**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/GM2 ≲ 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.;