Equatorially Asymmetric Magnetic Fields and Their Impact on Black Hole Accretion Dynamics

TL;DR

This study uses axisymmetric GRMHD simulations of a $a=0.9375$ Kerr black hole with a Fishbone–Moncrief torus to explore how equatorially asymmetric magnetic fields, implemented via a polar offset in the vector potential at deformation angles $z_o=30^{\circ},45^{\circ},60^{\circ}$, alter accretion dynamics and relativistic outflows. By varying the initial plasma-$\beta$ ($\beta=0.001,0.005,0.007$) and employing a robust jet/wind classification, the authors find that stronger magnetic fields and smaller deformations promote more collimated, magnetically dominated winds and persistent horizon flux asymmetries, while higher deformation weakens coherence and reduces jet power; these effects are most pronounced in the inner disk and polar regions and are accompanied by MRI-driven turbulence as evidenced by PSD slopes in $\dot{M}$. The work demonstrates that equatorially asymmetric magnetic geometries can produce asymmetric winds, time-variable accretion, and memory of initial field deformation in the horizon flux, offering a plausible pathway to link 2D GRMHD results with observed jet variability and asymmetries, though three-dimensional simulations are required for a complete observational connection. Overall, the paper highlights the intricate coupling between magnetic field geometry, plasma conditions, and relativistic outflows in black hole accretion systems and motivates future 3D studies to capture obliquity effects, precession, and non-axisymmetric instabilities.

Abstract

We investigate the impact of equatorial asymmetry in the magnetic field geometry on accretion dynamics around a spinning black hole using axisymmetric general relativistic magnetohydrodynamic simulations. We consider a Fishbone--Moncrief torus orbiting a Kerr black hole with spin parameter $a = 0.9375$, threaded by large-scale magnetic fields that are asymmetric about the equatorial plane. The degree of equatorial asymmetry in the magnetic field is parametrized by an angle, with values of $30^\circ$, $45^\circ$, and $60^\circ$. We examine how this equatorially asymmetric initial magnetic field configuration influences the magnetic field structure, accretion flow morphology, and angular momentum transport across a range of initial plasma beta values ($β= 0.007, 0.005, 0.001$). We find that such deformation in the magnetic field leads to noticeable changes in the inner disk structure, asymmetric outflow patterns in the poloidal plane, and time-dependent variations in accretion rates. These effects are generally more pronounced at lower beta values, where magnetic pressure dominates; in particular, the $30^\circ$ case at $β= 0.001$ exhibits strong and persistent asymmetric inflows and outflows. Our results demonstrate that equatorially asymmetric magnetic field configurations can significantly influence the structure and variability of relativistic accretion flows. These findings motivate future extensions to full three-dimensional studies, where black hole magnetosphere can be explored in a more general setting.

Figures (15)

• Figure 1: Initial magnetic field configuration for simulations with deformation angles $30^\circ,\, 45^\circ,\, \text{and } 60^\circ$, shown at $t = 0$ for $\beta = 0.005$. The left three panels show the logarithmic rest-mass density distributions in the poloidal plane for each deformation angle, while the right three panels display the corresponding plasma-$\beta = 2P/B^{2}$ parameter. White lines overlaid on each panel represent magnetic field streamlines, highlighting the initial magnetic topology.
• Figure 2: Angular profiles of time-averaged quantities at fixed radii for the simulation with initial $\beta = 0.005$ and deformation angle $45^\circ$. Plotted are the variations of Lorentz factor, velocity, magnetization parameter, and density as functions of $\theta'$ at three representative radii ($r = 5$, $20$, and $50$). The values are averaged over the quasi-steady period $t = 9,000$ to $11,000$$t_{g}$.
• Figure 3: Time-averaged Lorentz factor profile, $\log_{10}(\Gamma - 1)$ as a function of $\theta'$ at $r = 5\,r_g$. It shows the variation with plasma beta ($\beta = 0.001,\, 0.005,\, 0.007$) for deformation angles $30^\circ$, $45^\circ$, and $60^\circ$, respectively. All profiles are time-averaged over $t = 9000\text{--}11{,}000\,t_g$.
• Figure 4: Time-averaged 2D distribution of key physical quantities for the fiducial run with $\beta = 0.005$, averaged over $t = 9000$–$11000$$t_{g}$ across the simulation domain ($x\text{--}z$ plane). From left to right: rest-mass density $\rho$, plasma-$\beta^{-1}$, magnetization parameter $\sigma = b^2/\rho$, Alfvén Mach number $\mathcal{M}_{\rm A}$, and mass flux, $\dot{\rm{m}}$ = -$\sqrt{-g}\rho u^{r}$ . Each row corresponds to a different deformation: (top) $30^\circ$, (middle) $45^\circ$, and (bottom) $60^\circ$. The first three panels in each row are overplotted with magnetic field contours, as well as the jet boundary (black dashed line) and wind boundary (white dashed line).
• Figure 5: Same as Figure \ref{['fig:figure_4']}, but for a fixed deformation of $30^\circ$, showing the variation with plasma-$\beta$. Each row corresponds to a different value of $\beta$: top—$\beta = 0.001$, middle—$\beta = 0.005$, and bottom—$\beta = 0.007$. All quantities are time-averaged over $t = 9000$–$11000\,t_{g}$ across the simulation domain (r–$\theta$ plane).