The first stages of planet formation take place in protoplanetary disks that are largely made up of gas. Understanding how the gas affects planetesimals in the protoplanetary disk is therefore essential. In this paper, we discuss whether or not gas flow can erode planetesimals. We estimate how much shear stress is exerted onto the planetesimal surface by the gas as a function of disk and planetesimal properties. To determine whether erosion can take place, we compare this with previous measurements of the critical stress that a pebble-pile planetesimal can withstand before erosion begins. If erosion takes place, we estimate the erosion time of the affected planetesimals. We also illustrate our estimates with two-dimensional numerical simulations of flows around planetesimals using the lattice Boltzmann method. We find that the wall shear stress can overcome the critical stress of planetesimals in an eccentric orbit within the innermost regions of the disk. The high eccentricities needed to reach erosive stresses could be the result of shepherding by migrating planets. We also find that if a planetesimal erodes, it does so on short timescales. For planetesimals residing outside of $1 \ \rm{au}$, we find that they are mainly safe from erosion, even in the case of highly eccentric orbits.
Aeolian-erosion is a destructive process which can erode small-size planetary objects through their interaction with a gaseous environment. Aeolian-erosion operates in a wide range of environments and under various conditions. Aeolian-erosion has been extensively explored in the context of geophysics in terrestrial planets. Here we show that aeolian-erosion of cobbles, boulders and small planetesimals in protoplanetary-discs can constitute a significant barrier for the early stages of planet formation. We use analytic calculations to show that under the conditions prevailing in protoplanetary-…
Small, pebble-sized objects and large bodies of planetesimal size both play important roles in planet formation. They form the evolutionary steps of dust growth in their own respect. However, at later times, they are also thought to provide background populations of mass that larger bodies might feed upon. What we suggest in this work is that starting at times of viscous stirring, planetesimals on eccentric orbits could simply explode as they become supersonic in comparison to small, porous planetary bodies entering Earth's atmosphere. We present a toy model of planetesimal motion and destruct…
In parabolic flight experiments we studied the wind induced erosion of granular beds composed of spherical glass beads at low gravity and low ambient pressure. Varying g-levels were set by centrifugal forces. Expanding existing parameter sets to a pressure range between $p=300-1200\,$Pa and to g-levels of $g=1.1-2.2\,\rm m\,s^{-2}$ erosion thresholds are still consistent with the existing model for wind erosion on planetary surfaces by Shao & Lu (2000). These parameters were the lowest values that could technically be reached by the experiment. The experiments decrease the necessary range of e…
The asteroid belt is an open window on the history of the Solar System, as it preserves records of both its formation process and its secular evolution. The progenitors of the present-day asteroids formed in the Solar Nebula almost contemporary to the giant planets. The actual process producing the first generation of asteroids is uncertain, strongly depending on the physical characteristics of the Solar Nebula, and the different scenarios produce very diverse initial size-frequency distributions. In this work we investigate the implications of the formation of Jupiter, plausibly the first gia…
A planetesimal moves through the gas of its protoplanetary disc where it experiences a head wind. Though the ambient pressure is low, this wind can erode and ultimately destroy the planetesimal if the flow is strong enough. For the first time, we observe wind erosion in ground based and microgravity experiments at pressures relevant in protoplanetary discs, i.e. down to $10^{-1}\, \rm mbar$. We find that the required shear stress for erosion depends on the Knudsen number related to the grains at the surface. The critical shear stress to initiate erosion increases as particles become comparable…
The coagulation of microscopic dust into planetesimals is the first step towards planet formation. The size and shape of the growing aggregates determine the efficiency of this early growth. It has been proposed that fluffy ice aggregates can grow very efficiently, suffering less from the bouncing and radial drift barriers. While the collision velocity between icy aggregates of similar size is thought to stay below the fragmentation threshold, they may nonetheless lose mass from collisions with much smaller projectiles. We investigate the effect of these erosive collisions on the ability of po…
Wind erosion is a destructive mechanism that completely dissolves a weakly bound object like a planetesimal into its constituent particles, if the velocity relative to the ambient gas and the local gas pressure are sufficiently high. In numerical simulations we study the influence of such wind erosion on pebble and planetesimal accretion by a planetary body up to $10 R_\mathrm{Earth}$. Due to the rapid size reduction of an in-falling small body, the accretion outcome changes significantly. Erosion leads to a strong decrease in the accretion efficiency below a threshold size of the small body o…
