Planetesimal Disk Research Articles

Bulk and Atmospheric Metallicities as Direct Probes of Sequentially Varying Accretion Mechanisms of Gas and Solids Onto Planets

Core accretion is the standard scenario of planet formation, wherein planets are formed by sequential accretion of gas and solids, and is widely used to interpret exoplanet observations. However, no direct probes of the scenario have been discussed yet. Here, we introduce an onion-like model as one idealization of sequential accretion and propose that bulk and atmospheric metallicities of exoplanets can be used as direct probes of the process. Our analytical calculations, coupled with observational data, demonstrate that the trend of observed exoplanets supports the sequential accretion hypothesis. In particular, accretion of planetesimals that are ≳100 km in size is most favored to consistently explain the observed trends. The importance of opening gaps in both planetesimal and gas disks following planetary growth is also identified. A new classification is proposed, wherein most observed planets are classified into two interior statuses: globally mixed and locally (well) mixed. Explicit identification of the locally (well) mixed status enables reliable verification of sequential accretion. During the JWST era, the quality and volume of observational data will increase drastically and improve exoplanet characterization. This work provides one key reference of how both the bulk and atmospheric metallicities can be used to constrain gas and solid accretion mechanisms of planets.

Gravitational interactions of binary systems in the massive planetesimal disc

Gravitational interactions of binary systems in the massive planetesimal disc

The Solar System could have formed in a low-viscosity disc: A dynamical study from giant planet migration to the Nice model

Context. In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating generally inwards, making the Grand Tack scenario impossible. Aims. We explore what resonant chains of multiple giant planets can form in a low-viscosity disc, and whether these configurations can evolve into forming the Solar System in the post gas disc phase. Methods. We used hydrodynamical simulations with the code FARGOCA to study the migration of the giant planets in a disc with viscosity parameter of α = 10−4. After a transition phase to a gas-less configuration, we studied the stability of the obtained resonant chains through their interactions with a disc of leftover planetesimals by performing N-body simulations using rebound. Results. The gaps opened by giant planets are wider and deeper for lower viscosity, reducing the damping effect of the disc. Thus, when planets enter a resonance, the resonant angle remains closer to circulation, making the chain weaker. Exploring numerous configurations, we found five stable resonant chains of four or five planets. In a thin (cold) PPD, the four giant planets revert their migration and migrate outwards. After disc dispersal, under the influence of a belt of planetesimals, some resonant chains undergo an instability phase while others migrate smoothly over a billion years. For three of our resonant chains, about ~1% of the final configurations pass the four criteria to fit the Solar System. The most successful runs are obtained for systems formed in a cold PPD with a massive planetesimal disc. Conclusions. This work provides a fully consistent study of the dynamical history of the Solar System’s giant planets, from the protoplanetary disc phase up to the giant planet instability. Although building resonant configurations is difficult in low-viscosity discs, we find it possible to reproduce the Solar System from a cold, low-viscosity protoplanetary disc.

Giant planet formation in the Solar System

The formation history of Jupiter has been of interest due to its ability to shape the solar system’s history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here we explore through N-body simulations the implications of the simplest disc and pebble accretion model with steady-state accretion and an assumed ring structure in the disc at 5 AU on the formation of the giant planets in the solar system. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter to control the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in logr, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets indicating that systems with more massive planets are more violent. We compute the average formation time for proto-Jupiter to reach 10 Earth masses to be 〈tc,J〉=1.1±0.3 Myr and for proto-Saturn 〈tc,S〉=3.3±0.4 Myr, while for the ice giants this increases to 〈tc,I〉=4.9±0.1 Myr. The formation timescales of the cores of the gas giants are distinct at >95% confidence, suggesting that they formed sequentially.

Extensive Pollution of Uranus and Neptune’s Atmospheres by Upsweep of Icy Material during the Nice Model Migration

In the Nice model of Solar System formation, Uranus and Neptune undergo an orbital upheaval, sweeping through a planetesimal disk. The region of the disk from which material is accreted by the ice giants during this phase of their evolution has not previously been identified. We perform direct N-body orbital simulations of the four giant planets to determine the amount and origin of solid accretion during this orbital upheaval. We find that the ice giants undergo an extreme bombardment event, with collision rates as high as ∼3 per hour assuming km-sized planetesimals, increasing the total planet mass by up to ∼0.35%. In all cases, the initially outermost ice giant experiences the largest total enhancement. We determine that, for some plausible planetesimal properties, the resulting atmospheric enrichment could potentially produce sufficient latent heat to alter the planetary cooling timescale according to existing models. Our findings suggest that substantial accretion during this phase of planetary evolution may have been sufficient to impact the atmospheric composition and thermal evolution of the ice giants, motivating future work on the fate of deposited solid material.

