Collisionless Accretion of Finite-Angular-Momentum Plasma onto a Spinning Black Hole

The gist: The first fully kinetic simulations of collisionless plasma accreting onto a black hole reveal that the accretion flow behaves similarly to magnetically arrested disk (MAD) regimes and that pair production enables the Blandford-Znajek process by supplying plasma to the jet funnel.

Simulation Setup

The simulations utilize a GPU-based general relativistic particle-in-cell (GRPIC) code framework Aperture to perform fully kinetic, 2D axisymmetric simulations of finite angular momentum plasma accreting onto a BH The simulations are conducted in horizonpenetrating spherical Kerr-Schild coordinates, x µ = (t, r, θ, φ) = (x 0, x1, x2, x3), and assume a dimensionless BH spin of a = 0.998. The simulations start from the Luepker Torus [17] which is initialized with inner and outer radii, rin = 6.2rg and rout ≈ 73rg, respectively. The torus is initialized with a uniform magnetic field described by the vacuum Wald solution [21], with strength B0 far from the BH.

Accretion Dynamics and Instabilities

The simulations observe the development of the MRI in addition to other kinetic instabilities The MRI triggers accretion at a given location in the torus once it has had time to grow – after approximately one local Keplerian orbit – thereafter leading to the development of a geometrically thick, magnetized, and turbulent accretion flow. Although weak, the initial vertical magnetic field provides a deep reservoir of magnetic flux which accumulates onto the BH as the result of accretion and eventually saturates, leading to flux eruptions similar to those typically seen in the magnetically arrested disk (MAD) accretion regime [24–27]. The most striking feature is perhaps the funnel region, where in the run without pair production, BHthreading magnetic field lines become a vacuum, with the particles in the accretion disk inhibited from populating them. In contrast, the run with pair production is able to continuously supply plasma to the funnel zone by producing e± pairs via quasi-periodic discharges [28].

Magnetic Flux Saturation and Eruptions

Both simulations attain a saturation of the normalized flux at around ϕ ∼ 50, after which point a flux eruption is triggered, significantly reducing ΦH and M˙ H. These eruptions are similar to those seen in GRMHD simulations in the MAD accretion regime They also resemble eruptions witnessed in kinetic simulations of Bondi accretion [15, 16]. Regardless of whether pair production is active, our simulations show similar saturated ϕ-values and hint at similar eruption recurrence times (∼500rg/c). In contrast, without pair production, there is no plasma to hold the magnetic field lines in place once the eruption is triggered, and the magnetic flux can escape the BH within a few rg/c.

Angular Momentum Transport

The most crucial aspect of finite-angular-momentum BH accretion is how the plasma sheds its angular momentum to be able to fall into the BH. We analyze the angular momentum transport in our simulations by isolating contributions from individual stresses following the formalism of [32]. The plasma contribution, L˙plasma, is typically negative, which results from material infall, U r < 0. Negative L˙plasma first appears at a given radius after roughly one local Keplerian period. Removing the plasma advection term, the rest of the angular momentum transport, L˙total − L˙plasma, is almost exclusively positive, indicating efficient removal of angular momentum. In particular, the Maxwell stress dominates the outward angular momentum transport in both simulations.

Kinetic Instabilities and Anisotropy Regulation

The regulation of pressure anisotropy in our simulations is imposed by kinetic mirror and firehose instabilities [33] These are triggered through the global fluidlevel dynamics. For the Maxwell stress to dominate the angular momentum transfer even in high-βpl regions, it indicates that ∆p is regulated to ≪ p. The regulation of pressure anisotropy in our simulations is imposed by kinetic mirror and firehose instabilities [33] These are triggered through the global fluidlevel dynamics. Although Figs. 3b and 3c show the simulation with pair production, we have checked that the run without pair production exhibits similar ∆p-regulation.

Particle Acceleration

We find that the strongest nonthermal particle acceleration occurs in the jet funnel and equatorial current sheet. The accretion flow remains largely thermal in our simulations In contrast, local box simulations of the MRI turbulence have shown that particles can be accelerated to a nonthermal power law [34, 37]. We believe that this is due in part to our limited scale separation in these global simulations, as well as to their axisymmetric nature, which prevents the MRI turbulence from fully developing. Our results highlight the magnetospheric region as the dominant source of the highest-energy particles. The cutoff at Γ = 10 is due to the pair production threshold.

