Planetesimals In Protoplanetary Disks Research Articles

Surviving the heat: multiwavelength analysis of V883 Ori reveals that dust aggregates survive the sublimation of their ice mantles

ABSTRACT Investigating the response of icy dust aggregates to water ice sublimation is essential for understanding the formation and properties of planetesimals in protoplanetary discs. However, their fate remains unclear, as previous studies suggest that aggregates could either survive or completely fall apart to (sub)μm-sized grains. Protoplanetary discs around stars undergoing accretion outbursts represent a unique laboratory to study the ice sublimation process, as the water snowline is pushed outward to regions accessible to current observatories. In this work, we aim to understand the aggregates’ response to ice sublimation by focusing on V883 Ori, a system currently undergoing a powerful accretion outburst. We present new analysis of archival high-resolution ALMA observations of the protoplanetary disc of V883 Ori at 0.88, 1.3, 2.0, and 3.1 mm, and derive new radial spectral index profiles, which we compare with predictions from one-dimensional dust evolution simulations. In the region of V883 Ori where water ice has sublimated, we find lower spectral indices than previously obtained, indicating the presence of cm-sized particles. Coupled with our dust evolution models, we find that the only way to explain their presence is to assume that they formed before the outburst and survived the sublimation process. The resilience of dust aggregates to such intense events leads us to speculate that it may extend to other environments with more gentle heating, such as pebbles drifting through the water snowline in quiescent protoplanetary discs. In that case, it may alter the formation pathway of dry planetesimals interior to the snowline.

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.

Binaries are softer than they seem: effects of an external potential on the scattering dynamics of binaries

ABSTRACT Binary evolution is influenced by dynamical scattering with other stars in dense environments. Heggie’s law states that, due to their environments, hard binaries (whose orbital energy surpasses the typical energy of single stars) tend to harden (increase their orbital energy), while soft binaries typically soften. Here, we show that Heggie’s law sometimes needs to be revised, by accounting for an external potential, for example, for binaries in nuclear stellar discs or active galactic nucleus discs, that are affected by the central massive black hole, or binary planetesimals in protoplanetary discs, affected by the host star. We find that in such environments, where the Hill radius is finite, binary-single scattering can have different outcomes. In particular, a three-body encounter could be cut short due to stars being ejected beyond the Hill radius, thereby ceasing to participate in further close interactions. This leads to a systematic difference in the energy changes brought about by the encounter, and in particular slows binary hardening, and even causes some hard binaries to soften, on average, rather than harden. We use our previously derived analytical, statistical solution to the bound chaotic three-body problem to quantitatively characterise the revision of the hardening-softening phase transition and evolution of binaries. We also provide an analytical calculation of the mean hardening rate of binaries in any environment (also reproducing the results of detailed N-body simulations). We show that the latter exhibits a non-trivial dependence on the Hill radius induced by the environment.

A close-encounter method for simulating the dynamics of planetesimals

The dynamics of planetesimals plays an important role in planet formation because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in the gaseous environment of protoplanetary discs, their orbits are nearly circular and planar due to the effect of gas drag. However, mutual close encounters of the planetesimals increase eccentricities and inclinations until an equilibrium between stirring and damping is reached. After disc dissipation there is no more gas that damps the motion and mutual close encounters as well as encounters with planets stir the orbits again. After disc dissipation there is no gas that can damp the motion, and mutual close encounters and encounters with planets can stir the orbits. The large number of planetesimals in protoplanetary discs makes it difficult to simulate their dynamics by means of directN-body simulations of planet formation. Therefore, we developed a novel method for the dynamical evolution of planetesimals that is based on following close encounters between planetesimal-mass bodies and gravitational stirring by planet-mass bodies. To separate the orbital motion from the close encounters we employ a Hamiltonian splitting scheme, as used in symplecticN-body integrators. Close encounters are identified using a cell algorithm with linear scaling in the number of bodies. A grouping algorithm is used to create small groups of interacting bodies which are integrated separately. Our method can simulate a large number of planetesimals interacting through gravity and collisions at low computational cost. The typical computational time is of the order of minutes or hours, up to a few days for more complex simulations, compared to several hours or even weeks for the same setup with fullN-body. The dynamical evolution of the bodies is sufficiently well reproduced. This will make it possible to study the growth of planetesimals through collisions and pebble accretion coupled to their dynamics for a much larger number of bodies than previously accessible with fullN-body simulations.

