Particle-in-cell Simulations of the Magnetorotational Instability in Stratified Shearing Boxes

Abstract: The magnetorotational instability (MRI) plays a crucial role in regulating the accretion efficiency in astrophysical accretion disks. In low-luminosity disks 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 disks using shearing boxes with net vertical field. We use pair plasmas, with initial $\beta=100$ and concentrate on sub-relativistic plasma temperatures ($k_BT \lesssim mc^2$). Our 2D and 3D runs show disk expansion, particle and magnetic field outflows, and a dynamo-like process. They also produce magnetic pressure dominated disks with (Maxwell stress dominated) viscosity parameter $\alpha \sim 0.5-1$. By the end of the simulations, the dynamo-like magnetic field tends to dominate the magnetic energy and the viscosity in the disks. Our 2D and 3D runs produce fairly similar results, and are also consistent with previous 3D MHD simulations. Our simulations also show nonthermal particle acceleration, approximately characterized by power-law tails with temperature dependent spectral indices $-p$. For temperatures $k_BT \sim 0.05-0.3\, mc^2$, we find $p\approx 2.2-1.9$. 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 modeling from first principles potentially observable stratified MRI effects in low-luminosity accretion disks around black holes.