Supermassive PopIII Stars: Formation & Fate

• Supermassive PopIII Stars are metal-free, rapidly accreting primordial stars forming in atomic-cooling haloes with masses from 10⁴ to 10⁶ M₀, key to early black hole seeding.
• Their growth is driven by high accretion rates (∼0.1–1 M₀/yr) via disk-mediated inflows, where intermittent fragmentation does not hinder but often fuels their mass build-up.
• These stars feature inflated, cool envelopes with weak ionizing feedback, and their evolution is sensitive to rotation and angular momentum loss, influencing collapse versus explosion outcomes.

Searching arXiv for the cited SMS/Pop III literature and closely related work on formation, evolution, rotation, instability, and observability. Supermassive Population III stars are metal-free, rapidly accreting primordial stars that occupy the extreme high-mass end of Pop III star formation, typically at $M_\ast \sim 10^{4-5}\,M_\odot$ and, in some direct-collapse models, up to $\lesssim 10^6\,M_\odot$. They are studied primarily as progenitors of heavy black-hole seeds in the early universe, because their direct collapse can yield black holes of $\sim 10^5{-}10^6\,M_\odot$, alleviating the growth-time problem posed by the existence of quasars at $z\gtrsim 6{-}7$ (Hosokawa, 2018, Haemmerlé, 2022). Their formation, structure, stability, and observability are controlled by the coupled physics of atomic-cooling haloes, suppressed $\mathrm{H_2}$ cooling, extreme accretion, radiation-pressure support, angular-momentum transport, and general-relativistic instability (Woods et al., 2021, Matsukoba et al., 2020).

1. Cosmological setting and formation environments

Supermassive Pop III stars are associated with rare metal-free atomic-cooling haloes whose virial temperatures reach $T_{\rm vir}\sim 10^4$ K, enabling atomic hydrogen cooling while suppressing the usual minihalo mode of Pop III star formation. Across the literature summarized here, the relevant hosts lie in the approximate halo-mass range $M_{\rm halo}\sim 10^{7-8}\,M_\odot$ and formation-redshift range $z\sim 10{-}20$, with some studies examining even later-forming pristine haloes that were delayed by external ionizing fields (Chen et al., 2014, Woods et al., 2021, Sullivan et al., 22 Jan 2025). In the standard direct-collapse picture, strong Lyman–Werner backgrounds dissociate $\mathrm{H_2}$, the gas collapses nearly isothermally at $T\sim 8000{-}10^4$ K, fragmentation is reduced, and central inflow rates become high enough to assemble a supermassive protostar (Regan et al., 2018, Hosokawa, 2018).

This environment is not unique to externally irradiated haloes. Dynamical heating during rapid halo assembly can also delay cooling and maintain warm, massive clouds until collapse, yielding a subset of atomic-cooling haloes with very high central supply rates (Toyouchi et al., 2022). At the same time, internal Lyman–Werner feedback from one Pop III source inside an atomic-cooling halo does not appear to be an efficient way to create a second supermassive star after a dense core has already formed. In simulations with two nearby collapsing clumps, a realistic internal field of $\lesssim 10^6\,M_\odot$0 reduces $\lesssim 10^6\,M_\odot$1 in low-density gas but does not heat the core to the atomic-cooling regime; accretion rates and final stellar masses decrease rather than increase, and SMS formation is not facilitated (Sullivan et al., 22 Jan 2025).

The rarity of the required conditions is a recurring result. Strong LW fields, dynamical heating, or both can create suitable primordial clouds, but the pathway is highly selective. This suggests that SMSs represent a special mode of Pop III star formation rather than the generic outcome of metal-free collapse (Regan et al., 2018, Toyouchi et al., 2022).