Secular Gravitational Instability of Drifting Dust in Protoplanetary Disks: Formation of Dusty Rings without Significant Gas Substructures

Abstract Secular gravitational instability (GI) is one promising mechanism for creating annular substructures and planetesimals in protoplanetary disks. We perform numerical simulations of secular GI in a radially extended disk with inwardly drifting dust grains. The results show that, even in the presence of dust diffusion, dust rings form via secular GI while the dust grains are moving inward, and the dust surface density increases by a factor of 10. Once secular GI develops into a nonlinear regime, the total mass of the resultant rings can be a significant fraction of the dust disk mass. In this way, a large amount of drifting dust grains can be collected in the dusty rings and stored for planetesimal formation. In contrast to the emergence of remarkable dust substructures, secular GI does not create significant gas substructures. This result indicates that observations of a gas density profile near the disk midplane enable us to distinguish the mechanisms for creating the annular substructures in the observed disks. The resultant rings start decaying once they enter the inner region stable to secular GI. Because the ring-gap contrast smoothly decreases, it seems possible that the rings are observed even in the stable region. We also discuss the likely outcome of the nonlinear growth and indicate the possibility that a significantly developed region of secular GI may appear as a gap-like substructure in dust continuum emission as dust growth into larger solid bodies and planetesimal formation reduce the total emissivity.

Physical models of streaming instabilities in protoplanetary discs

ABSTRACT We develop simple, physically motivated models for drag-induced dust–gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary discs. The models explain, based on the physics of gaseous epicyclic motion and dust–gas drag forces, the most important features of the streaming instability and its simple generalization, the disc settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas mass ratio surpasses one, the slow growth rate of the streaming instability compared to the settling instability for smaller grains, and the main physical processes underlying the growth of the most unstable modes in different regimes. As well as providing helpful simplified pictures for understanding the operation of an interesting and fundamental astrophysical fluid instability, our models may prove useful for analysing simulations and developing non-linear theories of planetesimal growth in discs.

The aeolian-erosion barrier for the growth of metre-size objects in protoplanetary discs

ABSTRACT Aeolian erosion is a destructive process that 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 discs small bodies ($10\!-\!10^4 \, \rm {m}$) are highly susceptible to gas-drag aeolian erosion. At this size-range aeolian erosion can efficiently erode the planetesimals down to tens-cm size and quench any further growth of such small bodies. It thereby raises potential difficulties for channels suggested to alleviate the metre-size barrier. Nevertheless, the population of ∼decimetre-size cobbles resulting from aeolian erosion might boost the growth of larger (>km size) planetesimals and planetary embryos through increasing the efficiency of pebble-accretion, once/if such large planetesimals and planetary embryos exist in the disc.

The tensile strength of dust aggregates consisting of small elastic grains: constraints on the size of condensates in protoplanetary discs

ABSTRACT A consensus view on the formation of planetesimals is now exposed to a threat, since recent numerical studies on the mechanical properties of dust aggregates tend to dispute the conceptual picture that submicrometer-sized grains conglomerate into planetesimals in protoplanetary discs. With the advent of precise laboratory experiments and extensive computer simulations on the interaction between elastic spheres comprising dust aggregates, we revisit a model for the tensile strength of dust aggregates consisting of small elastic grains. In the framework of contact mechanics and fracture mechanics, we examine outcomes of computer simulations and laboratory experiments on the tensile strength of dust aggregates. We provide a novel analytical formula that explicitly incorporates the volume effect on the tensile strength, namely, the dependence of tensile strength on the volume of dust aggregates. We find that our model for the tensile strength of dust aggregates well reproduces results of computer simulations and laboratory experiments, if appropriate values are adopted for the elastic parameters used in the model. Moreover, the model with dust aggregates of submicrometer-sized grains is in good harmony with the tensile strength of cometary dust and meteoroids derived from astronomical observations. Therefore, we reaffirm the commonly believed idea that the formation of planetesimals begins with conglomeration of submicrometer-sized grains condensed in protoplanetary discs.

