Modeling the Galactic Chemical Evolution of Helium

We examine the galactic chemical evolution (GCE) of $^4$He in one-zone and multi-zone models, with particular attention to theoretical predictions and empirical constraints on IMF-averaged yields. Published models of massive star winds and core collapse supernovae span a factor of 2 -- 3 in the IMF-averaged $^4$He yield, $y\mathrm{_{He}^{CC}}$. Published models of intermediate mass, asymptotic giant branch (AGB) stars show better agreement on the IMF-averaged yield, $y\mathrm{_{He}^{AGB}}$, and they predict that more than half of this yield comes from stars with $M=4-8 M_\odot$, making AGB $^4$He enrichment rapid compared to Fe enrichment from Type Ia supernovae. Although our GCE models include many potentially complicating effects, the short enrichment time delay and mild metallicity dependence of the predicted yields makes the results quite simple: across a wide range of metallicity and age, the non-primordial $^4$He mass fraction $\Delta Y = Y-Y_{\mathrm{P}}$ is proportional to the abundance of promptly produced $\alpha$-elements, like oxygen, with $\Delta Y/Z_{\mathrm{O}} \approx (y\mathrm{_{He}^{CC}}+y\mathrm{_{He}^{AGB}})/y\mathrm{_{O}^{CC}}$. Reproducing solar abundances with our fiducial choice of the oxygen yield $y\mathrm{_{O}^{CC}}=0.0071$ implies $y\mathrm{_{He}^{CC}}+y\mathrm{_{He}^{AGB}} \approx 0.022$, i.e., $0.022M_\odot$ of net $^4$He production per solar mass of star formation. Our GCE models with this yield normalization are consistent with most available observations, though the implied $y\mathrm{_{He}^{CC}}$ is low compared to most of the published massive star models. More precise measurements of $\Delta Y$ in stars and gas across a wide range of metallicity and [$\alpha$/Fe] ratio could test our models more stringently, either confirming the simple picture suggested by our calculations or revealing surprises in the evolution of the second most abundant element.