Global Electron Thermodynamics in Radiatively Inefficient Accretion Flows

In the collisionless plasmas of radiatively inefficient accretion flows, heating and acceleration of ions and electrons is not well understood. Recent studies in the gyrokinetic limit revealed the importance of incorporating both the compressive and Alfvenic cascades when calculating the partition of dissipated energy between the plasma species. In this paper, we use a covariant analytic model of the accretion flow to explore the impact of compressive and Alfvenic heating, Coulomb collisions, compressional heating, and radiative cooling on the radial temperature profiles of ions and electrons. We show that, independent of the partition of heat between the plasma species, even a small fraction of turbulent energy dissipated to the electrons makes their temperature scale with a virial profile and the ion-to-electron temperature ratio smaller than in the case of pure Coulomb heating. In contrast, the presence of compressive cascades makes this ratio larger because compressive turbulent energy is channeled primarily into the ions. We calculate the ion-to-electron temperature in the inner accretion flow for a broad range of plasma properties, mass accretion rates, and black hole spins and show that it ranges between $5 \lesssim T_i/T_e \lesssim 40$. We provide a physically motivated expression for this ratio that can be used to calculate observables from simulations of black hole accretion flows for a wide range of conditions.