We investigate the possibility of erosion of planetesimals in a protoplanetary disk. We use theory and direct numerical simulations (Lattice Boltzmann Method) to calculate the erosion of large -- much larger than the mean-free-path of gas molecules -- bodies of different shapes in flows. We find that erosion follows a universal power-law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about hundred years) erodes away if the semi-major axis of their orbit lies in the inner disk -- less than about $10$ au. Even planetesimals in circular orbits erode away in approximately ten thousand years if the semi-major axis of their orbits are $\lessapprox 0.6$au.
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 e…
Detections of planets in eccentric, close (separations of ~20 AU) binary systems such as αCen or γCep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities resulting in destruction, rather than growth, of objects with sizes of up to several hundred km in collisions of similar-size bodies. It was recently suggested that gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disk…
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…
Models for the steady state collisional evolution of low eccentricity planetesimal belts identify debris disks with hot dust at 1AU, like eta Corvi and HD69830, as anomalous since collisional processing should have removed most of the planetesimal mass over their >1 Gyr lifetimes. This paper looks at the effect of large planetesimal eccentricities (e>>0.3) on their collisional lifetime and the amount of mass that can remain at late times M_{late}. For an axisymmetric planetesimal disk with common pericentres and eccentricities e, we find that M_{late} \propto e^{-5/3}(1+e)^{4/3}(1-e)^{-3}. For…
About $20\%$ of exoplanets discovered by radial velocity surveys reside in stellar binaries. To clarify their origin one has to understand the dynamics of planetesimals in protoplanetary disks within binaries. The standard description, accounting for only gas drag and gravity of the companion star has been challenged recently, as the gravity of the protoplanetary disk was shown to play a crucial role in planetesimal dynamics. An added complication is the tendency of protoplanetary disks in binaries to become eccentric, giving rise to additional excitation of planetesimal eccentricity. Here, fo…
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…
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…
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…
Context: Since circumstellar dust in debris disks is short-lived, dust-replenishing requires the presence of a reservoir of planetesimals. These planetesimals in the parent belt of debris disks orbit their host star and continuously supply the disk with fine dust through their mutual collisions. Aims: We aim to understand effects of different collisional parameters on the observational appearance of eccentric debris disks. Methods: The collisional evolution of selected debris disk configurations was simulated with the numerical code ACE. Subsequently, selected observable quantities are simulat…
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-…
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…
Terrestrial planets are believed to be formed via giant impacts of Mars-sized protoplanets. Planets formed via giant impacts have highly eccentric orbits. A swarm of planetesimals around the planets may lead to eccentricity damping for the planets via the equipartition of random energies (dynamical friction). However, dynamical friction increases eccentricities of planetesimals, resulting in high velocity collisions between planetesimals. The collisional cascade grinds planetesimals to dust until dust grains are blown out due to radiation pressure. Therefore, the total mass of planetesimals de…
Planet formation in small-separation (~20 AU) eccentric binaries such as gamma Cephei or alpha Centauri is believed to be adversely affected by the presence of the stellar companion. Strong dynamical excitation of planetesimals by the eccentric companion can result in collisional destruction (rather than growth) of 1-100 km objects, giving rise to the "fragmentation barrier" for planet formation. We revise this issue using a novel description of secular dynamics of planetesimals in binaries, which accounts for the gravity of the eccentric, coplanar protoplanetary disk, as well as gas drag. By …
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 onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies 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. Our semi-analy…
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 disk. 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 ex…
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 Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple…
Many massive objects have been found in the outer region of the Solar system. How they were formed and evolved has not been well understood, although there have been intensive studies on accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner…
Planet formation around one component of a tight, eccentric binary system such as $γ$ Cephei (with semimajor axis around 20 AU) is theoretically challenging because of destructive high-velocity collisions between planetesimals. Despite this fragmentation barrier, planets are known to exist in such orbital configurations. Here we present a novel numerical framework for carrying out multi-annulus coagulation-fragmentation calculations of planetesimal growth, which fully accounts for the specifics of planetesimal dynamics in binaries, details of planetesimal collision outcomes, and the radial tra…
