= One-third spectrum of a multitemperature disk
{title2=$F_\nu\propto\nu^{1/3}$}
For a <blackbody> disk with $T\propto r^{-3/4}$, the substitution $x=h\nu/(k_BT)$ in $F_\nu\propto\nu^3\int r(e^x-1)^{-1}dr$ produces $F_\nu\propto\nu^{1/3}\int x^{5/3}(e^x-1)^{-1}dx$. When the inner and outer temperatures make the limits approximately zero and infinity, that convergent integral is independent of <frequency>. The law applies between the outer-edge turnover and the hot inner-disk cutoff.
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