On the maximum amplitude and coherence of the kilohertz quasi‐periodic oscillations in low‐mass X‐ray binaries

I study the behaviour of the maximum rms fractional amplitude, r max , and the maximum coherence, Q max , of the kilohertz quasi‐periodic oscillations (kHz QPOs) in a dozen low‐mass X‐ray binaries. I find that (i) the maximum rms amplitudes of the lower‐ and upper‐kHz QPOs, r ℓ max and r u max , respectively, decrease more or less exponentially with increasing luminosity of the source; (ii) the maximum coherence of the lower‐kHz QPO, Q ℓ max , first increases and then decreases exponentially with luminosity, at a faster rate than both r ℓ max and r u max ; (iii) the maximum coherence of the upper‐kHz QPO, Q u max , is more or less independent of luminosity; and (iv) r max and Q max show the opposite behaviour with hardness of the source, consistent with the fact that there is a general anticorrelation between luminosity and spectral hardness in these sources. Both r max and Q max in the sample of sources, and the rms amplitude and coherence of the kHz QPOs in individual sources show a similar behaviour with hardness. This similarity argues against the interpretation that the drop of coherence and rms amplitude of the lower‐kHz QPO at high QPO frequencies in individual sources is a signature of the innermost stable circular orbit around a neutron star. I discuss possible interpretations of these results in terms of the modulation mechanisms that may be responsible for the observed variability.