Particle-in-cell simulations of the magnetorotational instability in stratified shearing boxes

The magnetorotational instability (MRI) plays a crucial role in regulating the accretion efficiency in astrophysical accretion discs. In low-luminosity discs around black holes, such as Sgr A* and M87, Coulomb collisions are infrequent, making the MRI physics effectively collisionless. The collisionless MRI gives rise to kinetic plasma effects that can potentially affect its dynamic and thermodynamic properties. We present 2D and 3D particle-in-cell (PIC) plasma simulations of the collisionless MRI in stratified discs using shearing boxes with net vertical field. We use pair plasmas, with initial ß = 100 and concentrate on subrelativistic plasma temperatures (kBT mc2). Our 2D and 3D runs show disc expansion, particle and magnetic field outflows, and a dynamo-like process. They also produce magnetic pressure dominated discs with (Maxwell stress dominated) viscosity parameter a ~ 0.5 1. By the end of the simulations, the dynamo-like magnetic field tends to dominate the magnetic energy and the viscosity in the discs. Our 2D and 3D runs produce fairly similar results, and are also consistent with previous 3D MHD (magnetohydrodynamic) simulations. Our simulations also show non-thermal particle acceleration, approximately characterized by power-law tails with temperature-dependent spectral indices - p. For temperatures kBT ~ 0.05 - 0.3 mc2, we find p 2.2 1.9. The maximum accelerated particle energy depends on the scale separation between MHD and Larmor-scale plasma phenomena in a way consistent with previous PIC results of magnetic reconnection-driven acceleration. Our study constitutes a first step towards modelling from first principles potentially observable stratified MRI effects in low-luminosity accretion discs around black holes.