Supermassive black holes (SMBHs) power quasars less than a billion years after the Big Bang, and one proposed origin is the direct collapse of gas in rare primordial haloes where strongly convergent, cold accretion flows drive violent supersonic turbulence that postpones star formation until a sudden, catastrophic baryon collapse forms supermassive stars (SMSs) of tens of thousands of solar masses, leaving massive black hole seeds. Latif, Whalen, Khochfar, Herrington and Woods (Nature 607, 48, 2022) demonstrated this channel in a single halo simulation, and their closing discussion left three open points: the SMS masses are upper limits until ionising ultraviolet (UV) feedback from the stars is quantified once they evolve onto hot, blue tracks; the paper showed that turbulence-driven collapse need only occur in about 10% of haloes capable of forming quasars by z > 6 to account for the observed quasar counts, but the actual fraction that undergoes collapse, and the statistical distribution of seed masses in a full cosmological volume, remain undetermined; and the paper conjectured that cosmic-web topology governed the numbers of these rare, strong cold-flow convergences, so the demographics of the first quasars may have been set by the structure of the cosmic web — a conjecture yet to be tested. This problem asks for those three quantifications.

Background

Quasars are extremely luminous galactic nuclei powered by accreting supermassive black holes (SMBHs, roughly 10610^6–101010^{10} solar masses). More than 200 quasars are now known at redshift z>6z > 6, when the Universe was less than a billion years old, and explaining how SMBHs grew so large so fast has been an open problem in astrophysics for two decades. One leading resolution is the direct-collapse black hole (DCBH) scenario: rather than growing from the ∼100\sim 100 solar-mass remnants of ordinary first stars (so-called Population III stars, the metal-free first stellar generation), gas in a primordial halo collapses almost isothermally into a short-lived supermassive star (SMS, 10410^4–10510^5 solar masses) that ends its life in a general-relativistic instability collapse, leaving a massive seed black hole that can grow to quasar scale by Eddington-limited accretion. Classical DCBH models required a strong external Lyman–Werner (LW) ultraviolet background — radiation between 11.2 and 13.6 eV that photodissociates molecular hydrogen (H2\mathrm{H}_2), the main coolant in metal-free gas — to suppress H2\mathrm{H}_2 cooling and fragmentation in an atomic-cooling halo (a halo massive enough, about 10710^7–10810^8 solar masses, to cool via atomic hydrogen at about 10410^4 K); the needed LW flux is uncertain by orders of magnitude. Simulations such as Wise et al. (Nature 566, 85, 2019) realized this LW-suppressed channel. Separately, cosmological simulations had predicted that rare, narrow streams of cold gas penetrating to halo centres (cold flows, or cold accretion) converging in low-shear environments could build massive seeds, but could not resolve the collapse itself. Latif et al. (2022) closed that gap for one halo: converging cold flows drove supersonic turbulence that prevented star formation until the halo suddenly collapsed, forming two SMSs of 31,000 and 40,000 solar masses with no need for an LW background, supersonic streaming velocities, or even atomic cooling, and they argued that this channel needs to operate in only about 10% of the 11–2×10−82 \times 10^{-8} per comoving cubic megaparsec haloes capable of hosting z>6z > 6 quasars to match observed quasar counts. The same paper's closing discussion, however, delimited what remains unknown, and those points are the subject of this problem: (1) its SMS masses are upper limits, because ionising UV from the SMSs themselves, once they contract onto hot, blue evolutionary tracks, could reduce their accretion rates, and quantifying this feedback requires treating the stellar ionising radiation field self-consistently with the accretion flow — the paper cites radiation-hydrodynamical (RHD) simulations, cosmological simulations that simultaneously follow the collapse and the stellar radiation field, as the setting in which such feedback operates; (2) the paper showed that delayed collapse only has to occur in about 10% of the haloes capable of forming quasars by z>6z > 6 (numbered at 11–2×10−82 \times 10^{-8} per comoving cubic megaparsec in large-scale simulations) to account for the observed quasar counts, but the actual fraction of these haloes that undergoes turbulence-driven collapse, and the statistical distribution of the resulting black hole seed masses in a full cosmological volume, are undetermined (single-halo or few-halo zoom-ins cannot yield them, since the relevant haloes are exponentially rare); and (3) the paper conjectured that, because the topology of cold flows in the primordial Universe governed the numbers of these rare reservoirs, the demographics of the first quasars may ultimately have been determined by the structure of the cosmic web — the filamentary network of dark matter and gas arising from gravitational instability — a conjecture that has yet to be tested with larger samples of haloes.

Problem Statement

Determine how the turbulence-driven, Lyman–Werner-free direct-collapse channel demonstrated by Latif et al. (2022) in a single halo is realized in the high-redshift halo population, addressing the open points delimited by that paper: (1) quantify how ionising ultraviolet feedback from the supermassive stars themselves, once they evolve onto hot, blue tracks, alters their accretion rates and final masses, testing the paper's caveat that the reported SMS masses should be taken as upper limits; this requires treating the stellar ionising radiation field self-consistently with the accretion flow. (2) Determine what fraction of the haloes capable of forming quasars by z > 6 (the population numbered at about 11–2×10−82 \times 10^{-8} per comoving cubic megaparsec in large-scale simulations, which is the reference population for this fraction) actually undergo turbulence-driven delayed collapse — the paper showed that occurrence in only about 10% of these haloes would suffice to account for the observed z > 6 quasar counts — and derive the statistical distribution of black hole seed masses this produces in a full cosmological volume, so the channel's contribution to the observed high-z quasar abundance can be tested. (3) Test the paper's conjecture that, because the topology of cold flows in the primordial Universe governed the numbers of these rare convergent-flow reservoirs, the demographics of the first quasars may ultimately have been determined by the structure of the cosmic web, using larger samples of haloes than the single halo simulated to date. Together, the three deliverables would convert the single-halo existence proof of Latif et al. (2022) into the population demographics of cold-flow-born quasar seeds.

References

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