Pebble dynamics and accretion onto rocky planets. I. Adiabatic and convective models (1801.07707v4)

Abstract: We present nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of Mars- to Earth-mass planetary embryos. The simulations extend from the surface of the embryos to a few vertical disk scale heights, with \rev{a spatial} dynamic range \rev{of} $\sim! 1.4\times 10^5$. Our results confirm that "pebble"-sized particles are readily accreted, with accretion rates continuing to increase up to metre-size "boulders" for a 10\% MMSN surface density model. The gas mass flux in and out of the Hill sphere is consistent with the Hill rate, $\Sigma\Omega R_\mathrm{H}^2 = 4\, 10^{-3}$ M$\oplus$ yr$^{-1}$. While smaller size particles mainly track the gas, a net accretion rate of $\approx 2\,10^{-5}$ M$\oplus$ yr$^{-1}$ is reached for 0.3--1 cm particles, even though a significant fraction leaves the Hill sphere again. Effectively all pebble-sized particles that cross the Bondi sphere are accreted. The resolution of these simulations is sufficient to resolve accretion-driven convection. Convection driven by a nominal accretion rate of $10^{-6}$ M$_\oplus$ yr$^{-1}$ does not significantly alter the pebble accretion rate. We find that, due to cancellation effects, accretion rates of pebble-sized particles are nearly independent of disk surface density. As a result, we can estimate accurate growth times for specified particle sizes. For 0.3--1 cm size particles, the growth time from a small seed is $\sim$0.15 million years for an Earth mass planet at 1 AU and $\sim$0.1 million years for a Mars mass planet at 1.5 AU.

• The paper demonstrates that pebble accretion rates scale linearly with particle size, challenging the conventional s^(2/3) prediction.
• The study employs high-resolution, nested-grid hydrodynamic simulations to capture complex gas flows, including horseshoe orbits, around rocky embryos.
• The paper finds that while convection alters gas dynamics, it does not significantly enhance pebble accretion, indicating intricate interactions within planetary atmospheres.

Addressing Pebble Dynamics and Accretion onto Rocky Planets: A Computational Study

The paper conducted by Popovas et al. presents a detailed investigation into the dynamics and accretion of pebble-sized particles onto terrestrial planetary embryos using advanced numerical simulations. The simulations encompass the region from the planet's surface to several disk scale heights. By employing nested-grid, high-resolution hydrodynamic simulations, the authors address several gaps in our understanding of pebble accretion within protoplanetary disks. The work focuses on evaluating the accretion rates, influenced by both adiabatic and convective atmospheric processes, for embryos ranging from Mars- to Earth-mass.

Overview of Methodology

The authors utilized the DISPATCH framework to model the gas flow around planetary embryos and the trajectory of particles ranging from 10 μm to 1 meter in size. The simulations were carried out in a three-dimensional Cartesian domain, allowing the paper of gas dynamics on both large (several disk scale heights) and small (a few percent of a planet's radius) scales. A significant aspect of this work involves capturing complex gas flows, including horseshoe orbits, and the role they play in facilitating or hindering pebble accretion.

The paper explored the interplay between particle size, gas density, and accretion efficiency. The authors subjected the embryos to varying disk conditions, including differences in mass, temperature, and density related to Minimum Mass Solar Nebula (MMSN) models. The simulations prioritize capturing not just the radial flows but also the vertical dynamics of the system, essential for understanding pebble accretion in three-dimensional environments.

Key Results and Insights

1. Particle Accretion Rates: The results indicate that the accretion rates of particles scale linearly with size, in contrast to the s2/3 scaling predicted under assumptions of unperturbed shear flow. This discrepancy arises from the complex flow structures around the embryos, which disrupt the simple scaling laws derived from idealized conditions.
2. Gas Flow Dynamics: The simulations reveal that the detailed flow patterns, particularly the presence of horseshoe orbits, significantly affect particle accretion. Gas flows near the Hill sphere, influenced by the embryo's mass and disk conditions, manifest in different accretion efficacies for varied particle sizes. Smaller particles, being closely coupled with the gas, often follow paths that lead them around instead of onto the planet.
3. Convection's Role in Accretion: The paper introduces a scenario with accretion-driven convection to assess its impact on pebble accretion. Interestingly, while convection alters gas flow patterns significantly, it does not drastically increase accretion rates. This finding suggests a complex relationship between atmospheric convection and pebble dynamics, warranting further investigation.
4. Numerical Robustness: Despite using a single node for computation, the nested-grid approach proves capable of resolving intricate flow patterns and particle dynamics with high fidelity. The efficient handling of numerical resolution across different spatial scales is pivotal to the paper's success.

Implications and Future Directions

The implications of this research are significant for theoretical models of planet formation. The paper underscores the importance of accounting for atmospheric dynamics and pebble motion in three dimensions. Recognizing these interactions could refine predictions regarding planetary growth timescales from small seeds to full-size rocky planets.

For the future, integrating more realistic equations of state and including pebble destruction processes, such as ablation in atmospheres, will enhance the model's fidelity. Additionally, including radiative energy transfer in the simulations could provide deeper insights into the thermal and dynamic evolution of planetary embryos situated in pressure bumps within protoplanetary disks.

This research constitutes an important step in understanding the complexities of planet formation via pebble accretion. The authors provide a solid foundation for further studies aimed at bridging theoretical predictions with observational constraints in planet formation and disk dynamics.