Metals versus Non-metals: Chemical Evolution of Hydrogen and Helium Isotopes in the Milky Way

TL;DR

This paper addresses a fundamental degeneracy in Galactic chemical evolution: metal yields, ISM ejection, and radial gas flows can produce similar present-day metallicities, complicating inferences about stellar yields. By incorporating non-metal isotopes—specifically D/H and $^3\text{He}/^4\text{He}$—in multi-zone GCE models, the authors show that these non-metals respond differently to the same yield and transport changes, enabling a break in the degeneracy. They forecast that about four additional measurements of $^3\text{He}/^4\text{He}$ within ~3 kpc of the Sun could determine the primordial ratio with ~30% precision, while the D/H–O/H–$^3\text{He}/^4\text{He}$ three-way relationship constrains the scale of metal yields and tests BBn. The study highlights both the observational challenges and the broad astrophysical payoff: refined constraints on stellar evolution, improved GCE modeling, and a new empirical handle on the primordial helium abundance.

Abstract

Star formation drives changes in the compositions of galaxies, fusing H and He into heavier nuclei. This paper investigates the differences in abundance evolution between metal and non-metal isotopes using recent models of Galactic chemical evolution appropriate for the thin disk epoch. A strong degeneracy arises between metal yields from stellar populations and the mean Galactocentric radial velocity of the interstellar medium (ISM). Similar metallicities arise when increases (decreases) in metal yields are combined with increases (decreases) to the gas flow velocity. A similar degeneracy exists between metal yields and the rate of gas ejection from the ISM. We demonstrate that this degeneracy can be confidently broken with precise measurements of the hydrogen (D/H) and helium ($^3$He/$^4$He) isotope ratios in the Galactic ISM. At fixed O/H, higher metal yields lead to higher D/H and lower $^3$He/$^4$He. Measurements available to date are not sufficiently precise or numerous to draw confident conclusions. A detailed inventory of non-metal isotopes in the Milky Way would provide critical empirical constraints for stellar and galactic astrophysics, as well as a new test of Big Bang Nucleosynthesis. We forecast that only $\sim$4 additional measurements of $^3$He/$^4$He within $\sim$$3$ kpc of the Sun are required to measure the primordial $^3$He/$^4$He ratio at $\sim$30\% precision. In parallel, empirical benchmarks on metal yields also have the power to inform stellar models, since absolute yield calculations carry factor of $\sim$$2-3$ uncertainties related to various complex processes (e.g., rotational mixing, convection, mass loss, failed supernovae).

Figures (5)

• Figure 1: Evolution of the ISM O abundance with time at $R = 8$ kpc in our four GCE models. Models using ejection of ISM gas from the disk versus those using radial flows within the disk (see discussion in Section \ref{['sec:gce:ejection-vs-radialflows']}) are color coded red and blue, respectively. Models using the $y / Z_\odot = 1$ scale of stellar yields versus those using $y / Z_\odot = 2$ (see discussion in Section \ref{['sec:gce:yields']}) are marked as solid and dashed lines, respectively. Summary: Models enrich on different timescales depending on the scale of metal yields but otherwise lead to the same O/H abundances in the ISM at the present day.
• Figure 2: Present day radial profiles of the $^3\text{He}/^4\text{He}$ and D/H ratios (top), the O abundance (bottom left), and the surface density of gravitational accretion (bottom right). Top panels show measurements of the non-metal isotope ratios available in the literature (see discussion in Section \ref{['sec:data']}). The lower left panel highlights the $R \sim 4 - 11$ kpc range as the region of the MW where these data reside. Summary: Overall, our GCE models have similar profiles in metallicity, but different yield scales lead to different normalizations in the D/H and $^3\text{He}/^4\text{He}$ profiles.
• Figure 3: The relationship between O/H, D/H, and $^3\text{He}/^4\text{He}$. Each panel shows the relationship between a pair of two quantities traced by the present-day ISM between $R = 3$ and $12$ kpc. Lines are colored and styled based on the GCE model with yield scales $y / Z_\odot = 1$ or $2$ (solid or dashed) and adopting ejection or radial gas flows (red or blue). Our adopted primordial isotope ratios (see Section \ref{['sec:gce:yields']}) are shown as a black $\times$ in the left panel and black dotted lines in the middle and right panels. At present, the Sun is the only astrophysical system with a measurement in all three of these panels, though the measurement corresponds to the protosolar composition as opposed to the present day Mahaffy1998. Grey lines in the middle panel show the D/H-O/H relation computed by Weinberg2017a for $y/Z_\odot = 1$ (solid) and $y / Z_\odot = 2$ (dashed). The black square in the right panel shows our measurement of the $^3\text{He}/^4\text{He}$ ratio in the Orion Nebula Cooke2022 assuming solar metallicity D'Orazi2009. Summary: This three-way relationship between O/H, D/H, and $^3\text{He}/^4\text{He}$ can provide measurements of both the scale of stellar yields and the primordial D/H and $^3\text{He}/^4\text{He}$ ratios simultaneously.
• Figure 4: The effects of failed supernovae (top) and rotation (bottom) on population-averaged massive star yields, computed with vice's vice.yields.ccsne.fractional function using stellar model predictions available in the literature (see discussion in Section \ref{['sec:discussion:yield-scale']}). Top: The yields of various elements under the W18 (black diamonds) and N20 (green circles) explosion mechanisms from Sukhbold2016, relative to the case where all massive stars explode as a CCSN at the ends of their lives Griffith2021. Bottom: The yields of the same elements assuming initial rotational velocities of $v_\text{rot} = 150$ km/s (red $\times$'s) and $v_\text{rot} = 300$ km/s (blue squares), relative to the non-rotating case ($v_\text{rot} = 0$). Summary: Failed supernovae and rotation each individually introduce factor of a $\gtrsim$few uncertainties in the predicted yields of most metals, so an empirical benchmark would provide an important test for stellar models.
• Figure 5: An inference of the primordial $^3\text{He}/^4\text{He}$ ratio, $( ^3\text{He}/^4\text{He} )_p$, using available measurements from the literature combined with mock data from our GCE model using ejection with the $y / Z_\odot = 2$ yield scale (see discussion in Section \ref{['sec:gce']}). The black square and gold $\times$ symbol indicate measurements of $^3\text{He}/^4\text{He}$ in the Orion Nebula by Cooke2022 and in Jupiter's atmosphere by Mahaffy1998, respectively. Red circles show mock measurements drawn from the GCE model at the present day at Galactocentric radii of $R = 5$, 7, 9, and 11 kpc, offset by measurement uncertainties of $\sigma([\text{O/H}]) = 0.02$ and $\sigma(^3\text{He}/^4\text{He}) = 0.13 \times 10^{-4}$ (see discussion in Section \ref{['sec:discussion:primordial-he-ratio']}). The red dashed line shows the line of best-fit to these data, with the intercept at O/H $= 0$ marked as the inferred primordial isotope rate of $(^3\text{He}/^4\text{He})_p = (1.06 \pm 0.32) \times 10^{-4}$. The grey dashed line marks the value of $( ^3\text{He}/^4\text{He} )_p$ used as input to our GCE models. Summary: Measurements of the $^3\text{He}/^4\text{He}$ ratio along $\sim$$4$ additional sightlines within distances of $\lesssim$$3$ kpc, each achieving similar precision as Cooke2022, would provide a measurement of $( ^3\text{He}/^4\text{He} )_p$ with $\sim$$30$% precision.