Collisionless Accretion onto Black Holes: Dynamics and Flares

We study the accretion of collisionless plasma onto a rotating black hole from first principles using axisymmetric general-relativistic particle-in-cell simulations. We carry out a side-by-side comparison of these results to analogous general-relativistic magnetohydrodynamic simulations. Although there are many similarities in the overall flow dynamics, three key differences between the kinetic and fluid simulations are identified. Magnetic reconnection is more efficient, and rapidly accelerates a nonthermal particle population, in our kinetic approach. In addition, the plasma in the kinetic simulations develops significant departures from thermal equilibrium, including pressure anisotropy that excites kinetic-scale instabilities, and a large field-aligned heat flux near the horizon that approaches the free-streaming value. We discuss the implications of our results for modeling event-horizon scale observations of Sgr A* and M87 by GRAVITY and the Event Horizon Telescope.

Figure 1

Comparison of fluid and kinetic simulations of accretion onto a rotating BH. The color shows $n/n_0$, which corresponds to the plasma number density in GRMHD simulations (left) and ion and positron number density in GRPIC simulations (right) in a region close to the BH ($20r_g$). The region inside the BH event horizon, $r_h=r_g(1+\sqrt{1-a^2})$, is shown by a black circle. Thin black lines represent the magnetic field lines, a thick black line outlines the ergosphere. The same quantities are shown at a time of $160r_g/c$ (a) and $300r_g/c$ (b). Several current sheets form and reconnect (a), leading to a flaring state (b).

Figure 2

Evolution of averaged quantities in GRPIC (solid lines) and GRMHD (dotted) simulations. (a) Time evolution of the accretion rate in units of the Bondi accretion rate, $\dot{M}/{\dot{M}}_B$; (b) magnetic flux on the horizon normalized by its initial value $\mathrm{\Phi }/{\mathrm{\Phi }}_0$. The gray dashed lines give the exponential fit for the decay rate of $\mathrm{\Phi }/{\mathrm{\Phi }}_0$, highlighting the difference of the reconnection rate. (c) Mean profiles of number density, $⟨n/n_0⟩$; (d) temperature, $⟨T⟩$, and (e) plasma-$\beta =⟨P⟩/⟨P_B⟩$, as a function of radius $r/r_g$, averaged over $t=[100-200]r_g/c$. The runs initialized with the turbulent magnetic field are shown by a darker color (loops), with a vertical uniform magnetic field—a lighter color (no loops).

Figure 3

Anisotropy and heat flux in GRPIC simulation initialized with ${\beta }_0=10$. Each row corresponds to a different moment in time: $40r_g/c$ (a)–(c), and $100r_g/c$ (d)–(f). First column: number density (left) and magnetic field (right) fluctuations. Second column: temperature anisotropy $T_{\parallel }/T_{\perp }$ (left) and the ratio of nonideal and ideal matter stress-energy tensor components in the tetrad frame ${\mathcal{T}}^{(0)(3)}/{\mathcal{T}}^{(3)(3)}$, which represents the ratio of parallel heat flux $q_{\parallel }$ and parallel pressure $P_{\parallel }$. The black circle and black lines represent the event horizon, ergosphere, and magnetic field lines as in Fig. 1. Third column: probability density as a function of ${\beta }_{\parallel }=P_{\parallel }/P_B$ and temperature anisotropy $T_{\perp }/T_{\parallel }$. White dashed lines correspond to the boundaries of the growth rate of mirror (top) and firehose (bottom) instabilities exceeding 10% of the ion cyclotron frequency calculated using [33]. A mirror instability develops and saturates at $40r_g/c$, for which we show a zoom into the structure of the instability (a).

Figure 4

Panel (a) shows the presence (yes or no) of energetic electrons with $\gamma \ge 8$ throughout the GRPIC simulation at $300r_g/c$ [shown in Fig. 1, right]. To avoid low density regions near the axis, we show regions above the density threshold, $n>n_0/2$. Panel (b) shows particle spectra measured inside the outflowing bubble (blue) and in the current sheet (purple), which are outlined in (a) by the respective colors.