Spectral fitting of the spin a ≡ cJ/GM 2 in the microquasar GRS 1915+105 estimate values higher than a = 0.98. However, there are certain doubts about this (nearly) extremal number. Confirming a high value of a > 0.9 would have significant concequences for the theory of high-frequency quasiperiodic oscillations (HF QPOs). Here we discuss its possible implications assuming several commonly used orbital models of 3:2 HF QPOs. We show that the estimate of a > 0.9 is almost inconsistent with two hot-spot (relativistic precession and tidal disruption) models and the warped disc resonance model. In contrast, we demonstrate that the epicyclic resonance and discoseismic models assuming the c-and g-modes are favoured. We extend our discussion to another two microquasars that display the 3:2 HF QPOs. The frequencies of these QPOs scale roughly inversely to the microquasar masses, and the differences in the individual spins, such as a = 0.9 compared to a = 0.7, represent a generic problem for most of the discussed geodesic 3:2 QPO models. To explain the observations of all the three microquasars by one unique mechanism, the models would have to accommodate very large non-geodesic corrections.

We study epicyclic oscillations of fluid tori around black holes (in the Paczyński-Wiita potential) and derive exact analytic expressions for their radial and vertical eigenfrequencies r and z to second-order accuracy in the width of the torus. We prove that pressure effects make the eigenfrequencies smaller than those for free particles. However, the particular ratio z / r ¼ 3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies r and z are about 15% higher than the ones corresponding to free particles. Our results therefore suggest that previous estimates of black hole spins from QPOs have produced values that are too high.

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M 0 = 2.2 ± 0.3M ⊙ . We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j = cJ/GM 2 . Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ∼ M 0 [1 + 0.55( j + j 2 )]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M ⊙ . We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.