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We study the Fourier time lags due to the Comptonization of disc-emitted photons in a spherical, uniform, and stationary X-ray corona, which located on the rotational axis of the black hole. We use monk , a general relativistic Monte Carlo radiative transfer code, to calculate Compton scattering of photons emitted by a thin disc with a Novikov–Thorne temperature profile. We find that the model time lags due to Comptonization remain constant up to a characteristic frequency and then rapidly decrease to zero at higher frequencies. We provide equations that can be used to determine the time lags and cross-spectra for a wide range of values for the corona radius, temperature, optical depth, height, and for various accretion rates and black hole masses. We also provide an equation for the X-ray luminosity of a single corona, as a function of its characteristics and location above the disc. Remarkably, the observed X-ray time lags of nearby, bright active galaxies can be successfully reproduced by inverse Comptonization process of multiple dynamic coronae. [ABSTRACT FROM AUTHOR]

Relativistic Fe K emission lines from accretion discs and from disc winds encode key information about black holes, and their accretion and feedback mechanisms. We show that these two processes can in principle produce indistinguishable line profiles, such that they cannot be disentangled spectrally. We argue that it is likely that in many cases both processes contribute to the net line profile, and their relative contributions cannot be constrained purely by Fe K spectroscopy. In almost all studies of Fe K emission to date, a single process (either disc reflection or wind Compton scattering) is assumed to dominate the total line profile. We demonstrate that fitting a single process emission model (pure reflection or pure wind) to a hybrid line profile results in large systematic biases in the estimates of key parameters, such as mass outflow rate and spin. We discuss various strategies to mitigate this effect, such as including high-energy data covering the Compton hump, and the implications for future X-ray missions. [ABSTRACT FROM AUTHOR]