[Paper Review] Planetesimal formation at the gas pressure bump following a migrating planet I. Basic characteristics of the new formation model

Yuhito Shibaike, Y. Alibert|arXiv (Cornell University)|Oct 20, 2020

Astrophysics and Star Formation Studies42 references4 citations

TL;DR

This paper proposes a new mechanism for planetesimal formation in protoplanetary discs, where planetesimals form via streaming instability at gas pressure bumps created by a migrating first-generation planet. As the planet migrates inward, the pressure bump and associated planetesimal formation region spread across broad radial regions, enabling widespread planetesimal distribution—key for population synthesis models.

ABSTRACT

To avoid known difficulties in planetesimal formation such as the drift or fragmentation barriers, many scenarios have been proposed. However, in these scenarios, planetesimals form in general only at some specific locations in protoplanetary discs. On the other hand, it is generally assumed in planet formation models and population synthesis models, that planetesimals are broadly distributed in the protoplanetary disc. Here we propose a new scenario in which planetesimals can form in broad areas of the discs. Planetesimals form at the gas pressure bump formed by a first-generation planet (e.g. formed by pebble accretion) and the formation region spreads inward in the disc as the planet migrates. We use a simple 1D Lagrangian particle model to calculate the radial distribution of pebbles in the gas disc perturbed by a migrating embedded planet. We consider that planetesimals form by streaming instability at the points where the pebble-to-gas density ratio on the mid-plane becomes larger than unity. We also study the effect of some key parameters like the ones of the gas disc model, the pebble mass flux, the migration speed of the planet, and the strength of turbulence. We find that planetesimals form in wide areas of the discs provided the flux of pebbles is typical and the turbulence is not too strong. The planetesimal surface density depends on the pebble mass flux and the migration speed of the planet. The total mass of the planetesimals and the orbital position of the formation area depend strongly on the pebble mass flux. We also find that the profile of the planetesimal surface density and its slope can be estimated by very simple equations. We show that our new scenario can explain the formation of planetesimals in broad areas. The simple estimates we provide for the planetesimal surface density profile can be used as initial conditions for population synthesis models.

Motivation & Objective

• Address the limitation of existing planetesimal formation models that restrict formation to specific locations in protoplanetary discs.
• Overcome the drift and fragmentation barriers in classical planetesimal formation by leveraging localized pebble accumulation at gas pressure bumps.
• Explain how planetesimals can form in broad, continuous regions of discs, consistent with population synthesis model assumptions.
• Provide a physically motivated mechanism that links planetesimal formation to the migration of a first-generation planet.
• Develop simple analytical estimates for planetesimal surface density profiles to serve as initial conditions for population synthesis models.

Proposed method

• Use a 1D Lagrangian super-particle model to simulate radial pebble distribution in a gas disc perturbed by a migrating embedded planet.
• Model planetesimal formation via streaming instability at locations where the mid-plane pebble-to-gas density ratio exceeds unity.
• Fix pebble Stokes number and planet mass to isolate the basic characteristics of the new formation scenario.
• Vary key parameters: gas disc surface density profile (p), temperature profile (q), pebble mass flux ($\dot{M}_{\rm peb}$), migration speed (Type I or II), and turbulence strength.
• Apply conservation of solid mass to derive a simple analytical estimate for planetesimal surface density: $\Sigma_{\rm pl} \propto \dot{M}_{\rm peb} / v_{\rm mig}$.
• Compare numerical results with analytical predictions to validate the model and assess parameter dependencies.

Experimental results

Research questions

• RQ1 Can planetesimal formation occur across broad radial regions in protoplanetary discs, rather than being confined to specific locations?
• RQ2 How does the migration of a first-generation planet influence the spatial distribution and total mass of formed planetesimals?
• RQ3 What is the dependence of planetesimal surface density on pebble mass flux, migration speed, and disc parameters?
• RQ4 How do Type I versus Type II migration of the planet affect the radial extent and surface density profile of planetesimals?
• RQ5 Can simple analytical equations accurately predict the planetesimal surface density profile and its slope?

Key findings

• Planetesimals form in broad regions of the disc when pebble flux is typical and turbulence is not too strong, due to the inward migration of the pressure bump.
• The planetesimal surface density is proportional to the pebble mass flux and inversely proportional to the migration speed of the planet, as per the analytical estimate $\Sigma_{\rm pl} \propto \dot{M}_{\rm peb} / v_{\rm mig}$.
• The slope of the planetesimal surface density profile is $p - q - 1.5$, where $-p$ and $-q$ are the power-law indices of the gas surface density and temperature profiles.
• The slope is independent of migration type (Type I or II), though the total mass and radial extent differ due to migration speed.
• With Type II migration (slower), the planetesimal surface density is higher and the radial distribution is broader than with Type I migration.
• In low-pebble-flux or high-density disc cases, the planetesimal surface density exceeds analytical estimates due to pebble accumulation before conversion to planetesimals.