Chondrules are silicate spheroids found in meteorites, serving as important fossil records of the early solar system. In order to form chondrules, chondrule precursors must be heated to temperatures much higher than the typical conditions in the current asteroid belt. One proposed mechanism for chondrule heating is the passage through bow shocks of highly eccentric planetesimals in the protoplanetary disk in the early solar system. However, it is difficult for planetesimals to gain and maintain such high eccentricities. In this paper, we present a new scenario in which planetesimals in the ast…
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…
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…
Planets migrate due to the recoil they experience from scattering solid (planetesimal) bodies. To first order, the torques exerted by the interior and exterior disks cancel, analogous to the cancellation of the torques from the gravitational interaction with the gas (type I migration). Assuming the dispersion-dominated regime and power-laws characterized by indices α and β for the surface density and eccentricity profiles, we calculate the net torque on the planet. We consider both distant encounters and close (orbit-crossing) encounters. We find that the close and distant encounter torques ha…
We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system (TBS). The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disk. The gas disk is assumed eccentric with a constant precession rate. Gravitational interactions between the planetesimals are ignored. All bodies are assumed coplanar. A comparison with full N-body simulations shows that the map is of the order of 100 times faster, while prese…
We present the Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK), a new method for simultaneously modeling, in 3-D, the collisional and dynamical evolution of planetesimals in a debris disk with planets. SMACK can simulate azimuthal asymmetries and how these asymmetries evolve over time. We show that SMACK is stable to numerical viscosity and numerical heating over 10^7 yr, and that it can reproduce analytic models of disk evolution. We use SMACK to model the evolution of a debris ring containing a planet on an eccentric orbit. Differential precession create…
We study the final architecture of planetary systems that evolve under the combined effects of planet-planet and planetesimal scattering. Using N-body simulations we investigate the dynamics of marginally unstable systems of gas and ice giants both in isolation and when the planets form interior to a planetesimal belt. The unstable isolated systems evolve under planet-planet scattering to yield an eccentricity distribution that matches that observed for extrasolar planets. When planetesimals are included the outcome depends upon the total mass of the planets. For system masses exceeding about …
We develop an idealized dynamical model to predict the typical properties of outer extrasolar planetary systems, at radii beyond 5 AU. Our hypothesis is that dynamical evolution in outer planetary systems is controlled by a combination of planet-planet scattering and planetary interactions with an exterior disk of small bodies ("planetesimals"). Using 5,000 long duration N-body simulations, we follow the evolution of three planets surrounded by a 50 Earth mass primordial planetesimal disk. For large planet masses (above that of Saturn) the influence of the disk is modest, and we recover the ob…
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…
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…
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…
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…
Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical "Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from th…
Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a …
Iapetus, the outermost regular satellite of Saturn, has a drastic albedo dichotomy and an equatorial circumferential ridge that reaches heights of 20 km and widths of 70 km. This moon is thought to have formed concurrently with Saturn, and so would have experienced an intense bombardment after its formation. The ridge, which has been inferred to be one of the most ancient features on Iapetus' surface, could reasonably be expected to have been eroded by impacts; however, it has retained long continuous sections and a nearly pristine triangular shape with ridge slopes reaching $\sim$ 40$^{\circ}…
In recent years, a number of eccentric debris belts have been observed in extrasolar systems. The most common explanation for their shape is the presence of a nearby eccentric planetary companion. The gravitational perturbation from such a companion would induce periodic eccentricity variations on the planetesimals in the belt, with a range of precession frequencies. The overall expected shape is an eccentric belt with a finite minimum width. However, several observed eccentric debris discs have been found to exhibit a narrower width than the theoretical expectation. In this paper, we study tw…
We present results from a suite of N-body simulations that follow the accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5--4.0 AU and the collisional growth is followed until the completion of planetary accretion (> 100 Myr). All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We var…
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…
