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Following the previous research on epicyclic oscillations of accretion disksaround black holes (BHs) and neutron stars (NSs), a new model of high-frequencyquasi-periodic oscillations (QPOs) has been proposed (CT model), which dealswith oscillations of fluid in marginally overflowing accretion tori (i.e., toriterminated by cusps). According to preliminary investigations, the modelprovides better fits of the NS QPO data compared to the relativistic precession(RP) model. It also implies a significantly higher upper limit on the Galacticmicroquasars BH spin. A short analytic formula has been noticed to wellreproduce the model's predictions on the QPO frequencies in Schwarzschildspacetimes. Here we derive an extended version of this formula that applies torotating compact objects. We start with the consideration of Kerr spacetimesand derive a formula that is not restricted to a particular specific angularmomentum distribution of the inner accretion flow, such as Keplerian orconstant. Finally, we consider Hartle-Thorne spacetimes and include correctionsimplied by the NS oblateness. For a particular choice of a single parameter,our relation provides frequencies predicted by the CT model. For another value,it provides frequencies predicted by the RP model. We conclude that the formulais well applicable for rotating oblateness NSs and both models. We brieflyillustrate application of our simple formula on several NS sources and confirmthe expectation that the CT model is compatible with realistic values of the NSmass and provides better fits of data than the RP model.

Simple analytic formula relating the mass and spin of accreting compact objects to their rapid X-ray variability