Schwarzschild and Ledoux are Equivalent on Evolutionary Timescales

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 convection zone and adjacent radiative zone, including both thermal compositional buoyancy forces. As expected, regions are unstable according convective. Initially, is Schwarzschild-unstable Ledoux-stable due composition gradient. Over many overturn timescales grows via entrainment. The saturates at size originally predicted by although in this final state criteria agree. Therefore, should be used determine stellar zones, except possibly during short-lived evolutionary stages entrainment persists.