General Analysis of Type I Planetary Migration with Stochastic Perturbations

TL;DR

This paper investigates how stochastic turbulence in protoplanetary disks influences Type I planetary migration, revealing that turbulence can allow some planetary cores to survive inward migration and providing statistical predictions of their distribution.

Contribution

It introduces a generalized framework combining Fokker-Planck and iterative map methods to analyze stochastic effects on planetary migration, highlighting survival probabilities.

Findings

Survival fraction of planets ranges from 1% to 10%.

Stochastic torques can cause outward diffusion of planetary cores.

Survival probability decreases exponentially over time.

Abstract

This paper presents a generalized treatment of Type I planetary migration in the presence of stochastic perturbations. In many planet-forming disks, the Type I migration mechanism, driven by asymmetric torques, acts on a short time scale and compromises planet formation. If the disk also supports MHD instabilities, however, the corresponding turbulent fluctuations produce additional stochastic torques that modify the steady inward migration scenario. This work studies the migration of planetary cores in the presence of stochastic fluctuations using complementary methods, including a Fokker-Planck approach and iterative maps. Stochastic torques have two main effects: [1] Through outward diffusion, a small fraction of the planetary cores can survive in the face of Type I inward migration. [2] For a given starting condition, the result of any particular realization of migration is uncertain, so that results must be described in terms of the distributions of outcomes. In addition to exploring different regimes of parameter space, this paper considers the effects of the outer disk boundary condition, varying initial conditions, and time-dependence of the torque parameters. For disks with finite radii, the fraction of surviving planets decreases exponentially with time. We find the survival fractions and decay rates for a range of disk models, and find the expected distribution of locations for surviving planets. For expected disk properties, the survival fraction lies in the range $0.01 < p_S < 0.1$.