2021MNRAS.507...55M

We present a new release of the RELTRANS model to fit the complex cross-spectrum of accreting black holes as a function of energy. The model accounts for continuum lags and reverberation lags self-consistently in order to consider the widest possible range of X-ray variability time-scales. We introduce a more self-consistent treatment of the reverberation lags, accounting for how the time variations of the illuminating flux change the ionization level of the accretion disc. This process varies the shape of the reflection spectrum in time causing an additional source of lags besides the light crossing delay. We also consider electron densities in the accretion disc up to 10²⁰ cm^–3, which are found in most of the stellar mass black holes and in some active galactic nuclei. These high densities increase the amplitude of the reverberation lags below 1 keV since the reflection flux enhances in the same energy range. In addition, we investigate the properties of hard lags produced by variations in the power-law index of the continuum spectrum, which can be interpreted as due to roughly 3 per cent variability in the corona's optical depth and temperature. As a test case, we simultaneously fit the lag-energy spectra in a wide range of Fourier frequency for the black hole candidate MAXI J1820+0701820 observed with NICER. The best fit shows how the reverberation lags contribute even at the longer time-scales where the hard lags are important. This proves the importance of modelling these two lags together and self-consistently in order to constrain the parameters of the system.