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Hot, Retrograde Tilted MADs: Misaligned, Precessing, and Shaped by Electromagnetic Torques

Sajal Gupta, Jason Dexter

TL;DR

This work tackles how misaligned, magnetically arrested disks around spinning black holes realign or precess, addressing inconsistencies in prior results for prograde versus retrograde configurations. It employs 3D GRMHD simulations and derives torque equations in ideal GRMHD, evaluating them in a frame aligned with the disk to quantify electromagnetic and hydrodynamic contributions to alignment. The key findings are that prograde MADs align with the black hole spin via a two-stage process—rapid flux-saturation–driven alignment followed by a slower, spin-insensitive phase—whereas retrograde MADs stay misaligned and undergo solid-body precession at rates about four times higher than weakly magnetized flows at the same spin. An empirical model is developed to explain the two-stage prograde alignment and the potential for retrograde alignment, with implications for interpreting low-frequency quasi-periodic oscillations in black hole X-ray binaries.

Abstract

Tilted accretion disks in the magnetically arrested (MAD) state may be present in X-ray binaries and active galactic nuclei such as Sgr A* and M87. We have carried out 3D global GRMHD simulations to study the evolution of these accretion flows as a function of black hole spin and misalignment angle. Prograde MADs align with the spin through a two-stage process: an initial rapid alignment phase that operates on the magnetic flux saturation timescale, followed by a slower, spin-independent phase. In contrast, retrograde MADs remain persistently misaligned regardless of the black hole spin, displaying solid-body precession at rates four times higher than weakly magnetized flows at the same spin magnitude. By deriving torque equations in ideal GRMHD and evaluating them in a frame aligned with instantaneous disk orientation, we demonstrate that electromagnetic (EM) torques always act to align the disk with the BH spin, but are countered by opposing hydrodynamic fluxes in retrograde flows. We further develop a preliminary empirical model to explain the cause of two-stage prograde alignment and discuss the possibility of alignment in the retrograde MAD. Strongly magnetized, retrograde, misaligned accretion disks provide a candidate scenario for the low-frequency quasi-periodic oscillations in black hole X-ray binaries.

Hot, Retrograde Tilted MADs: Misaligned, Precessing, and Shaped by Electromagnetic Torques

TL;DR

This work tackles how misaligned, magnetically arrested disks around spinning black holes realign or precess, addressing inconsistencies in prior results for prograde versus retrograde configurations. It employs 3D GRMHD simulations and derives torque equations in ideal GRMHD, evaluating them in a frame aligned with the disk to quantify electromagnetic and hydrodynamic contributions to alignment. The key findings are that prograde MADs align with the black hole spin via a two-stage process—rapid flux-saturation–driven alignment followed by a slower, spin-insensitive phase—whereas retrograde MADs stay misaligned and undergo solid-body precession at rates about four times higher than weakly magnetized flows at the same spin. An empirical model is developed to explain the two-stage prograde alignment and the potential for retrograde alignment, with implications for interpreting low-frequency quasi-periodic oscillations in black hole X-ray binaries.

Abstract

Tilted accretion disks in the magnetically arrested (MAD) state may be present in X-ray binaries and active galactic nuclei such as Sgr A* and M87. We have carried out 3D global GRMHD simulations to study the evolution of these accretion flows as a function of black hole spin and misalignment angle. Prograde MADs align with the spin through a two-stage process: an initial rapid alignment phase that operates on the magnetic flux saturation timescale, followed by a slower, spin-independent phase. In contrast, retrograde MADs remain persistently misaligned regardless of the black hole spin, displaying solid-body precession at rates four times higher than weakly magnetized flows at the same spin magnitude. By deriving torque equations in ideal GRMHD and evaluating them in a frame aligned with instantaneous disk orientation, we demonstrate that electromagnetic (EM) torques always act to align the disk with the BH spin, but are countered by opposing hydrodynamic fluxes in retrograde flows. We further develop a preliminary empirical model to explain the cause of two-stage prograde alignment and discuss the possibility of alignment in the retrograde MAD. Strongly magnetized, retrograde, misaligned accretion disks provide a candidate scenario for the low-frequency quasi-periodic oscillations in black hole X-ray binaries.
Paper Structure (3 sections, 2 equations, 1 figure)

This paper contains 3 sections, 2 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Methods
  3. Governing Equations

Figures (1)

  • Figure 1: Top panel: Poloidal slice snapshots of density ($\rho$) for high-spin prograde ($a \approxeq 0.94$) and retrograde ($a \approxeq -0.94$) cases, captured during their respective flux saturation time. Both flows are initially tilted by $16^\circ$ from the $+ z$ axis (see equation \ref{['eq:diskinclinationeq']}) The white line denotes the averaged disk plane, and black and white arrows indicate the directions of the BH and disk angular momenta, respectively. Middle panel: Evolution of normalized magnetic flux threading the event horizon. Bottom panel: Disk tilt evolution from the event horizon to $20\,r_g$. The figure demonstrates that prograde flows align with the BH spin axis, whereas retrograde flows remain misaligned. Here, for comparison to the prograde case, the tilt evolution for retrograde flow was shown relative to $+z$-axis.