Subgrid Mean-field Dynamo Model with Dynamical Quenching in General Relativistic Magnetohydrodynamic Simulations

Abstract

Large-scale magnetic fields are relevant for a number of dynamical processes in accretion disks, including driving turbulence, reconnection events, and launching outflows. Numerical simulations have indicated that the initial strengths and configurations of the large-scale magnetic fields have a direct imprint on the outcome of an accretion disk evolution. To facilitate future self-consistent simulations that include intrinsic dynamo processes, we derive and implement a subgrid model of a helical large-scale dynamo with dynamical quenching in general-relativistic resistive magnetohydrodynamical simulations of geometrically thin accretion disks. By incorporating previous numerical and analytical results of helical dynamos, our model features only one input parameter, the viscosity parameter $α_\text{SS}$. We demonstrate that our model can reproduce butterfly diagrams seen in previous local and global simulations. With rather aggressive parameter choice of $α_\text{SS}=0.02$ and black hole spin $a_\text{BH}=0.9375$, our thin-disk model launches weak collimated polar outflows with Lorentz factor $\simeq 1.2$, but no polar outflow is present with less vigorous turbulence or less positive $a_\text{BH}$. With negative $a_\text{BH}$, we find the field configurations to appear more similar to Newtonian cases, whereas for positive $a_\text{BH}$, the poloidal field loops become distorted and the cycle period becomes sporadic or even disappears. Moreover, we demonstrate how $α_\text{SS}$ can avoid to be prescribed and instead be determined by the local plasma beta. Such a fully dynamical subgrid dynamo allows for self-consistent amplification of the large-scale magnetic fields.

Figures (13)

• Figure 1: The time series of the density-weighted averages of (a) the inverse plasma beta, and (b) the squared magnetic strengths for the non-dynamo run A0 and the fiducial dynamo run A1.
• Figure 2: Same as Fig. \ref{['fig:A1_ts_A']} but shown the the time series of (a) accretion rate at the horizon, and (b) normalized magnetic flux at the horizon.
• Figure 3: Snapshots of run A1 for the distribution of the density (left), the plasma beta with magnetic field lines (middle), and the radial velocity (right), at $t=10^4t_\text{g}$ (top) and $t=2\times 10^5t_\text{g}$ (bottom).
• Figure 4: For run A1, distribution of line-integral convolution of the poloidal magnetic field $\bm B_\text{pol}$ at two representative snapshots ($t=10^4$ and $2\times10^5t_g$). Colors indicate the values calculated from the curl of the fields in the code unit to reflect the field orientation. For each panel, the black dot at $r=0$ indicates the outer horizon, and the thin black curve denotes the ergosphere.
• Figure 5: For run A1, the space-time diagram at $r=20r_\text{g}$ for (a) the azimuthal magnetic field $B_\phi$, (b) $B_\phi$ normalized by its maximal amplitude at each fixed time (to reveal the polarity), and (c) the plasma beta.