The relationship between warm and hot gas-phase metallicity in massive elliptical galaxies and the influence of active galactic nucleus feedback

Context. Warm ionized gas is ubiquitous at the centers of X-ray bright elliptical galaxies. While it is believed to play a key role in the feeding and feedback processes of supermassive black holes, its origins remain under debate. Existing studies have primarily focused on the morphology and kinematics of warm ionized gas. Aims. This work aims to provide a new perspective on warm (similar to 10 000 K) ionized gas and its connection to X-ray-emitting hot gas (> 10(6 )K) by measuring and comparing their metallicities. Methods. We conducted a joint analysis of 13 massive elliptical galaxies using MUSE/VLT and Chandra observations. Emission-line ratios, including [OIII]/H beta, [NII]/H alpha, were measured using MUSE observations to infer the ionization mechanisms. We derive metallicities of the warm ionized gas using HII, and LINER calibrations. We also computed the warm phase metallicity using X-ray/EUV, and pAGB star models. For two sources at higher redshifts, the direct Te method was also used to measure warm gas metallicities. The metallicity of the hot gas was measured using Chandra X-ray observations. Results. Our observations reveal that most sources exhibit composite ionization, with contributions from both star formation and LINER-like emission. The four sources with the lowest star formation rates in our sample - Centaurus, M87, M84, and Abell 496 - are dominated by LINER emission. A positive linear correlation was found between the gas-phase metallicities of the warm and hot phases, ranging from 0.3 to 1.5 Z(circle dot). In some sources the warm gas metallicity shows a central drop. A similar radial trend has been reported for the hot gas metallicity in some galaxy clusters. Conclusions. The ionization mechanisms of cooling flow elliptical galaxies are diverse, suggesting multiple channels for powering the warm ionized gas. The positive correlation found in warm and hot gas metallicities suggest the intimate connection between the two gas phases, likely driven by gas cooling and/or mixing. The large variation in the warm gas metallicity further suggests that cold gas mass derived under the assumption of solar metallicity for the CO-to-H2 conversion factor needs to be revised by approximately an order of magnitude.