The Origin of the Slow-to-Alfvén Wave Cascade Power Ratio in Shear-Driven Accretion Flows

The partition of turbulent heating between ions and electrons in radiatively inefficient accretion flows plays a crucial role in determining the observational appearance of accreting black holes. Recent studies of particle heating from collisionless damping of turbulent energy have shown that this partition of energy between ions and electrons is dictated by the ratio of the energy injected into the slow and Alfvén wave cascades. In this talk, I will present the mechanism by which turbulent energy is injected into slow- and Alfvén- wave cascades in magnetized shear flows. I will show that this ratio depends on the particular (rϕ) components of the Maxwell and Reynolds stress tensors that cause the transport of angular momentum, the shearing rate, and the orientation of the mean magnetic field relative to the shear. I will then use numerical magnetohydrodynamic shearing-box simulations with background conditions relevant to black hole accretion disks to compute the magnitudes of the stress tensors for turbulence driven by the magneto-rotational instability (MRI) and infer the injection power ratio between slow and Alfvén wave cascades. I will connect these results to the predictions of linear theory of the dynamics of the Maxwell and Reynolds stress tensors during the growth of the MRI, to formulate a subgrid model for the slow-to-Alfvén wave cascade power ratio and consequently the ion-to-electron heating ratio that can be incorporated into global simulations of electron thermodynamics in accretion flows.