Radiation spectrum

The distribution of emitted or received electromagnetic power, radiative flux or specific intensity across frequency or wavelength. The spectral quantity and interval convention must be specified: $F_{\nu }$ and $F_{\lambda }$ differ by the change-of-variable factor, while $\nu F_{\nu }$ gives energy flux per logarithmic frequency interval. This physical spectrum is distinct from the spectrum of a linear operator or a spectrum in topology.

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.