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

Technical Summary: Magnetic Fields in Extreme Primordial Halos

Problem Statement
The James Webb Space Telescope (JWST) has revealed the existence of supermassive black holes (SMBHs) at high redshifts, posing a challenge to standard formation models. One proposed channel for these early SMBHs is the direct collapse of massive primordial gas clouds within rare, high-sigma peaks of the cosmic density field. While previous studies have established that such halos host highly supersonic turbulence capable of amplifying magnetic fields, the dynamical role of these fields in extreme environments—specifically those driven by convergent cosmic filament flows—remains unclear. It is debated whether magnetic fields in such regimes can reach equipartition to suppress fragmentation and influence the formation of massive seeds, or if the extreme turbulence dominates the dynamics, rendering magnetic effects secondary.

Methodology
The authors conducted cosmological magneto-hydrodynamical (MHD) zoom-in simulations using the ENZO code, focusing on a specific dark matter halo identified in a previous study (Latif et al. 2022). This halo forms at the intersection of cosmic filaments, growing from $3.0 \times 10^5 M_\odot$ at $z=35$ to $1.4 \times 10^{12} M_\odot$ at $z=6$.

• Setup: The simulations utilize a $25 \text{ Mpc } h^{-1}$ cosmological box with adaptive mesh refinement (AMR), achieving a maximum spatial resolution of $\sim 20 \text{ AU}$ in the innermost regions.
• Initial Conditions: Three simulations were performed with different initial uniform magnetic field strengths: $B_0 = 10^{-14}$, $10^{-10}$, and $10^{-8} \text{ G}$ (proper units). These values span the range of upper limits for primordial magnetic fields established by Planck.
• Physics: The model includes primordial chemistry (solving for 9 species including $H_2$), self-gravity, and radiative cooling. A pressure floor is applied at the highest refinement level to satisfy the Truelove criterion and prevent artificial fragmentation.
• Resolution Constraints: The simulations employ a Jeans resolution of 64 cells per Jeans length. The authors note that while this is sufficient to resolve turbulent eddies, it may not fully capture small-scale dynamo amplification, particularly given the highly supersonic nature of the flows ($M \sim 30-60$), which is known to reduce dynamo efficiency.

Key Results

1. Dominance of Turbulence: The collapse dynamics are overwhelmingly dominated by highly supersonic turbulence driven by convergent cold flows from intergalactic scales. Turbulent Mach numbers reach values of $10\text{--}20$ within the halo, and sonic Mach numbers reach $30-60$.
2. Magnetic Field Amplification:
   • Magnetic fields are amplified beyond what is expected from simple spherical compression ($B/\rho^{2/3}$ increases toward the center).
   • Counter-intuitively, the simulation with the weakest initial field ($10^{-14} \text{ G}$) shows the most dramatic relative amplification due to shear flows, as the weak field offers negligible damping.
   • Despite amplification, the magnetic energy density ($E_B$) remains orders of magnitude below the kinetic energy density ($E_K$), with $E_B/E_K \ll 1$ throughout the halo. The fields never reach equipartition.
3. Jeans Mass Analysis:
   • The turbulent Jeans mass ($M_{J,turb}$) is the dominant scale for collapse across all radii, reaching $\sim 10^4 M_\odot$ in the central regions.
   • The magnetic Jeans mass ($M_{J,mag}$) only becomes comparable to the thermal Jeans mass on limited scales ($10^{-2} - 3 \text{ pc}$) and only in simulations with stronger initial fields. It never exceeds the thermal or turbulent contributions significantly.
   • This contrasts with "typical" atomic cooling halos where magnetic pressure can dominate on intermediate scales.
4. Morphological Evolution:
   • The large-scale morphology (four cold streams converging) remains unaffected by the initial magnetic field strength.
   • At sub-parsec scales, the simulations show the formation of disc-like structures. The strongest field case ($10^{-8} \text{ G}$) develops a binary core structure, whereas the weaker field cases show a single clump. The authors caution that this binary feature may be stochastic given the low number statistics.
   • Magnetic fields do not suppress the formation of these structures; the collapse proceeds to form central massive objects of $\sim 10^4 M_\odot$ regardless of the initial seed.
5. Timescales: Stronger initial magnetic fields systematically delay the onset of collapse and slow the subsequent evolution by approximately 13 kyr (compared to 4 kyr for the weakest field) due to additional magnetic pressure support.

Significance and Claims
The paper concludes that in extreme primordial halos formed at the intersection of cosmic filaments, turbulence is the primary regulator of collapse dynamics, not magnetic fields.

• Contrast with Typical Halos: The findings differ significantly from simulations of more typical atomic cooling halos, where magnetic fields can reach sufficient strength to suppress fragmentation and dominate the Jeans mass on intermediate scales. In this extreme regime, the high Mach numbers disfavor the efficiency of the small-scale dynamo, preventing magnetic fields from becoming dynamically relevant.
• Implications for Quasar Formation: The results support the formation of central massive objects (seeds for early quasars) with masses of a few times $10^4 M_\odot$ even in the presence of magnetic fields. The magnetic fields do not fundamentally alter the collapse pathway or the resulting mass scale, which is set by the turbulent pressure.
• Modesty on Future Evolution: The authors note that while magnetic fields are subdominant during the collapse, they may still play a role in the subsequent evolution of the formed supermassive star or black hole (e.g., via magnetic braking or jet launching), but this requires further investigation. They also emphasize that the lack of small-scale dynamo resolution in their setup means the results reflect the impact of initial seeds rather than full saturation, though the extreme physical conditions of the halo appear to be the limiting factor for amplification.