Transporting solids of different sizes is an essential process in the evolution of protoplanetary disks and planet formation. Large solids are supposed to drift inward; high-temperature minerals found in comets are assumed to have been transported outward. From low-gravity experiments on parabolic flights we studied the light-induced erosion of dusty bodies caused by a solid-state greenhouse effect and photophoresis within a dust bed's upper layers. The gravity levels studied were 0.16g, 0.38g, 1g, and 1.7g. The light flux during the experiments was 12 +/- 2 kW/m^2 and the ambient pressure was…
The formation of the first planetesimals and the final growth of planetary cores relies on the abundance of small pebbles. The efficiencies of both the streaming instability (SI) process, suggested to catalyze the early growth of planetesimals, and the pebble-accretion process, suggested to accelerate the growth of planetary cores, depend on the sizes of solids residing in the disk. In particular, these processes were found to be sensitive to size distribution of solids, and efficient planetesimal formation and growth through these channels require a limited pebble size distribution. Here we s…
Disruptive collisions have been regarded as an important process for planet formation, while non-disruptive, small-scale collisions (hereafter called erosive collisions) have been underestimated or neglected by many studies. However, recent studies have suggested that erosive collisions are also important to the growth of planets, because they are much more frequent than disruptive collisions. Although the thresholds of the specific impact energy for disruptive collisions (Q_RD^*) have been investigated well, there is no reliable model for erosive collisions. In this study, we systematically c…
In protoplanetary disks, dust grains rich in metallic iron can attract each other magnetically. If they are magnetized to values near saturation, the magnetically induced collision speeds are high enough to knock off the non-magnetized, loosely bound silicates. This process enriches the surviving portions of the dust grains in metallic iron, which further enhances the magnetically mediated collisions. The magnetic enhancement to the collisional cross-section between the iron rich dust results in rapid grain growth leading to planetesimal formation. While this process of knocking off silicates,…
The discovery of numerous debris disks around white dwarfs (WDs), gave rise to extensive study of such disks and their role in polluting WDs, but the formation and evolution of these disks is not yet well understood. Here we study the role of aeolian (wind) erosion in the evolution of solids in WD debris disks. Aeolian erosion is a destructive process that plays a key role in shaping the properties and size-distribution of planetesimals, boulders and pebbles in gaseous protoplanetary disks. Our analysis of aeolian erosion in WD debris disks shows it can also play an important role in these env…
Recent observations from NASA's Kepler mission detected the first planets in circumbinary orbits. The question we try to answer is where these planets formed in the circumbinary disk and how far inside they migrated to reach their present location. We investigate the first and more delicate phase of planet formation when planetesimals accumulate to form planetary embryos. We use the hydrodynamical code FARGO to study the evolution of the disk and of a test population of planetesimals embedded in it. With this hybrid hydrodynamical--N--body code we can properly account for the gas drag force on…
The growth of small planetesimals into large planetary embryos occurs much before the dispersal of the gas from the protoplanetary disk. The planetesimal - gaseous-disk interactions give rise to migration and orbital evolution of the planetesimals/planets. Small planetesimals are dominated by aerodynamic gas drag. Large protoplanets, $m\sim0.1M_{\oplus}$, are dominated by type I migration \emph{differential} torque. There is an additional mass range, $m\sim10^{21}-10^{25}g$ of \emph{intermediate mass} planetesimals (IMPs), where gravitational interactions with the disk dominate over aerodynami…
One of first the stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. At this stage gas-planetesimal interactions play a key role in the dynamical evolution of \emph{single} intermediate-mass planetesimals ($m_{p}\sim10^{21}-10^{25}g$) \emph{through gas dynamical friction} (GDF). A significant fraction of all Solar system planetesimals (asteroids and Kuiper-belt objects) are known to be binary planetesimals (BPs). H…
One of the first stages of planet formation is the growth of small planetesimals. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. Due to their different aerodynamic properties, planetesimals of different sizes and shapes experience different drag forces from the gas during this time. Such differential forces produce a wind-shearing (WISH) effect between close by, different size planetesimals. For any two planetesimals, a WISH radius can be considered, at which the differential acceleration due to the wind becomes greater than the mutual gravit…
