Compression-Driven Kinetic Instabilities in Magnetically Arrested Disks

Abstract

Event horizon-scale observations of low-luminosity black hole accretion flows favor magnetically arrested disks, characterized by dynamically important magnetic fields ($β\lesssim1$, where $β$ is the ratio of plasma thermal pressure to magnetic pressure) and a two-temperature transrelativistic plasma. Motivated by plasma conditions in the synchrotron-emitting regions of these models, we perform 2D particle-in-cell simulations of electron-ion plasmas with a realistic mass ratio, subject to continuous compression perpendicular to the mean magnetic field $\boldsymbol{B}_0$. Conservation of particle magnetic moments drives pressure anisotropy $P_{\perp}>P_{\parallel}$, triggering anisotropy-driven instabilities. For ion plasma beta $β_{i0}=0.5$ and ion temperature $k_{\text{B}}T_{i0}/m_i c^2=0.05$, the ion pressure anisotropy is regulated by the ion cyclotron instability, while the mirror mode influences the late-time electron anisotropy. Both species develop nonthermal components at high energies, consistent with stochastic acceleration by cyclotron-scale fluctuations. We characterize how the onset and time evolution of the plasma instabilities, as well as the resulting ion and electron anisotropies and energy spectra, vary with $β_{i0}$, $k_{\text{B}}T_{i0}/m_i c^2$, electron-to-ion temperature ratio $T_{e0}/T_{i0}$, and the compression rate. Increasing the thermal energy toward relativistic values raises the anisotropy thresholds for all instabilities observed in our simulations, allowing larger anisotropies to develop. For $T_{e0}/T_{i0}<1$, as expected in collisionless two-temperature accretion flows, the growth of mirror and whistler instabilities is delayed or suppressed, leading to increasingly adiabatic evolution of the electrons. Our findings can be used to inform global fluid models of black hole accretion.

Figures (19)

• Figure 1: Plots of the pressure anisotropy $\Delta P\equiv P_{\perp}-P_{\parallel}$ normalized by the comoving magnetic energy density $b^2$ in the poloidal $(r,\theta)$ plane for a MAD weakly collisional GRMHD simulation from dhruv_egrmhd_variability_2025. The gray circle in the center represents the black hole. The left panel shows a single snapshot at azimuth $\phi=\pi$ while the right panel plots the time- and azimuth-averaged value. We find most of the accretion disk is driven toward $\Delta P>0$.
• Figure 2: Radiative transfer diagnostics for a weakly collisional MAD $a_{*}=+0.94$ simulation ($a_*\equiv Jc/GM^2$ is the dimensionless black hole spin). Left panel: Time-averaged total intensity image at 230 GHz plotted as brightness temperature. Middle panel: Normalized emission map highlighting regions in the simulation domain that contribute to the observed image (left panel). Note that most of the emission for the MAD model originates close to the black hole and near the midplane. Right panel: Emission-weighted distribution of the fluid plasma $\beta$ and temperature $P_{\rm{gas}}/\rho c^2$.
• Figure 3: Time series of the box-averaged squared magnetic field perturbations in panel (a) and particle anisotropy in panel (b) for the fiducial simulation with $T_{e0}/T_{i0}=1$, $\beta_{i0}=0.5$, and $\Theta_{i0}=0.05$. The gray dash-dot line in panel (a) is $\propto(1+qt)^4$ and is the expected evolution of the $\vert\boldsymbol{B}_0\vert^2$ due to flux-freezing. The black dashed line in panel (b) follows $(1+qt)^2-1$ and is the expected growth rate if the particles underwent pure adiabatic compression. The gray vertical lines in panel (a) mark the snapshot times shown in Figure \ref{['fig:fiducial_sim_snapshots']}: the dotted line denotes $t=0.78\,q^{-1}$ (top row) and the dashed line denotes $t=1.30\,q^{-1}$ (bottom row).
• Figure 4: Snapshots for fiducial simulation with $T_{e0}/T_{i0}=1$, $\Theta_{i0}=0.05$, $\beta_{i0}=0.5$. Left to right: the perturbations in the x (first column), y (second column) and z (third column) component of the magnetic field normalized by the mean field, and the perturbations in the ion number density normalized by the initial ion number density (fourth column) at two timestamps. The first row shows results at $t=0.78\,q^{-1}$, and the second row shows the same quantities at a later time $t=1.30\,q^{-1}$ once the mirror mode is activated. This is evident by the spatial anticorrelation in the field and number density perturbations.
• Figure 5: Spatial power spectrum of the magnetic field components for the fiducial simulation plotted at two different time intervals. The top row corresponds to $0.73\,q^{-1} \leq t \leq 0.83\,q^{-1}$ and the bottom row to $1.25\,q^{-1} \leq t \leq 1.35\,q^{-1}$. The first three columns plot the logarithm of the 2D power spectrum $\vert\delta\tilde{B}^{i}\,(k_x,ky)\vert$, and the rightmost column shows a 1D slice of $\delta\tilde{B}^{x}$ and $\delta\tilde{B}^z$ along $k_y$. For the time interval $1.25\,q^{-1} \leq t \leq 1.35\,q^{-1}$, in panel (h) we also plot a 1D slice of $\delta\tilde{B}^{y}$ along the wave vector of the oblique mirror mode as measured over that time range (indicated by the dotted white line in panel (f)). The field perturbation in each panel is normalized by its corresponding maximum amplitude.