 Multitemperature blackbody disk

A multitemperature blackbody disk adds the radiation from annuli with different effective temperatures. For a steady, radiatively efficient accretion disk, the inner annuli are hotter and dominate higher photon frequencies, while cooler outer annuli contribute at lower frequencies. With $T(r)\propto r^{-3/4}$, integrating the Planck law produces the intermediate-frequency slope $F_{\nu }\propto {\nu }^{1/3}$. This slope applies between the outer thermal turnover and inner high-frequency cutoff, rather than across the entire spectrum.^[ref]