Using integral field spectroscopic data of 24 nearby spiral galaxies obtained with the Multi-Unit Spectroscopic Explorer ( MUSE ) , we derive empirical calibrations to determine the metallicity of the diffuse ionized gas ( DIG ) and/or of the low-ionisation emission region ( LI ( N ) ER ) in passive regions of galaxies .
To do so , we identify a large number of H ii –DIG/LIER pairs that are close enough to be chemically homogeneous and we measure the metallicity difference of each DIG/LIER region relative to its H ii region companion when applying the same strong line calibrations .
The O3N2 diagnostic ( = log [ ( [ O iii ] /H \beta ) / ( [ N ii ] /H \alpha ) ] ) shows a minimal offset ( 0.01–0.04 dex ) between DIG/LIER and H ii regions and little dispersion of the metallicity differences ( 0.05 dex ) , suggesting that the O3N2 metallicity calibration for H ii regions can be applied to DIG/LIER regions and that , when used on poorly resolved galaxies , this diagnostic provides reliable results by suffering little from DIG contamination .
We also derive second-order corrections which further reduce the scatter ( 0.03–0.04 dex ) in the differential metallicity of H ii -DIG/LIER pairs .
Similarly , we explore other metallicity diagnostics such as O3S2 ( = log ( [ O iii ] /H \beta + [ S ii ] /H \alpha ) ) and N2S2H \alpha ( = log ( [ N ii ] / [ S ii ] ) + 0.264log ( [ N ii ] /H \alpha ) ) and provide corrections for O3S2 to measure the metallicity of DIG/LIER regions .
We propose that the corrected O3N2 and O3S2 diagnostics are used to measure the gas-phase metallicity in quiescent galaxies or in quiescent regions of star-forming galaxies .