= Accretion-powered effective-temperature scaling
{title2=$T_{\rm eff}\propto t^{1/4}$}
For constant supply, negligible seed <mass> and fixed emitting radius, $M=\dot Mt$ and $L_{\rm acc}\propto t$. Thermal emission with $L=4\pi r_0^2\sigma_{\rm SB}T_{\rm eff}^4$ therefore gives the quarter-power law. It describes an effective surface <temperature>. A homologous ideal-gas interior at the same fixed radius instead has <virial temperature> proportional to <mass> and hence to time; its absolute <temperature> requires a structural model.
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