**Publication date:** Jun 2015

**Abstract:**

Estimations of black hole spin in the three Galactic microquasars GRS

1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on

spectral and timing X-ray measurements and various theoretical concepts.

Among others, a non-linear resonance between axisymmetric epicyclic

oscillation modes of an accretion disc around a Kerr black hole has been

considered as a model for the observed high-frequency quasi-periodic

oscillations (HF QPOs). Estimates of spin predicted by this model have

been derived based on the geodesic approximation of the accreted fluid

motion. Here we assume accretion flow described by the model of a

pressure-supported torus and carry out related corrections to the mass-

spin estimates. We find that for dimensionless black hole spin a ≡

cJ/GM^{2} ≲ 0.9, the resonant eigenfrequencies are very close to

those calculated for the geodesic motion. Their values slightly grow

with increasing torus thickness. These findings agree well with results

of a previous study carried out in the pseudo-Newtonian approximation.

The situation becomes different for a ≳ 0.9, in which case the resonant

eigenfrequencies rapidly decrease as the torus thickness increases. We

conclude that the assumed non-geodesic effects shift the lower limit of

the spin, implied for the three microquasars by the epicyclic model and

independently measured masses, from a ~ 0.7 to a ~ 0.6. Their

consideration furthermore confirms compatibility of the model with the

rapid spin of GRS 1915+105 and provides highly testable predictions of

the QPO frequencies. Individual sources with a moderate spin (a ≲ 0.9)

should exhibit a smaller spread of the measured 3:2 QPO frequencies than

sources with a near-extreme spin (a ~ 1). This should be further

examined using the large amount of high-resolution data expected to

become available with the next generation of X-ray instruments, such as

the proposed Large Observatory for X-ray Timing (LOFT).

**Authors:**

Šrámková, E.; Török, G.; Kotrlová, A.; Bakala, P.; Abramowicz, M. A.; Stuchlík, Z.; Goluchová, K.; Kluźniak, W.;