H₃⁺ fractional abundance. Left panel: H₃⁺ vs. H column densities. The H column density corresponds to the obscuring material of the ∼4 μm continuum derived from the continuum differential extinction model (Sect. 3.1). The dashed lines indicate constant H₃⁺ fractional abundances between 10⁻⁶ and 10⁻⁸ in steps of 1 dex. The red circles are the observed (U)LIRGs. The black star corresponds to the average columns in the GC from Goto et al. (2008) and Oka et al. (2019). Upper limits for Seyfert-type AGN are indicated by the empty black squares. Middle panel: H₃⁺ fractional abundance as a function of the observed 2–10 keV X-ray luminosity. Right panel: Blue shaded area is the predicted H₃⁺ fractional abundance (left y-axis) as a function of ζ_H2/n_H estimated using Eq. 2 from Neufeld & Wolfire (2017) for x_e in the range (1.5–5) × 10⁻⁴ (Sect. 3.1). The horizontal red shaded area indicates the range of H₃⁺ fractional abundances measured in these (U)LIRGs. The dashed green line (right y-axis) is f_H2 as function of ζ_H2/n_H using Eq. 2 from González-Alfonso et al. (2013).