Evidence for harmonic relationships in the high-frequency quasi-periodic oscillations of XTE J1550-564 and GRO J1655-40

We continue to investigate the X-ray properties of the black hole binary XTE J1550-564. By grouping observations (1998-1999) according to the type of low-frequency quasiperiodic oscillation (LFQPO) identified in a previous paper, we show evidence that two high-frequency QPOs (HFQPOs) occur simultaneously near 184 and 276 Hz. We can model the QPO profiles while assuming that the central frequencies are related by a 3:2 ratio. In one group, there is some evidence of a broad feature at the fundamental frequency of 92 Hz. We also investigate the 2000 April outburst, and we confirm the suggestion of Miller et al. that a 270 Hz QPO is accompanied by a second feature near 180 Hz. The histogram for the 28 individual HFQPO detections in XTE J1550-564 shows two peaks near 184 and 276 Hz, while there is a notable exception in the 143 Hz QPO detected on 1998 October 15. Similarly, all of the 13 HFQPO detections in the black hole binary GRO J1655-40 occur at two frequencies that are related by a 3:2 ratio. We next investigate all of the energy spectra for XTE J1550-564, and we find a systematic increase in the strength of the power-law component as the stronger of the two HFQPOs shifts from 276 to 184 Hz. A strikingly similar result is seen in the spectra of GRO J1655-40 when the stronger HFQPO shifts from 450 to 300 Hz. The fundamental HFQPO frequencies for the two X-ray sources scale as M-1, which is consistent with the hypotheses that these HFQPOs represent some kind of oscillation rooted in general relativity (GR) and that the two black holes have similar values of the dimensionless spin parameter. We discuss physical mechanisms that may explain these HFQPOs. A resonance between orbital and radial coordinate frequencies is one possibility suggested by Abramowicz & Kluzniak. For XTE J1550-564, this would imply moderate values for the dimensionless spin parameter (0.1 < a(*) < 0.6), with similar results for GRO J1655-40. A resonance between polar and radial coordinate frequencies allows additional values for a(*) above 0.9. There remain serious uncertainties regarding the physical mechanism whereby resonances in coordinate frequencies may produce HFQPOs. We also discuss models for "diskoseismic'' oscillations. In this case, the concept that the inner disk behaves as a resonance cavity in GR has certain attractions for explaining HFQPOs, but integral harmonics are not predicted for the three types of diskoseismic modes derived for adiabatic perturbations in a thin accretion disk.