Dependence of time-lags upon luminosity in neutron-star low-mass X-ray binaries

Kilohertz quasi-periodic oscillations (kHz QPOs) are fast variability features in the emission of neutron-star low-mass X-ray binaries (LMXBs) that are believed to have their origin in the innermost regions of binary systems, close to the central object. Studying this variability allows us to probe the extreme conditions under which matter interacts with the system, helping us understand the mechanism responsible for the kHz QPOs and the way matter behaves as it gets closer to the neutron star. Using timing analysis techniques, it has been shown that the fractional rms amplitude of the lower kHz QPOs decreases exponentially with the luminosity of the source in which the QPOs occur. We show here, for the first time, that the slope of the time-lag spectrum of the lower kHz QPO in 8 neutron-star LMXBs follows the same trend with luminosity. This strong correlation suggests that a single property of the system is responsible for the energy-dependent rms amplitude and time lags of the kHz QPOs in these sources. Since time-dependent Comptonisation with feedback between the corona and the accretion disc is currently the only mechanism that can explain both the lags and rms spectra of the QPO, and since the properties of the corona in these sources change with luminosity, we propose that the QPOs arise from the onset of resonance in a coupled oscillation between the disc and the corona. This resonance would be excited over a narrow range of sizes, electron temperatures and optical depths of the corona when variability at the appropriate frequency appears in the disc