2. Assembly by rapid accretion and disk-mediated inflow

The decisive control parameter is the mass accretion rate onto the protostar. In atomic-cooling gas, characteristic inflow rates are $\lesssim 10^6\,M_\odot$2, and several stellar-evolution studies adopt a critical rate near $\lesssim 10^6\,M_\odot$3 for maintaining the SMS state; recent work also quotes a broader range $\lesssim 10^6\,M_\odot$4 (Regan et al., 2018, Matsukoba et al., 2020, Sullivan et al., 22 Jan 2025). Above this threshold, the protostar remains bloated and cool; below it, sustained contraction toward a hot main-sequence Pop III configuration becomes possible.

Three-dimensional and two-dimensional calculations consistently show that the inflow is neither smooth nor monolithic. Primordial disks around forming SMSs are self-gravitating and fragment when the Toomre parameter

$\lesssim 10^6\,M_\odot$5

falls to $\lesssim 10^6\,M_\odot$6, producing spiral arms and massive clumps (Matsukoba et al., 2020). In detailed disk calculations, raw accretion can fluctuate by 9 orders of magnitude, but the $\lesssim 10^6\,M_\odot$7-yr averaged rates remain typically $\lesssim 10^6\,M_\odot$8, with quiescent intervals shorter than the surface Kelvin–Helmholtz timescale,

$\lesssim 10^6\,M_\odot$9

so the star does not have time to contract into a strong ionizing source (Matsukoba et al., 2020). This result is central: disk fragmentation does not automatically destroy the SMS channel; rather, clump migration and tidal disruption can feed the central object in bursts.

Cosmological simulations add an important dynamical qualification. In haloes irradiated by $\sim 10^5{-}10^6\,M_\odot$0, supercritical accretion can persist for $\sim 10^5{-}10^6\,M_\odot$1 yr and produce stars of $\sim 10^5{-}10^6\,M_\odot$2, but mild fragmentation and N-body interactions can eject the most massive objects from the halo center, shutting off subsequent growth (Regan et al., 2018). By contrast, somewhat less extreme $\sim 10^5{-}10^6\,M_\odot$3 haloes produce central Pop III stars of $\sim 10^5{-}10^6\,M_\odot$4 that may remain coupled to the inflow and later feed their black-hole remnants more effectively (Regan et al., 2018). A plausible implication is that “best SMS-forming” conditions and “best central BH-seed” conditions do not always coincide.

A separate 3D RHD study of dynamically heated atomic-cooling haloes reached a similar bifurcation. One halo sustained the cool bloating phase and grew unimpeded to $\sim 10^5{-}10^6\,M_\odot$5, whereas another supplied the protostar more weakly; there the star spent most of its life as a hot main-sequence source and its growth was terminated around $\sim 10^5{-}10^6\,M_\odot$6 by photoevaporation of the circumstellar disk (Toyouchi et al., 2022). In those simulations, the resulting primordial IMF over $\sim 10^5{-}10^6\,M_\odot$7 is approximately top-heavy, following $\sim 10^5{-}10^6\,M_\odot$8 with a steeper decline at $\sim 10^5{-}10^6\,M_\odot$9 (Toyouchi et al., 2022).

3. Stellar structure, inflated envelopes, and weak ionizing feedback

At sufficiently high accretion rates, SMSs enter the “supergiant protostar” stage. The defining structural relation is

$z\gtrsim 6{-}7$0

which yields radii exceeding $z\gtrsim 6{-}7$1 after the star accretes more than $z\gtrsim 6{-}7$2, and radii of order $z\gtrsim 6{-}7$3 AU at $z\gtrsim 6{-}7$4 (Hosokawa, 2018, Regan et al., 2018). The luminosity is near the Eddington limit, while the effective temperature stays low, typically $z\gtrsim 6{-}7$5 K, because the inflated atmosphere is regulated by opacity physics in the cool outer envelope (Hosokawa, 2018, Matsukoba et al., 2020). The result is a star with enormous bolometric luminosity but very weak ionizing output.