Unknotting of quasi-two-dimensional ferrogranular networks by in-plane homogeneous magnetic fields

Our ongoing research addresses, by means of experiments and computer simulations, the aggregation process that takes place in a shaken granular mixture of glass and magnetized ferrous alloy beads when the shaking amplitude is suddenly decreased. After this quenching, the magnetized beads form a transient network that coarsens in time into compact clusters, following a viscoelastic phase separation. Here we focus on the quasi-two-dimensional case, analyzing in computer simulations the effects of a magnetic field parallel to the system plane. Our results evidence that the field drastically changes the structure of the forming network: chains and elongated clusters parallel to the field are favored whereas perpendicular connecting structures tend to be suppressed, leading to the unknotting of the networks which are observed at zero field. Importantly, we found that moderate field strengths lead to the formation of larger clusters at intermediate time intervals than in the case of weak and strong fields. Moreover, the latter tend to limit the overall growth of the clusters at longer time scales. These results may be relevant in different systems governed by similar magnetically driven aggregation processes as, for example, in the formation of iron-rich planetesimals in protoplanetary discs or for magnetic separation systems.

Revealing the dust grain size in the inner envelope of the Class I protostar Per-emb-50

Context. A good constraint of when the growth of dust grains from sub-micrometer to millimeter sizes occurs, is crucial for planet formation models. This provides the first step towards the production of pebbles and planetesimals in protoplanetary disks. Currently, it is well established that Class II objects have large dust grains. However, it is not clear when in the star formation process this grain growth occurs. Aims. We use multi-wavelength millimeter observations of a Class I protostar to obtain the spectral index of the observed flux densities αmm of the unresolved disk and the surrounding envelope. Our goal is to compare our observational results with visibility modeling at both, 1.3 and 2.7 mm simultaneously. Methods. We present data from NOEMA at 2.7 mm and SMA at 1.3 mm of the Class I protostar, Per-emb-50. We model the dust emission with a variety of parametric and radiative-transfer models to deduce the grain size from the observed emission spectral index. Results. We find a spectral index in the envelope of Per-emb-50 of αenv = 3.3 ± 0.3, similar to the typical ISM values. The radiative-transfer modeling of the source confirms this value of αenv with the presence of dust with a amax ≤ 100 μm. Additionally, we explore the backwarming effect, where we find that the envelope structure affects the millimeter emission of the disk. Conclusions. Our results reveal grains with a maximum size no larger than 100 μm in the inner envelope of the Class I protostar Per-emb-50, providing an interesting case to test the universality of millimeter grain growth expected in these sources.

Are Pebble Pile Planetesimals Doomed?

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 extrapolation of erosion thresholds from verified to currently still unknown values at the conditions of planetesimals in protoplanetary discs. We apply our results to the stability of planetesimals. In inner regions of protoplanetary discs, pebble pile planetesimals below a certain size are not stable but will be disassembled by a head wind.

Diffusion and Concentration of Solids in the Dead Zone of a Protoplanetary Disk

Abstract The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the mid-plane needs to be efficient, and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the mid-plane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment, we use the local-shearing-box approximation to simulate a particle-gas system with an Ohmic dead zone including mutual drag force between the gas and the solids. We systematically compare the evolution of the system with ideal or non-ideal MHD, with or without backreaction drag force from particles on gas, and with varying solid abundances. Similar to previous investigations of dead-zone dynamics, we find that particles of dimensionless stopping time do not sediment appreciably more than those in ideal magnetorotational turbulence, resulting in a vertical scale height an order of magnitude larger than in a laminar disk. Contrary to the expectation that this should curb the formation of planetesimals, we nevertheless find that strong clumping of solids still occurs in the dead zone when solid abundances are similar to the critical value for a laminar environment. This can be explained by the weak radial diffusion of particles near the mid-plane. The results imply that the sedimentation of particles to the mid-plane is not a necessary criterion for the formation of planetesimals by the streaming instability.

