Curve of growth

In astronomy, the curve of growth describes the equivalent width of a spectral line as a function of the column density of the material from which the spectral line is observed.

[1] The curve of growth describes the dependence of the equivalent width

, which is an effective measure of the strength of a feature in a emission or absorption spectrum, on the column density

Because the spectrum of a single spectral line has a characteristic shape, being broadened by various processes from a pure line, by increasing the optical depth

of a medium that either absorbs or emits light, the strength of the feature develops non-trivially.

[2] In the case of the combined natural line width, collisional broadening and thermal Doppler broadening, the spectrum can be described by a Voigt profile and the curve of growth exhibits the approximate dependencies depicted on the right.

, increasing the thickness of the medium leads to a linear increase of absorption and the equivalent line width grows linearly

Eventually, the growth will be dominated by the Lorentzian tails of the profile, which decays as