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tokens: of A for to match is then (taking ). This factor could include contributions from the turnaround time at each end of the corona or from other physical processes. magnetohydrodynamic calculations (Edwin Roberts 1983 ) show that magnetic fields affect the frequency of various modes of oscillation. Detailed calculations of expected values of A are beyond the scope of this work. Remillard McClintock ( 2006 ; fig. 10) show that QPO frequency correlates with disc flux in hard/steep power-law-intermediate states. The observations presented here have a weaker disc component, which is not unambiguously detected but may be clearer at soft energies, so this could be investigated, for example, with NICER . While the QPO is most dominant at high energies, it is also strongly detected in the 3–10 keV band, which is also covered by NICER . Owing to the more frequent coverage of MAXI J1820+070 by NICER , a more detailed analysis of the QPO progression can be made with these data. 4.3 Coronal temperature The corona also shows changes in its mean properties: the temperature anticorrelates with flux. This has been observed in other individual XRBs (Joinet, Kalemci Senziani 2008 ; Motta, Belloni Homan 2009 ) and AGN (Lubiński et al. 2010 ). This could happen because pair production from photon collisions is regulating the temperature (Svensson 1984 ; Zdziarski 1985 ; Fabian et al. 2015 ): at higher fluxes, there are more photons, which allows sufficient pairs to be produced at lower temperatures. The coronal temperatures observed here are allowed by the pair thermostat, being below the pair-production limit that is observed to limit accreting sources as a population (Fabian et al. 2015 ). The lower temperatures than the pair limit can be explained by a deviation from a pure thermal distribution, which is expected as the cooling time-scale is less than the collision time-scale (Fabian et al. 2017 ). The presence of a non-thermal tail to the particle distribution reduces the critical temperature (Fabian et al. 2017 ). These considerations do not take substructure in the corona into account; this remains a potential caveat when estimating the coronal compactness from its total luminosity and size. We consider this correlation in more detail by comparing the corona’s radiative compactness with its electron temperature. We take electron temperatures from our fits and calculate the coronal compactness following the methodology of Fabian et al. ( 2015 ). We take the luminosity from the total direct flux of our best-fittng models at a distance of 3.5 kpc. Calculation of the compactness also requires a radius; the coronal prescription used here (including contributions from two points) does not readily convert to an equivalent spherical size so we try several prescriptions. First, we consider a fiducial size for all observations. We also consider the effect of a shrinking radius, as could be implied by the reduction in illumination of the outer disc with time. We reduce