Resolving the extended interstellar medium of infrared galaxies II. Fine-structure line emission

We investigate how star formation and active galactic nuclei (AGNs) shape the ionized and neutral interstellar medium in 67 nearby luminous and ultraluminous infrared galaxies from the Great Observatories All-sky LIRG Survey (GOALS). Combining mid-infrared (MIR) spectral mapping from the Spitzer Infrared Spectrograph with far-infrared (FIR) spectroscopy from the Herschel Photodetector Array Camera and Spectrometer, we measure fine-structure emission lines in aperture grids extending to projected galactocentric distances of about 14 kpc. We compare the measurements with CLOUDY photoionization models to constrain the ionization parameter, hydrogen density, stellar age, and metallicity. In starburst-dominated galaxies, the combined MIR+FIR fits yield a decreasing ionization parameter with radius, approximately constant hydrogen densities, uniformly young stellar populations, and flat metallicity profiles. MIR-only fits instead yield an increasing ionization parameter with radius, highlighting the importance of FIR diagnostics, particularly the [C II] emission associated with photodissociation regions, in constraining the multiphase gas. In the strongest AGN-dominated system, the nucleus and inner extended regions show elevated [Ne III]/[Ne II] and suppressed [C II]/[O I] ratios, while the outermost regions, at projected distances of about 6 kpc and beyond, show values typical of star-forming regions. This suggests that the AGN may affect gas excitation out to about 5 kpc. Our results demonstrate the importance of combining MIR and FIR diagnostics to recover radial trends that can be hidden in galaxy-integrated measurements. Together with Paper I, they provide a benchmark for spatially resolved studies of gas and dust in starbursts and AGN-hosting galaxies.