Formation of planetesimals

Formation of planetesimals is discussed. The following subject areas are covered: (1) nebular structure; (2) aerodynamics of the solid bodies in the nebula; (3) problems with gravitational instability; (4) particle growth by coagulation; properties of fractal aggregates; and (5) coagulation and settling of fractal aggregates

Dust retention in protoplanetary disks

Context: Protoplanetary disks are observed to remain dust-rich for up to several million years. Theoretical modeling, on the other hand, raises several questions. Firstly, dust coagulation occurs so rapidly, that if the small dust grains are not replenished by collisional fragmentation of dust aggregates, most disks should be observed to be dust poor, which is not the case. Secondly, if dust aggregates grow to sizes of the order of centimeters to meters, they drift so fast inwards, that they are quickly lost. Aims: We attempt to verify if collisional fragmentation of dust aggregates is effective enough to keep disks 'dusty' by replenishing the population of small grains and by preventing excessive radial drift. Methods: With a new and sophisticated implicitly integrated coagulation and fragmentation modeling code, we solve the combined problem of coagulation, fragmentation, turbulent mixing and radial drift and at the same time solve for the 1-D viscous gas disk evolution. Results: We find that for a critical collision velocity of 1 m/s, as suggested by laboratory experiments, the fragmentation is so effective, that at all times the dust is in the form of relatively small particles. This means that radial drift is small and that large amounts of small dust particles remain present for a few million years, as observed. For a critical velocity of 10 m/s, we find that particles grow about two orders of magnitude larger, which leads again to significant dust loss since larger particles are more strongly affected by radial drift.Comment: Letter accepted 3 July 2009, included comments of language edito

The Physics of Protoplanetesimal Dust Agglomerates. Vi. Erosion of Large Aggregates as a Source of Micrometer-Sized Particles

Observed protoplanetary disks consist of a large amount of micrometer-sized particles. Dullemond and Dominik (2005) pointed out for the first time the difficulty in explaining the strong mid-IR excess of classical T-Tauri stars without any dust-retention mechanisms. Because high relative velocities in between micrometer-sized and macroscopic particles exist in protoplanetary disks, we present experimental results on the erosion of macroscopic agglomerates consisting of micrometer-sized spherical particles via the impact of micrometer-sized particles. We find that after an initial phase, in which an impacting particle erodes up to 10 particles of an agglomerate, the impacting particles compress the agglomerate's surface, which partly passivates the agglomerates against erosion. Due to this effect the erosion halts within our error bars for impact velocities up to ~30 m/s. For larger velocities, the erosion is reduced by an order of magnitude. This outcome is explained and confirmed by a numerical model. In a next step we build an analytical disk model and implement the experimentally found erosive effect. The model shows that erosion is a strong source of micrometer-sized particles in a protoplanetary disk. Finally we use the stationary solution of this model to explain the amount of micrometer-sized particles in observational infrared data of Furlan et al. (2006)

High Velocity Dust Collisions: Forming Planetesimals in a Fragmentation Cascade with Final Accretion

In laboratory experiments we determine the mass gain and loss in central collisions between cm to dm-size SiO2 dust targets and sub-mm to cm-size SiO2 dust projectiles of varying mass, size, shape, and at different collision velocities up to ~56.5 m/s. Dust projectiles much larger than 1 mm lead to a small amount of erosion of the target but decimetre targets do not break up. Collisions produce ejecta which are smaller than the incoming projectile. Projectiles smaller than 1 mm are accreted by a target even at the highest collision velocities. This implies that net accretion of decimetre and larger bodies is possible. Independent of the original size of a projectile considered, after several collisions all fragments will be of sub-mm size which might then be (re)-accreted in the next collision with a larger body. The experimental data suggest that collisional growth through fragmentation and reaccretion is a viable mechanism to form planetesimals

Coagulation of small grains in disks: the influence of residual infall and initial small-grain content

Turbulent coagulation in protoplanetary disks is known to operate on timescale far shorter than the lifetime of the disk. In the absence of mechanisms that replenish the small dust grain population, protoplanetary disks would rapidly lose their continuum opacity-bearing dust. This is inconsistent with infrared observations of disks around T Tauri stars and Herbig Ae/Be stars, which are usually optically thick at visual wavelengths and show signatures of small (a<~ 3um) grains. A plausible replenishing mechanism of small grains is collisional fragmentation or erosion of large dust aggregates, which model calculations predict to play an important role in protoplanetary disks. If optically thick disks are to be seen as proof for ongoing fragmentation or erosion, then alternative explanations for the existence of optically thick disks must be studied carefully. In this study we explore two scenarios. First, we study the effect of residual, low-level infall of matter onto the disk surface. We find that infall rates as low as 10^{-11} Msun/yr can, in principle, replenish the small grain population to a level that keeps the disk marginally optically thick. However, it remains to be seen if the assumption of such inflow is realistic for star+disk systems at the age of several Myrs, at which winds and jets are expected to have removed any residual envelope. In summary, fragmentation or erosion still appear to be the most promising processes to explain the abundant presence of small grains in old disks.Comment: 10 pages, 4 figures, A&A in pres

Chondrules and Nebular Shocks

Beneath the fusion-encrusted surfaces of the most primitive stony meteorites lies not homogeneous rock, but a profusion of millimeter-sized igneous spheres. These chondrules, and their centimeter-sized counterparts, the calcium-aluminum-rich inclusions, comprise more than half of the volume fraction of chondritic meteorites. They are the oldest creations of the solar system. Their chemical composition matches that of the solar photosphere in all but the most volatile of elements, reflecting their condensation from the same pristine gas that formed the sun. In this invited editorial, we review the nebular shock wave model of Desch and Connolly (Meteoritics and Planetary Science 2002, 37, 183) that seeks to explain their origin. While the model succeeds in reproducing the unique petrological signatures of chondrules, the origin of the required shock waves in protoplanetary disks remains a mystery. Outstanding questions are summarized, with attention paid briefly to competing models.Comment: Invited editorial in Meteoritics and Planetary Science, vol. 37, no.

