On the evolution of the snow line in protoplanetary discs II: Analytic approximations

TL;DR

This paper derives an analytic model for the evolution of the snow line in protoplanetary discs with dead zones, explaining its implications for planet formation and water delivery to Earth.

Contribution

It provides a fully analytic solution for the snow line radius in discs with dead zones, incorporating effects of ionisation and turbulence.

Findings

The snow line is farther out than in fully turbulent models.

In the solar system, the snow line remained outside Earth's orbit.

Dead zones can explain Earth's low water content.

Abstract

We examine the evolution of the snow line in a protoplanetary disc that contains a dead zone (a region of zero or low turbulence). The snow line is within a self-gravitating part of the dead zone, and we obtain a fully analytic solution for its radius. Our formula could prove useful for future observational attempts to characterise the demographics of planets outside the snow line. External sources such as comic rays or X-rays from the central star can ionise the disc surface layers and allow the magneto-rotational instability to drive turbulence there. We show that provided that the surface density in this layer is less than about 50 g/cm^2, the dead zone solution exists, after an initial outbursting phase, until the disc is dispersed by photoevaporation. We demonstrate that the snow line radius is significantly larger than that predicted by a fully turbulent disc model, and that in our own solar system it remains outside of the orbital radius of the Earth. Thus, the inclusion of a dead zone into a protoplanetary disc model explains how our Earth formed with very little water.