The Primordial Abundance of Deuterium: Ionization correction

We determine the relative ionization of deuterium and hydrogen in low metallicity damped Lyman-alpha (DLA) and sub-DLA systems using a detailed suite of photoionization simulations. We model metal-poor DLAs as clouds of gas in pressure equilibrium with a host dark matter halo, exposed to the Haardt & Madau (2012) background radiation of galaxies and quasars at redshift z~3. Our results indicate that the deuterium ionization correction correlates with the H I column density and the ratio of successive ion stages of the most commonly observed metals. The N(N II) / N(N I) column density ratio provides the most reliable correction factor, being essentially independent of the gas geometry, H I column density, and the radiation field. We provide a series of convenient fitting formulae to calculate the deuterium ionization correction based on observable quantities. The ionization correction typically does not exceed 0.1 per cent for metal-poor DLAs, which is comfortably below the current measurement precision (2 per cent). However, the deuterium ionization correction may need to be applied when a larger sample of D/H measurements becomes available.