Trans-iron nucleosynthesis in zero-metallicity rotating massive stars: primary neutron sources, the seed-absence limit, and yield scaling with mass, rotation, mergers, and explosion physics

Whether zero-metallicity (Population III) massive stars can synthesize elements heavier than the iron peak through internally generated neutron sources is an open question of first-stars nucleosynthesis. Rotation can drive primary neutron production via $^{22}\mathrm{Ne}(\alpha,n)$ even in metal-free stars, but the complete absence of iron-peak seeds may preclude any neutron-capture flow beyond zinc: the only self-consistent coupled evolution-plus-explosion models computed so far (rotating 15 and 25 solar-mass stars with a 524-isotope network) produce no appreciable trans-iron material at $Z=0$, while production up to the first and, in a few cases, second s-process peaks appears already at $[\mathrm{Fe}/\mathrm{H}]=-5$ and $-4$. The open problem asks for a determination across the full massive-star mass range — including convective shell mergers, proton-ingestion neutron bursts, and self-consistent explosion physics — of whether any internal channel can produce trans-iron elements in a metal-free star, and of how the ejected yields scale with rotation and explosion physics, with direct consequences for interpreting neutron-capture abundance patterns in extremely and ultra metal-poor stars and the onset of early chemical evolution.

Background

Stars are classified by metallicity $Z$, the mass fraction of elements heavier than helium. The first, metal-free generation (Population III, Pop III) formed from gas left by Big Bang nucleosynthesis, which contains essentially no elements beyond lithium; at $Z=0$ the conventional iron-abundance notation $[\mathrm{Fe}/\mathrm{H}]$ (the logarithmic iron-to-hydrogen number ratio relative to the Sun) reads $[\mathrm{Fe}/\mathrm{H}]=-\infty$. Massive stars (roughly above $10\,M_\odot$) end their lives as core-collapse supernovae and dominated the earliest chemical enrichment of the Universe, so their nucleosynthetic yields set the initial conditions of Galactic chemical evolution.

Elements heavier than the iron peak are made mainly by neutron-capture processes. The slow neutron-capture process (s-process) operates during quiescent hydrostatic burning: neutrons released by $^{22}\mathrm{Ne}(\alpha,n)^{25}\mathrm{Mg}$ near the end of core helium burning are captured by pre-existing iron-peak seed nuclei, and the capture flow climbs in atomic mass until it stalls at nuclei with magic neutron numbers $N=50$ (the strontium region, first s-peak) and $N=82$ (the barium region, second s-peak). In massive stars this "weak" s-process is classically secondary: both the neutron source (built from initial CNO nitrogen) and the iron seeds scale with the star's initial metallicity, so standard non-rotating models predict negligible s-process yields at $[\mathrm{Fe}/\mathrm{H}]\lesssim-2$.

Rotation changes this. Rotationally induced internal mixing transports carbon and oxygen made in the helium core into the hydrogen-burning shell, where they are processed into primary $^{14}\mathrm{N}$ (freshly synthesized, independent of the initial metallicity) and then into primary $^{22}\mathrm{Ne}$ — a neutron source that no longer scales with $Z$. Parameterized post-processing by Pignatari et al. (2008) first showed that such rapidly rotating stars ("spinstars") could produce large amounts of trans-iron nuclei at low metallicity, but also that the resulting very high neutron-to-seed ratio destroys the iron seeds. Full grids of rotating models with s-process networks extending to bismuth (Frischknecht et al. 2012, 2016; Limongi & Chieffi 2018 down to $[\mathrm{Fe}/\mathrm{H}]=-3$) confirmed rotation-boosted s-process production at low but nonzero metallicity, while non-rotating $Z=0$ grids (Chieffi & Limongi 2004; Heger & Woosley 2010) produce essentially nothing beyond zinc. However, the Geneva grids stopped at the end of central oxygen burning — missing the late convective shell mergers and the explosion — and no coupled $Z=0$ calculation with a trans-iron network existed before 2024.

