FORGE'd in FIRE II: The Formation of Magnetically-Dominated Quasar Accretion Disks from Cosmological Initial Conditions

TL;DR

This study demonstrates that cosmological inflows can naturally form magnetically dominated quasar accretion disks where the magnetic pressure far exceeds thermal pressure (β ≪ 1) and the toroidal field dominates. The disks are sustained by flux-freezing, with rapid advection of magnetic flux from large scales feeding a robust mean toroidal field, leading to trans-Alfvénic turbulence, efficient angular-momentum transport, and the potential for super-Eddington accretion. In contrast, simulations without magnetic fields fragment catastrophically and fail to produce substantial inflow, highlighting magnetic fields as essential for disk stability and SMBH growth in these environments. The work also situates these flux-frozen disks in the broader context of strongly magnetized disk literature, distinguishing them from MAD and magnetically elevated models and suggesting new pathways for interpreting quasar accretion physics from galactic to sub-pc scales.

Abstract

In a companion paper, we reported the self-consistent formation of quasar accretion disks with inflow rates $\sim 10\,{\rm M_{\odot}\,yr^{-1}}$ down to <300 Schwarzschild radii from cosmological radiation-magneto-thermochemical-hydrodynamical galaxy and star formation simulations. We see the formation of a well-defined, steady-state accretion disk which is stable against star formation at sub-pc scales. The disks are optically thick, with radiative cooling balancing accretion, but with properties that are distinct from those assumed in most previous accretion disk models. The pressure is strongly dominated by (primarily toroidal) magnetic fields, with a plasma $β\sim 10^{-4}$ even in the disk midplane. They are qualitatively distinct from magnetically elevated or arrested disks. The disks are strongly turbulent, with trans-Alfvenic and highly super-sonic turbulence, and balance this via a cooling time that is short compared to the disk dynamical time, and can sustain highly super-Eddington accretion rates. Their surface and 3D densities at $\sim 10^{3}-10^{5}$ gravitational radii are much lower than in a Shakura-Sunyaev disk, with important implications for their thermo-chemistry and stability. We show how the magnetic field strengths and geometries arise from rapid advection of flux with the inflow from much weaker galaxy-scale fields in these 'flux-frozen' disks, and how this stabilizes the disk and gives rise to efficient torques. Re-simulating without magnetic fields produces catastrophic fragmentation with a vastly smaller, lower-$\dot{M}$ Shakura-Sunyaev-like disk.

Figures (30)

