In this study, we analyse the characteristics of stellar populations and the
interstellar medium (ISM) in 15,107 early-type central galaxies from the SPIDER
survey. Using optical spectra from the Sloan Digital Sky Survey (SDSS), we
investigate stellar age (Age), metallicity (Z), visual extinction (AV​), and Hα equivalent width (EWHα) to understand the evolution
of the baryonic content in these galaxies. Our analysis explores the
relationship between these properties and central velocity dispersion
(σ) and halo mass (Mhalo​) for isolated centrals (ICs) and group
centrals (GCs). Our results confirm that both ICs and GCs' stellar populations
and gas properties are mainly influenced by σ, with Mhalo​
playing a secondary role. Higher σ values correspond to older, more
metal-rich stellar populations in both ICs and GCs. Moreover, fixed σ
values we observe younger Ages at higher values of Mhalo​, a consistent
trend in both ICs and GCs. Furthermore, we investigate the ionisation source of
the warm gas and propose a scenario where the properties of ionised gas are
shaped by a combination of cooling within the intra-cluster medium (ICM) and
feedback from Active Galactic Nuclei (AGN) assuming a Bondi accretion regime.
We observe inherent differences between ICs and GCs, suggesting that the ratio
between AGN kinetic power and ICM thermal energy influences EWHα in ICs.
Meanwhile, gas deposition in GCs appears to involve a more complex interplay
beyond a singular AGN-ICM interaction.Comment: 14 pages, 11 figures, accepted for publication in the MNRA