Dynamics of planetesimal formation Áron Süli Eötvös University Dept. of Astronomy

Overview This talk reviews our current understanding of terrestrial planets formation. Very short historical overview Structure of the gas disk The orbital velocity of the gas disk The stages of the planetesimal and planet formation

Introduction The study of planet formation has a long history. The idea that the Solar System formed from a rotating disk of gas and dust – the Nebula Hypothesis – dates back to Kant, Laplace in the 18th century. A quantitative description of terrestrial planet formation was given by the late 1960s, when Viktor Safronov published his now classic monograph The core accretion theory for gas giant planet formation were developed in the early 1980s.

Introduction More recently, a wealth of new observations has led to renewed interest in the problem: The most dramatic development has been the identification of extrasolar planets. The discovery of protoplanetary disks and of the Solar System’s Kuiper Belt have been almost as influential in focusing theoretical attention on the initial conditions for planet formation Geochemical and cosmochemical analyses performed with laboratory instruments produced data on the chemical and isotopic composition of the planets giving constraints on the chronology of their accretion and thermal evolution. Remarkable increase in computer performance has allowed modelers to undertake increasingly realistic simulations of the dynamical process of terrestrial planet accretion. Sufficient level of reliability to be integrated in a comprehensive view of the early evolution of the inner solar system.

Introduction The formation of terrestrial planets from micron-sized dust particles requires growth through at least 12 orders of magnitude in size scale. The formation is usually ordered in time and by the relevant different dominant physical processes involved. Planetesimal formation: Planetesimals are defined as bodies that are large enough (R  1 - 100 km) that their orbital evolution is dominated by mutual gravitational interactions rather than aerodynamic drag. Embryo formation: Embryos are between planetesimals and planets (100 < R < 1 - 2000 km). Giant planets probably form at roughly the same time as planetary embryos. Terrestrial planet formation: after the disappearance of gas from, the embryos’ orbits become unstable, and their mutual collisions give birth to a small number of terrestrial planets coupling to gas: drag collision (sticky) Stage I gravity collision Stage II coupling to gas: migration gravity collision Stage III

Protoplanetary disk structure Protoplanetary disks form because the diffuse gas has too much angular momentum to collapse directly to stellar densities Disks survive as structures in quasi-equilibrium because its specific angular momentum increases with radius. To accrete, angular momentum must be lost from, or redistributed within the disk gas, and this process requires time scales that are much longer than the orbital or dynamical time scale. Since angular momentum transport is slow, it is assumed that the disk is static This approximation suffices for a first study of the temperature density, and composition profiles of protoplanetary disks, which are critical inputs for models of planet formation. Lets begin with the gas component of the disk

Protoplanetary disk: Vertical structure of the gas vertical component of the gravitational acceleration vertical pressure gradient Equation of state           Approximation     mid-plane density surface density   vertical scale height orbital frequency        

Protoplanetary disk: Orbital velocity of the gas The radial velocity component of the gas can be determined from the momentum equation           This slight difference is in the heart of the so-called meter-size barrier problem

Stage I: from dust to planetesimals   Aerodynamic drag on solid particles             Aerodynamic drag is important to understand both the vertical and radial distribution of solid material

Stage I: from dust to planetesimals Dust settling: dust grains sediment into a thin layer at the mid-plane of the disks                   In the absence of turbulence micron-sized particles sediment out of the upper layers a time scale that is short compared to the disk lifetime.

Stage I: from dust to planetesimals Previously both turbulence and growth via collision were negelcted. Lets consider a single particle settling with coagulation in a laminar disk:              

Stage I: from dust to planetesimals – turbulence   The sedimentation timescale and the volume density of grains near the mid-plane depend on the severity of turbulence in the disk gas, as strong turbulence inhibits sedimentation. Even in laminar disks, though, the volume density of grains in the mid-plane could not reach arbitrarily large values, because the sedimentation of an excessive amount of solids would itself generate turbulence in the disk via the so-called Kelvin-Helmoltz instability.

Stage I: from dust to planetesimals   Radial drift of solid particles             radial drift velocity      

Stage I: from dust to planetesimals – m-size barrier problem radial drift velocity min timescale   barrier   Planetesimal formation must be rapid, Radial redistribution of solids is very likely to occur Radial drift with coagulation: relative velocity between particles of different sizes -> coagulation. But the relative velocities are too large -> FRAGMENTATION

Stage I: from dust to planetesimals – an alternative Planetesimals may form due to the collective gravity of massive swarms of small particles via the Goldreich-Ward mechanism, if they are concentrated at some locations, such as local maxima of the gas density distribution inter-vortex regions. These models can explain the formation of planetesimals of size 100 km or larger without passing through intermediate small sizes, circumventing the meter-size barrier problem. Evidence: The size distribution of objects in the asteroid belt and in the Kuiper belt, where most of the mass is concentrated in 100km objects The existence and the properties of binary Kuiper belt objects (have angular momenta too large to form single objects)  

Stage II: from planetesimals to embryos  

Stage II: from planetesimals to embryos  

Stage II: from planetesimals to embryos     The detailed physics of the collision is neglected, it is assumed that the bodies agglomerate into a single object.   The collisional cross section is enhanced by the gravity of the bodies: this is called gravitational focusing Using conservation of energy conservation of angular momentum the cross section for collision:            

Stage II: from planetesimals to embryos           The initially more massive body grows faster than its less massive cousin. This phenomenon is called runaway growth

Stage II: from planetesimals to embryos     The growth rate of the embryos gets slower as the bodies increase in size. The relative velocities are too high -> collisions between smaller bodies leads to disruption. Only collisions between small and large bodies can lead to growth! This phase is called oligarchic growth.

Stage II: from planetesimals to embryos   The maximum mass of a protoplanet, the isolation mass after the runaway and oligarhic growth can be estimated: The body can accrete material only from within its feeding zone, which gives:   feeding zone  

Stage II: from planetesimals to embryos – the giants  

Stage III: from embryos to terrestrial planets The final assembly of terrestrial planets starts once the oligarchs have depleted the planetesimal disk (dynamical friction can no longer maintain low e and i) The largest bodies start to interact strongly, collide, and scatter smaller bodies across a significant radial extent of the disk. Numerical N-body simulations show that this final stage is by far the slowest, with large collisions continuing out to at least 100 Myr The process is chaotic: identical initial conditions can give rise to a range of outcomes The typical result: 2 to 4 planets are formed on well-separated and stable orbits, with eccentricities and inclinations that are comparable of the real planets Quasi-tangent collisions of Mars-mass embryos onto the proto-planets are frequent. These collisions are expected to generate satellites (the formation of the Moon) The accretion timescale in the simulations is ~30-100 Myr, in general agreement with the timescale of Earth accretion deduced from radioactive chronometers A small fraction of the original planetesimals typically remain in the asteroid belt on stable orbits

Stage III: from embryos to terrestrial planets

Thank you for your attention Summary Remarks: turbulance, collisions, migration, chemical composition, water, ... the formation of terrestrial planets can be divided in three stages the mechanisms responsible to create particles of cm scale are identified the formation of planetesimals faces a sever problem: the meter-size barrier the final assembly of terrestrial planets is well understood, and the outcomes statistically agree with the inner Solar System the extraordinary diversity of the discovered planetary systems poses new challenges to the theories Thank you for your attention