A PROCEDURE FOR CORRECTING THE APPARENT OPTICAL DEPTHS OF MODERATELY SATURATED INTERSTELLAR ABSORPTION LINES

摘要

Presently, most observations of absorption lines from interstellar and intergalactic matter have sufficient resolution to show most of the structure at differing radial velocities of the absorber. This added information allows one to go beyond the practice of just obtaining equivalent widths. As with measurements of W_λ, however, it is important to sense and correct for the fact that some parts of a profile may arise from absorption peaks that are strong enough to be saturated. This effect may be unrecognized, or at least underappreciated, in those cases where the narrowest velocity structures are degraded by the convolution of the true spectrum by the instrumental profile. Using a procedure that is virtually identical to the curve-of-growth method for equivalent widths, one can compare at any velocity the apparent optical depths τ_a of two lines that have significantly different transition probabilities. If their ratio is smaller than the ratio of the lines' values of fλ, the actual saturation is more severe than that indicated by the values of τ_a. This paper describes a simple procedure for selectively boosting the τ_a of the weaker of the two lines so that the unresolved saturated structure is accounted for. This enables one to obtain a very nearly correct answer for the column density per unit velocity. (However, the lost velocity detail is not restored.) Two synthetic test examples of very complex, saturated profiles are analyzed with this method in order to show how well it works. A demonstration with real observations is also presented. An explicit, easily computed formula that is a very close approximation to the real correction factors is given, to make data analysis and error estimation more convenient.