2:3 Twin Quasi-Periodic Oscillations in Magnetohydrodynamic Accretion   Flows
  We study the radial and vertical oscillations in the three-dimensional magnetohydrodynamic (MHD) accretion flows around black holes. General relativistic effects are taken into account by using pseudo-Newtonian potential. We find that the structure of MHD flows is changed at $3.8 r_{\rm s}\leq r\leq 6.3 r_{\rm s}$ and the two pairs of quasi-periodic oscillations (twin QPOs) are excited in that region. The time evolution of the power spectrum density (PSD) indicates that these twin QPOs are most likely to be produced by the resonance between the Keplerian frequency $\nu_{\rm K}$ and the epicyclic frequency $\nu_{\kappa}$. The PSD shows that the lower peak frequency $\nu_{\rm l}$ corresponds to $\nu_{\rm K}$, while the upper peak frequency $\nu_{\rm u}$ corresponds to $\nu_{\rm K} + \nu_{\kappa}$. The ratio of two peak frequencies is close to 2:3. The results provide the first direct evidence for the excitation of the resonant disk oscillation in the MHD accretion flows. 
Yoshiaki Kato