Are spectral and timing correlations similar in different spectral states in black hole X-ray binaries?

We study the outbursts of the black hole X-ray binaries MAXI J1659-152, SWIFT J1753.5-0127, and GX 339-4 with the Swift X-ray Telescope (XRT). The bandpass of the XRT has access to emission from both components of the accretion flow: the accretion disk and the corona/hot flow. This allows a correlated spectral and variability study, with variability from both components of the accretion flow. We present for the first time a combined study of the evolution of spectral parameters (disk temperature and radius) and timing parameters (frequency and strength) of all power spectral components in different spectral states. Comparison of the correlations in different spectral states shows that the frequency and strength of the power spectral components exhibit dependencies on the disk temperature that are different in the (low-)hard and the hard-intermediate states (HIMSs); most of these correlations that are clearly observed in the HIMS (in MAXI J1659-152 and GX 339-4) are not seen in the (low-)hard state (in GX 339-4 and SWIFT J1753.5-0127). Also, the responses of the individual frequency components to changes in the disk temperature are markedly different from one component to the next. Hence, the spectral-timing evolution cannot be explained by a single correlation that spans both these spectral states. We discuss our findings in the context of the existing models proposed to explain the origin of variability.