Bodies In Protoplanetary Disks Research Articles

The dissolution of planetesimals in electrostatic fields

ABSTRACT Planetesimals or smaller bodies in protoplanetary discs are often considered to form as pebble piles in current planet formation models. They are supposed to be large but loose, weakly bound clusters of more robust dust aggregates. This makes them easy prey for destructive processes. In microgravity experiments, we apply strong electric fields on clusters of slightly conductive dust aggregates. We find that this generates enough tensile stress on the fragile clusters to sequentially rip off the aggregates from the cluster. These experiments imply that electric fields in protoplanetary discs can dissolve pebble pile planetesimals. This process might induce a bias for the local planetesimal reservoir in regions with strong fields. Planetesimals prevail with certain kinds of compositions where they are either good isolators or compacted bodies. The less lucky ones generate pebble clouds that might be observable as signposts of electrostatic activity in protoplanetary discs.

Drag forces on porous aggregates in protoplanetary disks

Context. In protoplanetary disks, particle–gas interactions are a key part of the early stages of pre-planetary evolution. As dust particles grow into porous aggregates, treating drag forces of aggregates in the same way as those of monolithic compact spheres has always been an approximation. Aims. The substructures and building blocks of aggregates may respond differently to different drag regimes than the overall size of the porous body would suggest. The influence of porosity and substructure size on the drag on porous bodies is studied. Methods. We measured centimeter-sized porous aggregates with volume filling factors as low as ~10−4 for the first time in low-pressure wind tunnel experiments. Various substructures of different sizes down to micrometer (μm) resolution are tested. Knudsen numbers for the centimeter-sized superstructure are between 0.005 and 0.1 and Reynolds numbers are between 5 and 130. Results. We find that bodies are subject to increasingly large drag forces with increasing porosity, significantly larger than previously thought. In the parameter range measured, drag can increase by a factor of 23, and extrapolation suggests even larger values. We give an empirically determined model for an adjusted drag force. Conclusions. Our findings imply that the coupling of highly porous bodies in protoplanetary disks is significantly stronger than assumed in previous works. This decreases collision velocities and radial drift speeds and might allow porous bodies to grow larger under certain conditions before they become compacted.

New Growth Mechanism of Dust Grains in Protoplanetary Disks with Magnetically Driven Disk Winds

Abstract We discovered a new growth mode of dust grains to kilometer-size bodies in protoplanetary disks that evolve via viscous accretion and magnetically driven disk winds (MDWs). We solved an approximate coagulation equation of dust grains with time-evolving disks that consist of both gas and solid components using a one-dimensional model. With grain growth, all solid particles initially drift inward toward the central star due to the gas drag force. However, the radial profile of gas pressure, P, is modified by the MDW that disperses the gas in an inside-out manner. Consequently, a local concentration of solid particles is created by the converging radial flux of drifting dust grains at the location with a convex-upward profile of P. When the dimensionless stopping time, St, exceeds unity there, the solid particles spontaneously reach the growth-dominated state because of the positive feedback between the suppressed radial drift and the enhanced accumulation of dust particles that drift from the outer part. Once the solid particles are in the drift-limited state, the above-mentioned condition of St for dust growth is equivalent to Σd/Σg ≳ η, where Σd/Σg is the dust-to-gas surface-density ratio and η is the dimensionless radial pressure-gradient force. As a consequence of the successful growth of dust grains, a ring-like structure containing planetesimal-size bodies is formed at the inner part of the protoplanetary disks. Such a ring-shaped concentration of planetesimals is expected to play a vital role in the subsequent planet formation.

Dust dynamics in 2D gravito-turbulent discs

The dynamics of solid bodies in protoplanetary disks are subject to the properties of any underlying gas turbulence. Turbulence driven by disk self-gravity shows features distinct from those driven by the magnetorotational instability (MRI). We study the dynamics of solids in gravito-turbulent disks with two-dimensional (in the disk plane), hybrid (particle and gas) simulations. Gravito-turbulent disks can exhibit stronger gravitational stirring than MRI-active disks, resulting in greater radial diffusion and larger eccentricities and relative speeds for large particles (those with dimensionless stopping times $t_{stop} \Omega > 1$, where $\Omega$ is the orbital frequency). The agglomeration of large particles into planetesimals by pairwise collisions is therefore disfavored in gravito-turbulent disks. However, the relative speeds of intermediate-size particles $t_{stop} \Omega \sim 1$ are significantly reduced as such particles are collected by gas drag and gas gravity into coherent filament-like structures with densities high enough to trigger gravitational collapse. First-generation planetesimals may form via gravitational instability of dust in marginally gravitationally unstable gas disks.

