A series of Exosat observations of the 'atoll' source 4U/MXB 1636 - 53 shows that duration and temperature of the X-ray bursts strongly correlate with the X-ray spectral and fast variability characteristics of the persistent emission of the source. This implies that spectral shape, fast variability, and burst duration and temperature all correlate well with accretion rate M. This provides a strong argument that in the atoll sources, source-state is determined by M, just as in the Z sources. These observations also show that the persistent X-ray intensity can vary independently from the other mentioned characteristics. Therefore, intensity is probably not a good measure for the accretion rate.
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Klis et al. (1990) studied this question.