The formation of cold gas giants similar to Jupiter and Saturn in orbit and mass is a great challenge for planetesimal-driven core accretion models because the core growth rates far from the star are low. Here we model the growth and migration of single protoplanets that accrete planetesimals and gas. We integrated the core growth rate using fits in the literature to $N$-body simulations, which provide the efficiency of accreting the planetesimals that a protoplanet migrates through. We take into account three constraints from the solar system and from protoplanetary discs: (1) the masses of t…
When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are…
We examined the excitations of planetesimals caused by the resonances of a giant planet in a protoplanetary gas disk. The highly excited planetesimals generate bow shocks, the mechanism of which results in chondrule formation, crystallization of silicate dust, and evaporation of icy planetesimals. The planetesimals beyond 2:1 resonance migrate owing to the gas drag and obtain the maximum eccentricity around 3:1 resonance, which is located at approximately half the planetary distance. The eccentricity depends on the parameters of the planetesimals and the Jovian planet, such as size and locatio…
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 o…
The growth and migration of planetesimals in a young protoplanetary disc are fundamental to planet formation. In all models of early growth, there are several processes that can inhibit grains from reaching larger sizes. Nevertheless, observations suggest that growth of planetesimals must be rapid. If a small number of 100 km sized planetesimals do manage to form in the disc, then gas drag effects could enable them to efficiently accrete small solids from beyond their gravitationally focused cross-section. This gas drag-enhanced accretion can allow planetesimals to grow at rapid rates, in prin…
Aims. We investigate the feasibility of planetesimal growth in circumbinary protoplanetary disks around the observed systems Kepler- 16 and Kepler-34 under the gravitational influence of a precessing eccentric gas disk. Methods. We embed the results of our previous hydrodynamical simulations of protoplanetary disks around binaries into an N-body code to perform 3D, high-resolution, inter-particle gravity-enabled simulations of planetesimal growth and dynamics that include the gravitational force imparted by the gas. Results. Including the full, precessing asymmetric gas disk generates high ecc…
Using ab initio simulations we investigate whether water ice is stable in the cores of giant planets, or whether it dissolves into the layer of metallic hydrogen above. By Gibbs free energy calculations we find that for pressures between 10 and 40 Mbar the ice-hydrogen interface is unstable at temperatures above approximately 3000 K, far below the temperature of the core-mantle boundaries in Jupiter and Saturn that are of the order of 10000 K. This implies that the cores of solar and extrasolar giant planets are at least partially eroded.
Regular satellites of giant planets are formed by accretion of solid bodies in circumplanetary disks. Planetesimals that are moving on heliocentric orbits and are sufficiently large to be decoupled from the flow of the protoplanetary gas disk can be captured by gas drag from the circumplanetary disk. In the present work, we examine the distribution of captured planetesimals in circumplanetary disks using orbital integrations. We find that the number of captured planetesimals reaches an equilibrium state as a balance between continuous capture and orbital decay into the planet. The number of pl…
We investigate the effects of gas-disk gravity on the planetesimal dynamics in inclined binary systems, where the circumprimary disk plane is tilted by a significant angle ($i_B$) with respect to the binary disk plane. Our focus is on the Lidov-Kozai mechanism and the evolution of planetesimal eccentricity and inclination. Using both analytical and numerical methods, we find that, on one hand, the disk gravity generally narrows down the Kozai-on region, i.e., the Lidov-Kozai effect can be suppressed in certain parts of (or even the whole of) the disk, depending on various parameters. In the Ko…
To avoid known difficulties in planetesimal formation such as the drift or fragmentation barriers, many scenarios have been proposed. However, in these scenarios, planetesimals form in general only at some specific locations in protoplanetary discs. On the other hand, it is generally assumed in planet formation models and population synthesis models, that planetesimals are broadly distributed in the protoplanetary disc. Here we propose a new scenario in which planetesimals can form in broad areas of the discs. Planetesimals form at the gas pressure bump formed by a first-generation planet (e.g…
When gas giant protoplanets grow sufficiently massive, circumplanetary disks would form. While solid bodies captured by the circumplanetary disks likely contribute to the growth of the planets and regular satellites around them, some of captured bodies would remain in planet-centered orbits after the dispersal of the disk. We examine capture and subsequent orbital evolution of planetesimals in waning circumplanetary gas disks using three-body orbital integration. We find that some of captured planetesimals can survive in the circumplanetary disk for a long period of time under such weak gas dr…
