Particle Acceleration in Stratified 2D MRI Turbulence: From Reconnection to First- and Second-Order Fermi and Shear Acceleration

Low-luminosity accretion disks around black holes are weakly collisional, potentially enabling nonthermal particle acceleration. Local two-dimensional particle-in-cell simulations of the stratified magnetorotational instability (MRI) in pair plasmas by Sandoval et al. (2024; hereafter S24) revealed nonthermal populations with maximum energies proportional to the scale-separation ratio ω c,0/Ω 0, where ω c,0 and Ω 0 are the initial particle cyclotron and Keplerian frequencies, respectively. We identify the acceleration mechanisms involved and quantify their scale-separation dependence. Acceleration occurs primarily within large-scale current sheets associated with an MRI dynamo. Particles are initially injected by non-ideal electric fields during reconnection driven by plasmoid splitting, attaining energies independently of scale separation. They subsequently undergo rapid first-order Fermi-like acceleration occurring within converging flows between newly formed, separating plasmoids. During this stage, energies grow at a rate proportional to the instantaneous non-relativistic cyclotron frequency, independently of ω c,0/Ω 0. This fast acceleration rate implies a maximum energy proportional to ω c,0/Ω 0. Particles then continue interacting repeatedly with plasmoids, undergoing slower, predominantly second-order Fermi acceleration, with a subdominant contribution from shear acceleration. This stage increases particle energies by only a factor of a few over several orbits, regardless of ω c,0/Ω 0. The combination of these three stages implies a maximum energy proportional to ω c,0/Ω 0, explaining the scaling found by S24 and suggesting that the MRI may accelerate particles to ultrarelativistic energies in low-luminosity disks. Testing these results in three dimensions remains an important next step.