Small-N collisional dynamics – IV. Order in the realm of not-so-small-N

In this paper, the fourth in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and interactions that produce direct collisions between any two particles. Our long-term goal is to predict the probability of a given collision event occurring over the course of an interaction, as a function of the numbers and properties of the particles. In previous papers, we varied the number of interacting particles, as well as the distributions of particle radii and masses. Here, we refine the methods developed in these preceding studies, and arrive at a final and robust methodology that can be used to study collisional dynamics in a variety of astrophysical contexts, ranging from stars in star clusters, galaxies in galaxy groups and clusters and even the collisional growth of planetesimals in protoplanetary disks. We further present and refine the concept of a Collision Rate Diagram (CRD), the primary tool we use to quantify the relative rates for different collision scenarios to occur. The agreement between our final theoretical model and the results of numerical scattering simulations is excellent.

Planetesimal formation near the snowline: in or out?

The formation of planetesimals in protoplanetary disks is not well-understood. Streaming instability is a promising mechanism to directly form planetesimals from pebble-sized particles, provided a high enough solids-to-gas ratio. However, local enhancements of the solids-to-gas ratio are difficult to realize in a smooth disk, which motivates the consideration of special disk locations such as the snowline. In this article we investigate the viability of planetesimal formation by streaming instability near the snowline due to water diffusion and condensation. We adopt a viscous disk model, and numerically solve the transport equations for vapor and solids on a cylindrical, 1D grid. We take into account radial drift of solids, gas accretion on to the central star, and turbulent diffusion. We study the importance of the back-reaction of solids on the gas and of the radial variation of the mean molecular weight of the gas. We find that water diffusion and condensation can locally enhance the ice surface density by a factor 3--5 outside the snowline. Assuming that icy pebbles contain many micron-sized silicate grains that are released during evaporation, the enhancement is increased by another factor $\sim$$2$. In this `many-seeds' model, the solids-to-gas ratio interior to the snowline is enhanced as well, but not as much as just outside the snowline. In the context of a viscous disk, the diffusion-condensation mechanism is most effective for high values of the turbulence parameter $\alpha$ ($10^{-3}$--$10^{-2}$). Therefore, assuming young disks are more vigorously turbulent than older disks, planetesimals near the snowline can form in an early stage of the disk. In highly turbulent disks, tens of Earth masses can be stored in an annulus outside the snowline, which can be identified with recent ALMA observations.

Prometheus Induced Vorticity in Saturn’s F Ring

Saturns rings are known to show remarkable real time variability in their structure. Many of which can be associated to interactions with nearby moons and moonlets. Possibly the most interesting and dynamic place in the rings, probably in the whole Solar System, is the F ring. A highly disrupted ring with large asymmetries both radially and azimuthally. Numerically non zero components to the curl of the velocity vector field (vorticity) in the perturbed area of the F ring post encounter are witnessed, significantly above the background vorticity. Within the perturbed area rich distributions of local rotations is seen located in and around the channel edges. The gravitational scattering of ring particles during the encounter causes a significant elevated curl of the vector field above the background F ring vorticity for the first 1-3 orbital periods post encounter. After 3 orbital periods vorticity reverts quite quickly to near background levels. This new found dynamical vortex life of the ring will be of great interest to planet and planetesimals in proto-planetary disks where vortices and turbulence are suspected of having a significant role in their formation and migrations. Additionally, it is found that the immediate channel edges created by the close passage of Prometheus actually show high radial dispersions in the order ~20-50 cm/s, up to a maximum of 1 m/s. This is much greater than the value required by Toomre for a disk to be unstable to the growth of axisymmetric oscillations. However, an area a few hundred km away from the edge shows a more promising location for the growth of coherent objects.

THE MASS AND SIZE DISTRIBUTION OF PLANETESIMALS FORMED BY THE STREAMING INSTABILITY. I. THE ROLE OF SELF-GRAVITY

ABSTRACT We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the Athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the Athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power law, , with , which equates to a differential size distribution of , with . We find no significant trends with resolution from a convergence study of up to 5123 grid zones and particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time ), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.

Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks

Planetesimals in gaseous protoplanetary disks may grow by collecting dust particles. Hydrodynamical studies show that small particles generally avoid collisions with the planetesimals because they are entrained by the flow around them. This occurs when $St$, the Stokes number, defined as the ratio of the dust stopping time to the planetesimal crossing time, becomes much smaller than unity. However, these studies have been limited to the laminar case, whereas these disks are believed to be turbulent. We want to estimate the influence of gas turbulence on the dust-planetesimal collision rate and on the impact speeds. We used three-dimensional direct numerical simulations of a fixed sphere (planetesimal) facing a laminar and turbulent flow seeded with small inertial particles (dust) subject to a Stokes drag. A no-slip boundary condition on the planetesimal surface is modeled via a penalty method. We find that turbulence can significantly increase the collision rate of dust particles with planetesimals. For a high turbulence case (when the amplitude of turbulent fluctuations is similar to the headwind velocity), we find that the collision probability remains equal to the geometrical rate or even higher for $St\geq 0.1$, i.e., for dust sizes an order of magnitude smaller than in the laminar case. We derive expressions to calculate impact probabilities as a function of dust and planetesimal size and turbulent intensity.

Secular diffusion in discrete self-gravitating tepid discs II. Accounting for swing amplification via the matrix method

The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is investigated using the inhomogeneous Balescu-Lenard equation expressed in terms of angle-action variables. The matrix method is implemented numerically in order to model the induced gravitational polarization. Special care is taken to account for the amplification of potential fluctuations of mutually resonant orbits and the unwinding of the induced swing amplified transients. Quantitative comparisons with ${N-}$body simulations yield consistent scalings with the number of particles and with the self-gravity of the disc: the fewer particles and the colder the disc, the faster the secular evolution. Secular evolution is driven by resonances, but does not depend on the initial phases of the disc. For a Mestel disc with ${Q \sim 1.5}$, the polarization cloud around each star boosts up its secular effect by a factor of the order of a thousand or more, promoting accordingly the dynamical relevance of self-induced collisional secular evolution. The position and shape of the induced resonant ridge are found to be in very good agreement with the prediction of the Balescu-Lenard equation, which scales with the square of the susceptibility of the disc. In astrophysics, the inhomogeneous Balescu-Lenard equation may describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic centre. It could be used as a valuable check of the accuracy of ${N-}$body integrators over secular timescales.

Planetesimal formation in self-gravitating discs – dust trapping by vortices

The mechanism through which meter-sized boulders grow to km-sized planetesimals in protoplanetary discs is a subject of active research, since it is critical for planet formation. To avoid spiralling into the protostar due to aerodynamic drag, objects must rapidly grow from cm-sized pebbles, which are tightly coupled to the gas, to large boulders of 1-100m in diameter. It is already well known that over-densities in the gaseous component of the disc provide potential sites for the collection of solids, and that significant density structures in the gaseous component of the disc (e.g., spiral density waves) can trap solids efficiently enough for the solid component of the disc to undergo further gravitational collapse due to their own self-gravity. In this work, we employ the PENCIL CODE to conduct local shearing sheet simulations of massive self-gravitating protoplanetary discs, to study the effect of anticyclonic transient vortices, or eddies, on the evolution of solids in these discs. We find that these types of structures are extremely efficient at concentrating small and intermediate-sized dust particles with friction times comparable to, or less than, the local orbital period of the disc. This can lead to significant over-densities in the solid component of the disc, with density enhancements comparable to, and even higher, than those within spiral density waves; increasing the rate of gravitational collapse of solids into bound structures.

Secular diffusion in discrete self-gravitating tepid discs

The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When applied to the secular evolution of an isolated stationary self-gravitating Mestel disc, this formalism predicts initially the importance of the corotation resonance in the inner regions of the disc leading to a regime involving radial migration and heating. It predicts in particular the formation of a "ridge like" feature in action space, in agreement with simulations, but over-estimates the timescale involved in its appearance. Swing amplification is likely to resolve this discrepancy. In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit may also describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic center.