Radiation hydrodynamic simulations for the origin of quasi-periodic oscillations for accretion onto supermassive black holes

ABSTRACT Quasi-periodic oscillation (QPO) has been detected in several accreting supermassive black hole (SMBH) systems, including active galactic nuclei (AGNs) and tidal disruption events (TDEs). However, despite that several models have been proposed, the physical origin of QPO is still unclear. In this paper, we performed radiation hydrodynamic simulations of accretion flow by injecting mass at a fixed radius, i.e. 10 Schwarzschild radius with different mass accretion rates, and setting the black hole (BH) mass to $10^7\,{\rm M}_{\odot }$. We find that there are QPO signals by analyzing the mass inflow rates as a function of time from the simulations for different radii. The QPO frequencies from our simulations are well consistent with the radial epicyclic frequencies from analytic calculations for radius greater than a critical radius 3.8 Schwarzschild radius. This critical radius corresponds to the maximum epicyclic frequency, i.e. $\nu _{\rm r,max}$, in the radial direction. We proposed that $\nu _{\rm r,max}$ can be a good proxy for the observed QPO $\nu _{\rm QPO}$. Furthermore, assuming that our simulation results can be scaled to different BH masses $M_{\rm BH}$, we find that the theoretical relation of $\nu _{\rm r,max}$ as a function of $M_{\rm BH}$ can well match $\nu _{\rm QPO}$ as a function of $M_{\rm BH}$ for a sample of AGN and TDE. Finally, we discuss the effects of the BH mass, general relativity (GR), and other possible factors including the size of the mass injecting radius, viscosity and magnetic field on the simulation results.