Randomness and retention: using weak mean motion resonances to constrain Neptune’s late-stage migration

ABSTRACT Planet–planetesimal interactions cause a planet to migrate, manifesting as a random walk in semimajor axis. In models for Neptune’s migration involving a gravitational upheaval, this planetesimal-driven migration is a side-effect of the dynamical friction required to damp Neptune’s orbital eccentricity. This migration is noisy, potentially causing Trans-Neptunian Objects (TNOs) in mean motion resonance to be lost. With N-body simulations, we validate a previously derived analytic model for resonance retention and determine unknown coefficients. We identify the impact of random-walk (noisy) migration on resonance retention for resonances up to fourth order lying between 39 and 75 au. Using a population estimate for the weak 7:3 resonance from the well-characterized Outer Solar System Origins Survey (OSSOS), we rule out two cases: (1) a planetesimal disc distributed between 13.3 and 39.9 au with ≳ 30 Earth masses in today’s size distribution and Tmig ≳ 40 Myr and (2) a top-heavy size distribution with ≳2000 Pluto-sized TNOs and Tmig ≳10 Myr, where Tmig is Neptune’s migration time-scale. We find that low-eccentricity TNOs in the heavily populated 5:2 resonance are easily lost due to noisy migration. Improved observations of the low-eccentricity region of the 5:2 resonance and of weak mean motion resonances with Rubin Observatory’s Legacy Survey of Space and Time will provide better population estimates, allowing for comparison with our model’s retention fractions and providing strong evidence for or against Neptune’s random interactions with planetesimals.

Tidal Disruption of Planetesimals from an Eccentric Debris Disk Following a White Dwarf Natal Kick

The surfaces of many white dwarfs are polluted by metals, implying a recent accretion event. The tidal disruption of planetesimals is a viable source of white dwarf pollution and offers a unique window into the composition of exoplanet systems. The question of how planetary material enters the tidal disruption radius of the white dwarf is currently unresolved. Using a series of N-body simulations, we explore the response of the surrounding planetesimal debris disk as the white dwarf receives a natal kick caused by anisotropic mass loss on the asymptotic giant branch. We find that the kick can form an apse-aligned, eccentric debris disk in the range 30–240 au, which corresponds to the orbits of Neptune, the Kuiper Belt, and the scattered disk in our solar system. In addition, many planetesimals beyond 240 au flip to counterrotating orbits. Assuming an isotropic distribution of kicks, we predict that approximately 80% of white dwarf debris disks should exhibit significant apsidal alignment and a fraction of counterrotating orbits. The eccentric disk is able to efficiently and continuously torque planetesimals onto radial, star-grazing orbits. We show that the kick causes both an initial burst in tidal disruption events as well as an extended period of 100 Myr where tidal disruption rates are consistent with observed mass accretion rates on polluted white dwarfs.

Can the giant planets of the Solar System form via pebble accretion in a smooth protoplanetary disc?

Context. Prevailing N-body planet formation models typically start with lunar-mass embryos and show a general trend of rapid migration of massive planetary cores to the inner Solar System in the absence of a migration trap. This setup cannot capture the evolution from a planetesimal to embryo, which is crucial to the final architecture of the system. Aims. We aim to model planet formation with planet migration starting with planetesimals of ~10−6−10−4 M⊕ and reproduce the giant planets of the Solar System. Methods. We simulated a population of 1000-5000 planetesimals in a smooth protoplanetary disc, which was evolved under the effects of their mutual gravity, pebble accretion, gas accretion, and planet migration, employing the parallelized N-body code SyMBAp. Results. We find that the dynamical interactions among growing planetesimals are vigorous and can halt pebble accretion for excited bodies. While a set of results without planet migration produces one to two gas giants and one to two ice giants beyond 6 au, massive planetary cores readily move to the inner Solar System once planet migration is in effect. Conclusions. Dynamical heating is important in a planetesimal disc and the reduced pebble encounter time should be considered in similar models. Planet migration remains a challenge to form cold giant planets in a smooth protoplanetary disc, which suggests an alternative mechanism is required to stop them at wide orbits.

