Fast modelling of ionization balance in the intergalactic medium: I- implications for the IGM metallicity

Abstract

Ionization balance in the intergalactic medium (IGM) underpins the interpretation of quasar absorption spectra by linking observed ionic columns to the underlying gas density, temperature, metallicity, and ionizing radiation field. Yet the relevant microphysical timescales (ionization, recombination, and cooling) can be comparable to the timescales over which the ultraviolet background (UVB) and thermodynamic state evolve. As a result, ion populations may exhibit strong history dependence. We present a fast, metals-inclusive, zero-dimensional framework to evolve the IGM across redshifts. The framework follows a coupled thermal and ionization evolution of a Lagrangian gas parcel in a redshift-dependent UVB. The model integrates stiff, time-dependent rate equations for H, He, and 107 metal ions (C, N, O, Ne, Mg, Si, S, Fe) while self-consistently evolving the thermodynamics via photoheating and standard cooling channels. We validate the approach by comparing its predictions to full three-dimensional hydrodynamical non-equilibrium calculations, finding that it recovers the IGM thermal and ionization histories to good accuracy over a wide redshift range, including the characteristic heating associated with He ii reionization. The framework efficiently maps ionization histories into cosmic metal-ion abundances and ionization corrections relevant for metallicity inference. As an application, we predict the cosmic C iv density parameter, ΩCIV, and use it to infer the origin of metal ions in the IGM and IGM metallicities from observational measurements, obtaining values in reasonable agreement with literature constraints. We also discuss the possible implications for the non-equilibrium ionization (NEI) in the IGM. Our framework is designed for rapid parameter studies, enabling controlled tests of how reionization timing, UVB spectral hardness, self-shielding, and spatial UVB inhomogeneity (e.g., patchy reionization and local sources) propagate into the IGM thermal/ionization history and metal-line observables, providing a practical bridge between micro-physical modeling and absorption-line analyses.