= Hertzsprung-Russell slope of a stellar homology sequence
{c}
{title2=$d\log L/d\log T_{\rm eff}=4Y/(Y-2X)$}
For a <stellar homology> sequence with $R\propto M^X$ and $L\propto M^Y$, the <Stefan–Boltzmann law> gives $T_{\rm eff}\propto M^{(Y-2X)/4}$. Eliminating mass gives the displayed <Hertzsprung-Russell diagram> slope when $Y\ne2X$. The usual horizontal axis decreases in <temperature> toward the right, reversing the visual left-to-right sign. The relation is between logarithmic variables and depends on the specified structural assumptions.
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