We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result-a radial planetesimal distribution-can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus here they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time dependent formation rates and location of primary pebble accretion. We show that large α-values of 0.01 (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around 0.001 (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles (∼ mm to dm) and the pebble flux reaches a critical value, which is after a few thousand years at 2 − 3 au and after a few hundred thousand years at 20 − 30 au. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution which helps to explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.
Mean and local cerebral blood flows were lower during sevoflurane than during isoflurane anesthesia. This difference cannot be explained by differing changes in glucose utilization because glucose utilization was decreased to the same extent in both groups.
Context. The formation of gas giant planets by the accretion of 100 km diameter planetesimals is often thought to be inefficient. A diameter of this size is typical for planetesimals and results from self-gravity. Many models therefore use small kilometer-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals that are distributed radially in a minimum-mass solar-nebula way. Aims. We use a dynamical model for planetesimal formation to investigate the effect of various initial radial density distributions on the resulting planet population. In doing so, we highlight the directive role of the early stages of dust evolution into pebbles and planetesimals in the circumstellar disk on the subsequent planet formation. Methods. We implemented a two-population model for solid evolution and a pebble flux-regulated model for planetesimal formation in our global model for planet population synthesis. This framework was used to study the global effect of planetesimal formation on planet formation. As reference, we compared our dynamically formed planetesimal surface densities with ad hoc set distributions of different radial density slopes of planetesimals. Results. Even though required, it is not the total planetesimal disk mass alone, but the planetesimal surface density slope and subsequently the formation mechanism of planetesimals that enables planetary growth through planetesimal accretion. Highly condensed regions of only 100 km sized planetesimals in the inner regions of circumstellar disks can lead to gas giant growth. Conclusions. Pebble flux-regulated planetesimal formation strongly boosts planet formation even when the planetesimals to be accreted are 100 km in size because it is a highly effective mechanism for creating a steep planetesimal density profile. We find that this leads to the formation of giant planets inside 1 au already by pure 100 km planetesimal accretion. Eventually, adding pebble accretion regulated by pebble flux and planetesimal-based embryo formation as well will further complement this picture.
Recent laboratory experiments indicate that destructive collisions of icy dust particles occur with much lower velocities than previously thought. These fragmentation velocities play a crucial role in planet formation because they set the maximum grain size in collisional growth models. When these new velocities are considered from laboratory experiments in dust evolution models, a growth to pebble sizes (typically millimeter-to decimeter-sized particles) in protoplanetary disks is difficult. This may contradict (sub-) millimeter observations and challenge the formation of planetesimals and planets. We investigate the conditions that are required in dust evolution models for growing and trapping pebbles in protoplanetary disks when the fragmentation speed is 1 m s −1 in the entire disk. In particular, we distinguish the parameters controlling the effects of turbulent velocities (δt), vertical stirring (δz), radial diffusion (δr), and gas viscous evolution (α), always assuming that particles cannot diffuse faster (radially or vertically) than the gas (i.e., δr,z,t ≤ α). We compare our models with observations of protoplanetary disks at both the near-infrared and millimeter regimes. To form pebbles and produce effective particle trapping, the parameter that controls the particle turbulent velocities must be small (δt 10 −4). In these cases, the vertical settling can limit the formation of pebbles, which also prevents particle trapping. Therefore the parameter that sets the vertical settling and stirring of the grains must be δz < 10 −3. Our results suggest that different combinations of the particle and gas diffusion parameters can lead to a large diversity of millimeter fluxes and dust-disk radii. When pebble formation occurs and trapping is efficient, gaps and rings have higher contrast at millimeter emission than in the near-infrared. In the case of inefficient trapping, structures are also formed at the two wavelengths, producing deeper and wider gaps in the near-infrared. Our results highlight the importance of obtaining observational constraints of gas and particle diffusion parameters and the properties of gaps at short and long wavelengths to better understand basic features of protoplanetary disks and the origin of the structures that are observed in these objects.
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