• Figure 1: Image of the gas surface density in our fiducial cosmological simulation. We show projected gas density on a logarithmic scale (increasing dark-to-bright, dynamic range rescaled in each panel from a median $N_{H} \sim 10^{19}\,{\rm cm^{-2}}$ at the largest scale to $\sim 10^{8}$ times larger at the smallest scale). Multiple scales are shown to illustrate the dynamic range of the simulation, which zooms in down to $\approx 80\,$au scales around a $\sim 10^{7}\,M_{\odot}$ SMBH in the center of a massive galaxy at redshift $z\approx 4.4$ in a $\sim (100\,{\rm Mpc})^{3}$ cosmological box. The simulations include explicit multi-band radiation-magnetohydrodynamics, detailed thermochemistry/cooling, self-gravity with resolved individual (proto)star formation, accretion, evolution, and feedback, and many other physical processes (§ \ref{['sec:methods']}). Tidally captured gas streams from an encounter with a massive star-forming cloud complex triggered via gravitational torques in a galaxy-scale merger fall into the BH radius of influence (BHROI) at a few $\sim$ pc and circularize at $\sim 0.1-1\,$pc to form an accretion disk which we follow down to $\sim 300$ BH Schwarzschild radii.
• Figure 2: As Fig. \ref{['fig:image.zoom']}, showing face-on ( top) and edge-on ( bottom) projections (relative to the nuclear disk) with order-of-magnitude different spatial scales (dynamic range a factor of $\sim 100$ in each panel, rescaled as Fig. \ref{['fig:image.zoom']}). We focus on sub-pc scales; for discussion of the dynamics on larger scales driving these flows see Paper I. The dashed circle at right denotes the inner accretion boundary at $r < 80\,$au. We see the disk circularization radius from the inflowing filament. The disk is thin but has complex structure with spiral arms and multiple warps and some large-scale arms at different angles tracing new inflow with slightly different impact parameter.
• Figure 3: Magnetic field strengths as a function of BH-centric radius $r$. We measure $\langle |{\bf B}|^{2} \rangle^{1/2}$ in spherical annuli from our inner boundary at $\sim 80\,$au to $>$ Mpc scales, and show the corresponding $\langle B_{i}^{2} \rangle^{1/2}$ for the radial, toroidal, and poloidal components of the field (with directions defined relative to the angular momentum vector of the BH accretion disk at $r<0.1\,$pc). Inside $\ll 10\,$pc, the resolution is uniformly $<0.01\,M_{\odot}$ and star formation follows the STARFORGE individual-resolved-stars physics. Outside of this radius the resolution is lower and the FIRE prescriptions form stellar population particles representing multiple stars sampling an assumed IMF (see § \ref{['sec:methods']}). Intergalactic sub-nG magnetic fields are amplified by the turbulent and galactic dynamo to "typical" ISM magnetic field strengths of $\sim 1-15\,{\rm \mu G}$ at $\sim 1-10\,$kpc (labeled), but the fields are amplified and approach kG at $r \sim 100\,$au. At most radii the fields are roughly isotropic (representing the dis-ordered ISM and CGM without a preferred direction), with a mild radial bias in the infall region, before becoming predominantly toroidal where the clear rotating thin BH accretion disk forms (see Fig. \ref{['fig:image.zoom']}).
• Figure 4: Wedge plot showing various disk properties (colormaps labeled) including: 3D gas density $n_{\rm gas}$, gas temperature $T$, plasma $\beta\equiv c_{s}^{2}/v_{A}^{2}$, ratio of toroidal to total field strength $|B_{\rm tor}|/|{\bf B}|$, ratio of azimuthal to total velocity $|v_{\phi}|/|{\bf v}|$, ratio of magnetic pressure $P_{\rm B}$ to total non-rotational kinetic/turbulent ram pressure $P_{\rm turb}$, and "effective" total (including thermal+magnetic+turbulent support) local Toomre $Q_{\rm eff}$ parameter. The plot shows cylindrical coordinates $R,\,\phi$, but with the cylindrical radius $R$ stretched on a log scale from $\sim 80\,$au to $\sim 2\,$pc (labeled), to show the behavior over a large range of scales. All quantities are mass-weighted averages within each image pixel, in a slice through the disk midplane ($|z|/R<0.1$). Densities increase inwards; temperatures vary but tend to be mostly cold-to-warm at these scales; $\beta\ll1$ and decreases in the inner disk $R\lesssim 0.01\,$pc; the toroidal field and azimuthal (rotational) velocities dominate inside $\lesssim 0.1\,$pc; the magnetic pressure is crudely of order turbulent pressure but varies locally from $\sim 0.01-10$ times its value; and the effective stability parameter $Q_{\rm eff} \gg 1$ on all these scales.
• Figure 5: Radial profiles of properties versus spherical BH-centric distance $r$, from $<10^{-3}$ pc to $\sim 1\,$pc (properties are mass-averaged in concentric shells unless otherwise stated; for discussion of properties on larger (extra)galactic scales, see Paper I). Top left: Inflow rate (summing all gas with $v_{r} < 0$), outflow rate ($v_{r} > 0$), and star formation rate (stellar mass formed/accreted within the last dynamical time, in each shell). We see consistent inflow at up to $\sim 20\,{\rm M_{\odot}\,yr^{-1}}$. Top right: Toomre $Q$ parameter for the gas alone, separating thermal support ($c_{s}$), magnetic ($v_{A}$), turbulent ($v_{\rm turb}$) and total ($\delta v_{r,\,{\rm eff}}^{2} \equiv c_{s}^{2} + v_{A}^{2} + v_{\rm turb}^{2}$). The system is stable on all these scales, but the relatively modest thermal-only $Q$ produces some of the large-scale gravitoturbulence and some (very slow/weak) star formation. Middle left: Gas density (lines show mean, shaded range $\sim 90\%$ inclusion interval) weighted by mass (spikes correspond to denser arms/clumps) or volume. Middle right: Total contribution to the stress/pressure tensor (Frobenius norm of each tensor, lines show volume-weighted mean, shaded range $\sim 90\%$ interval), for kinetic ($\rho\,{\bf v}\,{\bf v}$), magnetic ($|{\bf B}|^{2}\,\mathbb{I}/8\pi -{\bf B}{\bf B}/4\pi$), thermal ($n\,k\,T\,\mathbb{I}$), and radiation ($\int {\rm d}\nu\,e_{\nu}\,\mathbb{D}_{\nu}$) energies. The thermal and radiation terms are in rough equilibrium as expected (the disk is optically thick) but are strongly dominated by magnetic and kinetic terms. Note the kinetic energy is primarily rotation of the disk, the turbulent kinetic energy is order-of-magnitude comparable to magnetic (turbulence is broadly trans-Alfvénic). Bottom left: Scale height $H/R$ directly measured (median or rms $z$, as labeled), and expected ($\approx \sigma/V_{c}$) from turbulent/magnetic/thermal support. Given the above, we see turbulent+magnetic support clearly dominate the disks' vertical structure. Bottom right: Magnetic field strength (rms volume-weighted value in solid, shaded shows $90\%$ range for total field strength), for total and by toroidal/poloidal/radial component. The fields rise to very large values at small $r$, and are toroidal-dominated in the disk but with non-negligible poloidal+radial terms. In a companion paper (Paper III) we note that all of these scalings can be reasonably approximated with a simple analytic similarity model.