One of the first stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. Due to their different aerodynamic properties, planetesimals of different sizes/shapes experience different drag forces from the gas at these stage. Such differential forces produce a wind-shearing effect between close by, different size planetesimals. For any two planetesimals, a wind-shearing radius can be considered, at which the differential a…
We report here on an extension of a previous study by Kirsh et al. (2009) of planetesimal-driven migration using our N-body code SyMBA (Duncan et al., 1998). The previous work focused on the case of a single planet of mass Mem, immersed in a planetesimal disk with a power-law surface density distribution and Rayleigh distributed eccentricities and inclinations. Typically 10^4-10^5 equal-mass planetesimals were used, where the gravitational force (and the back-reaction) on each planetesimal by the Sun and planetwere included, while planetesimal-planetesimal interactions were neglected. The runs…
Small scale jet-induced erosion experiments are useful for identifying the scaling of erosion with respect to the various physical parameters (gravity, grain size, gas velocity, gas density, grain density, etc.), and because they provide a data set for benchmarking numerical flow codes. We have performed experiments varying the physical parameters listed above (e.g., gravity was varied in reduced gravity aircraft flights). In all these experiments, a subsonic jet of gas impinges vertically on a bed of sand or lunar soil simulant forming a localized scour hole beneath the jet. Videography captu…
We investigate the formation process of planetesimals from the dust layer by the gravitational instability in the gas disk using local $N$-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the du…
Studies of internal structure of gas giant planets suggest that their envelopes are enriched with heavier elements than hydrogen and helium relative to their central stars. Such enrichment likely occurred by solid accretion during late formation stages of gas giant planets in which gas accretion dominates protoplanetary growth. Some previous studies performed orbital integration of planetesimals around a growing protoplanet with the assumption of an uniform circumstellar disc to investigate how efficiently the protoplanet captures planetesimals. However, not only planetesimals but also disc ga…
Sufficiently massive growing giant planets have circumplanetary disks, and the capture of solid bodies by the disks would likely influence the growth of the planets and formation of satellite systems around them. In addition to dust particles that are supplied to the disk with inflowing gas, recent studies suggest the importance of capture of planetesimals whose motion is decoupled from the gas, but orbital evolution of captured bodies in circumplanetary gas disks has not been studied in detail. In the present work, using three-body orbital integration and analytic calculations, we examine orb…
We analyze the dynamics of individual kilometer-size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non-linear gas drag stemming from an eccentric gas disk with a finite precession rate. We consider several precession rates and eccentricities for the gas, and compare the results with a static disk in circular orbit. The disk precession introduces three main differences with respect to the classical static case: (i) The equilibrium secular solutions generated by the gas drag are no longer fixed points i…
Planet formation begins with collisional growth of small planetesimals accumulating into larger ones. Such growth occurs while planetesimals are embedded in a gaseous protoplanetary disc. However, small-planetesimals experience collisions and gas-drag that lead to their destruction on short timescales, not allowing, or requiring fine tuned conditions for the efficient growth of $\sim$ metre-size objects. Here we show that $\sim10^{4}$ interstellar objects such as the recently detected 1I/2017-U1 ('Oumuamua) could have been captured, and become part of the young Solar System, together with up t…
Giant planet migration is an important phenomenon in the evolution of planetary systems. Recent works have shown that giant planet growth and migration can shape the asteroid belt, but these works have not considered interactions between planetesimals. We have calculated the evolution of planetesimal disks, including planetesimal-planetesimal collisions, during gas giant growth and migration. The numbers, locations, and impact velocities of these collisions depend on the specific growth and migration path. We find that giant planet growth alone has little effect on impact velocities, and most …
