Inferring the HII region escape fraction of ionizing photons from infrared emission lines in metal-poor star-forming dwarf galaxies

Context. Local metal-poor galaxies stand as ideal laboratories for probing the properties of the interstellar medium (ISM) in chemically unevolved conditions. Detailed studies of this primitive ISM can help gain insights into the physics of the first primordial galaxies that may be responsible for the reionization. Quantifying the ISM porosity to ionizing photons in nearby galaxies may improve our understanding of the mechanisms leading to Lyman continuum photon leakage from galaxies. The wealth of infrared (IR) tracers available in local galaxies and arising from different ISM phases allows us to constrain complex models in order to estimate physical quantities. Aims. Primitive galaxies with low metal and dust content have been shown to host a patchier and more porous ISM than their high-metallicity counterparts, with numerous density-bounded regions from where ionizing photons might leak out. To what extent this peculiar structure contributes to the leakage of ionizing photons remains to be quantitatively studied. Such effects can only be investigated by accounting for the complexity and inhomogeneity of the ISM. We aim to provide a new statistical framework to quantify various galactic observables by constraining a representative multiphase and multisector topology using a combination of 1D models. Methods. To address these questions, we built a refined grid of models that include density-bounded regions and a possible contribution of an X-ray source. Using MULTIGRIS, a new Bayesian code based on Monte Carlo sampling, we combined the models as sectors under various assumptions to extract the probability density functions of the parameters and infer the corresponding escape fractions from H II regions (f(esc,HII)). We applied this new code to a sample of 39 well-known local starbursting dwarf galaxies from the Dwarf Galaxy Survey. Results. We confirm previous results that hinted at an increased porosity to ionizing photons of the ISM in low-metallicity galaxies and provide, for the first time, quantitative predictions for f(esc,HII). The predicted f(esc,HII) for low-metallicity objects span a large range of values, up to similar to 60%, while the values derived for more metal-rich galaxies are globally lower. We also examine the influence of other parameters on the escape fractions, and find that the specific star-formation rate correlates best with f(esc;HII). Finally, we provide observational line ratios that could be used as tracers of the photons escaping from density-bounded regions. Among others, we discuss the possible caveats of diagnostics based on [C II]158 mu m in low-metallicity environments as we find a strong metallicity dependence of the fraction of [C II]158 mu m emitted in the different ISM phases. Conclusions. The new framework presented in this paper allows us to use suites of unresolved IR emission lines to constrain various galactic parameters, including the escape fraction of ionizing photons from H II regions. Although this multisector modeling remains too simple to fully capture the ISM complexity, it can be used to preselect galaxy samples with potential leakage of ionizing photons based on current and forthcoming spectral data in unresolved surveys of local and high-redshift galaxies.