Super-Eddington Accretion Disks around Supermassive black Holes

TL;DR

The study conducts four global 3D radiation-MHD simulations of super-Eddington accretion onto a $5\times10^8 M_\odot$ SMBH to probe how angular momentum is transported, how outflows form, and how radiative efficiency depends on magnetic flux geometry. Spiral density waves generated by MRI-driven turbulence drive strong Reynolds stresses in flux-free cases, while net vertical magnetic flux enhances Maxwell stresses; outflows with speeds of 0.1–0.4c emerge and radiative efficiency varies from ~5–7% at moderate rates to ~1% at the highest rates, with funnel regions becoming optically thick. The results reveal a complex interplay between radiation pressure, magnetic fields, and density waves that shapes the disk structure and observable signatures, including weaker X-ray emission due to thick winds. These findings improve understanding of AGN feedback and the radiative properties of super-Eddington disks.

Abstract

We use global three dimensional radiation magneto-hydrodynamical simulations to study accretion disks onto a $5\times 10^8M_{\odot}$ black hole with accretion rates varying from $\sim 250L_{Edd}/c^2$ to $1500 L_{Edd}/c^2$. We form the disks with torus centered at $50-80$ gravitational radii with self-consistent turbulence initially generated by the magneto-rotational instability. We study cases with and without net vertical magnetic flux. The inner regions of all disks have radiation pressure $\sim 10^4-10^6$ times the gas pressure. Non-axisymmetric density waves that steepen into spiral shocks form as gas flows towards the black hole. In simulations without net vertical magnetic flux, Reynolds stress generated by the spiral shocks are the dominant mechanism to transfer angular momentum. Maxwell stress from MRI turbulence can be larger than the Reynolds stress only when net vertical magnetic flux is sufficiently large. Outflows are formed with speed $\sim 0.1-0.4c$. When the accretion rate is smaller than $\sim 500 L_{Edd}/c^2$, outflows start around $10$ gravitational radii and the radiative efficiency is $\sim 5\%-7\%$ with both magnetic field configurations. With accretion rate reaching $1500 L_{Edd}/c^2$, most of the funnel region close to the rotation axis becomes optically thick and the outflow only develops beyond $50$ gravitational radii. The radiative efficiency is reduced to $1\%$. We always find the kinetic energy luminosity associated with the outflow is only $\sim 15\%-30\%$ of the radiative luminosity. The mass flux lost in the outflow is $\sim 15\%-50\%$ of the net mass accretion rates. We discuss implications of our simulation results on the observational properties of these disks.

Figures (17)

• Figure 1: Histories of spherically integrated mass accretion rate at $10r_g$ for the four simulations. Negative values of $\dot{M}$ mean gas flows towards the black hole. The time unit $t_0\equiv r_g/c$ corresponds to $5\times10^{-3}$ Keplerian orbital period at $10r_g$.
• Figure 2: Space-time diagram of azimuthally averaged density (top panels), radiation temperature (middle panels) and azimuthal component of magnetic field (bottom panels) at radius $20r_g$ for the run AGN33 (left) and AGNB52 (right). (Note that the color bar ranges differ between the left and right panels.) The butterfly diagram shows up in the run AGNB52 where a single loop of magnetic field is used initially but does not exist in AGN33 which adopts multiple loops of magnetic field in the initial torus.
• Figure 3: Snapshots of density $\rho/\rho_0$ (left panels a and c) and radiation energy density $E_r/a_rT_0^4$ (right panels b and d) at the inner $40r_g$ of the accretion disks for runs AGN33 (top panels a and b) and AGNB25 (bottom panels c and d). The length unit in the plot is $2r_g$. The snapshots are taken at times $2.73\times 10^4t_0$ and $2.53\times 10^4t_0$ for runs AGN33 and AGNB25 respectively. Notice the significant spiral arms in the disk, particularly for $E_r$.
• Figure 4: Slices of radiation energy density $E_r$ (color) and $r,\theta$ components of radiation flux $F_{r,r},\ F_{r,\theta}$ (streamlines) through the plane $\phi=\pi$ at the same times as in Figure \ref{['spiralimage']} for the two runs AGN33 (left panel) and AGNB25 (right panel).
• Figure 5: Time and azimuthally averaged spatial structures of density $\rho$ (color) and density weighted flow velocity $v_r, v_{\theta}$ (streamlines) at the inner regions of the disks. Color of the streamlines represents the velocity magnitude $v\equiv \sqrt{v_r^2+v_{\theta}^2}$. From left to right, they are for runs AGN150, AGN33, AGNB25, AGNB52 respectively. The dashed black lines indicate the locations where the integrated optical depth from the rotation axis along the horizontal direction is one.