Dynamics of the β Pictoris planetary system and its falling evaporating bodies

Context. For decades, the spectral variations of β Pictoris have been modelled as the result of the evaporation of exocomets close to the star, termed falling evaporating bodies (FEBs). Resonant perturbations by a hypothetical giant planet have been proposed to explain the dynamical origin of these stargrazers. The disk is now known to harbour two giant planets, β Pic b and c, orbiting the star at 9.9 and 2.7 au. While the former almost matches the planet formerly suspected, the recent discovery of the latter complicates the picture. Aims. We first question the stability of the two-planet system. Then we investigate the dynamics of a disk of planetesimals orbiting the star together with both planets to check the validity of the FEB generation mechanism. Methods. Symplectic N-body simulations are used to first determine which regions of the planetesimal disk are dynamically stable and which are not. Then we focus on regions where disk particles are able to reach high eccentricities, mainly thanks to resonant mechanisms. Results. The first result is that the system is dynamically stable. Both planets may temporarily fall in 7:1 mean-motion resonance (MMR). Then, simulations with a disk of particles reveal that the whole region extending between ~l.5 au and ~25 au is unstable to planetary perturbations. However, a disk below 1.5 au survives, which appears to constitute an active source of FEBs via high-order MMRs with β Pic c. In this new picture, β Pic b acts as a distant perturber that helps sustain the whole process. Conclusions. Our new simulations rule out the preceding FEB generation mechanism model, which placed their origin at around 4–5 au. Conversely, FEBs are likely to originate from a region much further in and related to MMRs with β Pic c. That mechanism also appears to last longer, as new planetesimals are able to continuously enter the MMRs and evolve towards the FEB state. Subsequently, the physical nature of the FEBs may differ from that previously thought, and presumably may not be icy.

Post-giant impact planetesimals sustaining extreme debris discs

ABSTRACT Extreme debris discs can show short-term behaviour through the evolution and clearing of small grains produced in giant impacts, and potentially a longer period of variability caused by a planetesimal population formed from giant impact ejecta. In this paper, we present results of numerical simulations to explain how a planetesimal populated disc can supply an observed extreme debris disc with small grains. We simulated a sample of giant impacts from which we form a planetesimal population. We then use the N-body code rebound to evolve the planetesimals spatially and collisionally. We adopt a simplistic collision criteria in which we define destructive collisions to be between planetesimals with a mutual impact velocity that exceeds two times the catastrophic disruption threshold, V*. We find that for some configurations, a planetesimal populated disc can produce a substantial amount of dust to sustain an observable disc. The semimajor axis at which the giant impact occurs changes the mass added to the observed disc substantially, while the orientation of the impact has less of an effect. We determine how the collision rate at the collision point changes over time and show that changes in semimajor axis and orientation only change the initial collision rate of the disc. Collision rates across all discs evolve at a similar rate.

