Abstract:
We expand the relativistic precession model to include nonequatorial and eccentric trajectories and apply it to
quasi-periodic oscillations (QPOs) in black hole X-ray binaries (BHXRBs) and associate their frequencies with the
fundamental frequencies of the general case of nonequatorial (with Carterʼs constant, Q ¹ 0) and eccentric (e ¹ 0)
particle trajectories, around a Kerr black hole. We study cases with either two or three simultaneous QPOs and
extract the parameters {e, rp, a, Q}, where rp is the periastron distance of the orbit, and a is the spin of the black
hole. We find that the orbits with [Q = -0 4] should have e 0.5 and rp ∼ 2–20 for the observed range of QPO
frequencies, where a ä [0, 1], and that the spherical trajectories {e = 0, Q ¹ 0} with Q = 2–4 should have
rs ∼ 3–20. We find nonequatorial eccentric solutions for both M82 X-1 and GROJ 1655-40. We see that these
trajectories, when taken together, span a torus region and give rise to a strong QPO signal. For two simultaneous
QPO cases, we found equatorial eccentric orbit solutions for XTEJ 1550-564, 4U 1630-47, and GRS 1915+105,
and spherical orbit solutions for BHXRBs M82 X-1 and XTEJ 1550-564. We also show that the eccentric orbit
solution fits the Psaltis–Belloni–Klis correlation observed in BHXRB GROJ 1655-40. Our analysis of the fluid
flow in the relativistic disk edge suggests that instabilities cause QPOs to originate in the torus region. We also
present some useful formulae for trajectories and frequencies of spherical and equatorial eccentric orbits
