Power-law spectrum ($F_{\nu }\propto {\nu }^{-\alpha }$)

A radiation spectrum whose spectral flux density follows a power law over a stated frequency range. For $F_{\nu }\propto {\nu }^{-\alpha }$, the spectral energy distribution satisfies $\nu F_{\nu }\propto {\nu }^{1-\alpha }$. Thus $\alpha =1$ gives equal energy flux in equal logarithmic frequency intervals. A spectral break invalidates extrapolation with a single index.

The local logarithmic slope with the displayed sign convention. Other fields sometimes use the opposite sign, so an index should be accompanied by its defining power-law spectrum.