The inner structure and thermodynamics of a thin accretion disc
Using three-dimensional general relativistic magnetohydrodynamic simulations with electron and proton thermodynamics and an electron cooling function, we probe the inner radial and vertical structure of weakly magnetized geometrically thin accretion discs around rapidly spinning black holes. We find that the thin, cold disc transitions to a thick, hot accretion flow at a radius dependent on the mass accretion rate due to proton-electron Coulomb decoupling. At high accretion rates, the disc truncates close to the innermost stable circular orbit $r\approx2r_g$, demonstrating that even in the canonical thin disc model, the plunging region should be treated with two-temperature physics. At intermediate accretion rates, the transition radius moves outward by a factor of two to $r\approx 5r_g$, forming a radiatively inefficient inner flow. The simulations also reveal extended cooling along the surface of the disc out to $\sim10r_g$, with 40\% of the total cooling at intermediate accretion rates occurring above the disc body. Two-temperature effects also impact the emission from within the plunging region of the black hole, leading to less thermal emission than predicted by single-temperature models. These results have implications for X-ray binary state transitions, the physical origin of the X-ray corona, and spin measurements that rely on determining the location of the innermost stable circular orbit.