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Curve of growth

Curve used to interpret spectral features in astronomy From Wikipedia, the free encyclopedia

Curve of growth
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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]

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Example of a curve of growth

Shape

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. For low optical depth corresponding to low , increasing the thickness of the medium leads to a linear increase of absorption and the equivalent line width grows linearly . Once the central Gaussian part of the profile saturates, and the Gaussian tails will lead to a less effective growth of . Eventually, the growth will be dominated by the Lorentzian tails of the profile, which decays as , producing a dependence of .[2]


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