Radiation GRMHD Models of Accretion onto Stellar-Mass Black Holes: II. Super-Eddington Accretion

We present a comprehensive analysis of super-Eddington black hole accretion simulations that solve the GRMHD equations coupled with angle-discretized radiation transport. The simulations span a range of accretion rates, two black hole spins, and two magnetic field topologies, and include resolution studies as well as comparisons with non-radiative models. Super-Eddington accretion flows consistently develop geometrically thick disks supported by radiation pressure, regardless of magnetic field configuration. Radiation generated in the inner disk drives substantial outflows, forming conical funnel regions that limit photon escape and result in very low radiation efficiency. The accretion flows are highly turbulent with thermal energy transport dominated by radiation advection rather than diffusion. Angular momentum is primarily carried outward by Maxwell stress, with turbulent Reynolds stress playing a subdominant role. Both strong and weak jets are produced. Strong jets arise from sufficient net vertical magnetic flux and rapid black hole spin and can effectively evacuate the funnel, enabling radiation to escape through strong geometric beaming. In contrast, weak jets fail to clear the funnel, which becomes obscured by radiation-driven outflows and leads to distinct observational signatures. Spiral structures are observed in the plunging region, behaving like density waves. These super-Eddington models are applicable to a variety of astronomical systems, including ultraluminous X-ray sources, little red dots, and black hole transients.

💡 Research Summary

This paper presents a systematic study of super‑Eddington accretion onto stellar‑mass black holes using three‑dimensional general‑relativistic magnetohydrodynamic (GRMHD) simulations that incorporate angle‑dependent radiation transport. The authors explore a parameter space that includes two black‑hole spins (a = 0.3 and 0.9375), two magnetic‑field topologies (single‑loop “SANE” and double‑loop configurations), and a range of mass‑accretion rates spanning roughly 10–150 Ṁ_Edd. Both intermediate‑resolution (2048 × 2048 × 1152) and low‑resolution (1152 × 1152 × 640) grids are employed, together with a higher‑angular‑resolution test, to assess numerical convergence.

The simulations are performed with the ATHENA K code in Cartesian Kerr‑Schild coordinates. Radiation is treated in a frequency‑integrated but multi‑angle fashion, allowing the authors to resolve photon trapping, anisotropic radiation pressure, and the formation of effective and scattering photospheres. The initial condition consists of a geometrically thick, radiation‑pressure‑supported torus threaded by a vertical magnetic field.

Key findings are as follows:

1. Disk Structure – All super‑Eddington runs develop a thick disk (H/R ≈ 0.3–0.5) whose pressure is dominated by radiation. The disk reaches a quasi‑steady state after ≈ 1.5 × 10⁴ r_g/c and remains stable for the remainder of the run (up to ≈ 6 × 10⁴ r_g/c).

2. Radiation‑Driven Outflows – Strong radiation generated in the inner disk launches powerful, conical outflows that carve a low‑density funnel along the rotation axis. The funnel limits photon escape, leading to a very low radiative efficiency (η_rad ≈ 10⁻³) in models where the funnel is filled with outflowing gas.

3. Angular Momentum Transport – Maxwell stress ⟨B_r B_φ⟩/4π carries 70–85 % of the total angular‑momentum flux, while Reynolds stress contributes only 10–20 %. The flows remain in the SANE regime (dimensionless magnetic flux φ < 4).

4. Energy Transport – Within the disk, radiation advection dominates over diffusion; the advected radiative energy is the primary channel for thermal energy transport. This contrasts with classic slim‑disk models that assume diffusion‑dominated cooling.

5. Jet Formation – Two jet regimes emerge:

   • Strong jets appear in high‑spin (a ≈ 0.94) models with sufficient net vertical magnetic flux (single‑loop). These jets are Poynting‑flux dominated, evacuate the funnel, and enable strong geometric beaming (opening angles ≈ 10°).
   • Weak jets occur in low‑spin or double‑loop configurations where the magnetic flux is insufficient. The jets cannot clear the funnel; radiation‑driven winds fill the polar region, suppressing beaming and reducing observable high‑energy emission.

6. Spiral Density Waves – In the plunging region inside the ISCO, coherent spiral density structures are observed. They behave like non‑linear density waves, modulating the inflow velocity and magnetic field topology.

7. Resolution and Numerical Checks – Increasing spatial resolution raises the measured accretion rate and jet power by ≈ 10–20 %. Raising angular resolution modestly (θ‑grid from 80 to 160) increases the radiation pressure in the funnel by ~5 %, slightly sharpening the beaming cone.

8. Comparison with Non‑Radiative Runs – Non‑radiative SANE simulations with identical spins and magnetic topologies show higher magnetic fluxes (φ ≈ 4–5) and thicker disks, confirming that radiation pressure softens the MRI turbulence and reduces magnetic field amplification.

9. Astrophysical Implications – The authors argue that the two jet regimes can explain the diversity of ultraluminous X‑ray sources (ULXs) and “little red dots” (LRDs). Strong‑jet systems would appear as highly beamed, hard X‑ray sources, while weak‑jet systems would exhibit softer spectra, larger variability, and signs of dense, optically thick winds. The results also have relevance for tidal‑disruption events and black‑hole X‑ray transients that exceed the Eddington limit.

Overall, the paper delivers a comprehensive, high‑fidelity picture of how radiation, magnetic fields, and black‑hole spin interact to shape super‑Eddington accretion flows. It bridges the gap between analytic slim‑disk theory and earlier, less detailed GRMHD simulations, and provides concrete predictions for the observational signatures of super‑Eddington disks and their jets.