Supporting evidence for the signature of the innermost stable circular orbit in Rossi X-ray data from 4U 1636-536

Analysis of archival Rossi X-ray Timing Explorer (RXTE) data on neutron star low-mass X-ray 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. Specifically, he has suggested that analysis of multiple sources shows trends in Q similar to those previously reported in individual sources, and he surmises that the ISCO therefore does not play a role in the observed sharp drop in Q in any source. We test this hypothesis for 4U 1636-536 by measuring precisely spectral colours 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 4U 1608-522; 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 4U 1636-536, and thus possibly for others.