Matching envelope-models to the simulations

  This matching is done in two steps, at a reference pressure chosen as deep in the box as it is possible without getting disturbed by boundary effects:

• The MLT parameter is changed to get the same density at the matching point.
• And then the factor in the expression for , is adjusted to get the same at the matching point.

Matching in this way, it turns out that the gradient of from the simulations converges to that of the envelopes in the bottom third or so, of the simulation box, making it a sensible contributor to the hydrostatic equilibrium in the envelopes inward of the matching point. The results of this envelope matching can be seen in Fig. 1 and Table 1.