The time derivative of the kilohertz quasi-periodic oscillations in 4U 1636-53

We analysed all archival Rossi X-ray Timing Explorer (RXTE) observations of the neutron star low-mass X-ray binary 4U 1636-53 up to 2010 May. In 528 out of 1280 observations we detected kilohertz quasi-periodic oscillations (kHz QPOs), with \tilde65 per cent of these detections corresponding to the so-called lower kHz QPO. Using this QPO we measured, for the first time, the rate at which the QPO frequency changes as a function of QPO frequency. For this we used the spread of the QPO frequency over groups of 10 consecutive measurements, sampling time-scales between 320 and 1600 s and the time derivative of the QPO frequency, ν$$dot QPO , over time-scales of 32-160 s. We found that (i) both the QPO-frequency spread and ν$$dot QPO decrease by a factor of \tilde3 as the QPO frequency increases. (ii) The average value of ν$$dot QPO decreases by a factor of \tilde2 as the time-scale over which the derivative is measured increases from less than 64 to 160 s. (iii) The relation between the absolute value of ν$$dot QPO and the QPO frequency is consistent with being the same both for the positive and negative QPO-frequency derivatives. We show that, if either the lower or the upper kHz QPO reflects the Keplerian frequency at the inner edge of the accretion disc, these results support a scenario in which the inner part of the accretion disc is truncated at a radius that is set by the combined effect of viscosity and radiation drag.