  Association of the high-frequency quasi-periodic oscillation (HFQPO) pairs
with the broad Fe K line in XTE J1550-564 and GRO J1655-40 is discussed based
on the magnetic coupling (MC) of a rotating black hole (BH) with its
surrounding disc. The 3:2 HFQPO pairs are interpreted by virtue of the inner
and outer hotspots arising from non-axisymmetric magnetic field, where the
inner hotspot is produced by a torque exerted at the inner edge of the disc,
and the outer hotspot is created by the screw instability of the large-scale
magnetic field. The very steep emissivity index is created predominantly by the
torque exerted at the inner edge of the disc. It turns out that the 3:2 HFQPO
pairs observed in the two sources can be fitted by tuning several model
parameters, such as the BH spin, and the main features of this model lie in
three aspects. (1) The condition for only one HFQPO is discussed based on the
two mechanisms for producing the 3:2 HFQPO pairs, (2) an explanation is given
for a systematic shift away from disc dominated flux with the increasing
power-law flux as the HFQPO pairs shift from the higher to lower frequencies,
which is consistent with the analysis given by Remillard et al. (2002), and (3)
the BH spin in XTE J1550-564 and GRO J1655-40 can be estimated by combining the
3:2 HFQPO pairs with the very steep emissivity index required for fitting the
broad Fe K emission line.

Astrophysics