Accretion-ejection instability and QPO in black-hole binaries.II. Relativistic effects

The Accretion-Ejection Instability has been proposed to explain the low frequency Quasi-Periodic Oscillation (QPO) observed in low-mass X-Ray Binaries, in particular Black-Hole candidates. Its frequency, typically a fraction of the Keplerian frequency at the disk inner radius, is exactly in the range indicated by observations. The variations of the frequency with the disk inner radius (extracted from spectral fits of the X-ray emission) might thus be a useful test. In this paper we discuss how changes in the rotation curve, due to relativistic effects when the disk approaches the central object, affect the physics of the instability, and thus this frequency-inner radius relation. We find that the relationship between the frequency of the mode and the Keplerian frequency at the inner disk radius ($r_{int}$) departs from the one obtained in a Keplerian disk, when $r_{int}$ approaches the last stable orbit. This might agree with the recently published results, showing a discrepancy between the behavior of the QPO in the micro quasar GRO J1655, compared to other sources such as XTE J1550 and GRS 1915. In a companion paper (Rodriguez et al., 2002, hereafter Paper I) we have presented detailed observational results for GRO J1655 and GRS 1915. We show how the opposite correlations found in these sources between the disk color radius (assumed to be close to its inner radius) and the QPO frequency could indeed be explained by our theoretical result.