Voigt Profile Fitting to Quasar Absorption Lines: An Analytic Approximation to the Voigt-Hjerting Function

The Voigt-Hjerting function is fundamental in order to correctly model the profiles of absorption lines imprinted in the spectra of bright background sources by intervening absorbing systems. In this work we present a simple analytic approximation to this function in the context of absorption line profiles of intergalactic HI absorbers. Using basic calculus tools, we derive an analytic expression for the Voigt-Hjerting function that contains only fourth order polynomial and Gaussian functions. In connection with the absorption coefficient of intergalactic neutral hydrogen, this approximation is suitable for modeling Voigt profiles with an accuracy of $10^{-4}$ or better for an arbitrary wavelength baseline, for column densities up to $N_{HI} = 10^{22} cm^{-2}$, and for damping parameters $a \lesssim 10^{-4}$, i.e. the entire range of parameters characteristic to all Lyman transitions arising in a variety of HI absorbing systems such as Lyman Alpha Forest clouds, Lyman Limit systems and Damped Lyman Alpha systems. We hence present an approximation to the Voigt-Hjerting function that is both accurate and flexible to implement in various types of programming languages and machines, and with which Voigt profiles can be calculated in a reliable and very simple manner.