Decisive constraints on redshift evolution of the stellar initial-mass function and coupled transient-progenitor parameters from cosmic transient rates

Whether the stellar initial-mass function (IMF) is universal or evolves with redshift remains unsettled. Gabrielli et al. (2024) introduced an observation-driven framework that infers a Larson-shaped IMF — high-mass slope $\xi$ and characteristic mass $m_c$ — by Bayesian matching of parametric models to the cosmic UV luminosity density, the local stellar mass density, and type Ia supernova, core-collapse supernova, and long gamma-ray burst rate data. They recovered an IMF compatible with local determinations, found no evidence for evolution of the slope but only a mild, uncertain evolution of the characteristic mass, and left open a set of coupled progenitor questions: the true maximum core-collapse progenitor mass (biased by failed/faint supernova incompleteness), the long-gamma-ray-burst progenitor mass range and remnant engine, the degeneracy between metallicity scatter and maximum progenitor metallicity, and the binary channel efficiencies behind the supernova Ia normalization. No resolution of these questions is yet reported in the literature, and the adjacent 2024–2026 literature remains active but contested.

Background

The stellar initial-mass function (IMF) specifies the relative number of stars formed as a function of initial mass in a newly born stellar population. Nearly every quantity derived from unresolved stellar populations — galaxy stellar masses, cosmic star-formation histories, chemical enrichment, and the ionizing-photon budget of cosmic reionization — depends on it, so IMF uncertainty propagates through most of galaxy evolution and cosmology. In the solar neighborhood the IMF is measured directly by counting stars: above roughly $1\,M_\odot$ it follows a nearly power-law shape with slope $\xi\approx-2.35$ (Salpeter 1955), flattening at lower masses in the parameterizations of Kroupa (2001) and Chabrier (2003). Whether this same IMF holds in all environments and at all cosmic times ("IMF universality") is unresolved: star-formation theory predicts that the IMF should respond to the temperature and density of star-forming gas, and hence to redshift, and the James Webb Space Telescope (JWST) era has intensified the debate because the surprising brightness of high-redshift galaxies can be reconciled with standard galaxy-formation models if early star formation produced a top-heavy IMF (relatively richer in massive stars).

A complementary, observation-driven route to the IMF uses stellar transients rather than star counts. Type Ia supernovae (SNe Ia) are thermonuclear explosions of accreting white dwarfs in binary systems; core-collapse supernovae (CCSNe) mark the deaths of massive stars; long gamma-ray bursts (LGRBs) are ultra-relativistic jets launched during the collapse of massive, usually low-metallicity, stars. Because the rates of these events, together with the cosmic ultraviolet (UV) luminosity density (the volume-averaged UV output of star-forming galaxies, which traces recent star formation) and the local stellar mass density, are integrals over the IMF weighted by stellar-evolution and binary physics, a parametric model fitted simultaneously to all of them constrains the IMF itself. Gabrielli et al. (2024) implemented this program: a Larson-shaped IMF $\phi(m)\propto m^{\xi}e^{-m_c/m}$, with high-mass slope $\xi$ and characteristic mass $m_c$, inserted into models of the UV luminosity density, stellar mass density, SN Ia, CCSN, and LGRB rates as functions of redshift, with all parameters constrained against empirical datasets by Bayesian Markov-Chain Monte Carlo (MCMC) sampling. They recovered an IMF statistically compatible with local determinations ($\xi=-2.53^{+0.24}_{-0.27}$, $m_c=0.10^{+0.24}_{-0.08}\,M_\odot$), estimated the fraction of SN Ia-progenitor binaries that actually explode ($N_{Ia}\approx3.5\times10^{-2}$), the maximum CCSN progenitor mass $M_{CC}^{up}\sim58^{+37}_{-23}\,M_\odot$, the LGRB progenitor mass bounds $M_{LGRB}^{low}<24\,M_\odot$ and $M_{LGRB}^{up}>51\,M_\odot$, and the maximum LGRB progenitor metallicity $Z_{max}=0.12^{+0.29}_{-0.05}\,Z_\odot$. Testing a redshift-dependent IMF (slope-evolution parameter $f_{imf}$, characteristic-mass-evolution parameter $\gamma$), they found no evidence for slope evolution ($f_{imf}<0.026$ at $1\sigma$) but a mild, uncertain increase of the characteristic mass with redshift ($\gamma_{imf}=0.53^{+0.21}_{-0.43}$).

