2025MNRAS.542..982B

Cygnus X-1 is a persistent, high-mass black hole X-ray binary (BHXRB) which in the hard state shows many similar properties to transient BHXRBs, along with intriguing differences, such as the lack of quasi-periodic oscillations. Here, we compare for the first time the detailed spectral-timing properties of Cyg X-1 with a transient BHXRB, MAXI J1820+070, combining data from XMM-Newton and NICER (Neutron Star Interior Composition Explorer) with contemporaneous INTEGRAL (International Gamma-Ray Astrophysics Laboratory) data to study the power spectra, rms spectra, and time lags over a broad 0.5-200 keV range. We select bright hard state MAXI J1820+070 data with similar power-spectral shapes to the Cyg X-1 data, to compare the source behaviours while accounting for the evolution of spectral-timing properties, notably the lags, through the hard state. Cyg X-1 shows no evidence for soft lags in the 1-10 Hz frequency range where they are clearly detected for MAXI J1820+070. Furthermore, the low-frequency hard lags and rms spectra evolve much more strongly during the hard state of Cyg X-1 than for MAXI J1820+070. We argue that these differences cannot be explained by the different black hole masses of these systems, but may be related to their different accretion rates and corresponding locations on the hardness-intensity diagram. We conjecture that there is a significant luminosity-dependence of coronal geometry in the hard state of BHXRBs, rather than an intrinsic difference between Cyg X-1 and transient BHXRBs. This possibility has also been suggested to explain a common time-lag feature that appears in the hard intermediate states of Cyg X-1 and transient BHXRBs.