Accretion and evolution of solar system bodies

We use a combination of analytical and numerical methods to study dynamical processes involved in the formation of planets and smaller bodies in the solar system. Our goal was to identify and understand critical processes and to link them in a numerical model of planetesimal accretion. We study effects of these processes by applying them in the context of the standard model of solar system formation, which involves accretion of the terrestrial planets and cores of the giant planet from small planetesimals. The principal focus of our research effort is the numerical simulation of accretion of a swarm of planetesimals into bodies of planetary size. Our computer code uses a Monte Carlo method to determine collisional interactions within the swarm. These interactions are not determined simply by a relative velocity, but rather by explicit distributions of keplerian orbital elements. The planetesimal swarm is divided into a number of zones in semimajor axis, which are allowed to interact. The present version of our code has the capability of following detailed distributions of size, eccentricity, and inclination in each zone

Accretion in Protoplanetary Disks by Collisional Fusion

The formation of a solar system is believed to have followed a multi-stage process around a protostar. Whipple first noted that planetesimal growth by particle agglomeration is strongly influenced by gas drag; there is a "bottleneck" at the meter scale with such bodies rapidly spiraling into the central star, whereas much smaller or larger particles do not. Thus, successful planetary accretion requires rapid planetesimal growth to km scale. A commonly accepted picture is that for collisional velocities $V_c$ above a certain threshold collisional velocity, ${V_{th}} \sim$ 0.1-10 cm s$^{-1}$, particle agglomeration is not possible; elastic rebound overcomes attractive surface and intermolecular forces. However, if perfect sticking is assumed for all collisions the bottleneck can be overcome by rapid planetesimal growth. While previous work has dealt explicitly with the influences of collisional pressures and the possibility of particle fracture or penetration, the basic role of the phase behavior of matter--phase diagrams, amorphs and polymorphs--has been neglected. Here it is demonstrated that novel aspects of surface phase transitions provide a physical basis for efficient sticking through collisional melting or amphorph-/polymorphization and fusion to extend the collisional velocity range of primary accretion to $\Delta V_c \sim$ 1-100 m s$^{-1}$, which bound both turbulent RMS speeds and the velocity differences between boulder sized and small grains $\sim$ 1-50 m s$^{-1}$. Thus, as inspiraling meter sized bodies collide with smaller particles in this high velocity collisional fusion regime they grow rapidly to km scales and hence settle into stable Keplerian orbits in $\sim$ 10$^5$ years before photoevaporative wind clears the disk of source material.Comment: 11 pages, 7 figures, 1 tabl

Planet formation around stars of various masses: Hot super-Earths

We consider trends resulting from two formation mechanisms for short-period super-Earths: planet-planet scattering and migration. We model scenarios where these planets originate near the snow line in ``cold finger'' circumstellar disks. Low-mass planet-planet scattering excites planets to low periastron orbits only for lower mass stars. With long circularisation times, these planets reside on long-period eccentric orbits. Closer formation regions mean planets that reach short-period orbits by migration are most common around low-mass stars. Above ~1 Solar mass, planets massive enough to migrate to close-in orbits before the gas disk dissipates are above the critical mass for gas giant formation. Thus, there is an upper stellar mass limit for short-period super-Earths that form by migration. If disk masses are distributed as a power law, planet frequency increases with metallicity because most disks have low masses. For disk masses distributed around a relatively high mass, planet frequency decreases with increasing metallicity. As icy planets migrate, they shepherd interior objects toward the star, which grow to ~1 Earth mass. In contrast to icy migrators, surviving shepherded planets are rocky. Upon reaching short-period orbits, planets are subject to evaporation processes. The closest planets may be reduced to rocky or icy cores. Low-mass stars have lower EUV luminosities, so the level of evaporation decreases with decreasing stellar mass.Comment: Accepted to ApJ. 13 pages of emulateap

The Progressive Self-Culture of a Lutheran Pastor

During his three years at the seminary the theological student is taught the qualifications and requirements of a Lutheran pastor, and he is informed of the tremendous responsibilities and the exacting demands which a call into the ministry will lay upon him when he has become a pastor of a congregation. But the seminary training is not able to convert the student into a full-fledged pastor. Only long years of hard study and practical experience and divine grace can equip a man successfully and completely for this greatest and hardest calling and work in this world. Unless the ministerial candidate, upon the entry into his life’s work, continues, with firm determination and fixed purpose all through his life, to erect a well-built superstructure upon the foundation which was laid with the help of his teachers at the seminary, he will soon find himself unable to cope with the problems of his calling, he will fail to render efficient service as a steward over God\u27s household, and he will forfeit the joy and the reward of a faithful shepherd of the f lock over which God has placed him