The observational driver is the population of extremely metal-poor (EMP, $[\mathrm{Fe}/\mathrm{H}]<-3$) and ultra metal-poor (UMP, $[\mathrm{Fe}/\mathrm{H}]<-5$) halo stars, believed to record the ejecta of one or a few first supernovae. Their neutron-capture abundances show large star-to-star spreads in [Sr/Fe] and [Ba/Fe] (Roederer et al. 2014), whose origin is debated.

Roberti, Limongi & Chieffi (2024) computed the first self-consistent evolution-plus-explosion models of rotating 15 and 25 $M_\odot$ stars at $Z=0$, $[\mathrm{Fe}/\mathrm{H}]=-5$ and $-4$, with a 524-isotope network up to bismuth and initial equatorial rotation velocities of 0–800 km/s. They found that rotation raises the neutron density at $Z=0$ to roughly $10^7\ \mathrm{cm^{-3}}$, yet the complete absence of iron-peak seeds inhibits production beyond Zn, as their neutron-exposure and seed-budget analysis showed. At $[\mathrm{Fe}/\mathrm{H}]=-5$ and $-4$, by contrast, rotating models reach the first s-peak ($N=50$), in a few cases the second ($N=82$) or even the strong component (lead), with partial destruction of the initial iron seeds ($^{64}\mathrm{Ni}$ surviving as an effective seed). The explosion was imposed as a one-dimensional thermal bomb — energy deposited instantaneously with a fixed ejected $^{56}\mathrm{Ni}$ mass and no mixing or fallback — and only two initial masses were computed. The authors list as explicit open limitations the uncalibrated rotational-mixing parameters ($f_c$, $f_\mu$) and the choice of convective stability criterion, the need for a deeper analysis of late convective shell mergers (penetration of the oxygen convective shell into carbon-rich layers; entanglement of the helium shell with hydrogen-rich layers), the thermal-bomb explosion treatment, and the restricted mass grid; the nuclear reaction rates were frozen at their October 2019 values.

Problem Statement

Determine whether massive stars born at zero metallicity ($Z=0$, $[\mathrm{Fe}/\mathrm{H}]=-\infty$) can synthesize and eject elements heavier than the iron peak (atomic number > 30, i.e. beyond zinc) through neutron-capture nucleosynthesis driven by internally produced (primary) neutron sources, and quantify how the ejected trans-iron yields depend on initial mass, initial rotation velocity, convective shell mergers, and the explosion and fallback physics. Concretely, the open question comprises: (i) whether the seed-free interior of a $Z=0$ star permits any internal neutron-capture channel to climb beyond Zn — the rotation-driven $^{22}\mathrm{Ne}(\alpha,n)$ s-process during helium burning, neutron bursts from H–He convective entanglement (proton ingestion), or C–O convective shell mergers — or whether substantial trans-iron production strictly requires pre-existing iron-peak seeds, i.e. a minimum metallicity near $[\mathrm{Fe}/\mathrm{H}]\approx-5$; (ii) the scaling of the trans-iron yields with rotation rate and initial mass across the massive-star range, beyond the two masses (15 and 25 $M_\odot$) computed so far with a trans-iron network; and (iii) how a self-consistent core-collapse explosion — the mass cut separating ejected from collapsing material, fallback of ejecta onto the remnant, and shock-induced modification of the nucleosynthesis — changes the ejected fraction of any trans-iron nuclei produced, relative to the thermal-bomb treatment. The determination bears directly on interpreting the diverse neutron-capture abundance patterns of extremely and ultra metal-poor stars, the putative second-generation descendants of the first stars, and on the initial conditions of early Galactic chemical evolution. Here 'significant' (equivalently 'substantial' or 'appreciable') trans-iron production means ejected production of nuclei beyond zinc at a non-negligible level, above the numerical noise of the nucleosynthesis calculation, as distinct from trace production.

References

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