A full spectral-timing model to map the accretion flow in black hole binaries: the low hard state of MAXI J1820+070

The nature and geometry of the accretion flow in the low/hard state of black hole binaries is currently controversial. While most properties are generally explained in the truncated disc/hot inner flow model, the detection of a broad residual around the iron line argues for strong relativistic effects from an untruncated disc. Since spectral fitting alone is somewhat degenerate, we combine it with the additional information in the fast X-ray variability and perform a full spectral-timing analysis for NICER and NuSTAR data on a bright low/hard state of MAXI J1820+070. For the first time, we model the variability with propagating mass accretion rate fluctuations by combining two separate current insights: that the hot flow is spectrally inhomogeneous, and that there is a discontinuous jump in viscous time-scale between the hot flow and variable disc. Our model naturally gives the 'double hump' shape of the power spectra, and the increasing high frequency variability with energy in the second hump. Including reflection quantitatively reproduces the switch in the lag-frequency spectra, from hard lagging soft at low frequencies (propagation through the variable flow) to the soft lagging hard at the high frequencies (reverberation from the hard X-ray continuum illuminating the disc). The light travel time derived from the model corresponds to a distance of $\sim$ 45 gravitational radii, supporting the truncated disc model geometry for the low/hard state. The propagation lags allow us to measure the viscous time-scale in the hot flow, and the results favour SANE rather than MAD models for this source.