Spectral Index

In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density on frequency. Given frequency and radiative flux, the spectral index 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 . In this case, the spectral index is given implicitly by

and at a given frequency, spectral index may be calculated by taking the derivative

The opposite sign convention is sometimes employed, in which the spectral index is given by

The spectral index of a source can hint at its properties. For example, using the positive sign convention, a spectral index of 0 to 2 at radio frequencies indicates thermal emission, while a steep negative spectral index typically indicates synchrotron emission.