Planet formation scenarios and the observed planetary dynamics in binaries pose a number of theoretical challenges, especially in what concerns circumbinary planetary systems. We explore the dynamical stirring of a planetesimal circumbinary disk in the epoch when the gas component disappears. For this purpose, following theoretical approaches by Heppenheimer (1978) and Moriwaki and Nakagawa (2004), we develop a secular theory for the dynamics of planetesimals in circumbinary disks. If the binary is eccentric and its components have unequal masses, a spiral density wave is generated, engulfing …
We study the dynamics of a vertically thin, dispersion-dominated disk of planetesimals with eccentricities $e$ and inclinations $i$ (normalized in Hill units) satisfying $e >> 1$, $i << e^{-2} << 1$. This situation may be typical for e.g. a population of protoplanetary cores in the end of the oligarchic phase of planet formation. In this regime of orbital parameters planetesimal scattering has an anisotropic character and strongly differs from scattering in thick ($i ~ e$) disks. We derive analytical expressions for the planetesimal scattering coefficients and compare them with numerical calcu…
We study planetesimal evolution in circumbinary disks, focusing on the three systems Kepler 16, 34 and 35 where planets have been discovered recently. We show that for circumbinary planetesimals, in addition to secular forcing, eccentricities evolve on a dynamical timescale, which leads to orbital crossings even in the presence of gas drag. This makes the current locations of the circumbinary Kepler planets hostile to planetesimal accretion. We then present results from simulations including planetesimal formation and dust accretion, and show that even in the most favourable case of 100% effic…
Standard models of planet formation explain how planets form in axisymmetric, unperturbed disks in single star systems. However, it is possible that giant planets could have already formed when other planetary embryos start to grow. We investigate the dynamics of planetesimals under the perturbation of a giant planet in a gaseous disk. Our aim is to understand the effect of the planet's perturbation on the formation of giant planet cores outside the orbit of the planet. We calculate the orbital evolution of planetesimals ranging from $10^{13}$ to $10^{20}$g, with a Jupiter-mass planet located …
Secular oscillations in multi-planet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This "secular chaos" readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets' properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-…
The planet candidate Fomalhaut b is bright in optical light but undetected in longer wavelengths, requiring a large, reflective dust cloud. The most recent observations find an extremely eccentric orbit (e ~ 0.8), indicating that Fomalhaut b cannot be the planet that is constraining the system's eccentric debris ring. An irregular satellite swarm around a super-Earth has been proposed, however, explaining the well-constrained debris ring requires an additional planet on an orbit that crosses that of the putative super-Earth. This paper expands upon a second theory: Fomalhaut b is a transient d…
We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about 60% - 80%. In each simulation, 3 - 4 terrestrial planets are formed inside "Jupiter" with m…
Circumbinary planetary systems recently discovered by Kepler represent an important testbed for planet formation theories. Planetesimal growth in disks around binaries has been expected to be inhibited interior to ~10 AU by secular excitation of high relative velocities between planetesimals, leading to their collisional destruction (rather than agglomeration). Here we show that gravity of the gaseous circumbinary disk in which planets form drives fast precession of both the planetesimal and binary orbits, resulting in strong suppression of planetesimal eccentricities beyond 2-3 AU and making …
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…
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）
A critical phase in the standard model for planet formation is the runaway growth phase. During runaway growth bodies in the 0.1--100 km size range (planetesimals) quickly produce a number of much larger seeds. The runaway growth phase is essential for planet formation as the emergent planetary embryos can accrete the leftover planetesimals at large gravitational focusing factors. However, torques resulting from turbulence-induced density fluctuations may violate the criterion for the onset of runaway growth, which is that the magnitude of the planetesimals' random (eccentric) motions are less…
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 …
Trans-Neptunian objects (TNOs) are icy/rocky bodies that move beyond the orbit of Neptune in a region known as the trans-Neptunian belt (or Edgeworth-Kuiper belt). In contrast to the predictions of accretion models that feature protoplanetary disk planetesimals evolving on dynamically cold orbits (with both very small eccentricities, e, and inclinations, i), in reality TNOs exhibit surprisingly wide ranges of orbital eccentricities and inclinations. Several theoretical models have addressed the origin and orbital evolution of the main dynamical classes of TNOs, but none have successfully repro…
The dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto-rotational turbulence in their natal protoplanetary gas disks. Using the local shearing box approximation, we perform numerical simulations of planetesimals moving as massless particles in a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of $α\sim 10^{-2}$, with root-mean-square density perturbations of $\sim$10%. We measure the statistical evolution of particle orbital pro…
