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.
Read more about Spectral Index: Spectral Index of Thermal Emission
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