Quasars observed at redshifts beyond six harbor black holes of a billion solar masses, and how their seeds formed remains unknown. One proposed channel is direct collapse: if pristine gas in galactic nuclei or pre-galactic haloes falls inward at rates exceeding a few tenths of a solar mass per year — far above ordinary first-star accretion rates — the inflowing matter contracts without ever igniting as a star, leaving a small black hole embedded in a massive, radiation-pressure-supported envelope (a 'quasistar') inside which the hole can grow at highly super-Eddington rates to 10^3-10^4 solar masses. The still-open core of that proposal, as formulated by Begelman (2008) and developed in the subsequent literature through the JWST era, is: whether the required high inflow rates are produced and sustained in realistic cosmological environments, how frequently; how the rapidly assembled, rotating envelopes are structured and how much mass they finally deliver to the black hole; and whether any observed population — in particular JWST's high-redshift AGNs and the enigmatic 'little red dots' — can be identified with these objects. Simulations have demonstrated feasibility in idealized settings and JWST has produced candidate heavy seeds, but no direct-collapse object has been confirmed, the incidence rate and seed-mass spectrum remain uncertain by orders of magnitude, and the envelope physics (rotation, opacity-driven mass loss) is still parametrized.

Background

Quasars at redshift z≳6z\gtrsim 6 power black holes of ∼109\sim10^9 solar masses (M⊙M_\odot) less than a billion years after the Big Bang. If the seeds of these black holes were ordinary stellar remnants, they would need to have grown at the Eddington limit — the maximum luminosity balance between gravity and radiation pressure — almost continuously since formation, which strains the available time. An alternative is that the seeds formed by direct collapse: the rapid accumulation of gas so fast that no star ever forms. The physical picture (Begelman, Volonteri & Rees 2006; Begelman 2008) is as follows. In ordinary first-star (Population III) formation, gas falls onto a growing core at ∼10−4\sim10^{-4}-10−2 M⊙ yr−110^{-2}\,M_\odot\,\mathrm{yr}^{-1}; nuclear ignition then halts contraction and a star results. But if the infall rate exceeds a few tenths of a solar mass per year — comparable to the natural gravitational inflow rate M˙∼v3/G\dot M\sim v^3/G of a self-gravitating system with internal velocity dispersion v≳10 km s−1v\gtrsim10\,\mathrm{km\,s^{-1}} — the core becomes so tightly bound before nuclear reactions ignite that the released energy cannot halt the collapse. The outcome is a low-entropy core that collapses to a black hole of ∼10\sim10-20 M⊙20\,M_\odot embedded in a high-entropy, radiation-pressure-dominated envelope of thousands to millions of solar masses. Because the accretion luminosity is limited only by the Eddington limit of the whole (much heavier) envelope, the embedded hole accretes at a rate super-Eddington for its own mass by a factor of order Menv/MBHM_{\rm env}/M_{\rm BH}, and can grow to 10310^3-104 M⊙10^4\,M_\odot in ∼105\sim10^5-10610^6 yr. The resulting object, powered by accretion rather than fusion and resembling an extreme red supergiant with a photospheric temperature of a few thousand kelvin, was dubbed a 'quasistar' (Begelman, Rossi & Armitage 2008). Reaching these high inflow rates requires gas that cannot cool much below the virial temperature of ∼104\sim10^4 K (an 'atomic-cooling halo'): it must be free of metals and lack molecular hydrogen (H2\mathrm{H}_2) cooling. Suppressing H2\mathrm{H}_2 is the central environmental difficulty — photodissociating radiation in the Lyman-Werner band (11-13.6 eV) can destroy it, but whether enough haloes experience the required irradiation history without prior metal-enriching star formation is contested. The envelope itself poses structural questions: simple scaling arguments allow two limiting density profiles (ρ∝r−2\rho\propto r^{-2} versus a nearly isothermal ρ∝r−1/2\rho\propto r^{-1/2}), and which applies once rotation and angular-momentum transport are included was left open. Because quasistars, like red giants, cannot maintain a photosphere below the temperature where opacity drops sharply (an 'opacity crisis' analogous to the Hayashi track forbidden zone), they are predicted to evaporate when they enter that region; the mass-loss response, including a super-Eddington bound-free opacity bump with an unresolved analogue in Luminous Blue Variables (unstable, intensely mass-losing supergiant stars), sets the final black hole mass. Modern work recasts part of the program in terms of supermassive stars (≳104 M⊙\gtrsim10^4\,M_\odot) that collapse through a general-relativistic radial instability once their cores exceed ∼3×104 M⊙\sim3\times10^4\,M_\odot (raised by up to a factor ∼5\sim5 by rotation), an alternative endpoint of the same rapid-accretion regime. Observationally, the James Webb Space Telescope (JWST) has now found accreting black holes at z≳10z\gtrsim10, including the overmassive black hole in the galaxy UHZ-1 whose mass rivals its host's stellar mass — a signature predicted for heavy seeds — and a population of compact, extremely red sources ('little red dots', z∼4z\sim4-99) whose physical nature is intensely debated, with proposed identifications ranging from dust-reddened active nuclei to the supermassive stars and late-stage quasistars of the direct-collapse scenario.

Problem Statement

Determine whether supermassive black holes formed by direct collapse, in the specific sense posed by Begelman (2008): (i) identify the astrophysical conditions under which galactic nuclei and pre-galactic haloes produce and sustain the very high gas inflow rates (≳0.1 M⊙ yr−1\gtrsim0.1\,M_\odot\,\mathrm{yr}^{-1}) required for collapse without a stellar precursor — including the relative roles of global versus local gravitational torques, merger- and turbulence-driven inflow, H2\mathrm{H}_2 formation and cooling, and early metal enrichment and prior star formation — and establish how frequently these conditions are realized in the cosmological population; (ii) determine the internal structure and evolution of the resulting rapidly assembled, rotating envelopes (quasistars), including angular-momentum transport and dissipation and the response to the opacity-driven forbidden region (the opacity crisis and its associated mass loss), which together fix the final black-hole seed masses, predicted to be ∼103\sim10^3-104 M⊙10^4\,M_\odot under simple parametrizations of the accretion efficiency; and (iii) predict and observationally test the frequency, typical masses, and spectroscopic/photometric signatures of these objects, so that the channel's role in the observed supermassive-black-hole population is decided at a single stated strength — confirmed as that population's predominant seeding channel, confirmed as only a sub-dominant contributor, or excluded — including against alternative interpretations of the candidate observations (in the current era, the high-redshift active nuclei and the 'little red dots' identified by JWST). These three components are jointly the problem, and each is settled by its own standard of evidence: (i) by a quantified incidence of the required inflow conditions in the cosmological population — a rate or fraction, not a qualitative demonstration of feasibility in idealized settings; (ii) by a determination of the rotating envelope's structure and its opacity-driven mass-loss response that fixes the final seed-mass scale rather than leaving it parametrized; and (iii) by the observational verdict, at the strength stated above, on the channel's role in the observed population. A determination of all three — the channel's incidence, its seed-mass scale, and its identifiable signatures — establishes whether supermassive black holes formed by direct collapse.

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