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We investigate how the stellar and gas-phase He abundances evolve asfunctions of time within simulated star-forming disc galaxies with differentstar formation histories. We make use of a cosmological chemodynamicalsimulation for galaxy formation and evolution, which includes star formation,as well as energy and chemical enrichment feedback from asymptotic giant branchstars, core-collapse supernovae, and Type Ia supernovae. The predictedrelations between the He mass fraction, $Y$, and the metallicity, $Z$, in theinterstellar medium of our simulated disc galaxies depend on the past galaxystar formation history. In particular, $dY/dZ$ is not constant and evolves as afunction of time, depending on the specific chemical element that we choose totrace $Z$; in particular, $dY/dX_{\text{O}}$ and $dY/dX_{\text{C}}$ increase asfunctions of time, whereas $dY/dX_{\text{N}}$ decreases. In the gas-phase, wefind negative radial gradients of $Y$, due to the inside-out growth of oursimulated galaxy discs as a function of time; this gives rise to longerchemical enrichment time scales in the outer galaxy regions, where we findlower average values for $Y$ and $Z$. Finally, by means of chemical evolutionmodels, in the galactic bulge and inner disc, we predict steeper $Y$ versus agerelations at high $Z$ than in the outer galaxy regions. We conclude that, forcalibrating the assumed $Y$-$Z$ relation in stellar models, C, N, and C+N arebetter proxies for the metallicity than O, because they show steeper and lessscattered relations.

He abundances in disc galaxies -- I. Predictions from cosmological chemodynamical simulations