Search

Context. Understanding planetesimal formation is an essential first step towards understanding planet formation. The distribution of these first solid bodies drives the locations where planetary embryos, which eventually form fully-fledged planets, grow. Aims. We seek to understand the parameter space of possible protoplanetary disk formation and evolution models of our Solar System. A good protoplanetary disk scenario for the Solar System must meet at least the following three criteria: (1) It must produce an extended gas and dust disk (e.g. 45 au for the dust); (2) within the disk, the local dust-to-gas ratio in at least two distinct locations must sufficiently increase to explain the early formation of the parent bodies of non-carbonaceous and carbonaceous iron meteorites; and (3) dust particles, which have condensed at high temperatures (i.e. calcium–aluminium-rich inclusions), must be transported to the outer disk. Though current protoplanetary disk models are able to satisfy one or two of these criteria, none have been successful in recreating all three. We aim to find scenarios that satisfy all three. Methods. In this study we used a 1D disk model that tracks the evolution of the gas and dust disks. Planetesimals are formed within the disk at locations where the streaming instability can be triggered. We explored a large parameter space to study the effect of the disk viscosity, the timescale of infall of material into the disk, the distance within which material is deposited into the disk, and the fragmentation threshold of dust particles. Results. We find that scenarios with a large initial disk viscosity (α > 0.05), a relatively short infall timescale (Tinfall < 100–200kyr), and a small centrifugal radius (RC~ 0.4 au; i.e. the distance within which material falls into the disk) result in disks that satisfy all three criteria needed to represent the protoplanetary disk of the Solar System. The large initial viscosity and short infall timescale result in a rapid initial expansion of the disk, which we dub the 'inflationary phase' of the disk. Furthermore, a temperature-dependent fragmentation threshold, which accounts for cold icy particles breaking more easily, results in larger and more massive disks. This, in turn, results in more 'icy' than 'rocky' planetesimals. Such scenarios are also better in line with our Solar System, which has small terrestrial planets and massive giant planet cores. Finally, we find that scenarios with large RC cannot transport calcium–aluminium-rich inclusions to the outer disk and do not produce planetesimals at two locations within the disk. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Context. It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like β-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall into their parent stars. Aims.We aim to develop a general, implementable, semi-analytical theory of secular eccentricity excitation of small bodies (planetesimals) in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Methods. Our semi-analytic model for the restricted planar three-body problem does not make use of series expansion and therefore is valid for any eccentricity value and semi-major axis ratio. The model is based on the application of the adiabatic principle, which is valid when the precession period of the longitude of pericentre of the planetesimal is much longer than the libration period in the mean motion resonance. In resonances of order larger than 1 this is true except for vanishingly small eccentricities. We provide prospective users with a Mathematica notebook with implementation of the model allowing direct use. Results. We confirm that the 4:1 mean motion resonance with a moderately eccentric (e' <≲ 0.1) planet is the most powerful one to lift the eccentricity of planetesimals from nearly circular orbits to star-grazing ones. However, if the planet is too eccentric, we find that this resonance is unable to pump the planetesimal's eccentricity to a very high value. The inclusion of the General Relativity effect imposes a condition on the mass of the planet to drive the planetesimals into star-grazing orbits. For a planetesimal at ~1 AU around a solar mass star (or white dwarf), we find a threshold planetary mass of about 17 Earth masses. We finally derive an analytical formula for this critical mass. Conclusions. Planetesimals can easily fall into the central star even in the presence of a single moderately eccentric planet, but only from the vicinity of the 4.1 mean motion resonance. For sufficiently high planetary masses the General Relativity effect does not prevent the achievement of star-grazing orbits. [ABSTRACT FROM AUTHOR]

Context. Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. Aims. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. Methods. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. Results. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw ≲ 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths. [ABSTRACT FROM AUTHOR]

Context. A large fraction of stars host one or multiple close-in super-Earth planets. There is an active debate about whether these planets formed in situ or at greater distances from the central star and migrated to their current position. It has been shown that part of their observed properties (e.g., eccentricity distribution) can be reproduced by N-body simulations of in situ formation starting with a population of protoplanets of high masses and neglecting the effects of the disk gas. Aims. We plan to reassess the in situ formation of close-in super-Earths through more complete simulations. Methods. We performed N-body simulations of a population of small planetary embryos and planetesimals that include the effects of disk-planet interactions (e.g., eccentricity damping, Type I migration). In addition, we also consider the accretion of a primitive atmosphere from a protoplanetary disk. Results. We find that planetary embryos grow very quickly well before the gas dispersal, and thus undergo rapid inward migration, which means that one cannot neglect the effects of a gas disk when considering the in-situ formation of close-in super-Earths. Owing to their rapid inward migration, super-Earths reach a compact configuration near the disk's inner edge whose distribution of orbital parameters matches the observed close-in super-Earths population poorly. On the other hand, simulations including eccentricity damping, but no Type I migration, reproduce the observed distributions better. Including the accretion of an atmosphere does not help reproduce the bulk architecture of observations. Interestingly, we find that the massive embryos can migrate inside the disk edge while capturing only a moderately massive hydrogen/helium atmosphere. By this process they avoid becoming giant planets. Conclusions. The bulk of close-in super-Earths cannot form in situ, unless Type I migration is suppressed in the entire disk inside 1 AU. [ABSTRACT FROM AUTHOR]