Several prior results define the obstacles. Pre-supernova imaging of hydrogen-rich type II supernovae shows an apparent dearth of luminous red supergiant (evolved massive-star) progenitors above $\log(L/L_\odot)\approx5.1$ (Smartt 2015), interpreted either as a maximum CCSN progenitor mass near $20\,M_\odot$ or as failed supernovae — direct collapse to black holes with a faint or absent explosion — which would remove exactly the most massive progenitors from observed CCSN samples. The LGRB central engine is debated between the collapsar scenario (a spinning black hole with a massive accretion disk launches the jet) and the magnetar scenario (a rapidly spinning, strongly magnetized neutron star powers it); discriminating them via progenitor masses requires far tighter mass bounds. Cosmic metallicity evolution is often encoded in the fundamental metallicity relation (FMR), an empirical relation between gas-phase metallicity, stellar mass, and star-formation rate whose behavior at $z\gtrsim3$ is poorly calibrated; in the framework this couples structurally to the dispersion $\sigma_Z$ of galaxy metallicities, producing a degeneracy with $Z_{max}$. Finally, the SN Ia normalization $N_{Ia}$ conflates single-degenerate (white dwarf accreting from a companion star) and double-degenerate (two white dwarfs merging) channels whose efficiencies are set by binary evolution.

Problem Statement

Determine, within the multi-transient-rate framework of Gabrielli et al. (2024) or an equivalent observation-driven joint analysis of the same datasets, whether the stellar IMF evolves with redshift — obtaining decisive constraints on the slope-evolution parameter $f_{imf}$ and the characteristic-mass-evolution parameter $\gamma$ (equivalently on $\xi(z)$ and $m_c(z)$) — while simultaneously pinning down the progenitor parameters that the same rate data jointly constrain, with the framework's identified biases and degeneracies explicitly corrected: (1) treat failed/faint-supernova incompleteness in observed CCSN samples so that the inferred $M_{CC}^{up}$ estimates the true maximum CCSN progenitor mass rather than the maximum mass of observable progenitors; (2) break the structural degeneracy between the metallicity scatter $\sigma_Z$ and the maximum LGRB progenitor metallicity $Z_{max}$ using any published independent high-redshift metallicity measurements or an independently calibrated cosmic-metallicity evolution, explicitly cited; (3) marginalize over residual uncertainties in the intrinsic LGRB-rate reconstruction (beaming, luminosity function, relativistic effects) so that the progenitor mass bounds $M_{LGRB}^{low/up}$ tighten enough to discriminate a black-hole collapsar remnant from a neutron-star magnetar remnant, with the discriminating statistic and its threshold stated explicitly; and (4) decompose the SN Ia normalization $N_{Ia}$ into physically motivated single-degenerate and double-degenerate channel efficiencies using published binary-population-synthesis inputs and binary-fraction constraints as functions of mass and redshift, explicitly cited. The joint analysis of UV luminosity density, stellar-mass-density, SN Ia, CCSN, and LGRB-rate data, applying all four corrections (1)–(4) jointly in the same analysis, yields both (i) the IMF-evolution inference — posteriors that either establish significant evolution of the IMF slope and/or characteristic mass with redshift or quantify a universality bound at stated confidence — and (ii) the correspondingly tightened progenitor-parameter posteriors ($M_{CC}^{up}$, $M_{LGRB}^{low/up}$ and remnant engine, $Z_{max}$, channel efficiencies).

References

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