Abstract

Context. The ionization fraction in the neutral interstellar medium (ISM) plays a key role in the physics and chemistry of the ISM, from controlling the coupling of the gas to the magnetic field to allowing fast ion-neutral reactions that drive interstellar chemistry. Most estimations of the ionization fraction have relied on deuterated species such as DCO+, whose detection is limited to dense cores representing an extremely small fraction of the volume of the giant molecular clouds that they are part of. As large field-of-view hyperspectral maps become available, new tracers may be found. The growth of observational datasets is paralleled by the growth of massive modeling datasets and new methods need to be devised to exploit the wealth of information they contain.Aims. We search for the best observable tracers of the ionization fraction based on a grid of astrochemical models, with the broader aim of finding a general automated method applicable to searching for tracers of any unobservable quantity based on grids of models.Methods. We built grids of models that randomly sample a large range of physical conditions (unobservable quantities such as gas density, temperature, elemental abundances, etc.) and computed the corresponding observables (line intensities, column densities) and the ionization fraction. We estimated the predictive power of each potential tracer by training a random forest model to predict the ionization fraction from that tracer, based on these model grids.Results. In both translucent medium and cold dense medium conditions, we found several observable tracers with very good predictive power for the ionization fraction. Many tracers in cold dense medium conditions are found to be better and more widely applicable than the traditional DCO+/HCO+ ratio. We also provide simpler analytical fits for estimating the ionization fraction from the best tracers, and for estimating the associated uncertainties. We discuss the limitations of the present study and select a few recommended tracers in both types of conditions.Conclusions. The method presented here is very general and can be applied to the measurement of any other quantity of interest (cosmic ray flux, elemental abundances, etc.) from any type of model (PDR models, time-dependent chemical models, etc.).