Clumpy Outflows from Super-Eddington Accreting Black Holes I: Radiation Hydrodynamics Simulations and Observational Implications

TL;DR

This work addresses how clumpy outflows form in super-Eddington accreting black holes and how they imprint observable signatures. It employs high-resolution 2D radiation-hydrodynamics simulations (no magnetic fields, GR effects neglected) around a $M_{\rm BH}=10^7\,M_\odot$ black hole, with radiation pressure driving fragmentation of disk winds. The simulations yield clumps of size $~10$–$100\,r_g$, density $\sim10^{-12}$–$10^{-13}\ { m g\,cm^{-3}}$, optical depths $\tau\sim1$–$10$, and velocities $0.05$–$0.2\,c$ distributed over $100$–$1000\,r_g$, with ~5 clumps along a typical line of sight and a covering factor $\sim0.22$, broadly consistent with XRISM observations of PDS 456. The results emphasize that sufficient spatial resolution and inner-region interactions are essential for clump formation, and they highlight the need for future 3D radiation-transfer studies to connect directly with observed spectra and refine the physical understanding of clump generation mechanisms.

Abstract

Recent advances in X-ray spectroscopic observation have enabled researchers to reveal distinct clumpy structures in the super-Eddington outflows from the supermassive black hole in PDS 456 (XRISM Collaboration 2025), initiating detailed investigation of fine-scale structures in accretion-driven outflows. In this study, we conduct high-resolution, two-dimensional radiation-hydrodynamics simulations with time-varying and anisotropic initial and boundary conditions to reproduce outflows launched from super-Eddington accretion flows and analyze their statistical properties. The resulting clumpy outflows extend across a wide range of radial distances and polar angles, exhibiting typical properties such as a size of ~10 rg (where rg is the gravitational radius), a velocity of ~0.05-0.2 c (where c is the speed of light), and about five clumps along the line of sight. Although the velocities are slightly smaller, these characteristics reasonably resemble those obtained from the XRISM observation. The gas density of the clumps is on the order of 10^{-13}-10^{-12} g cm^{-3}, and their optical depth for electron scattering is approximately 1-10. The clumpy winds accelerated by radiation force are considered to originate from the region within <~300 rg.

Figures (9)

• Figure 1: Visualization of the initial conditions and disk boundary. The 2D density distribution is displayed using pseudo-colors, while velocity vectors are overlaid as arrows. The black solid curve indicates the disk boundary. The cylindrical coordinates are defined as $R=r\cos\theta$ and $z=r\sin\theta$.
• Figure 2: Left: The same figure as Figure \ref{['fig_ICBC']} but for time snapshot $t=1.6\times 10^5~r_{\rm g}/c$. Although highly dynamical, the outflow structures are quasi-steady at this time. The clumpy outflows are clearly visible. Right: 2D distribution for force ratio (radiation force/gravity). The red regions indicate areas where outward radiation forces dominate, while the blue regions correspond to areas where inward gravity is predominant. The disk boundary can marginally capture the boundary between the inflow and outflow motion. In the sky region, radiation forces are the main driver for the outflows.
• Figure 3: Left: 2D density distribution for clumpy outflows. These clumps are selected such that their ionization parameters are within the observational range. Dashed gray curves show five directions at polar angles: $9^\circ$, $14^\circ$, $19^\circ$, $29^\circ$, and $44^\circ$, while solid gray curve indicates the disk boundary. Middle: 1D density profiles along the 5 polar angles as shown in the left panel. For better visualization, density profiles are offset by different values, as indicated in the legend. Along each radial profile, the selected clump outflow is highlighted with bold black curves. Right: The same plot as the middle panel, but for radial velocity with no offsets.
• Figure 4: The angular number distribution for clumpy outflows in simulation. The color-coded regions are integrated distribution for all data snapshots ranging from $t=0.9\times 10^5~r_{\rm g}/c$ to $t=1.7\times 10^5~r_{\rm g}/c$, with time step $\delta t=200 ~r_{\rm g}/c$, while the solid black curve is the time-averaged number distribution. Note that for polar angles $30^\circ \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr <\crcr{ } \sim\crcr}}} \theta \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr <\crcr{ } \sim\crcr}}} 45^\circ$, the line-of-sights penetrate through the disk region (light-gray shaded region), and for $\theta \mathrel{ \vcenter{\m@th\f@size4 \ialign{$$\cr >\crcr{ } \sim\crcr}}} 45^\circ$, line-of-sights are entirely embedded in disk region (gray shaded region)
• Figure 5: Statistical distribution of properties for clumpy outflows. Left: Distribution in the clump density and clump size plane. The probability distributions for density and size are shown as side plots in the right and upper side of this panel, respectively. The solid red curves indicate the relation where $\tau = \rho \kappa_{\rm es}\Delta r=1$ and $10$. Right: The same distribution as left panel but for clump radial velocity and clump location plane.