A Global Three Dimensional Radiation Magneto-hydrodynamic Simulation of Super-Eddington Accretion Disks

TL;DR

This paper investigates super-Eddington accretion onto black holes using a global 3D radiation-MHD simulation that directly solves the time-dependent radiative transfer equation, avoiding FLD/M1 closures.It finds that vertical energy transport from magnetic buoyancy substantially enhances cooling, yielding radiative efficiencies around 4–5% and radiative luminosities near 10 L_Edd for a ~22 M_Edd accretion rate, with a strong, radiation-driven axial outflow that carries significant energy and mass.These results diverge from slim-disk expectations and previous simulations by showing efficient photon escape before advection, modest beaming, and robust MRI-driven turbulence, with important implications for ULXs and early SMBH growth via radiative and mechanical feedback.

Abstract

We study super-Eddington accretion flows onto black holes using a global three dimensional radiation magneto-hydrodynamical simulation. We solve the time dependent radiative transfer equation for the specific intensities to accurately calculate the angular distribution of the emitted radiation. Turbulence generated by the magneto-rotational instability provides self-consistent angular momentum transfer. The simulation reaches inflow equilibrium with an accretion rate ~220L_edd/c^2 and forms a radiation driven outflow along the rotation axis. The mechanical energy flux carried by the outflow is ~20% of the radiative energy flux. The total mass flux lost in the outflow is about 29% of the net accretion rate. The radiative luminosity of this flow is ~10L_edd. This yields a radiative efficiency ~4.5%, which is comparable to the value in a standard thin disk model. In our simulation, vertical advection of radiation caused by magnetic buoyancy transports energy faster than photon diffusion, allowing a significant fraction of the photons to escape from the surface of the disk before being advected into the black hole. We contrast our results with the lower radiative efficiencies inferred in most models, such as the slim disk model, which neglect vertical advection. Our inferred radiative efficiencies also exceed published results from previous global numerical simulations, which did not attribute a significant role to vertical advection. We briefly discuss the implications for the growth of supermassive black holes in the early universe and describe how these results provided a basis for explaining the spectrum and population statistics of ultraluminous X-ray sources.

Figures (16)

• Figure 1: Accretion rate history. The Eddington accretion rate $\dot{M}$ and time $t_s$ are defined in Table \ref{['Table:parameters']}.
• Figure 2: Space-time diagram of density (top), gas temperature (middle) and azimuthal component of magnetic field (bottom) at $r=10r_s$ (left) and $r=20r_s$ (right). Units for $\rho$, $T$ and $B_{\phi}$ are $\rho_0,\ T_0, \ \sqrt{P_0}$. The white lines at the top panels show the approximate locations of electron scattering photosphere measured from the nearby surfaces of the disk.
• Figure 3: Snapshot of disk structures for density (left) and radiation energy density (right) at time $1.13\times 10^4t_s$. Units for $\rho$ and $E_r$ are $\rho_0$ and $a_rT_0^4$ respectively.
• Figure 4: Averaged radial profiles of mass flux between time $10570t_s$ and $12080t_s$. The red line is the net mass flux ($\dot{M}_{\rm sum}$). The solid and dashed black lines are the inward and outward mass flux along radial directions ($\dot{M}_{\rm in}$ and $\dot{M}_{\rm out}$), while the blue line is the total mass flux along the vertical direction within each radius ($\dot{M}_{\rm z}$). The dotted vertical line indicates the location of $r_{\text{ISCO}}$.
• Figure 5: Left: time and azimuthally averaged density and streamlines for gas velocity. The color bar at the top of the figure shows the ratio between velocity magnitude and speed of light. The solid red line shows the location of electron scattering photosphere measured from the top and bottom of the simulation box, while the dashed red line shows the location of photosphere for effective absorption opacity. Right: time and azimuthally averaged radiation energy density and streamlines for lab frame flux. The color bar at the top of the figure represents $|{\hbox{\boldmath $F$}}_r/(cE_r)|$.