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 resonan
ce 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<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).
The innermost stable cicular orbit (ISCO) of an accretion disc orbiting a neutron star (NS) is often assumed a unique prediction of general relativity. However, it has been argued that ISCO also appears around highly elliptic bodies described by Newt
onian theory. In this sense, the behaviour of an ISCO around a rotating oblate neutron star is formed by the interplay between relativistic and Newtonian effects. Here we briefly explore the consequences of this interplay using a straightforward analytic approach as well as numerical models that involve modern NS equations of state. We examine the ratio K between the ISCO radius and the radius of the neutron star. We find that, with growing NS spin, the ratio K first decreases, but then starts to increase. This non-monotonic behaviour of K can give rise to a neutron star spin interval in which ISCO appears for two very different ranges of NS mass. This may strongly affect the distribution of neutron stars that have an ISCO (ISCO-NS). When (all) neutron stars are distributed around a high mass M0, the ISCO-NS spin distribution is roughly the same as the spin distribution corresponding to all neutron stars. In contrast, if M0 is low, the ISCO-NS distribution can only have a peak around a high value of spin. Finally, an intermediate value of M0 can imply an ISCO-NS distribution divided into two distinct groups of slow and fast rotators. Our findings have immediate astrophysical applications. They can be used for example to distinguish between different models of high-frequency quasiperiodic oscillations observed in low-mass NS X-ray binaries.
In the context of high-frequency quasi-periodic oscillation (HF QPOs) we further explore the appearance of an observable signal generated by hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwar
zschild spacetime. The aim of our investigation is to reveal whether observable characteristics of the Fourier power-spectral density can help us to distinguish between the two competing models, namely, the idea of bright spots orbiting on the surface of an accretion torus versus the scenario of intrinsic oscillations of the torus itself. We take the capabilities of the present observatories (represented by the Rossi X-ray Timing Explorer, RXTE) into account, and we also consider the proposed future instruments (represented here by the Large Observatory for X-ray Timing, LOFT).
High frequency quasi-periodic oscillations (HF QPOs) appear in the X-ray variability of several accreting low-mass binaries. In a series of works it was suggested that these QPOs may have connection to inhomogeneities orbiting close to an inner edge
of the accretion disc. In this paper we explore the appearance of an observable signal generated by small radiating circular hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. Our consideration takes into account the capabilities of observatories that have been operating in the past two decades represented by the Rossi X-ray Timing Explorer (RXTE) and the proposed future instruments represented by the Large Observatory for X-ray Timing (LOFT). For these purposes we choose such model parameters that lead to lightcurves comparable to those observed in Galactic black hole sources, in particular the microquasar GRS 1915+105. We find that when a weak signal corresponding to the hot-spot Keplerian frequency is around the limits of the RXTE detectability, the LOFT observations can clearly reveal its first and second harmonics. Moreover, in some specific situations the radial epicyclic frequency of the spot can be detected as well. Finally, we also compare the signal produced by the spots to the signal produced by axisymmetric epicyclic disc-oscillation modes and discuss the key differences that could be identified via the proposed future technology. We conclude that the ability to recognize the harmonic content of the signal can help to distinguish between the different proposed physical models.
At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41Hz, 67Hz, 113Hz, and 167Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a>0.98. We use the idea of oscilla
tions induced by the hump of the orbital velocity profile (related to locally non-rotating frames - LNRF) in discs orbiting near-extreme Kerr black holes, which are characterized by a humpy frequency f_h, that could excite the radial and vertical epicyclic oscillations with frequencies f_r, f_v. Due to non-linear resonant phenomena the combinational frequencies are allowed as well. Assuming mass M=14.8M_sun and spin a=0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies f_h=41Hz, f_r=67Hz, (f_h+f_r)=108Hz, (f_v-f_r)=170Hz corresponding quite well to the observed ones. For black-hole parameters being in good agreement with those given observationally, the forced resonant phenomena in non-linear oscillations, excited by the hump-induced oscillations in a Keplerian disc, can explain high-frequency QPOs in GRS 1915+105 within the range of observational errors.