Motion of Planetesimals in the Hill Sphere of the Star Proxima Centauri

The motion of planetesimals initially located in the feeding zone of the planet Proxima Centauri c, at distances of 500 AU from the star to the star’s Hill sphere radius of 1200 AU was considered. In the analyzed non-gaseous model, the primary ejection of planetesimals from most of the feeding zone of an almost formed planet c to distances greater than 500 AU from the star occurred during the first 10 million years. Only for planetesimals originally located at the edges of the planet’s feeding zone, the fraction of planetesimals that first reached 500 AU over the time greater than 10 million years was more than half. Some planetesimals could reach the outer part of the star’s Hill sphere over hundreds of millions of years. Approximately 90% of the planetesimals that first reached 500 AU from Proxima Centauri first reached 1200 AU from the star in less than 1 million years, given the current mass of the planet c. No more than 2% of planetesimals with aphelion orbital distances between 500 and 1200 AU followed such orbits for more than 10 million years (but less than a few tens of millions of years). With a planet mass equal to half the mass of the planet c, approximately 70–80% of planetesimals increased their maximum distances from the star from 500 to 1200 AU in less than 1 million years. For planetesimals that first reached 500 AU from the star under the current mass of the planet c, the fraction of planetesimals with orbital eccentricities greater than 1 was 0.05 and 0.1 for the initial eccentricities of their orbits eo = 0.02 and eo = 0.15, respectively. Among the planetesimals that first reached 1200 AU from the star, this fraction was approximately 0.3 for both eo values. The minimum eccentricity values for planetesimals that have reached 500 and 1200 AU from the star were 0.992 and 0.995, respectively. In the considered model, the disk of planetesimals in the outer part of the star’s Hill sphere was rather flat. Inclinations i of the orbits for more than 80% of the planetesimals that first reached 500 or 1200 AU from the star did not exceed 10°. With the current mass of the planet c, the percentage of such planetesimals with i 20° did not exceed 1% in all calculation variants. The results may be of interest for understanding the motion of bodies in other exoplanetary systems, especially those with a single dominant planet. They can be used to provide the initial data for models of the evolution of the disk of bodies in the outer part of Proxima Centauri’s Hill sphere, which take into account gravitational interactions and collisions between bodies, as well as the influence of other stars. The strongly inclined orbits of bodies in the outer part of Proxima Centauri’s Hill sphere can primarily result from bodies that entered the Hill sphere from outside. The radius of Proxima Centauri’s Hill sphere is an order of magnitude smaller than the radius of the outer boundary of the Hills cloud in the Solar System and two orders of magnitude smaller than the radius of the Sun’s Hill sphere. Therefore, it is difficult to expect the existence of a similarly massive cloud around this star as the Oort cloud around the Sun.

Col-OSSOS: The Distribution of Surface Classes in Neptune's Resonances

The distribution of surface classes of resonant trans-Neptunian objects (TNOs) provides constraints on the protoplanetesimal disk and giant planet migration. To better understand the surfaces of TNOs, the Colours of the Outer Solar System Origins Survey acquired multiband photometry of 102 TNOs and found that the surfaces of TNOs can be well described by two surface classifications: BrightIR and FaintIR. These classifications both include optically red members and are differentiated predominantly based on whether their near-infrared spectral slope is similar to their optical spectral slope. The vast majority of cold classical TNOs, with dynamically quiescent orbits, have the FaintIR surface classification, and we infer that TNOs in other dynamical classifications with FaintIR surfaces share a common origin with the cold classical TNOs. Comparison between the resonant populations and the possible parent populations of cold classical and dynamically excited TNOs reveal that the 3:2 has minimal contributions from the FaintIR class, which could be explained by the ν 8 secular resonance clearing the region near the 3:2 before any sweeping capture occurred. Conversely, the fraction of FaintIR objects in the 4:3 resonance, 2:1 resonance, and the resonances within the cold classical belt suggest that the FaintIR surface formed in the protoplanetary disk between ≳34.6 and ≲47 au, though the outer bound depends on the degree of resonance sweeping during migration. The presence and absence of the FaintIR surfaces in Neptune’s resonances provides critical constraints for the history of Neptune’s migration, the evolution of the ν 8, and the surface class distribution in the initial planetesimal disk.

Planetesimal Accretion at Short Orbital Periods

Abstract Formation models in which terrestrial bodies grow via the pairwise accretion of planetesimals have been reasonably successful at reproducing the general properties of the Solar System, including small-body populations. However, planetesimal accretion has not yet been fully explored in the context of the wide variety of recently discovered extrasolar planetary systems, in particular those that host short-period terrestrial planets. In this work, we use direct N-body simulations to explore and understand the growth of planetary embryos from planetesimals in disks extending down to ≃1 day orbital periods. We show that planetesimal accretion becomes nearly 100% efficient at short orbital periods, leading to embryo masses that are much larger than the classical isolation mass. For rocky bodies, the physical size of the object begins to occupy a significant fraction of its Hill sphere toward the inner edge of the disk. In this regime, most close encounters result in collisions, rather than scattering, and the system does not develop a bimodal population of dynamically hot planetesimals and dynamically cold oligarchs, as is seen in previous studies. The highly efficient accretion seen at short orbital periods implies that systems of tightly packed inner planets should be almost completely devoid of any residual small bodies. We demonstrate the robustness of our results to assumptions about the initial disk model, and we also investigate the effects that our simplified collision model has on the emergence of this non-oligarchic growth mode in a planet-forming disk.

