The first, metal-free (Population III, Pop III) stars formed at cosmic dawn, but when this mode of star formation was terminated — and whether any of it persisted into or beyond the epoch of reionization — remains unsettled. Mebane, Mirocha & Furlanetto (2018) showed with a feedback-limited semi-analytic model that massive Pop III star formation can in principle continue down to z∼6z\sim6 at ∼10−4\sim10^{-4}–10−5 M⊙ yr−1 Mpc−310^{-5}\,M_\odot\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}, with the predicted end redshift dominated by two uncertain inputs: the prescription for Pop II star formation in low-mass halos and the Pop III initial mass function. Liu & Bromm (2020) posed the complementary question for z≲6z\lesssim6 and found that predictions range from termination at the end of reionization to Pop III formation continuing to the present day, hinging on turbulent metal mixing in massive halos. The question is now observationally live: JWST has produced candidate pristine galaxies at z≃5.7z\simeq5.7–6.6 and even z=3.19z=3.19, together with first constraints on the Pop III ultraviolet luminosity function, although spectroscopic follow-up has already ruled out zero metallicity for the most prominent candidate. This record formulates the determination of the Pop III star-formation end redshift — its history, dominant sensitivities, and falsifiable observational signatures — as an open problem.

Background

Population III (Pop III) stars are the first, metal-free generation of stars, formed from primordial hydrogen and helium in the early universe; all later, metal-enriched generations are called Population II (Pop II) and Population I. In the standard picture, Pop III formation begins at redshift z∼20z\sim20–3030 (larger redshift means earlier cosmic time) inside dark-matter 'minihalos' of ∼106 M⊙\sim10^{6}\,M_\odot, where gas can cool only through molecular hydrogen (H2_2), which favours gas clouds that fragment little and are thought to yield massive stars. H2_2 is fragile: a metagalactic ultraviolet Lyman–Werner (LW) background (photons of 11.2–13.6 eV that photodissociate H2_2) raises the minimum halo mass able to cool, and once that minimum passes the atomic-cooling threshold (Tvir∼104T_{\rm vir}\sim10^{4} K, M∼108 M⊙M\sim10^{8}\,M_\odot, above which hydrogen line cooling operates without molecules), pristine gas can no longer collapse in minihalos. Conversely, once supernova ejecta raise a halo's metallicity above a critical value (Zcrit∼10−3.5 Z⊙Z_{\rm crit}\sim10^{-3.5}\,Z_\odot), metal-line cooling enables ordinary low-mass (Pop II) star formation. The Pop III initial mass function (IMF; the distribution of stellar birth masses) remains unconstrained by observation, though simulations favour a top-heavy distribution of a few to a few hundred M⊙M_\odot (reviewed by Klessen & Glover 2023). The heaviest Pop III stars, roughly 140140–260 M⊙260\,M_\odot, are predicted to die as pair-instability supernovae (PISNe) with a distinctive nucleosynthetic signature.

Mebane, Mirocha & Furlanetto (2018) asked how long massive Pop III star formation can persist. They built a per-halo, feedback-limited semi-analytic model: halo growth rates are taken from abundance matching (statistically pairing dark-matter halos with galaxies by matching their cumulative number densities) against the observed galaxy population, and within each halo star formation proceeds at maximum efficiency until self-consistently computed feedback — the LW background, supernova-driven ejection of gas and metals, photoionization, and chemical enrichment above ZcritZ_{\rm crit} — halts it. Their headline results: the massive Pop III star-formation rate density (SFRD) rises to ∼10−4 M⊙ yr−1 Mpc−3\sim10^{-4}\,M_\odot\,{\rm yr}^{-1}\,{\rm Mpc}^{-3} and then declines, but can in principle continue down to z∼6z\sim6 at 10−410^{-4}–10−5 M⊙ yr−1 Mpc−310^{-5}\,M_\odot\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}; Pop II stars dominate the total SFRD and radiation backgrounds before Pop III formation ends; and surviving Pop III halos contain at most ∼103 M⊙\sim10^{3}\,M_\odot of massive Pop III stars with absolute UV magnitudes MAB=−5M_{\rm AB}=-5 to −10-10, far beyond direct imaging. Crucially, the predicted end redshift is dominated by two uncertain inputs: the Pop II star-formation prescription in low-mass halos — energy-regulated (inefficient) versus momentum-regulated (efficient) feedback, parameterized by supernova coupling efficiencies ϵk\epsilon_{\rm k} and ϵp\epsilon_{\rm p}, with efficient Pop II formation choking off Pop III earlier — and the Pop III IMF. The authors flag further neglected or simplified physics: X-ray feedback (which can either catalyze H2_2 formation or heat gas and suppress fragmentation), photoheating of the intergalactic medium (IGM), halo mergers, a single star-forming region with a single star in isolation per halo, homogeneous metal mixing, and a fixed re-accretion prescription for ejected gas.