This weak ionizing output is the main reason radiative feedback fails to halt SMS growth under sustained high accretion. In the bloated state, the ionizing photon production is negligible compared to that of a hot ZAMS-like Pop III star of the same mass; H II regions remain compact or absent, and accretion continues (Hosokawa, 2018, Toyouchi et al., 2022). Even when accretion is variable, if low-$z\gtrsim 6{-}7$6 episodes remain shorter than $z\gtrsim 6{-}7$7, the star re-inflates before contracting to $z\gtrsim 6{-}7$8 K (Matsukoba et al., 2020). This makes intermittent accretion compatible with long-term SMS growth.

The envelope structure is not that of a fully relaxed classical $z\gtrsim 6{-}7$9 polytrope. In rapidly accreting models it consists of a compact nuclear-burning core, an extended radiative envelope, and a low-mass convective outer layer, with significant structural diversity when cosmological accretion histories are imposed directly (Woods et al., 2021). In KEPLER models fed by realistic halo inflows, SMSs can range from highly bloated configurations to nearly fully thermally relaxed, almost fully convective objects, depending on the time history of the accretion (Woods et al., 2021). This suggests that effective temperature and feedback may be more heterogeneous than constant-$\mathrm{H_2}$0 models imply.

Mass loss by radiation-driven winds does not eliminate the SMS channel in metal-free gas. Steady, optically thick wind calculations for rapidly accreting super-giant protostars show that the wind velocity never reaches escape speed, because once the temperature falls below $\mathrm{H_2}$1 K the opacity drops sharply owing to hydrogen recombination and the acceleration ceases (Nakauchi et al., 2016). In realistic non-steady cases such outflows would fall back, so net mass loss is negligible compared to $\mathrm{H_2}$2 (Nakauchi et al., 2016). A distinct line of work on porous, super-Eddington atmospheres instead finds continuum-driven winds and reduced ionizing emission, but still concludes that non-rotating SMSs can collapse to supermassive black holes, whereas rotationally stabilized ones may be eroded down to stars of a few $\mathrm{H_2}$3 (Dotan et al., 2012). The coexistence of these results reflects differing assumptions about atmospheric porosity, rotation, and evolutionary phase.

4. Rotation, GR stability, and collapse to black-hole seeds

SMSs are radiation-pressure dominated and evolve close to the Eddington limit, with $\mathrm{H_2}$4 in rotating Pop III models (Haemmerlé, 2022). Their surface rotation is then constrained by the $\mathrm{H_2}$5-limit,

$\mathrm{H_2}$6

so that $\mathrm{H_2}$7 for $\mathrm{H_2}$8 (Haemmerlé, 2022). Even this “slow” surface rotation is dynamically important for GR stability. To keep the star below the $\mathrm{H_2}$9-limit while accreting from a disk, the specific angular momentum of inflowing gas must satisfy

$T_{\rm vir}\sim 10^4$0

meaning that more than $T_{\rm vir}\sim 10^4$1 of the Keplerian angular momentum must be removed before gas joins the star (Haemmerlé, 2022). The centrifugal barrier is therefore one of the central theoretical constraints on SMS formation.

Rotation stabilizes SMSs against GR collapse. In hylotropic and GENEC-based analyses, even $T_{\rm vir}\sim 10^4$2 shifts the GR instability threshold upward; for Pop III SMSs under typical atomic-cooling conditions, realistic values $T_{\rm vir}\sim 10^4$3 still allow final masses of a few $T_{\rm vir}\sim 10^4$4, while more extreme accretion and rotation can in principle produce much larger masses in merger-driven environments (Haemmerlé, 2022). By contrast, KEPLER models evolved in realistic cosmological flows but without rotation reach $T_{\rm vir}\sim 10^4$5 before undergoing direct collapse during or at the end of main-sequence H burning at $T_{\rm vir}\sim 10^4$6 Myr, largely independent of halo mass, spin, or merger history (Woods et al., 2021). This indicates that the collapse mass is model-dependent: it varies with the treatment of accretion history, rotation, and internal angular-momentum transport.

