Schwarzschild and Ledoux are equivalent on evolutionary timescales

TL;DR

This study uses 3D hydrodynamical simulations to compare Schwarzschild and Ledoux criteria, finding they become equivalent over evolutionary timescales, supporting the use of Schwarzschild criterion for stellar convection zone sizing.

Contribution

The paper demonstrates through simulation that Schwarzschild and Ledoux criteria converge over time, clarifying their applicability in stellar evolution models.

Findings

Convection zone growth aligns with Schwarzschild predictions.

Schwarzschild and Ledoux criteria agree in the long-term.

Entrainment affects convection zone evolution temporarily.

Abstract

Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are unstable according to the Ledoux criterion are convective. Initially, the radiative zone adjacent to the convection zone is Schwarzschild-unstable but Ledoux-stable due to a composition gradient. Over many convective overturn timescales the convection zone grows via entrainment. The convection zone saturates at the size originally predicted by the Schwarzschild criterion, although in this final state the Schwarzschild and Ledoux criteria agree. Therefore, the Schwarzschild criterion should be used to determine the size of stellar convection zones, except possibly during short-lived evolutionary stages in which entrainment persists.