Liu & Bromm (2020) posed the question for the post-reionization universe directly ('When did Population III star formation end?') and found that radiative feedback confines potential late-time Pop III formation to massive halos (M≳109 M⊙M\gtrsim10^{9}\,M_\odot), where the survival of pristine pockets depends on turbulent metal mixing; predictions ranged from termination at the end of reionization (z∼5z\sim5) to Pop III formation continuing to z=0z=0 at ∼10−7 M⊙ yr−1 Mpc−3\sim10^{-7}\,M_\odot\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}. The question has since become observational: the James Webb Space Telescope (JWST) has begun to constrain the Pop III ultraviolet luminosity function (UV LF; the comoving number density of galaxies per absolute UV magnitude) at z≃5.6z\simeq5.6–6.6 and has produced candidate pristine galaxies — while spectroscopic follow-up has already shown how easily such candidates fail. A complementary probe is the global 21-cm signal — the sky-averaged brightness of the 21-cm hyperfine emission line of neutral hydrogen, measured relative to the microwave background — whose shape during cosmic dawn responds to the timing and radiative output of the first stars. What is missing is a determination of the Pop III star-formation end redshift, with its dominant sensitivities quantified and falsifiable observational signatures attached.

Problem Statement

Determine when Population III (metal-free) star formation effectively ended — the full history of the Pop III star-formation rate density (SFRD) from cosmic dawn to its termination, or to the present day if it never fully terminates — and whether any late-time Pop III formation is observable.

That determination comprises the following jointly supporting parts:

  1. The Pop III SFRD history and an effective end redshift zendz_{\rm end}, under a stated, physically motivated criterion for 'ended' (for example, the SFRD falling below a stated fraction of its peak or below a stated detectability floor); where the reported value of zendz_{\rm end} depends on the chosen criterion, that dependence must be stated. This should cover at least the massive, supernova-producing component tracked by the source model, and, where possible, the low-mass Pop III component.

  2. A quantified sensitivity analysis showing how zendz_{\rm end} depends on the inputs the source literature identifies as dominant: the Pop III initial mass function and per-site stellar multiplicity; the efficiency and regulation of Pop II star formation in low-mass halos (energy- versus momentum-regulated feedback and the coupling parameters ϵk\epsilon_{\rm k}, ϵp\epsilon_{\rm p}); and metal mixing, retention, and re-accretion (including inhomogeneous mixing and external enrichment). The physics that the source model neglected or simplified and that later work has only partly addressed — X-ray feedback, IGM photoheating, and halo mergers — enters the analysis where it proves material for zendz_{\rm end}.

  3. Falsifiable observational signatures of the predicted late-time Pop III formation — for example the Pop III ultraviolet luminosity function at z≈5.6z\approx5.6–6.6 and below, pair-instability supernova rates and light curves, or features of the global 21-cm signal — together with the observations that would confirm, bound, or rule out Pop III survival to a given redshift.

The end redshift can be determined theoretically (semi-analytic, seminumerical, or simulation-based) and observationally (through a survey-level detection or constraint on it), the two modes bearing on the same objective. A theoretical determination rests jointly on parts 1–3 and closes with predictions that observations can test. An observational determination is grounded in a survey-level detection or constraint on the end redshift, connected to parts 1–3 through the model predictions it confirms, bounds, or rules out; because metal-line non-detections bound metallicity but do not by themselves establish primordial composition, it requires control of contamination by extremely metal-poor Pop II populations and exotic alternatives.

References

  1. Mebane, R. H., Mirocha, J., & Furlanetto, S. R. (2018). The Persistence of Population III Star Formation. Monthly Notices of the Royal Astronomical Society, 479, 4544–4559. DOI: 10.1093/mnras/sty1833. URL: https://arxiv.org/abs/1710.02528
  2. Liu, B., & Bromm, V. (2020). When did Population III star formation end? Monthly Notices of the Royal Astronomical Society, 497, 2839–2854. DOI: 10.1093/mnras/staa2143. URL: https://arxiv.org/abs/2006.15260
  3. Mebane, R. H., Mirocha, J., & Furlanetto, S. R. (2020). The effects of population III radiation backgrounds on the cosmological 21-cm signal. Monthly Notices of the Royal Astronomical Society, 493, 1217–1226. DOI: 10.1093/mnras/staa280. URL: https://arxiv.org/abs/1910.10171
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