GANBISS: a new GPU accelerated N-body code for binary star systems

We present a GPU accelerated N-body integrator using the Bulirsch–Stoer method, called GANBISS (GPU accelerated n-body code for binary star systems). It is designed to simulate the dynamical evolution of planetesimal disks in binary star systems which contain some thousand disk objects. However, it can also be used for studies of non-interacting massless bodies where up to 50 million objects can be studied in a simulation. GANBISS shows the energy and angular momentum conservation behavior of non-symplectic integration methods. The code is written in CUDA C and can be run on NVIDIA GPUs of compute capability of at least 3.5. A comparison of GPU and CPU computations indicates a speed-up of the GPU performance of up to 100 times—depending on the number of disk objects.

Massive Protostellar Disks as a Hot Laboratory of Silicate Grain Evolution

Typical accretion disks around massive protostars are hot enough for water ice to sublimate. We here propose to utilize the massive protostellar disks for investigating the collisional evolution of silicate grains with no ice mantle, which is an essential process for the formation of rocky planetesimals in protoplanetary disks around lower-mass stars. We, for the first time, develop a model of massive protostellar disks that includes the coagulation, fragmentation, and radial drift of dust. We show that the maximum grain size in the disks is limited by collisional fragmentation rather than by radial drift. We derive analytic formulae that produce the radial distribution of the maximum grain size and dust surface density in the steady state. Applying the analytic formulae to the massive protostellar disk of GGD27-MM1, where the grain size is constrained from a millimeter polarimetric observation, we infer that the silicate grains in this disk fragment at collision velocities above ≈10 m s−1. The inferred fragmentation threshold velocity is lower than the maximum grain collision velocity in typical protoplanetary disks around low-mass stars, implying that coagulation alone may not lead to the formation of rocky planetesimals in those disks. With future measurements of grain sizes in massive protostellar disks, our model will provide more robust constraints on the sticking property of silicate grains.

Heavy-element accretion by proto-Jupiter in a massive planetesimal disc, revisited

ABSTRACT Planetesimal accretion is a key source for heavy-element enrichment in giant planets. It has been suggested that Jupiter’s enriched envelope is a result of planetesimal accretion during its growth, assuming it formed in a massive planetesimal disc. In this study, we simulate Jupiter’s formation in this scenario. We assume in situ formation and perform N-body simulations to infer the solid accretion rate. We find that tens-Earth masses of planetesimals can be captured by proto-Jupiter during the rapid gas accretion phase. However, if several embryos are formed near Jupiter’s core, which is an expected outcome in the case of a massive planetesimal disc, scattering from the embryos increases the eccentricity and inclination of planetesimals and therefore significantly reduces the accretion efficiency. We also compare our results with published semi-analytical models and show that these models cannot reproduce the N-body simulations especially when the planetesimal disc has a large eccentricity and inclination. We show that when the dynamical evolution of planetesimals is carefully modelled, the total mass of captured planetesimals Mcap,tot is 2M⊕ ≲ Mcap,tot ≲ 18M⊕. The metallicity of Jupiter’s envelope can be explained by the planetesimal accretion in our massive disc model despite the low accretion efficiency coming from the high eccentricity and inclination of planetesimals. Our study demonstrates the importance of detailed modelling of planetesimal accretion during the planetary growth and its implications to the heavy-element mass in gaseous planets.

Implications of Jupiter Inward Gas-driven Migration for the Inner Solar System

The migration history of Jupiter in the Sun’s natal disk remains poorly constrained. Here we consider how Jupiter’s migration affects small-body reservoirs and how this constrains its original orbital distance from the Sun. We study the implications of large-scale and inward radial migration of Jupiter for the inner solar system while considering the effects of collisional evolution of planetesimals. We use analytical prescriptions to simulate the growth and migration of Jupiter in the gas disk. We assume the existence of a planetesimal disk inside Jupiter’s initial orbit. This planetesimal disk received an initial total mass and size–frequency distribution (SFD). Planetesimals feel the effects of aerodynamic gas drag and collide with one another, mostly while shepherded by the migrating Jupiter. Our main goal is to measure the amount of mass in planetesimals implanted into the main asteroid belt (MAB) and the SFD of the implanted population. We also monitor the amount of dust produced during planetesimal collisions. We find that the SFD of the planetesimal population implanted into the MAB tends to resemble that of the original planetesimal population interior to Jupiter. We also find that unless very little or no mass existed between 5 au and Jupiter’s original orbit, it would be difficult to reconcile the current low mass of the MAB with the possibility that Jupiter migrated from distances beyond 15 au. This is because the fraction of the original disk mass that gets implanted into the MAB is very large. Finally, we discuss the implications of our results in terms of dust production to the so-called NC–CC isotopic dichotomy.

