Relativistic, Viscous, Radiation Hydrodynamic Simulations of Geometrically Thin Disks. I. Thermal and Other Instabilities
We introduce results from two-dimensional, general relativistic, viscous, radiation hydrodynamic numerical simulations of Shakura–Sunyaev thin disks accreting onto stellar-mass Schwarzschild black holes. We consider cases on both the gas- and radiation-pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates spanning the range from $\dot{M}=0.01{L}_{\mathrm{Edd}}/{c}^{2}$ to 10L Edd/c 2 . The simulations directly test the stability of this standard disk model on the different branches. We find clear evidence of thermal instability for all radiation-pressure-dominated disks, resulting universally in the vertical collapse of the disks, which in some cases then settle onto the stable, gas-pressure-dominated branch. Although these results are consistent with decades-old theoretical predictions, they appear to be in conflict with available observational data from black hole X-ray binaries. Additionally, we find evidence for a radiation-pressure-driven instability that breaks the unstable disks up into alternating rings of high and low surface density on a timescale comparable to the thermal collapse. Since radiation is included self-consistently in the simulations, we are able to calculate light curves and power density spectra (PDS). Mostly, we measure radiative efficiencies (ratio of luminosity to mass accretion rate) close to 6%, as expected for a nonrotating black hole. The PDS appear as broken power laws, with a break typically around 100 Hz. There is no evidence of significant excess power at any frequencies, i.e., no quasi-periodic oscillations are observed.