Radiative forces on macroscopic porous bodies in protoplanetary disks: laboratory experiments

In optically thin parts of protoplanetary disks photophoresis is a significant force not just for dust grains, but also for macroscopic bodies. The absolute strength on the supposedly highly porous objects is not known in detail as yet. We set up a low pressure torsion balance and studied photophoretic forces. We investigated the dependence on plate dimensions and on ambient pressure and considered the influence of channels through the plates. As samples for full (no channel) plates we used tissue with 2mm thickness and circular shape with diameters of 10mm, 30mm and 50mm. The influence of channels was probed on rectangular-shaped circuit boards of 35mm x 35mm area and 1.5mm thickness. The number of channels was 169 and 352. At low pressure, the absolute photophoretic force is proportional to the cross section of the plates. At high pressure, gas flow through the channels enhances the photophoretic force. The pressure dependence of the radiative force can (formally) be calculated by photophoresis on particles with a characteristic length. We derived two characteristic length scales l depending on the plate radius r_1, the channel radius r_2, and the thickness of the plate which equals the length of the channel d as l=r^{0.35} x d^{0.65}. The highest force is found at a pressure p_max = 15 x l^{-1}Pa mm. In total, the photophoretic force on a plate with channels can be well described by a superposition of the two components: photophoresis due to the overall size and cross section of the plate and photophoresis due to the channels, both with their characteristic pressure dependencies. We applied these results to the transport of large solids in protoplanetary disks and found that the influence of porosity on the photophoretic force can reverse the inward drift of large solids, for instance meter-sized bodies, and push them outward within the optically thin parts of the disk.

COLLIDING DECIMETER DUST

Collisional evolution is a key process in planetesimal formation and decimetre bodies play a key role in the different models. However, the outcome of collisions between two dusty decimetre bodies has never been studied experimentally. Therefore, we carried out microgravity collision experiments in the Bremen drop tower. The agglomerates consist of quartz with irregularly shaped micrometre-sized grains and the mean volume filling factor is 0.437 $\pm$ 0.004. The aggregates are cylindrical with 12 cm in height and 12 cm in diameter and typcial masses are 1.5 kg. These are the largest and most massive dust aggregates studied in collisions to date. We observed rebound and fragmentation but no sticking in the velocity range between 0.8 and 25.7 cm s$^{-1}$. The critical fragmentation velocity for split up of an aggregate is 16.2 $\pm$ 0.4 cm s$^{-1}$. At lower velocities the aggregates bounce of each other. In this velocity range the coefficient of restitution decreases with increasing collision velocity from 0.8 to 0.3. While the aggregates are very weak the critical specific kinetic energy for fragmentation $Q_{\mu =1}$ is a factor 6 larger than expected. Collisions of large bodies in protoplanetary discs are supposed to be much faster and the generation of smaller fragments is likely. In planetary rings collision velocities are of the order of a few cm s$^{-1}$ and are thereby in the same range investigated in these experiments. The coefficient of restitution of dust agglomerates and regolith covered ice particles, which are common in planetary rings, are similar.

Experiments on centimeter-sized dust aggregates and their implications for planetesimal formation

The first macroscopic bodies in protoplanetary disks are dust aggregates. We report on a number of experimental studies with dust aggregates formed from micron-size quartz grains. We confirm in laboratory collision experiments an earlier finding that producing macroscopic bodies by the random impact of sub-mm aggregates results in a well-defined upper-filling factor of 0.31 \pm 0.01. Compared to earlier experiments, we increase the projectile mass by about a factor of 100. The collision experiments also show that a highly porous dust-aggregate can retain its highly porous core if collisions get more energetic and a denser shell forms on top of the porous core. We measure the mechanical properties of cm-sized dust samples of different filling factors between 0.34 and 0.50. The tensile strength measured by a Brazilian test, varies between 1 kPa and 6 kPa. The sound speed is determined by a runtime measurement to range between 80 m/s and 140 m/s while Young's modulus is derived from the sound speed and varies between 7MPa and 25MPa. The samples were also subjected to quasi-static omni- and uni-directional compression todetermine their compression strengths and flow functions. Applied to planet formation, our experiments provide basic data for future simulations, explain the specific collisional outcomes observed in earlier experiments, and in general support a scenario where collisional growth of planetesimals is possible.

