Hydrogen emission from low column density gas: Case C

With modern detectors it is now possible to image dilute gas near powerful sources of ionizing radiation. This note concerns hydrogen emission expected from such gas. Hydrogen recombination lines are usually said to be formed under either Case A or Case B conditions. Case B occurs when the neutral hydrogen column density is large enough for Lyman lines to be optically thick. They undergo multiple scatterings and are eventually degraded into a Balmer line and Lyα or two-photon emission. Case A occurs when the neutral hydrogen column density is small enough for Lyman lines to be optically thin and so freely escape the cloud. Optical and infrared hydrogen lines are weaker in Case A than Case B since a significant fraction of the energy escapes as Lyman lines. Numerical simulations presented here show that when a photoionized cloud is optically thin in the Lyman lines its optical and infrared emission is not described by Case A. These lines will always be enhanced by continuum pumping unless the continuum source contains strong Lyman absorption lines. Continuum fluorescence in the Lyman lines will usually be competitive with recombination since the integrated continuous oscillator strength of the Lyman continuum is of order that of the Lyman lines. The line spectrum produced by a low column density cloud is mainly determined by the spectrum of the incident radiation field and the Lyman line optical depth. This situation was defined in the original literature as "Case C." It was not developed because the central stars of nebulae might have strong Lyman absorption lines, and so little pumping occurs in the interstellar case. This effect will be generally important for lower column density clouds in extragalactic sources, where Lyman lines are seldom in absorption. The purpose of this note is to draw attention to Case C and to motivate more precise calculations of emission in this limit.