Parametric epicyclic resonance in black hole disks: QPOs in micro-quasars

Non-linear acoustic coupling of modes in accretion disks allows a parametric resonance between epicyclic motions. In black hole disks, such a resonance first occurs, and is strongest, when the radial and vertical epicyclic frequencies are approximately in a 2:3 ratio, in agreement with the 300 and 450 Hz frequencies reported in GRO J1655-40 and the 184 and 276 Hz frequencies reported in XTE J1550-564. The first overtone in the same resonance is in a 5:3 ratio with the fundamental, in agreement with the 69.2 and 41.5 Hz frequencies reported in GRS 1915+105. The narrow width and the frequency stability of the corresponding QPOs follow from general properties of parametric resonance.