Abstract
The light curves of a diverse range of accreting objects show characteristic linear relationships between the short-term rms amplitude of variability and the flux as measured on longer time-scales. This behaviour is thought to be imprinted on the light curves by accretion rate fluctuations on different time-scales, propagating and coupling together through the accretion flow. Recently, a simple mathematical interpretation has been proposed for the rms-flux relation, where short-term variations are modulated by a single slower process. Here we show that this model was already considered and ruled out by another publication on the grounds that it did not produce the observed broad time-scale dependence of the rms-flux relation and associated lognormal flux distribution. We demonstrate the problems with the model via mathematical arguments and a case-study of Cyg X-1 data compared with numerical simulations. We also highlight another conclusion of our original work, which is that a linear rms-flux relation is easy to produce using a variety of models with positively skewed flux distributions. Observing such a relation in a non-accreting object (e.g. in solar flares) does not necessarily imply a phenomenological connection with the behaviour of accretion flows, unless the relation is seen over a similarly broad range of time-scales.
Highlights
An apparently universal feature of the aperiodic “flickering” flux variability seen from accreting compact objects is that they show a linear relationship between the rms amplitude of short-term variability and flux variations on longer timescales
This result has the corollary that the variability process is inherently non-linear and that, if the variability process is statistically stationary on long time-scales and stochastic fluctuations on different time-scales multiply together, the resulting flux distribution should be lognormal. Such lognormal flux distributions are observed from the data for X-ray binaries, active galactic nuclei (AGN), and accreting white dwarfs (Gaskell 2004; UMV05; Scaringi et al 2012). All of these results tie in with the idea that the particular rms-flux relation seen in accreting systems is linked to the common feature: the accretion flow itself, with variations produced by turbulent fluctuations in mass-accretion rate arising at different radii, which propagate through the flow so that variability is coupled together over and between a broad range of time-scales (Lyubarskii 1997; King et al 2004; Arévalo & Uttley 2006; Ingram & van der Klis 2013; Scaringi 2014; Cowperthwaite & Reynolds 2014; Hogg & Reynolds 2016)
To demonstrate that the K16 model for the rms-flux relation does not adequately describe the other key properties of the data described in the last section, even while it can reproduce the observed power spectrum, we conduct a simple case-study using the Cyg X-1 December 1996 hard state Rossi X-ray Timing Explorer (RXTE) observations that were used in UMV05
Summary
An apparently universal feature of the aperiodic “flickering” flux variability seen from accreting compact objects is that they show a linear relationship between the rms amplitude of short-term variability and flux variations on longer timescales. Such lognormal flux distributions are observed from the data for X-ray binaries, AGN, and accreting white dwarfs (Gaskell 2004; UMV05; Scaringi et al 2012) All of these results tie in with the idea that the particular rms-flux relation seen in accreting systems is linked to the common feature: the accretion flow itself, with variations produced by turbulent fluctuations in mass-accretion rate arising at different radii, which propagate through the flow so that variability is coupled together over and between a broad range of time-scales (Lyubarskii 1997; King et al 2004; Arévalo & