Measurement of Noisy Absorption Lines Using the Apparent Optical Depth Technique

To measure the column densities of interstellar and intergalactic gas clouds using absorption-line spectroscopy, the apparent optical depth (AOD) technique of Savage & Sembach can be used instead of a curve-of-growth analysis or profile fit. We show that the AOD technique, while an excellent tool when applied to data with good signal-to-noise ratio (S/N), will likely overestimate the true column densities when applied to data with low S/N. This overestimation results from the nonlinear relationship between the flux falling on a given detector pixel and the apparent optical depth in that pixel. We use Monte Carlo techniques to investigate the amplitude of this overestimation when working with data from the Far Ultraviolet Spectroscopic Explorer (FUSE) and the Space Telescope Imaging Spectrograph (STIS), for a range of values of S/N, line depth, line width, and rebinning. AOD measurements of optimally sampled, resolved lines are accurate to within 10% for FUSE LiF and STIS E140M data with S/N ≳ 7 per resolution element.