Recovering the properties of the interstellar medium through integrated spectroscopy: Application to the

Context. Deriving physical parameters from integrated galaxy spectra is paramount to interpret the cosmic evolution of the star formation, chemical enrichment, and energetic processes at play. Previous studies have highlighted the power of interstellar medium tracers but also the associated complexities that can be captured only through sophisticated modeling approaches. Aims. We developed modeling techniques to characterize the ionized gas properties in the subset of 2052 star-forming galaxies from the volume-limited, dwarf-dominated, z ∼ 0 ECO catalog (stellar mass range M* ∼ 108 − 11 M⊙). Our study sheds light on the internal distribution and average values of parameters such as the metallicity, ionization parameter, and electron density within galaxies. Methods. We used the MULTIGRIS statistical framework to evaluate the performance of various models using strong lines as constraints. The reference model involves physical parameters distributed as power laws with free parameter boundaries. Specifically, we used combinations of 1D photoionization models (i.e., considering the propagation of radiation toward a single cloud) to match optical H <ns0:sc>II</ns0:sc> region lines, in order to provide probability density functions of the inferred parameters. Results. The inference predicts nonuniform physical conditions within galaxies. The integrated spectra of most galaxies are dominated by relatively low-excitation gas with a metallicity around 0.3 Z⊙. Using the average metallicity in galaxies, we provide a new fit to the mass-metallicity relationship which is in line with direct abundance method determinations from the low-metallicity calibrated range up to high-metallicity stacks. The average metallicity shows a weakly bimodal distribution which may be due to external (e.g., refueling of non-cluster early-type galaxies) or internal processes (higher star-formation efficiency in metal-rich regions). The specific line set used for inference affects the results and we identify potential issues with the use of the [S <ns0:sc>II</ns0:sc>] line doublet. Conclusions. Complex modeling approaches may capture diverse physical conditions within galaxies but require robust statistical frameworks. Such approaches are limited by the inherent 1D model database as well as caveats regarding the gas geometry. Our results highlight, however, the possibility to extract useful and significant information from integrated spectra.