Linking planetary embryo formation to planetesimal formation II: The impact of pebble accretion in the terrestrial planet zone

The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolution of the disk. We connect a one dimensional two population model for solid evolution and pebble flux regulated planetesimal formation to the N-body code LIPAD. In our study we focus on the growth of planetesimals with an initial size of 100 km in diameter by planetesimal collisions and pebble accretion for the first 1 million years of a viscously evolving disk. We compare 18 different N-body simulations in which we vary the total planetesimal mass after 1 million years, the surface density profile of the planetesimal disk, the radial pebble flux and the possibility of pebble accretion. Pebble accretion leads to the formation of fewer, but substantially more massive embryos. The area of possible embryo formation is weakly influenced by the accretion of pebbles and the innermost embryos tend to form slightly earlier compared to the simulations in which pebble accretion is neglected. Pebble accretion strongly enhances the formation of super earths in the terrestrial planet region, but it does not enhance the formation of embryos at larger distances

Linking planetary embryo formation to planetesimal formation I: The impact of the planetesimal surface density in the terrestrial planet zone

The growth time scales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. We quantify the timescales and spatial distribution of planetary embryos via collisional growth and fragmentation of dynamically forming 100km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. We connect a one dimensional model for viscous gas evolution, dust and pebble dynamics and pebble flux regulated planetesimal formation to the N-body code LIPAD. Our framework enables us to study the formation, growth, fragmentation and evolution of planetesimals with an initial size of 100km in diameter for the first million years of a viscous disk. Our study shows the effect of the planetesimal surface density evolution on the preferential location and timescales of planetary embryo formation. A one dimensional analytically derived model for embryo formation based on the local planetesimal surface density evolution is presented. This model manages to reproduce the spatial distribution, formation rate and total number of planetary embryos at a fraction of the computational cost of the N-body simulations. The formation of planetary embryos in the terrestrial planet zone occurs simultaneously to the formation of planetesimals. The local planetesimal surface density evolution and the orbital spacing of planetary embryos in the oligarchic regime serve well as constraints to model planetary embryo formation analytically. Our embryo formation model will be a valuable asset in future studies regarding planet formation

The Importance of Disk Structure in Stalling Type I Migration

As planets form they tidally interact with their natal disks. Though the tidal perturbation induced by Earth and super-Earth mass planets is generally too weak to significantly modify the structure of the disk, the interaction is potentially strong enough to cause the planets to undergo rapid type I migration. This physical process may provide a source of short-period super-Earths, though it may also pose a challenge to the emergence and retention of cores on long-period orbits with sufficient mass to evolve into gas giants. Previous numerical simulations have shown that the type I migration rate sensitively depends upon the circumstellar disk's properties, particularly the temperature and surface density gradients. Here, we derive these structure parameters for 1) a self-consistent viscous-disk model based on a constant \alpha-prescription, 2) an irradiated disk model that takes into account heating due to the absorption of stellar photons, and 3) a layered-accretion disk model with variable \alpha-parameter. We show that in the inner viscously-heated regions of typical protostellar disks, the horseshoe and corotation torques of super-Earths can exceed their differential Lindblad torque and cause them to undergo outward migration. However, the temperature profile due to passive stellar irradiation causes type I migration to be inwards throughout much of the disk. For disks in which there is outwards migration, we show that location and the mass range of the "planet traps" depends on some uncertain assumptions adopted for these disk models. Competing physical effects may lead to dispersion in super-Earths' mass-period distribution.Comment: 12 pages, Submitted to Ap

