How to form planetesimals from mm-sized chondrules and chondrule aggregates (1501.05314v3)

Abstract: The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than $\sim$100 km in size. Instead, planetesimals appear to form top-down, with large $100-1000$ km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We use a hydrodynamic code to model the interaction between solid particles and the gas inside a shearing box inside the disk, considering particle sizes from sub-millimeter-sized chondrules to meter-sized rocks. We find that particles down to millimeter sizes can form dense particle clouds through the run-away convergence of radial drift known as the streaming instability. We make a map of the range of conditions (strength of turbulence, particle mass-loading, disk mass, and distance to the star) which are prone to producing dense particle clumps. Finally, we estimate the distribution of collision speeds between mm-sized particles. We calculate the rate of sticking collisions and obtain a robust upper limit on the particle growth timescale of $\sim$$10^5$ years. This means that mm-sized chondrule aggregates can grow on a timescale much smaller than the disk accretion timescale ($\sim$$10^6 - 10^7$ years). Our results suggest a pathway from the mm-sized grains found in primitive meteorites to fully formed asteroids. We speculate that asteroids may form from a positive feedback loop in which coagualation leads to particle clumping driven by the streaming instability. This clumping, in turn reduces collision speeds and enhances coagulation.} Future simulations should model coagulation and the streaming instability together to explore this feedback loop further.

Analysis of "How to form planetesimals from mm-sized chondrules and chondrule aggregates"

The formation of planetesimals, particularly from sub-meter scale chondrules and chondrule aggregates, has long been an enigmatic aspect of planetary sciences, challenging the coherence of bottom-up formation theories. The paper by Carrera, Johansen, and Davies provides a significant contribution to the understanding of this process, leveraging hydrodynamic simulations to explore the role of streaming instabilities in protoplanetary disks.

Key Findings

This research introduces a distinct perspective on planetesimal formation, positing that large bodies originate from the top-down gravitational collapse of dense particle clouds, rather than gradual accretion. Three pivotal conclusions are drawn from comprehensive 2D and 3D simulations:

1. Streaming Instability Thresholds: The paper methodically maps the parameter space of particle size (as characterized by the Stokes number, $\tau_f$) and concentration (quantified by $Z = \Sigma_{\rm solid} / \Sigma_{\rm total}$). It identifies conditions conducive to the streaming instability, identifying that particles as small as $\tau_f = 0.003$ can clump into high-density regions at $Z > 0.065$. This is considerably achievable with scenarios involving the break-up of icy aggregates around snow lines or enhanced local particle concentrations.
2. Influence of Disk Conditions: The interplay between particle size, turbulence (linked to the $\alpha$ viscosity parameter), and local disk properties is elaborated. Specifically, the paper finds that low turbulence allows particles to form larger aggregates, which are more likely to participate in streaming instabilities. The paper also emphasizes the potential for disk evolution—specifically gas depletion—to alter the effective stopping times of particles, making initially unfavorable regions of the disk become promising sites for planetesimal formation over time.
3. Coagulation of Millimeter-Sized Particles: A practical aspect of the paper evaluates the expected collision velocities for mm-sized particles, finding growth timescales under $10^5$ years for $R = 1$ mm aggregates. This is rapid in the context of protoplanetary disk lifetimes, suggesting that particles in this size range can grow efficiently through coagulation and participate in streaming instabilities once certain density thresholds are surpassed.

Implications

The outcomes of this paper bear significant implications for theoretical models of planet formation. By positing a path from chondrules to planetesimals that bypasses intermediate size scales, it challenges traditional pebble accretion scenarios and provides a plausible mechanism for the observed size distribution within the solar system's asteroid and Kuiper belts.

From a theoretical standpoint, these insights necessitate a revision of disk evolution models, particularly concerning the feedback mechanisms between particle coagulation, clumping, and streaming instability. Practically, the work underscores the importance of considering disk properties such as turbulent viscosity ($\alpha$) and solid concentration in future models and simulations aimed at reproducing observed distributions of protoplanetary materials.

Future Directions

The paper opens several avenues for future research. First, extending simulations to incorporate a concurrent treatment of coagulation and streaming instability could refine our understanding of size transition dynamics in particle aggregates. Incorporating more complex 3D simulations would also provide deeper insights into the role of kinetic heating and potential magnetic effects on clump formation.

Further observational efforts to map the distribution of chondrule sizes and aggregate masses in young planet-bearing systems will also be essential to test these theoretical findings against astrophysical reality. As a broader implication, improved understanding of initial planetesimal formation conditions will refine models of planetary system evolution, offering predictive power for the architecture of exoplanetary systems.

Overall, Carrera and colleagues have presented a robust and detailed examination of planetesimal formation, championing a paradigm shift in understanding the processes underlying the initial stages of planet formation. Their contributions form a critical foundation for the evolution of theoretical astrodynamics and the interpretation of observational data in protoplanetary environments.