Non-linear Development of Secular Gravitational Instability in Protoplanetary Disks

TL;DR

This paper presents long-term non-linear simulations of secular gravitational instability in protoplanetary disks, revealing dust concentration into rings that can migrate inward, advancing understanding of planetesimal formation.

Contribution

It introduces a new symplectic integrator-based numerical scheme for long-term simulation of secular GI and demonstrates its role in dust ring formation and migration.

Findings

Dust density increases by over 100 times in rings.

Dust rings tend to reach a critical line mass.

Dust rings migrate inward at a calculable low velocity.

Abstract

We perform non-linear simulation of secular gravitational instability (GI) in protoplanetary disks that has been proposed as a mechanism of the planetesimal formation and the multiple ring formation. Since the timescale of the growth of the secular GI is much longer than the Keplerian rotation period, we develop a new numerical scheme for a long term calculation utilizing the concept of symplectic integrator. With our new scheme, we first investigate the non-linear development of the secular GI in a disk without a pressure gradient in the initial state. We find that the surface density of dust increases by more than a factor of one hundred while that of gas does not increase even by a factor of two, which results in the formation of dust-dominated rings. A line mass of the dust ring tends to be very close to the critical line mass of a self-gravitating isothermal filament. Our results indicate that the non-linear growth of the secular GI provides a powerful mechanism to concentrate the dust. We also find that the dust ring formed via the non-linear growth of the secular GI migrates inward with a low velocity, which is driven by the self-gravity of the ring. We give a semi-analytical expression for the inward migration speed of the dusty ring.