Constraining the parameter space for the Solar Nebula

If we want to understand planetesimal formation, the only data set we have is our own Solar System. It is particularly interesting as it is so far the only planetary system we know of that developed life. Understanding the conditions under which the Solar Nebula evolved is crucial in order to understand the different processes in the disk and the subsequent dynamical interaction between (proto-)planets, once the gas disk is gone. Protoplanetary disks provide a plethora of different parameters to explore. The question is whether this parameter space can be constrained, allowing simulations to reproduce the Solar System. Models and observations of planet formation provide constraints on the initial planetesimal mass in certain regions of the Solar Nebula. By making use of pebble flux-regulated planetesimal formation, we perform a parameter study with nine different disk parameters like the initial disk mass, initial disk size, initial dust-to-gas ratio, turbulence level, and more. We find that the distribution of mass in planetesimals in the disk depends on the planetesimal formation timescale and the pebbles' drift timescale. Multiple disk parameters can influence pebble properties and thus planetesimal formation. However, it is still possible to draw some conclusions on potential parameter ranges. Pebble flux-regulated planetesimal formation seems to be very robust, allowing simulations with a wide range of parameters to meet the initial planetesimal constraints for the Solar Nebula. I.e., it does not require a lot of fine tuning.Comment: A&A accepte

Protoplanetary Disk Rings as Sites for Planetesimal Formation

Axisymmetric dust rings are a ubiquitous feature of young protoplanetary disks. These rings are likely caused by pressure bumps in the gas profile; a small bump can induce a traffic jam-like pattern in the dust density, while a large bump may halt radial dust drift entirely. The resulting increase in dust concentration may trigger planetesimal formation by the streaming instability (SI), as the SI itself requires some initial concentration. Here we present the first 3D simulations of planetesimal formation in the presence of a pressure bump modeled specifically after those observed by ALMA. In particular, we place a pressure bump at the center of a large 3D shearing box, along with an initial solid-to-gas ratio of $Z = 0.01$, and we include both particle back-reaction and particle self-gravity. We consider both mm-sized and cm-sized particles separately. For simulations with cm-sized particles, we find that even a small pressure bump leads to the formation of planetesimals via the streaming instability; a pressure bump does {\it not} need to fully halt radial particle drift for the SI to become efficient. Furthermore, pure gravitational collapse via concentration in pressure bumps (such as would occur at sufficiently high concentrations and without the streaming instability) is not responsible for planetesimal formation. For mm-sized particles, we find tentative evidence that planetesimal formation does not occur. This result, if it holds up at higher resolution and for a broader range of parameters, could put strong constraints on where in protoplanetary disks planetesimals can form. Ultimately, however, our results suggest that for cm-sized particles, planetesimal formation in pressure bumps is an extremely robust process.Comment: accepted to ApJ; 22 pages, 16 figure

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. II. The Effect of the Radial Gas Pressure Gradient

The streaming instability concentrates solid particles in protoplanetary disks, leading to gravitational collapse into planetesimals. Despite its key role in producing particle clumping and determining critical length scales in the instability's linear regime, the influence of the disk's radial pressure gradient on planetesimal properties has not been examined in detail. Here, we use streaming instability simulations that include particle self-gravity to study how the planetesimal initial mass function depends on the radial pressure gradient. Fitting our results to a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, we find a single value $p \approx 1.6$ describes simulations in which the pressure gradient varies by $\gtrsim 2$. An exponentially truncated power-law provides a significantly better fit, with a low mass slope of $p^\prime \approx 1.3$ that weakly depends on the pressure gradient. The characteristic truncation mass is found to be $\sim M_G = 4 \pi^5 G^2 \Sigma_p^3 / \Omega^4$. We exclude the cubic dependence of the characteristic mass with pressure gradient suggested by linear considerations, finding instead a linear scaling. These results strengthen the case for a streaming-derived initial mass function that depends at most weakly on the aerodynamic properties of the disk and participating solids. A simulation initialized with zero pressure gradient---which is {\em not} subject to the streaming instability---also yields a top-heavy mass function but with modest evidence for a different shape. We discuss the consistency of the theoretically predicted mass function with observations of Kuiper Belt planetesimals, and describe implications for models of early stage planet formation..Comment: 18 pages, 10 figures, 3 tables, accepted to Ap