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

TL;DR

This paper extends the original work on VPFIT by providing analytic derivatives for more complex absorption line models, improving precision and efficiency in spectral fitting.

Contribution

It introduces analytic derivatives for complex parameterizations in absorption line modelling, enhancing the capabilities of VPFIT beyond single column density parameters.

Findings

Analytic derivatives enable more accurate spectral modelling.

Enhanced VPFIT performance with complex parameterizations.

Improved optimization in absorption line analysis.

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.