Reduced gas accretion on super-Earths and ice giants
TL;DR: In this article, a series of 3D global, radiative hydrodynamical simulations reveal a steady-state gas flow, which enters through the poles and exits in the disk midplane.
Abstract: A large fraction of giant planets have gaseous envelopes that are limited to about 10% of their total mass budget. Such planets are present in the solar system (Uranus, Neptune) and are frequently observed in short periods around other stars (the so-called super-Earths). In contrast to these observations, theoretical calculations based on the evolution of hydrostatic envelopes argue that such low-mass envelopes cannot be maintained around cores exceeding five Earth masses. Instead, under nominal disk conditions, these planets would acquire massive envelopes through runaway gas accretion within the lifetime of the protoplanetary disk. In this work we show that planetary envelopes are not in hydrostatic balance, which slows down envelope growth. A series of 3D global, radiative hydrodynamical simulations reveal a steady-state gas flow, which enters through the poles and exits in the disk midplane. Gas is pushed through the outer envelope in about ten orbital timescales. In regions of the disk that are not significantly dust-depleted, envelope accretion onto cores of about five Earth masses can get stalled as the gas flow enters the deep interior. Accreted solids sublimate deep in the convective interior, but small opacity-providing grains are trapped in the flow and do not settle, which further prevents rapid envelope accretion. The transition to runaway gas accretion can however be reached when cores grow larger than typical super-Earths, beyond 15 Earth masses, and preferably when disk opacities are below κ = 1 cm2 /g. These findings offer an explanation for the typical low-mass envelopes around the cores of super-Earths.
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TL;DR: In this article, the authors explore the connection between a star's metallicity and the presence and properties of any associated planets by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets.
Abstract: Probing the connection between a star's metallicity and the presence and properties of any associated planets offers an observational link between conditions during the epoch of planet formation and mature planetary systems. We explore this connection by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets. After correcting for survey incompleteness, we measure planet occurrence: the number of planets per 100 stars with a given metallicity M. Planet occurrence correlates with metallicity for some, but not all, planet sizes and orbital periods. For warm super-Earths having P = 10–100 days and R_P = 1.0–1.7 R⊕, planet occurrence is nearly constant over metallicities spanning −0.4 to +0.4 dex. We find 20 warm super-Earths per 100 stars, regardless of metallicity. In contrast, the occurrence of warm sub-Neptunes (R_P= 1.7–4.0 R⊕) doubles over that same metallicity interval, from 20 to 40 planets per 100 stars. We model the distribution of planets as df ∝ 10^(βM) dM, where β characterizes the strength of any metallicity correlation. This correlation steepens with decreasing orbital period and increasing planet size. For warm super-Earths β = -0.3^(+0.2)_(-0.2), while for hot Jupiters β = +3.4^(+0.9)_(-0.8). High metallicities in protoplanetary disks may increase the mass of the largest rocky cores or the speed at which they are assembled, enhancing the production of planets larger than 1.7 R⊕. The association between high metallicity and short-period planets may reflect disk density profiles that facilitate the inward migration of solids or higher rates of planet–planet scattering.
261 citations
TL;DR: In this paper, the dependence of the pebble isolation mass on all relevant parameters of the protoplanetary disc was explored and a simple scaling law that captured the dependence on the local disc structure and the turbulent viscosity parameter α was derived.
Abstract: The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τ f
< 0.005 can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.
228 citations
TL;DR: In this article, it was shown that a difference of a factor of two in the pebble mass flux is enough to change the evolution from the terrestrial to the super-Earth growth mode.