Massive planetary cores ($\sim 10$ Earth masses) trigger rapid gas accretion to form gas giant planets \rev{such as} Jupiter and Saturn. We investigate the core growth and the possibilities for cores to reach such a critical core mass. At the late stage, planetary cores grow through collisions with small planetesimals. Collisional fragmentation of planetesimals, which is induced by gravitational interaction with planetary cores, reduces the amount of planetesimals surrounding them, and thus the final core masses. Starting from small planetesimals that the fragmentation rapidly removes, less ma…
We present numerical simulations of terrestrial planet formation that examine the growth continuously from planetesimals to planets in the inner Solar System. Previous studies show that the growth will be inside-out, but it is still common practice to assume that the entire inner disk will eventually reach a bi-modal distribution of embryos and planetesimals. For the combinations of disk mass, initial planetesimal radius and gas disk lifetime explored in this work the entire disk never reaches a simple bi-modal mass distribution. We find that the inside-out growth is amplified by the combined …
Episodic planetesimal disruptions triggered by dissipation of gas disk
Nanjing University（南京大学）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（教育部现代天文与天体物理重点实验室，南京大学）；State Key Laboratory of Critical Earth Material Cycling and Mineral Deposits & Lunar and Planetary Science Institute, School of Earth Sciences and Engineering, Nanjing University（南京大学地球科学与工程学院关键地球物质循环与矿床国家重点实验室及月球与行星科学研究所）；CAS Center for Excellence in Comparative Planetology（中国科学院比较行星学卓越创新中心）
Planetesimal belts are invoked to explain the prolonged existence of debris disks. Important parameters to model their collisional evolution and to compute the dust production rate are the intrinsic probability of collision $P_i$ and the mean impact velocity $U_c$. If a planet orbits close to the belt, the values of both these parameters are affected by its secular perturbations yielding a strong correlation between eccentricity $e$ and pericentre longitude $\varpi$. We adopt a new algorithm to compute both $P_i$ and $U_c$ in presence of various levels of secular correlation due to different r…
We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implement…
We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the mid-plane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebble-to-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten…
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust t…
Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a dead zone. In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism. We improve upon the previous study of the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. We performed 1D diffusion-advection simulations of drifting pebbles…
The collapse of dust particle clouds directly to km-sized planetesimals is a promising way to explain the formation of planetesimals, asteroids and comets. In the past, this collapse has been studied in stratified shearing box simulations with super-solar dust-to-gas ratio ε, allowing for streaming instability (SI) and gravitational collapse. This paper studies the non-stratified SI under dust-to-gas ratios from ε=0.1 up to ε=1000 without self-gravity. The study covers domain sizes of L=0.1 H, 0.01 H and 0.001 H, in terms of gas disk scale height H, using the PencilCode. They are performed in …
According to the sequential accretion model, giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. In order to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. We compute the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more dif…
Planetesimal formation stage represents a major gap in our understanding of the planet formation process. The late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution while the dust evolution models predict that planetesimal formation is only possible at some orbital distances. We want to test the importance of water snow line for triggering formation of the first planetesimals during the gas-rich phase of protoplanetary disk, when cores of giant planets have to form. We connect prescriptions for gas disk evolution, dust growth and fr…
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Re…
Accumulation of dust and ice particles into planetesimals is an important step in the planet formation process. Planetesimals are the seeds of both terrestrial planets and the solid cores of gas and ice giants forming by core accretion. Left-over planetesimals in the form of asteroids, trans-Neptunian objects and comets provide a unique record of the physical conditions in the solar nebula. Debris from planetesimal collisions around other stars signposts that the planetesimal formation process, and hence planet formation, is ubiquitous in the Galaxy. The planetesimal formation stage extends fr…
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 di…
Most detected planet-bearing binaries are in wide orbits, for which a high inclination, $i_B$, between the binary orbital plane and the plane of the planetary disk around the primary is likely to be common. In this paper, we investigate the intermediate stages - from planetesimals to planetary embryos/cores - of planet formation in such highly inclined cases. Our focus is on the effects of gas drag on the planetesimals' orbital evolution, in particular on the evolution of the planetesimals' semimajor axis distribution and their mutual relative velocities. We first demonstrate that a non-evolvi…