Context. The migration strength and direction of embedded low-mass planets depends on the disc structure. In discs with an efficient radiative transport, the migration can be directed outwards for planets with more than 3-5 Earth masses. This is due to the entropydriven corotation torque, a process that extends the lifetimes of growing planetary embryos. However, smaller mass planets are still migrating inwards and might be lost to the central star. Aims. We investigate the influence on the disc structure caused by a jump in the α parameter of the viscosity to model a dead-zone structure in the disc. We focus on M discs, which have a constant net mass flux. Using the resulting disc structure, we investigate the consequences for the formation of planetesimals and determine the regions of outward migration for proto-planets. Methods. We performed numerical hydrosimulations of M discs in the r-z-plane. We used the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation as well as a two-temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets was studied by using torque formulae. Results. Viscosity transitions inside the disc create transitions in density that stop inward migration for small planets through the so-called "planet trap" mechanism. This mechanism also works for planets down to MP > 0.5 MEarth, while in radiative discs with no viscosity transition the lowest mass with which inward migration can be avoided is 3-5 Earth masses. Additionally, the viscosity transitions change the pressure gradient in the disc, which facilitates planetesimal formation via the streaming instability. However, a very steep transition in viscosity is needed to achieve in a pressure bump in the disc. Conclusions. The transition in viscosity facilitates planetesimal formation and can stop the migration of small-mass planets (MP > 0.5 MEarth), but still does not halt inward migration of smaller planets and planetesimals that are affected by gas drag. A very steep, probably unrealistic viscosity gradient is needed to trap planets of smaller masses and halt gas-drag-driven planetesimal migration at a pressure bump. [ABSTRACT FROM AUTHOR]

Context. The strength and direction of migration of embedded low mass planets depends on the disc's structure. It has been shown that, in discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. Aims. In this paper we investigate the influence of a constant M-flux through the disc, as well as the influence of the disc's metallicity on the disc's thermodynamics. We focus on M discs, which have a net mass flux through them. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc. Methods. We perform numerical hydrosimulations of M discs with viscous heating, radiative cooling and stellar irradiation in 2D in the r-z-plane. We use the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets is studied by using torque formulae. Results. For a disc of gas surface density ΣG and viscosity v, we find that the discs thermal structure depends on the product ΣGv and the amount of heavy elements, while the migration of planets additionally to the mentioned quantities, depends on the amount of viscosity v itself. As a result of this, the disc structure can not be approximated by simple power laws. During the lifetime of the disc, the structure of the disc changes significantly in a non-linear way in the inner parts. In the late stages of the discs evolution (characterised by low M), outward migration is only possible if the metallicity of the disc is high. For low metallicity, planets would migrate inwards and could potentially be lost to the star. Conclusions. The presented disc structures and migration maps have important consequences on the formation of planets, as they can give hints on the different formation mechanisms for different types of planets as a function of metallicity. [ABSTRACT FROM AUTHOR]

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 (rP < 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. [ABSTRACT FROM AUTHOR]

The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time scales of several million years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height, and density. The commonly used disc structure of the minimum mass solar nebula (MMSN) is a simple power law in all these quantities. However, protoplanetary disc models with both viscous and stellar heating show several bumps and dips in temperature, scale height, and density caused by transitions in opacity, which are missing in the MMSN model. These play an important role in the formation of planets, since they can act as sweet spots for forming planetesimals via the streaming instability and affect the direction and magnitude of type-I migration. We present 2D simulations of accretion discs that feature radiative cooling and viscous and stellar heating, and they are linked to the observed evolutionary stages of protoplanetary discs and their host stars. These models allow us to identify preferred planetesimal and planet formation regions in the protoplanetary disc as a function of the disc's metallicity, accretion rate, and lifetime. We derive simple fitting formulae that feature all structural characteristics of protoplanetary discs during the evolution of several Myr. These fits are straightforward for applying to modelling any growth stage of planets where detailed knowledge of the underlying disc structure is required. [ABSTRACT FROM AUTHOR]