Resolving the extended interstellar medium of infrared galaxies I. Polycyclic aromatic hydrocarbon emission

We investigate spatial variations in polycyclic aromatic hydrocarbon (PAH) properties and photoelectric heating efficiency in 67 nearby luminous infrared galaxies from the Great Observatories All-sky LIRG Survey (GOALS). Using mid-infrared spectroscopy from Spitzer and far-infrared cooling-line maps from Herschel, we extract spectra in concentric annuli and matched aperture grids out to about 14 kpc. PAH features are measured with the CAFE spectral decomposition tool. We trace photoelectric heating efficiency by combining PAH emission with cooling lines after isolating the neutral-gas contribution. In starburst galaxies, the PAH 11.3/7.7 ratio rises out to about 5 kpc while 6.2/7.7 remains nearly constant, indicating predominantly large, neutral PAHs. Between 5 and 8 kpc, 11.3/7.7 continues to rise while inferred PAH sizes decrease. Beyond 8 kpc, 11.3/7.7 falls and 6.2/7.7 rises, indicating smaller, more ionized PAHs. These trends are consistent with PAH photodestruction near the central starburst. Strong active galactic nucleus (AGN) systems show more neutral PAHs and harder radiation fields in their nuclear and inner regions. Beyond about 5 kpc, PAHs become more ionized and approach the starburst locus as the radiation field weakens. Strong AGNs influence average PAH charge states at 6-14 kpc as effectively as moderate AGNs at 1-6 kpc. Photoelectric heating efficiency increases with radius in both starburst and AGN-hosting galaxies as the radiation field weakens. In starbursts, higher efficiency is associated with more neutral PAHs, while AGN-dominated systems show the opposite relation. These results provide quantitative, spatially resolved constraints on the extent of AGN effects on dust properties in a population of luminous infrared galaxies.