Population III (Pop III) stars — the first, essentially metal-free stellar generation — are expected to be born very massive, yet it is still not known how much mass they lose during their long-lived hydrostatic (main-sequence and core-helium-burning) evolution. Bahena and Klapp (2010) computed the evolution of 100, 150, 200, 250, and 300 solar-mass zero-metallicity stars deliberately omitting mass loss and rotation, and identified the uncertain role of mass loss as 'one of the major systematic uncertainties remaining in the study of metal-free stars': line-driven winds are expected to be inefficient at zero metallicity, while pulsational instability, rotation-induced loss, and luminous-blue-variable-type episodic eruptions are candidate mechanisms whose effectiveness, thresholds, and integrated amounts remain undetermined, as does the critical mass for onset of nuclear pulsational instability. Later work has resolved only pieces: follow-up models with prescribed mass-loss rates, wind theory at very low metallicity, a pulsation analysis restricted to 500–3000 solar masses, and rotating model grids with parametrized mass loss. The open problem is to determine, physically rather than by prescription, which mass-loss mechanisms operate in zero-metallicity stars of the relevant mass range, their thresholds and rate laws, the integrated mass lost and hence the pre-supernova masses as functions of initial mass and rotation, and the consequent shift of the boundaries between direct black-hole collapse, pulsational pair instability, and pair-instability supernova — including whether mass loss reconciles formation-simulation mass scales with abundance-inferred progenitor masses.

Background

Population III (Pop III) stars are the first generation of stars, formed from primordial hydrogen-helium gas before any heavy elements ('metals') had been synthesized. Their typical masses — described statistically by the initial mass function (IMF), the distribution of stellar masses at birth — remain uncertain: formation calculations (Omukai and Palla 2003) favor very massive stars, while comparisons of computed supernova nucleosynthesis with the chemical abundances observed in extremely metal-poor (EMP) halo stars — second-generation stars whose atmospheres record the yields of single Pop III progenitors — favor lower progenitor masses of roughly 20–40 solar masses (Umeda and Nomoto 2002; Heger and Woosley 2002; Klessen and Glover 2023; Koutsouridou et al. 2024). Whether Pop III stars lose mass matters because mass loss during evolution sets the pre-supernova (pre-SN) mass, and the pre-SN mass decides the final fate: in sufficiently massive helium cores, electron–positron pair creation softens the equation of state and triggers a runaway thermonuclear pair-instability supernova (PISN) that completely disrupts the star, while still more massive cores collapse directly into black holes; intermediate cores suffer repeated pulsational pair instability (PPI) pulses that shed mass before collapse (Heger and Woosley 2002).

Bahena and Klapp (2010) computed the quasi-static evolution — the long-lived hydrostatic main-sequence and core-helium-burning phases, as opposed to the terminal explosive event — of 100, 150, 200, 250, and 300 solar-mass zero-metallicity models, deliberately without mass loss or rotation, finding 200 and 300 solar-mass models end as pair-instability supernovae and the 100 solar-mass model collapses to a black hole. They posed the questions their omission left open: (i) the IMF/mass-scale tension above; (ii) whether and by which mechanisms — pulsational instability, rotation, or luminous blue variable (LBV)-type phenomena, i.e. episodic eruptions known in later stellar generations — metal-free stars lose mass during quasi-static phases, since line-driven winds (radiation pressure on metal absorption lines) are inefficient at very low metallicity (Kudritzki 2002); (iii) the critical mass for onset of nuclear pulsational instability, driven by the strong temperature sensitivity of nuclear energy generation (the so-called ε\varepsilon-mechanism), which they state 'is uncertain'; and (iv) how including mass loss and rotation would change lifetimes, convective-core evolution, surface properties, proximity to the Eddington limit (the luminosity at which radiation pressure balances gravity), and final fates. They concluded that 'the uncertain role of mass loss can be viewed as one of the major systematic uncertainties remaining in the study of metal-free stars'.

