GRMHD simulations of black hole accretion variabilities: Implications to hard state X-ray binary transients

TL;DR

This study addresses how magnetic field geometry and the plasma-$\beta$ regime shape accretion onto rapidly spinning black holes and drive variability across the black hole mass scale. Using high-resolution 3D GRMHD simulations with varied initial magnetic configurations, the authors identify three distinct accretion states—MAD, INT, and SANE—characterized by magnetic flux saturation, disk thickness, and jet/wind morphologies. A key contribution is the proposed unified framework in which magnetic flux accumulation and eruption mediate state transitions, offering explanations for hard-state phenomena observed in X-ray binaries (notably GRS 1915+105, Cyg X-1) and the extreme luminosities of HLX-1, consistent with cross-mass scalability. The work emphasizes a hierarchy of dynamical timescales driven by magnetic processes and shows that qualitative state distinctions persist in both 2D and 3D, though 3D dynamics require higher accretion rates to match 2D luminosities, pointing toward future radiative GRMHD investigations to connect to spectra.

Abstract

Using high-resolution general relativistic magnetohydrodynamic (GRMHD) simulations, we investigate accretion flows around spinning black holes and identify three distinct accretion states. Our results suggest the origin of the complex phenomenology observed across the black hole mass spectrum as the interplay between magnetic and gravitational fields. The magnetically arrested disk (MAD) state, characterized by strong magnetic fields (plasma-$β<< 1$), exhibits powerful jets, highly variable accretion, and significant sub-Keplerian motion. On the other hand, weakly magnetized disks (plasma-$β>> 1$), known as the standard and normal evolution (SANE) state, show steady accretion with primarily winds. An intermediate state bridges the gap between MAD and SANE regimes, with moderate magnetic support (plasma-$β\sim 1$) producing mixed outflow morphologies and complex variability. This unified framework has many implications including its possible connection to extreme variability of GRS 1915+105, particularly in its hard spectral states. It also suggests the possible origin of steady jets of Cyg X-1 and the unusually high luminosities (even super-Eddington based on stellar mass black hole) of HLX-1 without requiring super-Eddington mass accretion rates. Our simulations reveal a hierarchy of timescales that explain the rich variety of variability patterns, with magnetic processes driving transitions between states. Comparing two with three dimensional simulations demonstrates that while quantitative details differ, the qualitative features distinguishing different accretion states remain robust.

Figures (15)

• Figure 1: Schematic representation of the three accretion states and their transitions identified in our GRMHD simulations. The SANE state is characterized by weak magnetic fields (plasma-$\beta >> 1$) with low variability in accretion rate and weak jets. The MAD state features strong magnetic fields (plasma-$\beta << 1$) leading to magnetic stress dominated accretion with strong and powerful jets. The newly identified INT state (plasma-$\beta \sim 1-10$) bridges these extremes with moderate magnetic field strengths and mixed disk-jet characteristics, facilitating transitions between states (indicated by colored arrows). The bi-directional arrows represent the reversible nature of these transitions, with different colors indicating distinct transition pathways. This framework enlightens the possible origin of the complex variability patterns observed in systems like GRS 1915+105, the steady jets in Cyg X-1, and the high luminosities of ULXs like HLX-1.
• Figure 2: Initial magnetic field configurations for our three primary simulations. The color contours represent the logarithmic plasma-$\beta$, while the white lines show the magnetic field lines: (a) MAD configuration features a strong magnetic field structure near the equatorial plane with very low plasma-$\beta$ distribution and a very large initial torus. (b) INT configuration creates a smaller disk with relatively higher plasma-$\beta$. (c) SANE configuration shows a simpler poloidal field pattern with even higher plasma-$\beta$ and a very low density of magnetic field lines, and smaller loops compared to MAD and INT configurations.
• Figure 3: (a) Averaged density as a function of distance from black hole showing power-law relations; power-law indices are computed in the inner region $3-20 r_g$ where the simulation is well within converged and steady zone. (b) Shell averaged plasma-$\beta$ as a function of distance from black hole for 3D simulations. (c) Shell averaged radial velocity as a function of distance from black hole in units of speed of light for 3D simulations. (d) Ratio of angular velocity to the Keplerian angular velocity as a function of distance from the black hole for 3D simulations.
• Figure 4: Mass flow rates as functions of radius for the three accretion states from 3D simulations. Each panel shows the total mass accretion rate $\dot{M}_{\rm tot}$ (solid blue), inflow rate $\dot{M}_{\rm in}$ (dashed orange), and outflow rate $\dot{M}_{\rm out}$ (dash-dotted green). Gray dashed lines indicate power-law fits in the region $r = 3-20r_g$. (a) MAD state exhibits gradual inflow accumulation ($\dot{M}_{\rm in} \propto r^{0.39}$) and steep outflow scaling ($\dot{M}_{\rm out} \propto r^{2.03}$), characteristic of efficient magnetically-driven jet launching. (b) INT state shows intermediate behavior with $\dot{M}_{\rm in} \propto r^{0.67}$ and $\dot{M}_{\rm out} \propto r^{1.52}$. (c) SANE state displays steeper inflow accumulation ($\dot{M}_{\rm in} \propto r^{0.80}$) and shallower outflow scaling ($\dot{M}_{\rm out} \propto r^{1.45}$), reflecting mass-loaded winds. The relatively constant $\dot{M}_{\rm tot}$ across all states confirms quasi-steady-state conditions.
• Figure 5: Velocity contours for 3D simulations, time averaged from $t=20,000 r_g/c$ to $t=25,000 r_g/c$. The colors represent velocity magnitude and arrows show directions of velocity. The dashed orange line shows the disk boundary calculated from the aspect ratio. Left: MAD. Middle: INT. Right: SANE.