the earliest numerical models of Sun-like stars did not follow up on this work and continued to assume radiative equilibrium.

In his 1961 papers, Hayashi showed that the convective envelope of a star is determined by

where is unitless, and not the energy. Modelling stars as polytropes with index 3/2 (in other words, assuming they follow a pressure-density relationship of ), he found that is the maximum for a quasistatic

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