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The depths, widths, and shapes of absorption lines are the code of optical depth profiles. Line depth is the amplitude of the optical depth, which is absorber column density. Line width and shape mirror the total cross section. This is the atomic cross section convolved with a wavelength redistribution function, usually a Gaussian attributable to thermal Doppler broadening. The resulting optical depth profile is a Voigt function. In this chapter, we quantitatively described Voigt profiles in detail. The total absorption is the equivalent width and its functional dependence on column density and Doppler broadening is called the curve of growth. Expressions are derived for its three major regimes: the linear, flat, and damped “parts.” The measured equivalent width increases with increasing absorption redshift, and this must be calibrated out. Inverting absorption line profiles yields apparent optical depth (AOD) profiles, which can be converted into integrable column density profiles. We also describe how to compute the covering factor from doublets showing signs of partial covering and conclude with an in-depth discussion of Lyman-limit ionization breaks from optically thick absorbers.
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