Drop of coherence of the lower kilo-Hz QPO in neutron stars: Is there a link with the innermost stable circular orbit?

Using all available archival data from the Rossi X-ray Timing Explorer (RXTE), we follow the frequency of the kilo-Hz QPOs in three low luminosity neutron star low mass X-ray binaries; namely 4U 1636-536, 4U 1608-522, and 4U 1735-44. Following earlier work by Barret et al. (2005a,b), we focus our analysis on the lower kilo-Hz QPO, for which we study the dependency of its quality factor (Q = nu/Delta nu, where Delta nu is the FWHM) and amplitude as a function of frequency over a range covering from 500 Hz to 1000 Hz. As previously found for 4U 1636-536, we show that the quality factor of the lower kilo-Hz increases with frequency up to a maximum frequency around 800 Hz, beyond which an abrupt drop of its coherence is observed down to a limiting frequency where the QPO disappears completely. Simultaneously the amplitude of the QPOs is almost constant below the peak frequency and starts to decrease smoothly afterwards. The peak frequency is 850 Hz, 820 Hz, 740 Hz whereas the limiting frequency is 920 Hz, 900 Hz and 830 Hz for 4U 1636-536, 4U 1608-522 and 4U 1735-44 respectively. A ceiling of the lower QPO frequencies is also seen clearly in a frequency versus count rate diagram for all sources. This behavior is reproducible within an object and between objects. We suggest here that the drop of coherence of the lower QPO may be a geometry-related effect, which could be related to the last stable circular orbit.