MODELING MAGNETOROTATIONAL TURBULENCE IN PROTOPLANETARY DISKS WITH DEAD ZONES

Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive "dead zone" of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure of turbulence is well characterized by the vertical magnetic flux and three critical heights derived from the linear analysis of MRI in a stratified disk. In particular, the turbulent structure depends on the resistivity profile only through the critical heights and is insensitive to the details of the resistivity profile. We discover scaling relations between the amplitudes of various turbulent quantities (velocity dispersion, density fluctuation, vertical diffusion coefficient, and outflow mass flux) and vertically integrated accretion stresses. We also obtain empirical formulae for the integrated accretion stresses as a function of the vertical magnetic flux and the critical heights. These empirical relations allow to predict the vertical turbulent structure of a protoplanetary disk for a given strength of the magnetic flux and a given resistivity profile.

Decimetre dust aggregates in protoplanetary discs

The growth of planetesimals is an essential step in planet formation. Decimetre-size dust agglomerates mark a transition point in this growth process. In laboratory experiments we simulated the formation, evolution, and properties of decimetre-scale dusty bodies in protoplanetary discs. Small sub-mm size dust aggregates consisting of micron-size SiO$_2$ particles randomly interacted with dust targets of varying initial conditions in a continuous sequence of independent collisions. Impact velocities were 7.7 m/s on average and in the range expected for collisions with decimetre bodies in protoplanetary discs. The targets all evolved by forming dust \emph{crusts} with up to several cm thickness and a unique filling factor of 31% $\pm$3%. A part of the projectiles sticks directly. In addition, some projectile fragments slowly return to the target by gravity. All initially porous parts of the surface, i.e. built from the slowly returning fragments, are compacted and firmly attached to the underlying dust layers by the subsequent impacts. Growth is possible at impact angles from 0$^{\circ}$ (central collision) to 70$^{\circ}$. No growth occurs at steeper dust surfaces. We measured the velocity, angle, and size distribution of collision fragments. The average restitution coefficient is 3.8% or 0.29 m/s ejection velocity. Ejecta sizes are comparable to the projectile sizes. The high filling factor is close to the most compact configuration of dust aggregates by local compression ($\sim 33$%). This implies that the history of the surface formation and target growth is completely erased. In view of this, the filling factor of 31% seems to be a universal value in the collision experiments of all self-consistently evolving targets at the given impact velocities. We suggest that decimetre and probably larger bodies can simply be characterised by one single filling factor.

The Growth Mechanisms of Macroscopic Bodies in Protoplanetary Disks

The formation of planetesimals, the kilometer-sized planetary precursors, is still a puzzling process. Considerable progress has been made over the past years in the physical description of the first stages of planetesimal formation, owing to extensive laboratory work. This review examines the experimental achievements and puts them into the context of the dust processes in protoplanetary disks. It has become clear that planetesimal formation starts with the growth of fractal dust aggregates, followed by compaction processes. As the dust-aggregate sizes increase, the mean collision velocity also increases, leading to the stalling of the growth and possibly to fragmentation, once the dust aggregates have reached decimeter sizes. A multitude of hypotheses for the further growth have been proposed, such as very sticky materials, secondary collision processes, enhanced growth at the snow line, or cumulative dust effects with gravitational instability. We will also critically review these ideas.

Eolian Erosion of Dusty Bodies in Protoplanetary Disks

We discuss the possibility of the erosion of dusty bodies in protoplanetary disks by a subsonic laminar gas flow. Our analysis is based on wind tunnel experiments on centimeter-size dust targets in an air gas flow of 63 m s-1 at static gas pressures between 0.1 and 4.5 mbar. We compare the results to numerical calculations of gas flow through porous bodies and the resulting drag force on dust aggregates at the surface. Our studies imply that a dusty body can be efficiently eroded if the dynamic gas pressure of the surface flow exceeds gravity and/or cohesion. In protoplanetary disks, we find that objects on circular orbits might be relatively safe against erosion in a laminar gas flow even in a dense disk. However, if a body is stirred up to an eccentric orbit, its motion relative to the gas increases. Such objects can be significantly eroded if they consist of dust. As an extreme, a 100 m body with the rather low eccentricity of an Earth orbit might be eroded in a single orbit. This effect leads to a bias for planetesimals in low-eccentricity orbits, as objects with large eccentricities are destroyed more easily. Erosion of bodies in high-eccentricity orbits, and reaccretion of the dust aggregates by low-eccentricity planetesimals, might provide a special growth mode of planetesimals and protoplanets.