When collapse occurs, the generic outcome in the SMS regime is direct black-hole formation. In full GRMHD simulations of uniformly rotating, marginally unstable SMSs modeled as $T_{\rm vir}\sim 10^4$7 polytropes, collapse yields a black hole with $T_{\rm vir}\sim 10^4$8 and spin $T_{\rm vir}\sim 10^4$9, plus a hot, massive torus (Sun et al., 2017). After $M_{\rm halo}\sim 10^{7-8}\,M_\odot$0, an incipient jet is launched; the jet luminosity is $M_{\rm halo}\sim 10^{7-8}\,M_\odot$1 erg s$M_{\rm halo}\sim 10^{7-8}\,M_\odot$2, and the GW signal peaks at $M_{\rm halo}\sim 10^{7-8}\,M_\odot$3 mHz, placing $M_{\rm halo}\sim 10^{7-8}\,M_\odot$4 collapses in the LISA band and $M_{\rm halo}\sim 10^{7-8}\,M_\odot$5 collapses in the DECIGO/BBO band (Sun et al., 2017). In the more recent rotational analysis, the amount of mass left outside the horizon at collapse depends strongly on the spin profile: for atomic-cooling Pop III SMSs with realistic $M_{\rm halo}\sim 10^{7-8}\,M_\odot$6, little or no torus is expected, whereas higher-$M_{\rm halo}\sim 10^{7-8}\,M_\odot$7 merger-driven cases can retain $M_{\rm halo}\sim 10^{7-8}\,M_\odot$8 of the stellar mass in orbit (Haemmerlé, 2022).

5. Rare thermonuclear explosions and their observable transients

Direct collapse is not the only endpoint. A narrow mass range near $M_{\rm halo}\sim 10^{7-8}\,M_\odot$9 admits thermonuclear disruption instead of black-hole formation. Early modeling presented a $z\sim 10{-}20$0 Pop III progenitor as a supermassive PI SN with explosion energy $z\sim 10{-}20$1 erg and near-IR detectability to $z\sim 10{-}20$2 (Whalen et al., 2012). Subsequent calculations identified the trigger more precisely: a non-rotating $z\sim 10{-}20$3 primordial star becomes unstable because the general-relativistic contribution of radiation to gravity causes the core to contract during He burning; explosive helium burning then reverses collapse and completely unbinds the star (Chen et al., 2014). In those models, the same star collapses to a black hole if GR corrections are ignored, and a $z\sim 10{-}20$4 model collapses directly even with GR included, implying a very narrow explosion window (Chen et al., 2014).

The explosion energetics are extreme. KEPLER gives $z\sim 10{-}20$5 erg, while 2D CASTRO yields $z\sim 10{-}20$6 erg, well above the binding energy $z\sim 10{-}20$7 erg (Chen et al., 2014). The star is completely disrupted, leaves no compact remnant, and ejects nearly all of its mass. The nucleosynthesis is distinctive: about half of the stellar mass is expelled as heavy elements, but the yield is dominated by $z\sim 10{-}20$8-chain nuclei from C to Si, with $z\sim 10{-}20$9 (Chen et al., 2014). This differs sharply from ordinary pair-instability supernovae, which are triggered by pair creation in $\mathrm{H_2}$0 stars and can synthesize $\mathrm{H_2}$1 of $\mathrm{H_2}$2 (Chen et al., 2014).

Such explosions are also observationally unusual. They are not powered by radioactive decay but by shock heating, radiative diffusion, and ejecta–CSM interaction. Semi-analytic models informed by stellar-evolution and GR collapse simulations predict bolometric luminosities of $\mathrm{H_2}$3, source-frame durations of $\mathrm{H_2}$4 yr, and observer-frame durations of $\mathrm{H_2}$5 yr after cosmological time dilation (Jockel et al., 21 Jul 2025). The light curves are therefore quasi-persistent. Bright SMS explosions are predicted to be observable in long-wavelength JWST filters up to $\mathrm{H_2}$6 at $\mathrm{H_2}$7 mag, pulsating SMSs up to $\mathrm{H_2}$8, and Euclid or the Roman Space Telescope can detect SMS explosions at $\mathrm{H_2}$9 (Jockel et al., 21 Jul 2025). Deep Euclid fields could constrain the SMS rate down to $T\sim 8000{-}10^4$0, substantially deeper than current JWST bounds (Jockel et al., 21 Jul 2025).

