Quasiperiodic Oscillations

Quasiperiodic oscillations (QPOs) are generally observed in the PLD-HS state (see Many black-hole transients exhibit low-frequency QPOs roughly in the range 1-20 Hz [39]. (See [80] for a general review of QPO.)

QPOs of higher frequencies (> several 10 Hz) may be directly related to the black-hole accretion disks. For instance, the orbital frequency at the innermost stable orbit around a Schwarzschild hole is —220(M/ 10MQ)-1 Hz, and even higher for a Kerr hole. Several black-hole XBs do show high-frequency QPOs in the PLD-HS state in the range 40-450 Hz [39], suggesting that they originate in the inner disk near a black hole.

Remarkably, pairs of QPOs whose frequencies are commensurate in a 3:2 ratio were discovered from four black-hole XBs including one candidate. These are GRO J1655-40 at 450 and 300Hz [61,73], XTE J1550-564 at 276 and 184 Hz [41, 61] and a marginal QPO at 92 Hz (3:2:1 ratio) [61], GRS 1915+105 at 165 and 113 Hz [62], and H1743-322 at 242 and 166Hz [63]. Importantly, these QPO frequencies do not shift with changes in luminosity, unlike the kHz QPOs in the neutron-star LMXBs. The frequencies seem to be fixed for each individual sources. For these black-hole XBs, the QPO frequency is found to be inversely proportional to the measured black hole mass (^ M-1) [39], except for H1743-322 whose mass is still unknown. These results prompted attempts for interpreting the high-frequency QPOs of black-hole XBs in the framework of general relativity.

There are three fundamental oscillation modes in the disk around a spinning black hole, which produce the orbital frequency, the radial epicyclic frequency and the polar epicyclic frequency. Abramowicz and Kluzniak [2] were the first to propose that the commensurate QPOs result from resonance between these modes. They later considered the resonance between the polar and radial modes for explaining the 3:2 ratio [27]. Remillard et al. [61] found that the 3:2 ratio is possible for each of the three couplings, i.e. orbital/radial, orbital/polar, or radial/polar, at respectively different orbital radii (where resonance occurs) and different angular momentum parameter a* of a Kerr black hole, making use of the measured mass Mx.

Recently, Aschenbach [5] proposed a model that uniquely determines Mx and a*. He reported that the coupling of the polar and the radial epicyclic modes is possible with a frequency ratio of not only 3:2 but also 3:1, and with the associated Kepler frequencies being commensurate at a 3:1 ratio. These conditions restrict the spin to just one value, i.e., a* = 0.99616, which would be common to all 3:2 objects. The masses predicted from the measured QPO frequencies agree well with the dynamically determined masses (Table 16.1). Interestingly, at this high spin the topology of the particles' motion around the black hole unexpectedly changes such that their orbital velocity does not increase but decreases with decreasing distance in a region close to the innermost stable orbit [5]. This reversal of the velocity gradient might excite and maintain the radial epicyclic oscillations.

The commensurate high-frequency QPOs are unique to black holes and seem to be related to the black hole spin. Remarkably, these four sources with the commensurate QPOs all displayed jets, suggesting the role of the black hole spin in the jet production. Study of these QPOs is important as it may eventually lead to the determination of a* of black holes in XBs.

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