When the accretion rate is more than a small fraction of Eddington, the inner regions of accretion disks around black holes are expected to be radiation dominated. However, in the α-model, these regions are also expected to be thermally unstable. In this paper, we report two three-dimensional radiation magnetohydrodynamic simulations of a vertically stratified shearing box in which the ratio of radiation to gas pressure is ~10, and yet no thermal runaway occurs over a timespan 40 cooling times. Where the time-averaged dissipation rate is greater than the critical dissipation rate that creates hydrostatic equilibrium by diffusive radiation flux, the time-averaged radiation flux is held to the critical value, with the excess dissipated energy transported by radiative advection. Although the stress and total pressure are well correlated as predicted by the α-model, we show that stress fluctuations precede pressure fluctuations, contrary to the usual supposition that the pressure controls the saturation level of the magnetic energy. This fact explains the thermal stability. Using a simple toy model, we show that independently generated magnetic fluctuations can drive radiation pressure fluctuations, creating a correlation between the two while maintaining thermal stability.
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