Spectral index

In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density on frequency. Given frequency ${\displaystyle \nu }$ and radiative flux ${\displaystyle S}$, the spectral index ${\displaystyle \alpha }$ is given implicitly by

Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by

Spectral index is also sometimes defined in terms of wavelength ${\displaystyle \lambda }$. In this case, the spectral index ${\displaystyle \alpha }$ is given implicitly by

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