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GASP XXXII. Measuring the diffuse ionized gas fraction in ram-pressure stripped galaxies

The diffuse ionized gas (DIG) is an important component of the interstellar medium and it can be affected by many physical processes in galaxies. Measuring its distribution and contribution in emission allows us to properly study both its ionization and star formation in galaxies. Here, we measure for the first time the DIG emission in 38 gas-stripped galaxies in local clusters drawn from the GAs Stripping Phenomena in galaxies with MUSE survey (GASP). These galaxies are at different stages of stripping. We also compare the DIG properties to those of 33 normal galaxies from the same survey. To estimate the DIG fraction (C$_{DIG}$) and derive its maps, we combine attenuation corrected H$α$ surface brightness with $\rm [SII]/Hα$ line ratio. Our results indicate that we cannot use neither a single H$α$ or $\rm [SII]/Hα$ value, nor a threshold in equivalent width of H$α$ emission line to separate spaxels dominated by DIG and non-DIG emission. Assuming a constant surface brightness of the DIG across galaxies underestimates C$_{DIG}$. Contrasting stripped and non-stripped galaxies, we find no clear differences in C$_{DIG}$. The DIG emission contributes between 20\% and 90\% of the total integrated flux, and does not correlate with the galactic stellar mass and star-formation rate (SFR). The C$_{DIG}$ anti-correlates with the specific SFR, which may indicate an older ($>10^8$ yr) stellar population as ionizing source of the DIG. The DIG fraction shows anti-correlations with the SFR surface density, which could be used for a robust estimation of integrated C$_{DIG}$ in galaxies.