  Analysis of archival RXTE data on neutron stars binaries has shown that for
several sources the quality factor (Q) of the lower kilohertz Quasi-Periodic
Oscillations (QPO) drops sharply beyond a certain frequency. This is one
possible signature of the approach to the general relativistic innermost stable
circular orbit (ISCO), but the implications of such an interpretation for
strong gravity and dense matter are important enough that it is essential to
explore alternate explanations. In this spirit, Mendez has recently proposed
that Q depends fundamentally on mass accretion rate (as measured by spectral
hardness) rather than the frequency of the QPO. We test this hypothesis for
4U1636-536 by measuring precisely spectral colors simultaneously with the lower
QPO frequency and Q after correction for the frequency drift, over a data set
spanning eight years of RXTE observations. We find that in this source there is
no correlation between Q and spectral hardness. In particular, no apparent
changes in hardness are observed when Q reaches its maximum before dropping
off. We perform a similar analysis on 4U1608-522; another source showing a
sharp drop in the quality factor of its lower kHz QPO. We find that for this
source, positive and negative correlations are observed between spectral
hardness, frequency and Q. Consequently, if we are to search for a common
explanation for the sharp drop in the quality factor seen in both sources, the
spectral hardness is not a good candidate for the independent variable whereas
the frequency remains. Therefore, we conclude that the ISCO explanation is
viable for 4U1636-536, and thus possibly for others.
