The Spectral Index of a source of Electromagnetic Radiation is a scalar measure describing its spectrum, assuming the spectrum forms a Power Law. It is specifically the exponent of the Frequency that produces a term proportional to the Radiant Flux at the same frequency, i.e.,
S ∝ να
Confusingly, sometimes the term is used to mean the negative of this exponent. Also, sometimes spectral index refers to an exponent of the Wavelength rather than of the frequency.
In cases where the radiant flux by frequency is not a power law, it can be said that the spectral index varies by frequency. The concept seems less useful in this case.