Qualitative explanations of red giant formation

Recent research on giant formation has focused on the need for qualitative explanations. The explanations have the following general, qualitative form: the polytrope n assumes a certain value, that makes d ln r/d ln z take on a very large value; large increases in r can then be explained in terms of small changes in the variable z. This form is applicable to all the explanations current in the literature - they all have (1) either implicitly or explicitly, both a hydrostatic component and a luminosity-opacity component, and (2) a reliance on singular solutions. Dimensional analysis reveals that power laws that assume the polytrope n → 5 are identical in both the hydrostatic and luminosity-based explanations.