Relative f-values from interstellar absorption lines: advantages and pitfalls

Abstract

Interstellar absorption features seen in the ultraviolet and visible spectra of stars provide opportunities for comparing the strengths of different transitions out of the ground electronic states of atoms, ions and simple molecules. In principle, such measurements are straightforward since the radiative transfer is manifested as a simple exponential absorption law at any given radial velocity. Complications arise when the velocity structures of the lines are not completely resolved, or when the lines are either very strongly saturated or too weak to observe. Dynamic range limitations can compromise the comparisons of two transitions that have very different absorption f-values, but they can be mitigated if there are examples with very different column densities and transitions of intermediate strength that can help to bridge the large gap in line strengths. Attempts to unravel the effects of saturation include the use of a curve of growth when only equivalent widths are available, or the measurements of the ‘apparent optical depth’ when the line is mostly resolved by the instrument. Unfortunately, the application of the curve of growth for one constituent to that of another can sometimes create systematic errors, since the two may have different velocity structures. Likewise, unresolved fine velocity structures in features that have large optical depths can make the apparent optical depths misrepresent the smoothed versions of the true optical depths. One method to compare the strength of a very weak line to that of a very strong one is to measure the total absorption of the former and compare it with the strength of the damping wings of the latter. However in many circumstances, small amounts of gas at velocities well displaced from the line center can masquerade as damping wings. For this reason, it is important to check that these wings have the proper shape.