Abstract
Abstract We have proposed in previous papers that the high-frequency pair of quasi-periodic oscillations observed in black-hole binaries with a frequency ratio of $3:2$ are inertial-acoustic oscillations (nearly horizontal oscillations with no node in the vertical direction) or g-mode oscillations, which are resonantly excited on warped relativistic disks. The resonance occurs through horizontal motions. In this model, the dimensionless spin parameter, $a_*$, of the central sources can be estimated when their masses are known from other observations. This estimate is done for three sources (GRO J1665$-$40, XTE J1550$-$564, GRS 1915$+$105). For all of them, we have $a_*\leq 0.45$.
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