Subsequent work has resolved only parts of this. The promised follow-up (Bahena and Hadrava 2012) evolved 100–250 solar-mass models with a prescribed mass-loss rate, i.e. the rate was imposed rather than derived from physics. Wind theory confirms line driving is very inefficient at low metallicity, with the Wolf–Rayet wind scaling flattening below about 10−310^{-3} of solar metallicity because carbon and oxygen lines take over from iron-group lines (Kudritzki 2002; Vink and de Koter 2005). For the ε\varepsilon-mechanism, Sonoi and Umeda (2012) — extending Baraffe, Heger and Woosley (2001) — found by linear nonadiabatic analysis that only the radial fundamental mode of 500–3000 solar-mass Pop III main-sequence stars is unstable, with estimated mass loss below about 10% of the stellar mass and an explicit caveat that convection–pulsation interaction must be understood better; the 100–300 solar-mass range was not covered. Rotating and magnetic Pop III model grids exist (Ekström, Meynet and Maeder 2007, building on Meynet and Maeder 2002; Yoon, Dierks and Langer 2012; Martinet et al. 2023), but they inject mass loss through prescriptions, and Martinet et al. identify those prescriptions as the remaining systematic. Smith and Owocki (2006) argued that continuum-driven super-Eddington eruptions are largely metallicity-insensitive and could dominate Pop III very-massive-star mass loss, but this remains a hypothesis without a first-principles eruption theory. Recent activity (Sabhahit et al. 2023; Sabhahit, Vink and Sander 2026, computing hydrodynamical rather than parametrized mass-loss rates for very massive stars at low metallicity) shows the question is actively open, and the Glover and Klessen (2026) review states the field consensus that Pop III winds 'are probably not an important source of feedback from Pop. III star formation, although this is not yet completely settled'. No existing work determines, from the operating mechanisms themselves, the integrated mass lost by 100–300 solar-mass zero-metallicity stars during quasi-static evolution and its effect on their final fates.

Problem Statement

For zero-metallicity (Population III) stars with initial masses covering at least the 100100–300 M⊙300\,M_\odot range of the source models (Bahena and Klapp 2010), a required domain extended to the neighbouring very-massive-star regime treated by adjacent studies only as needed to locate the onset of the mechanisms in question, determine — from the physical operation of the mass-loss mechanisms themselves, not from an imposed prescription — the mass lost during the quasi-static (main-sequence and core-helium-burning) phases of evolution, and its consequences, as follows. (1) Mechanisms and thresholds: establish which of the candidate mechanisms operate at zero initial metallicity — line-driven winds (including any winds driven by self-produced or rotationally mixed-up carbon-nitrogen-oxygen material), mass loss driven by the ε\varepsilon-mechanism pulsational instability (determining the critical initial mass for its onset in and below the 100100–300 M⊙300\,M_\odot range, including the convection–pulsation coupling flagged by Sonoi and Umeda 2012), rotation-induced mass loss (via angular-momentum transport and approach to critical rotation velocity), and continuum-driven super-Eddington eruptions of the LBV type — and give, for each operating mechanism, its threshold conditions (Eddington proximity, surface composition, rotation rate) and rate law. (2) Integrated mass loss and pre-supernova masses: compute the total mass lost along the quasi-static evolution as a function of initial mass and initial rotation rate — i.e. the mapping from initial to pre-supernova mass — together with the resulting changes to lifetimes, convective-core masses, and surface properties relative to the mass-loss-free models of Bahena and Klapp (2010). (3) Final fates: determine how the computed mass loss shifts the boundaries, in the initial mass–rotation plane, between direct black-hole collapse, pulsational pair instability, and pair-instability supernova, relative to the mass-loss-free fate map. (4) Mass-scale reconciliation: assess whether the computed mass loss reconciles the very-massive-star mass scale favored by formation simulations with the roughly 2020–40 M⊙40\,M_\odot progenitor masses favored by extremely-metal-poor abundance comparisons, or whether the tension must instead be resolved by the initial mass function itself. Parts (1)–(4) are distinct sub-questions: progress on any one part does not by itself resolve the others. Scope boundary: mass ejection during the terminal explosion or collapse event is excluded; the question concerns the quasi-static phases. The determination of the IMF itself is not requested; it enters only as the reconciliation target of part (4).

References

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