Addendum: Precision in high resolution absorption line modelling, analytic Voigt derivatives, and optimisation methods

Abstract

The parent paper to this Addendum describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. In that paper, we show that Voigt function derivatives can be calculated analytically using Taylor series expansions and look-up tables, for the specific case of one column density parameter for each absorption component. However, in many situations, modelling requires more complex parameterisation, such as summed column densities over a whole absorption complex, or common pattern relative ion abundances. This Addendum provides those analytic derivatives.