Energy partition between Alfv\'enic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfv\'enic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In this model, the Alfv\'enic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfv\'enic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. We show that the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfv\'enic fluctuations. Combining this finding with our recent results found on hybrid-gyrokinetic simulations leads to an ion-to-electron heating prescription that takes into account both the driving of turbulence via MRI at MHD scales and the dissipation at kinetic scales. This prescription suggests that ions are heated at least twice as strongly as the electrons in the portion of accretion disc with near-azimuthal magnetic field, which can be a useful model in interpreting observations of hot accretion discs by the Event Horizon Telescope.