Conclusion

We have carried out the first global GRPIC simulations of collisionless BH accretion starting from a finite-angular-momentum plasma In our simulations, the MRI triggers accretion-mediating angular momentum transport – just like in GRMHD. As the plasma evolves, firehose and mirror instabilities limit its pressure anisotropy, providing an effective collisionality that causes the flow to behave like a magnetized fluid. As a result, fluid stresses, specifically magnetic torque, dominate the angular momentum transport. Our simulations also exhibit magnetic flux saturation and eruption phases typical of the MAD accretion state in GRMHD models Besides affirming a GRMHD description of angular momentum transport, our kinetic treatment makes several key advancements beyond fluid frameworks. Our code correctly handles vacuum regions and thus probes the role of pair production in enabling a BZ jet. Without pair production, our simulations do not exhibit a mechanism for efficiently mixing plasma from the accretion flow into the near-horizon polar regions. Without a plasma to support the necessary current, no BZ jet is launched. A kinetic approach also allows us to model and localize nonthermal particle acceleration. We find that the strongest nonthermal particle acceleration occurs in the jet funnel and equatorial current sheet. The accretion flow remains largely thermal in our simulations Relaxing the assumption of axisymmetry and enhancing the simulations’ dynamic range will enable future work to more thoroughly assess each of the above issues: particle acceleration in the accretion disk, mixing of the accreting plasma into the funnel region, and the dominant angular momentum transport mechanism.

Simulation Setup Details

The simulation setup requires enforcing several constraints on initial parameters to ensure physical relevance. The first constraint we need to satisfy is that the scale height of the torus, H, be at least several multiples of the most-unstable MRI wavelength, λMRI = 2πvA/omegaK. Furthermore, since our torus is geometrically thick, with H ∼ r, we phrase this as a requirement on r0, namely, r0 ≫ λMRI,0 ≡ 2π√σ0/omegaK(r0). We select σ0 = 1.8×10−4, yielding r0/λMRI,0 = 3.4. Our final constraint is that the radial grid spacing, ∆r = r∆(ln r) = (r/Nr) ln(rmax/rmin), resolves the plasma skin depth, d = (mec 2/(ne 2))1/2 everywhere.

Instability Analysis

To obtain the thresholds for mirror and firehose instabilities, we write down the dispersion relation for a plasma with a nonrelativistic bi-Maxwellian distribution at rest in a uniform background magnetic field B0. We consider the low-σi regime as appropriate for the accretion disk. It turns out that as long as σi ≪ 1, or, more precisely, kBT∥i/(mic 2) = β∥iσi/2 ≪ 1, the growth rate of mirror and firehose instabilities does not depend on the exact value of σi. In our calculations, we typically fix σi at a small value between 10−4 and 10−2. It appears that the oblique firehose and mirror instabilities constrain the plasma anisotropy (e.g., [47, 48]. These are non-propagating instabilities, meaning that ω is purely imaginary. We use Newton’s method with a purely imaginary starting trial solution to find the growth rate of these instabilities at a given β∥i, T⊥i/T∥i and k. We locate the T⊥i/T∥i value that gives a maximum growth rate of 10% the ion cyclotron frequency<ref:

1. Bold Header: Kinetic Accretion Modeling for Low-Luminosity AGN

This enables AI systems to accurately simulate accretion dynamics in collisionless, low-luminosity environments like M87 and Sgr A, moving beyond ideal MHD approximations by incorporating kinetic instabilities that regulate pressure anisotropy in the disk.

2. Bold Header: Nonthermal Particle Acceleration Prediction

The system can predict where nonthermal particles are generated by analyzing the spatial decomposition of particle energy, finding that the strongest nonthermal particle acceleration occurs in the jet funnel and equatorial current sheet.

3. Bold Header: Jet Sustenance Mechanism Assessment

AI systems can determine if a relativistic jet is sustained by pair production by assessing plasma availability, as the paper shows that Without pair production, our simulations do not exhibit a mechanism for efficiently mixing plasma from the accretion flow into the near-horizon polar regions.

4. Bold Header: Angular Momentum Transport Diagnosis

The system can diagnose whether magnetic torque or pressure anisotropy dominates angular momentum transport by calculating contributions to the stress-energy tensor, as the Maxwell stress dominates the outward angular momentum transport in both simulations after accounting for plasma advection.

5. Bold Header: Magnetic Flux Saturation and Eruption Forecasting

AI can forecast flux saturation and eruption phases typical of the magnetically arrested disk (MAD) regime by analyzing normalized flux evolution, noting that these events are similar to those seen in GRMHD simulations in the MAD accretion regime.