conditions encountered in the cores of gas giants, ice giants and of Earth like exoplanets now discovered with masses up to several times the mass of the Earth remains mostly unknown. Here, we report on theoretical predictions of the properties of silica, SiO$_2$, up to 4 TPa and about 20,000K using first principle molecular dynamics simulations based on density functional theory. For conditions found in the Super-Earths and in ice giants, we show that silica remains a poor electrical conductor up to 10 Mbar due to an increase in the Si-O coordination with pressure. For Jupiter and Saturn cores, we find that MgSiO$_3$ silicate has not only dissociated into MgO and SiO$_2$, as shown in previous studies, but that these two phases have likely differentiated to lead to a core made of liquid SiO$_2$ and solid (Mg,Fe)O.

MIGRATION AND GROWTH OF PROTOPLANETARY EMBRYOS. I. CONVERGENCE OF EMBRYOS IN PROTOPLANETARY DISKS

According to the core-accretion scenario, planets form in protostellar disks through the condensation of dust, coagulation of planetesimals, and emergence of protoplanetary embryos. At a few AU in a minimum mass nebula, embryos' growth is quenched by dynamical isolation due to the depletion of planetesimals in their feeding zone. However, embryos with masses ($M_p$) in the range of a few Earth masses ($M_\oplus$) migrate toward a transition radius between the inner viscously heated and outer irradiated regions of their natal disk. Their limiting isolation mass increases with the planetesimals surface density. When $M_p > 10 M_\oplus$, embryos efficiently accrete gas and evolve into cores of gas giants. We use numerical simulation to show that, despite streamline interference, convergent embryos essentially retain the strength of non-interacting embryos' Lindblad and corotation torque by their natal disks. In disks with modest surface density (or equivalently accretion rates), embryos capture each other in their mutual mean motion resonances and form a convoy of super Earths. In more massive disks, they could overcome these resonant barriers to undergo repeated close encounters including cohesive collisions which enable the formation of massive cores.

TWO-COMPONENT SECULAR GRAVITATIONAL INSTABILITY IN A PROTOPLANETARY DISK: A POSSIBLE MECHANISM FOR CREATING RING-LIKE STRUCTURES

The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. In the case where the dust to gas ratio is enhanced and turbulence is week, the instability grows, even in gravitationally stable disks, on a timescale of order $10^{4- 5}$yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", which was investigated previously as an instability of dust in a fixed background gas flow. In this work, we solve the equations of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. This may indicate that we should not neglect small terms in equation of motion if the growth rate is small. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, and hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii $\sim$100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.

Very high-density planets: a possible remnant of gas giants

Data extracted from the Extrasolar Planets Encyclopaedia (see http://exoplanet.eu) show the existence of planets that are more massive than iron cores that would have the same size. After meticulous verification of the data, we conclude that the mass of the smallest of these planets is actually not known. However, the three largest planets, Kepler-52b, Kepler-52c and Kepler-57b, which are between 30 and 100 times the mass of the Earth, have indeed density larger than an iron planet of the same size. This observation triggers this study that investigates under which conditions these planets could represent the naked cores of gas giants that would have lost their atmospheres during their migration towards the star. This study shows that for moderate viscosity values (10(25) Pa s or lower), large values of escape rate and associated unloading stress rate during the atmospheric loss process lead to the explosion of extremely massive planets. However, for moderate escape rate, the bulk viscosity and finite-strain incompressibility of the cores of giant planets can be large enough to retain a very high density during geological time scales. This would make those a new kind of planet, which would help in understanding the interior structure of the gas giants. However, this new family of exoplanets adds some degeneracy for characterizing terrestrial exoplanets.

PLANETARY POPULATIONS IN THE MASS-PERIOD DIAGRAM: A STATISTICAL TREATMENT OF EXOPLANET FORMATION AND THE ROLE OF PLANET TRAPS

The rapid growth in the number of known exoplanets has revealed the existence of several distinct planetary populations in the observed mass-period diagram. Two of the most surprising are, (1) the concentration of gas giants around 1AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenario, we showed that one can account for the positions of planets in the mass-period diagram. In this paper, we demonstrate quantitatively that most gas giants formed at planet traps tend to end up around 1 AU with most of these being contributed by dead zones and ice lines. In addition, we show that a large fraction of super-Earths and hot Neptunes are formed as "failed" cores of gas giants - this population being constituted by comparable contributions from dead zone and heat transition traps. Our results are based on the evolution of forming planets in an ensemble of disks where we vary only the lifetimes of disks as well as their mass accretion rates onto the host star. We show that a statistical treatment of the evolution of a large population of planetary cores initially caught in planet traps accounts for the existence of three distinct exoplantary populations - the hot Jupiters, the more massive planets at roughly orbital radii around 1 AU orbital, and the short period SuperEarths and hot Neptunes. There are very few evolutionary tracks that feed into the large orbital radii characteristic of the imaged Jovian planet, which agrees with recent surveys. Finally, we find that low-mass planets in tight orbits become the dominant planetary population for low mass stars ($M_* \le 0.7 M_{\odot}$).