The morphological, spectroscopic and kinematical properties of the warm interstellar medium (wim) in early-type galaxies (ETGs) hold key observational constraints to nuclear activity and the buildup history of these massive, quiescent systems. High-quality integral field spectroscopy (IFS) data with a wide spectral and spatial coverage, such as those from the CALIFA survey, offer an unprecedented opportunity for advancing our understanding of the wim in ETGs. This article centers on a 2D investigation of the wim component in 32 nearby (<~150Mpc) ETGs from CALIFA, complementing a previous 1D analysis of the same sample (Papaderos et al. 2013; P13). We include here Halpha intensity and equivalent width (EW) maps and radial profiles, diagnostic emission-line ratios, besides ionized-gas and stellar kinematics. This study is supplemented by tau-ratio maps as an efficient means to quantify the role of photoionization by pAGB stars, as compared to other mechanisms (e.g., AGN, low-level star formation). Additionally, we extend the tentative classification proposed in P13 by the type i+, which is assigned to a subset of type i ETGs exhibiting ongoing low-level star-formation (SF) in their periphery. This finding along with faint traces of localized SF in the extranuclear component of several of our sample ETGs points to a non-negligible contribution by OB stars to the total ionizing budget. We also demonstrate that, at the typical emission-line detection threshold of ~2AA in previous studies, most of the extranuclear wim emission in an ETG may evade detection, which could in turn prompt its classification as an entirely gas-devoid system. This study adds further observational evidence for a considerable heterogeneity among ETGs with regard to the physical properties and 2D kinematics of the wim component, and underscores the importance of IFS studies over their entire optical extent.
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