Modelling the cross-spectral variability of the black hole binary MAXI J1659-152 with propagating accretion rate fluctuations

Abstract

The power spectrum of the X-ray fluctuations of accreting black holes often consists of two broad humps. We quantitatively investigate the hypothesis that the lower frequency hump originates from variability in a truncated thin accretion disc, propagating into a large scale-height inner hot flow which, in turn, itself is the origin of the higher frequency hump. We extend the propagating mass accretion rate fluctuations model PROPFLUC to accommodate double hump power spectra in this way. Furthermore, we extend the model to predict the cross-spectrum between two energy bands in addition to their power spectra, allowing us to constrain the model using the observed time lags, which in the model result from both propagation of fluctuations from the disc to the hot flow, and inside the hot flow. We jointly fit soft and hard power spectrum, and the cross-spectrum between the two bands using this model for 5 Swift X-ray Telescope observations of MAXI J1659-152. The new double hump model provides a better fit to the data than the old single hump model for most of our observations. The data show only a small phase lag associated with the low frequency hump. We demonstrate quantitatively that this is consistent with the model. We compare the truncation radius measured from our fits with that measured purely by spectral fitting and find agreement within a factor of two. This analysis encompasses the first joint fits of stellar-mass black hole cross-spectra and power spectra with a single self-consistent physical model.

Multi-time-scale X-ray reverberation mapping of accreting black holes

“…We fit models to data for the real and imaginary parts of G (E, ν) as a function of energy, for a number of discrete frequency ranges (following Rapisarda et al 2016;Ingram et al 2016). Fitting for real and imaginary parts rather than amplitude and phase naturally avoids some mistakes and inaccuracies commonly found in the literature.…”

“…However, these lags do not show any reflection features in the lag-energy spectrum and for this reason they are thought to be associated with intrinsic variation of the continuum spectral shape. This is commonly interpreted as propagation of mass accretion rate fluctuations towards the black hole on a viscous timescale (Lyubarskii 1997;Kotov et al 2001;Arévalo & Uttley 2006;Ingram & van der Klis 2013;Rapisarda et al 2016). This intrinsic continuum lag reduces with increasing Fourier frequency, leaving the opportunity to detect a reverberation signature at high frequencies.…”

A physical model for the spectral-timing properties of accreting black holes

“…dominated by Comptonization from the hot flow. Fluctuations in the disc will propagate inwards through the hot flow, but with some lag time corresponding to the viscous time-scale for the fluctuation to drift from the disc inner edge to the innermost parts of the hot flow which dominate the Comptonized emissivity (Uttley et al 2014;Rapisarda et al 2016). However, such models are unable to explain why these lags are seen between different energy bands where the disc emission is negligible, nor why the lags also depend on the frequency of variability (Nowak et al 1999;De Marco et al 2015;Misra et al 2017).…”

Observations of X‐ray reverberation around black holes

“…This implies proper modelization of the continuum hard lags, as the latter are still significant in the frequency range of current detections. Several groups have been independently studying this problem, from an analytical (Ingram & van der Klis ; Mahmoud et al ; Mahmoud & Done ; Mastroserio et al ; Rapisarda et al , ) and numerical (Arévalo & Uttley ; Ingram & Done ) points of view, as well as in the context of magnetohydrodynamic (MHD) simulations (Hogg & Reynolds ), so that the number of available models is rapidly increasing.…”