The Role of Inhomogeneities in the Turbulent Accretion of Black Holes

Abstract

Observations of supermassive black holes by the Event Horizon Telescope reveal significant inhomogeneities, most likely related to density and magnetic field perturbations. To model these features, we conduct high-resolution 2D general-relativistic magnetohydrodynamics (GRMHD) simulations of a Fishbone-Moncrief torus around a Kerr black hole using the Black Hole Accretion Code $\texttt{BHAC}$. We compare unperturbed accretion with a case featuring plasma density bubbles with pressure balanced magnetic islands of different amplitudes. Power spectrum analysis of accretion time series, performed via the Blackman-Tukey method, shows that the perturbed case exhibits (1) steeper spectral indices compared to the unperturbed case, deviating from the characteristic $1/ω$ noise spectrum, and (2) increased correlation times, providing evidence for absorption of macro-structures at the event horizon. Spatial auto-correlation analysis of near-horizon turbulence confirms larger energy-containing coherent structures in the perturbed case altering the accretion rate. These results provide new insights for interpreting observations of supermassive black hole environments, where near-horizon turbulence may play a key role in the accretion process.

Figures (4)

• Figure 1: Left column: initial density contours for Run A (a) and B (b). Middle column: $\log$-snapshots of plasma parameter $\beta$ (left side) and density $\rho$ (right side) at $t=300 \ M$, for Run A (c) and B (d). The white circle represents the black hole event horizon area. Right column: same as middle column but at $t=3000 \ M$ for Run A (e) and B (f). In all plots, $r$ and $\theta$ are spheroidal Kerr-Schild coordinates.
• Figure 2: Left column: rest-mass accretion rate $\dot{M}$ (a) and accreted magnetic flux $\Phi$ (b) at the black hole horizon. Run A is depicted with solid orange lines, and Run B with dotted blue lines. Right column: power spectra of the accretion rate (c) and magnetic flux (d). In both panels, orange and blue dots denote data points from Runs A and B, respectively, while black and green solid lines indicate the corresponding power-law fits at low frequencies. The solid magenta line represents a general tendency common to both configurations at high frequencies.
• Figure 3: Top: Magnetic flux $\Phi$ for Run B (a). The solid black line shows the data and the shaded region indicates a selection window $T_w = 900\,M$. The inset (b) displays a convergence test of the correlation time $\tau_c$ as a function of the selection window length $T_w$. Bottom: normalized auto-correlation function $C(\tau)/C(0)$ of the magnetic flux $\Phi$ (c). Solid red and blue lines represent Runs A and B, respectively. Vertical dashed lines show correlation times $\tau_c^{A} = 12.75\,M$ (green) and $\tau_c^{B} = 30.25\,M$ (magenta), while the horizontal dashed black line denotes the $1/e$ threshold.
• Figure 4: Left column: Zoom-in of accretion rate $\dot{M}$ and magnetic flux $\Phi$ around one of the time series peaks (a). The dash-dotted black vertical line shows the time of the spatial analysis $t=2560 \ M$. Normalised auto-correlation function $C(\ell)/C(0)$ (b) of panels (c)-(d). Solid red and green lines depict Runs A and B, respectively. Vertical dashed lines mark $\ell$ values of $0.12\,M$ (blue) and $0.32\,M$ (magenta), while the horizontal dotted black line represents the $1/e$ threshold. Right column: Near-horizon density snapshots for Run A (c) and B (d) at $t=2560\,M$.