Planetesimal Dynamics in the Presence of a Giant Planet. II. Dependence on Planet Mass and Eccentricity

The presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and “accretion-friendly” locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect of a Jupiter-like planet on an external planetesimal disk, we generalize our findings to extrasolar planetary systems by varying the planet parameters. In particular, we focus on the dependence of the planetesimal relative velocities on the mass and eccentricity of the existing planet. We found that the velocity dispersion of identical-mass particles increases monotonically with increasing planet mass. Meanwhile, the dependence of the relative velocity between different-mass planetesimals on their mass ratio becomes weaker as the planet mass increases. While the relative velocities generally increase with increasing planet eccentricity, the velocity dispersion of lower-mass particles (m ≲ 1018 g) is almost independent of planet eccentricity owing to their strong coupling to gas. We find that the erosion limits are met for a wider range of parameters (planet mass/eccentricity, planetesimal mass ratio) when the planetesimal size decreases. Our results could provide some clues for the formation of Saturn’s core, as well as the architecture of some exoplanetary systems with multiple cold giant planets.

Extended planetary chaotic zones

ABSTRACT We consider the chaotic motion of low-mass bodies in two-body high-order mean-motion resonances with planets in model planetary systems, and analytically estimate the Lyapunov and diffusion time-scales of the motion in multiplets of interacting subresonances corresponding to the mean-motion resonances. We show that the densely distributed (though not overlapping) high-order mean-motion resonances, when certain conditions on the planetary system parameters are satisfied, may produce extended planetary chaotic zones – ‘zones of weak chaotization,’ – much broader than the well-known planetary connected chaotic zone, the Wisdom gap. This extended planetary chaotic zone covers the orbital range between the 2/1 and 1/1 resonances with the planet. On the other hand, the orbital space inner (closer to the host star) with respect to the 2/1 resonance location is essentially long-term stable. This difference arises because the adiabaticity parameter of subresonance multiplets specifically depends on the particle’s orbit size. The revealed effect may control the structure of planetesimal discs in planetary systems: the orbital zone between the 2/1 and 1/1 resonances with a planet should be normally free from low-mass material (only that occasionally captured in the first-order 3/2 or 4/3 resonances may survive); whereas any low-mass population inner to the 2/1 resonance location should be normally long-lived (if not perturbed by secular resonances, which we do not consider in this study).

Dynamical evolution of a self-gravitating planetesimal disk in the distant trans-Neptunian region

Aims. We study the dynamical evolution of a system consisting of the giant planets and a massive planetesimal disk over the age of the Solar System. The main question addressed in this study is whether distant trans-Neptunian objects could have come about as a result of the combined action of planetary perturbations and the self-gravity of the disk. Methods. We carried out a series of full N-body numerical simulations of gravitational interactions between the giant planets and a massive outer disk of planetesimals. Results. Our simulations show that the collective gravity of the giant planets and massive planetesimals produces distant trans-Neptunian objects across a wide range of the initial disk mass. The majority of objects that survive up through the age of the Solar System have perihelion distances of q > 40 au. In this region, there is a tendency toward a slow decrease in eccentricities and an increase in perihelion distances for objects with semimajor axes a > 150 au. Secular resonances between distant planetesimals play a major role in increasing their perihelion distances. This explains the origin of Sedna-type objects. In our integrations for the age of the Solar System, we registered times with both high and low clustering of longitudes of perihelion and arguments of perihelion for objects with q > 40 au, a > 150 au. The resulting distribution of inclinations in our model and the observed distribution of inclinations for distant trans-Neptunian objects have similar average values of around 20°. Conclusions. Distant trans-Neptunian objects are a natural consequence in the models that include migrating giant planets and a self-gravitating planetesimal disk.