Abstract: Super-Earths - planets with sizes between the Earth and Neptune - are found in tighter orbits than that of the Earth around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that also formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two clearly distinct formation pathways that are regulated by the pebble reservoir of the disc. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of two in the pebble mass flux is enough to change the evolution from the terrestrial to the super-Earth growth mode. If the pebble mass flux is small, then the initial embryos within the ice line grow slowly and do not migrate substantially, resulting in a widely spaced population of approximately Mars-mass embryos when the gas disc dissipates. Subsequently, without gas being present, the embryos become unstable due to mutual gravitational interactions and a small number of terrestrial planets are formed by mutual collisions. The final terrestrial planets are at most five Earth masses. Instead, if the pebble mass flux is high, then the initial embryos within the ice line rapidly become sufficiently massive to migrate through the gas disc. Embryos concentrate at the inner edge of the disc and growth accelerates through mutual merging. This leads to the formation of a system of closely spaced super-Earths in the five to twenty Earth-mass range, bounded by the pebble isolation mass. Generally, instabilities of these super-Earth systems after the disappearance of the gas disc trigger additional merging events and dislodge the system from resonant chains. Therefore, the key difference between the two growth modes is whether embryos grow fast enough to undergo significant migration. The terrestrial growth mode produces small rocky planets on wider orbits like those in the solar system whereas the super-Earth growth mode produces planets in short-period orbits inside 1 AU, with masses larger than the Earth that should be surrounded by a primordial H/He atmosphere, unless subsequently lost by stellar irradiation. The pebble flux - which controls the transition between the two growth modes - may be regulated by the initial reservoir of solids in the disc or the presence of more distant giant planets that can halt the radial flow of pebbles. (Less)
132 citations
TL;DR: In this article, the authors studied the growth and migration of an isolated planet in an evolving disc and showed that the growth of a giant planet requires a sufficiently high pebble flux to enable growth to outcompete migration.
Abstract: Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (r P
< 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5-10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50-100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.
127 citations
TL;DR: In this article, a model for gas-assisted pebble accretion and disk-planet tidal interaction was proposed to study the formation of super-Earth systems, and it was shown that up to 95% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations.
Abstract: At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to $\sim$95\% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction ($\gtrsim95\%$) of unstable systems with a sprinkling ($\lesssim5\%$) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (${\rm N\geq2}$) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet--planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths (abridged).
114 citations
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TL;DR: In this article, the authors presented a self-consistent, interactive simulation of the formation of the giant planets, in which for the first time both the gas and planetesimal accretion rates were calculated in a selfconsistent and interactive fashion.
2,931 citations
TL;DR: In this article, one-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a selfconsistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk.
Abstract: One-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a self-consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiqitous among low-mass YSOs, few constraints have until now been imposed on physical conditions in these disks. By fitting the results of time-dependent disk models to observed timescales of FU Orionis events, we estimate the magnitude of the effective viscous stress in the inner disk (r approximately less than 1 AU) to be, in accordance with an ad hoc 'alpha' prescription, the product of the local sound speed, pressure scale height, and an efficiency factor alpha of 10(exp -4) where hydrogen is neutral and 10(exp 3) where hydrogen is ionized. We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate sufficiently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass flux of dm(sub crit)/dt = 5 x 10(exp 7) solar mass/yr independent of the magnitude of alpha for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of dm(sub in)/dt = 1-10) x 10(exp -6) solar mass/yr produce observed FU Orionis timescales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propogate out to a distance of several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass flowing through the innermost disk annulus is equal to dm(sub in)/dt only in a time-averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals (approximately 1000 yr) of low-mass flux: (1-30) x 10(exp -8) solar mass/yr are punctuated by short intervals (approximately 100 yr) of high-mass flux: (1-30) x 10(exp -5) solar mass/yr. Timescales and mass fluxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems, respectively.
832 citations
TL;DR: A review of the current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multi-planet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems can be found in this paper.
Abstract: The basic geometry of the Solar System—the shapes, spacings, and orientations of the planetary orbits—has long been a subject of fascination as well as inspiration for planet-formation theories. For exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.
824 citations
TL;DR: In this paper, the structure of a gaseous envelope surrounding a protoplanet has been investigated in connection with the formation of the giant planets, and the most remarkable result is that a common relation between the core mass and the total mass holds irrespectively of the regions in the solar nebula.
Abstract: The structure of a gaseous envelope surrounding a protoplanet has been investigated in connection with the formation of the giant planets. Under the assumptions of spherical symmetry and hydrostatic equilibrium, the structure has been calculated for the regions of Jupiter, Saturn, Uranus and Neptune. Energy transfer in the envelope has been taken into account precisely. When the core mass increases beyond some critical value, the envelope cannot be in hydrostatic equilibrium and collapses onto the core. The most remarkable result is that a common relation between the core mass and the total mass holds irrespectively of the regions in the solar nebula. Therefore, at the collapse, the core mass becomes almost the same regardless of the regions in the nebula. This is consistent with the conclusion obtained from the theory of internal structure of the present giant planets. The grain opacity in the envelope should be about 1 cm2/g in order to explain the estimated core mass (about 10 Earth's mass) of the giant planets. This value of the grain opacity is larger than that expected before.
773 citations