He abundances in disc galaxies -- I. Predictions from cosmological
  chemodynamical simulations
  We investigate how the stellar and gas-phase He abundances evolve as
functions of time within simulated star-forming disc galaxies with different
star formation histories. We make use of a cosmological chemodynamical
simulation for galaxy formation and evolution, which includes star formation,
as well as energy and chemical enrichment feedback from asymptotic giant branch
stars, core-collapse supernovae, and Type Ia supernovae. The predicted
relations between the He mass fraction, $Y$, and the metallicity, $Z$, in the
interstellar medium of our simulated disc galaxies depend on the past galaxy
star formation history. In particular, $dY/dZ$ is not constant and evolves as a
function of time, depending on the specific chemical element that we choose to
trace $Z$; in particular, $dY/dX_{\text{O}}$ and $dY/dX_{\text{C}}$ increase as
functions of time, whereas $dY/dX_{\text{N}}$ decreases. In the gas-phase, we
find negative radial gradients of $Y$, due to the inside-out growth of our
simulated galaxy discs as a function of time; this gives rise to longer
chemical enrichment time scales in the outer galaxy regions, where we find
lower average values for $Y$ and $Z$. Finally, by means of chemical evolution
models, in the galactic bulge and inner disc, we predict steeper $Y$ versus age
relations at high $Z$ than in the outer galaxy regions. We conclude that, for
calibrating the assumed $Y$-$Z$ relation in stellar models, C, N, and C+N are
better proxies for the metallicity than O, because they show steeper and less
scattered relations.
