The dynamics of inner dead-zone boundaries in protoplanetary disks

TL;DR

This paper models the dynamic behavior of the boundary between MRI active and dead zones in protoplanetary disks, revealing a stable intermediate radius that likely defines the true boundary affecting disk evolution and planet formation.

Contribution

It introduces a reduced dynamical model showing how the active/dead zone interface can fluctuate and stabilize at an intermediate radius, providing new insights into disk structure and evolution.

Findings

Fronts propagate inward or outward depending on initial conditions.

The interface stalls at a stable intermediate radius.

This radius likely defines the true boundary in protoplanetary disks.

Abstract

In protoplanetary disks, the inner radial boundary between the MRI turbulent (`active') and MRI quiescent (`dead') zones plays an important role in models of the disk evolution and in some planet formation scenarios. In reality, this boundary is not well-defined: thermal heating from the star in a passive disk yields a transition radius close to the star (<0.1 au), whereas if the disk is already MRI active, it can self-consistently maintain the requisite temperatures out to a transition radius of roughly 1 au. Moreover, the interface may not be static; it may be highly fluctuating or else unstable. In this paper, we study a reduced model of the dynamics of the active/dead zone interface that mimics several important aspects of a real disk system. We find that MRI-transition fronts propagate inward (a `dead front' suppressing the MRI) if they are initially at the larger transition radius, or propagate outward (an `active front' igniting the MRI) if starting from the smaller transition radius. In both cases, the front stalls at a well-defined intermediate radius, where it remains in a quasi-static equilibrium. We propose that it is this new, intermediate stalling radius that functions as the true boundary between the active and dead zones in protoplanetary disks. These dynamics are likely implicated in observations of variable accretion, such as FU Ori outbursts, as well as in those planet formation theories that require the accumulation of solid material at the dead/active interface.