tokens: et al. ( 2018 ) and Stiele Kong ( 2018 ), but due to sparser observations, the correlation is not as tight as seen in this work. The trend observed by Mereminskiy et al. ( 2018 ) resembles the correlation observed for GRS 1915+105 (Shaposhnikov Titarchuk 2007 ). Such correlation has been previously observed in several BHBs (Vignarca et al. 2003 ) and provides a tight link between the QPO and the hard-component emission. In that work, the correlation was found on time-scales of minutes in GRS 1915+105 and on scales of days-months for other transient BHBs. Here, we follow the QPO over 5 d. Fürst et al. ( 2016 ) also observe an extremely tight correlation of the QPO centroid frequency and power-law index in GX 339–4 in the frequency range of 0.6–1 Hz and Γ of 1.66–1.8. The authors estimate the mass of the BH using a scaling relation provided by Shaposhnikov Titarchuk ( 2007 ). The typical evolution of the outburst of a transient BHB is described best in the HID, where a counterclockwise path is followed. In the right ‘vertical’ branch, corresponding to the LHS, the flux increases, the power-law index is well correlated with it and the frequencies of the timing features, although no peaked QPO is usually observed, also increase (see Motta, Belloni Homan 2009 ; Motta et al. 2011 ). Since the spectrum gradually softens, this branch is not really vertical. In the top ‘horizontal’ branch, the spectrum softens further, with the power-law index Γ increasing in absolute value. The flux usually continues to increase, although not as fast as before, and the QPO frequency is correlated with both flux and Γ. Given the shape of the PDS and the values of the power-law index, our observations are clearly on the HIMS branch. As described before, usually both the LHS and HIMS branches see a correlation between frequencies of variability components, the flux, and the power-law index. In our AstroSat data, we see the absence of a correlation with flux, although in the NICER data following our observation this correlation is present. This clearly shows that the QPO frequency is related to the energy spectral shape and not to the flux in either of the two main components. In a thermal-Comptonization scenario, the index of the hard component steepens as the population of electrons cools due to the increase in soft photon input (see e.g. Motta et al. 2009 ). However, from Fig. 4 we can see that this is not the case here, as the secular increase in disc flux is not followed by Γ. Another parameter that determines Γ is the optical depth of the cloud τ 0 : for a spherical cloud and input photon energy much lower than the temperature of the electron cloud kT e , we have , where (Sunyaev Truemper 1979 ; Sunyaev Titarchuk 1980 ). Therefore in order to keep Γ from varying when the cloud temperature decreases is to increase τ 0 in a very specific way. Fluctuations in this relation could in principle give rise to the observed fluctuations in Γ, but it would be very ad hoc.
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