The spectroscopic expectation is H/He-rich, metal-poor, Type IIn-like emission from an optically thick shock propagating through primordial circumstellar material (Jockel et al., 21 Jul 2025). A plausible implication is that some very red, weakly variable high-$T\sim 8000{-}10^4$1 sources could overlap in color–magnitude space with little red dots or AGN, and would require spectroscopy to distinguish.

6. Role in early black-hole demographics and open problems

SMSs remain one of the leading heavy-seed channels for the first quasars. In the simplest version of the scenario, a Pop III SMS forms in a rare atomic-cooling halo, accretes rapidly for $T\sim 8000{-}10^4$2Myr, and collapses to a $T\sim 8000{-}10^4$3 black hole that can later grow into the SMBHs powering quasars by $T\sim 8000{-}10^4$4 (Hosokawa, 2018, Haemmerlé, 2022). The difficulty of growing $T\sim 8000{-}10^4$5 Pop III remnants into $T\sim 8000{-}10^4$6 SMBHs under feedback-limited accretion is one of the main motivations for the SMS route (Matsukoba et al., 2020, Woods et al., 2021).

At the population level, however, the pathway is not guaranteed to be efficient. Fragmentation and dynamical ejection can create wandering SMS remnants rather than central seeds (Regan et al., 2018). Radiative feedback in some ACHs terminates growth near $T\sim 8000{-}10^4$7 instead of allowing the SMS regime (Toyouchi et al., 2022). Internal LW feedback inside a protogalaxy appears unlikely to rescue a cooled core and convert it into an SMS-forming cloud (Sullivan et al., 22 Jan 2025). These results indicate that the massive end of the Pop III IMF is broad and environmentally sensitive, spanning from $T\sim 8000{-}10^4$8 to $T\sim 8000{-}10^4$9, rather than producing a single canonical SMS mass (Toyouchi et al., 2022).

Multiple-object outcomes are another major theme. Cosmological flows can produce more than one massive disk or protostar in a single halo, raising the possibility of SMS binaries, supermassive X-ray binaries, and direct-collapse black-hole mergers detectable by LISA (Woods et al., 2021). In rotating collapse models, multimessenger signatures include ultra-long GRB-like jets, strong gravitational waves, and, in some cases, remnant tori that power extended electromagnetic emission (Sun et al., 2017, Haemmerlé, 2022). Rare thermonuclear explosions would add a separate class of long-lived infrared transients (Jockel et al., 21 Jul 2025).

Several uncertainties remain structural rather than merely parametric. The required angular-momentum extraction efficiency is extreme (Haemmerlé, 2022). Fully coupled 3D radiation-MHD simulations of SMS formation and evolution are still lacking (Haemmerlé, 2022). Surface temperatures and feedback strengths differ across stellar-evolution codes, especially when highly variable cosmological accretion is imposed (Woods et al., 2021). Wind physics is model-dependent, with one class of calculations finding fallback-dominated metal-free winds (Nakauchi et al., 2016) and another emphasizing super-Eddington porosity and continuum-driven mass loss with low ionizing output (Dotan et al., 2012). Finally, the narrow GR-instability explosion window near $\lesssim 10^6\,M_\odot$00 remains a special-case outcome rather than the dominant SMS fate (Chen et al., 2014).

Taken together, the current picture is internally coherent but not closed. Supermassive Pop III stars are best understood as a rare, rapidly accreting, weakly ionizing branch of primordial stellar evolution that can either collapse into heavy black-hole seeds or, in a narrow and physically distinctive regime, explode as extraordinarily energetic, Ni-poor thermonuclear transients. Their importance lies both in what they may have done—seeded the first quasars—and in how they might now be constrained: through the demographics of high-redshift black holes, the chemistry of early enrichment, long-duration infrared transients, and future gravitational-wave detections (Woods et al., 2021, Jockel et al., 21 Jul 2025).