Contrasting evolutionary pathways of fast- and slow-rotating galaxies in the green valley

We present an investigation of the evolutionary pathways of green valley (GV) galaxies, defined as galaxies with a distance to the star-forming main sequence in the range -1. 3<Δ_ ̊m SFMS <-0. 5, drawn from the SDSS-IV/MaNGA survey. Our goal is to examine the connection between the dynamical galaxy structure, specifically, its stellar angular momentum, and its key physical properties, including gas-phase metallicity, star formation history (SFH), and chemical enrichment history (ChEH). By exploring these correlations, we aim to constrain the physical processes that govern the evolution of green valley galaxies. We divided our sample into fast- and slow-rotating galaxies using a criterion motivated by the bimodal distribution of the stellar spin and compared their integrated stellar and gas-phase metallicities. Additionally, using a simple but comprehensive galaxy chemical evolution model, optimised to fit the gas-phase metallicity estimates and the integrated stellar spectra for each galaxy, we reconstructed the past star formation and chemical enrichment histories of the galaxies. The derived SFHs and ChEHs, along with parameters governing the gas-infall timescale and outflow strengths, offer valuable insights into the physical processes driving the evolution and quenching of our GV sample galaxies. We found that fast-rotating galaxies exhibit systematically higher metallicities in the gas and stellar phases compared to slow-rotating galaxies. However, in the gas phase, the difference is significant only at the low-mass end, while the stellar metallicity offset is observed consistently across the full stellar mass range. Our modelling framework yields simple but physically motivated explanations for these trends. At low stellar masses, the model predicts similar gas-infall and star formation timescales for fast- and slow-rotating galaxies, but the stronger outflows inferred for the slower population substantially reduce their chemical content in the gas and stars. At high masses, slow-rotating galaxies show shorter gas-infall and star formation timescales; the combination of a reduced pristine gas inflow and more efficient gas removal produces gas-phase metallicities that are comparable to those of fast-rotating galaxies, but systematically lower stellar metallicities. The systematic differences in stellar and gas-phase metallicity, as well as in model-inferred gas-accretion and outflow parameters, highlight the contrasting properties of fast- and slow-rotating galaxies in our GV sample. Interpreting these differences within our chemical evolution framework and combining evidence from theoretical studies suggests distinct past evolutions. Slow-rotating galaxies likely experienced more merger events, usually associated with strong gas removal processes, leading to their systematically lower metallicities. At low masses, stronger supernova-driven outflows reduce their chemical content while leaving star formation timescales similar to those of fast-rotating galaxies. At high masses, merger-triggered feedback from active galactic nuclei may rapidly deplete and suppress gas infall, producing the shorter star formation timescales seen in slow-rotating galaxies. Alternative environmental and assembly-driven scenarios are also discussed.