The diffuse ionized gas (DIG) is an important component of the interstellar medium that can provide insights into the different physical processes affecting the gas in galaxies. We utilise optical IFU observations of 71 gas-stripped and control galaxies from the Gas Stripping Phenomena in galaxies (GASP) survey, to analyze the gas properties of the dense ionized gas and the DIG, such as metallicity, ionization parameter log(q), and the difference between the measured $log[OI]/Halpha$ and the value predicted by star-forming models, given the measured log[OIII]/H$beta$ ($Delta log[OI]/Halpha$). We compare these properties at different spatial scales, among galaxies at different gas-stripping stages, and between disks and tails of the stripped galaxies. The metallicity is similar between the dense gas and DIG at a given galactocentric radius. The log(q) is lower for DIG compared to dense gas. The median values of log(q) correlate best with stellar mass, and the most massive galaxies show an increase in log(q) toward their galactic centers. The DIG clearly shows higher $Delta log[OI]/Halpha$ values compared to the dense gas, with much of the spaxels having LIER/LINER like emission. The DIG regions in the tails of highly stripped galaxies show the highest $Delta log[OI]/Halpha$, exhibit high values of log(q) and extend to large projected distances from star-forming areas (up to 10 kpc). We conclude that the DIG in the tails is at least partly ionized by a process other than star-formation, probably by mixing, shocks and accretion of inter-cluster and interstellar medium gas.
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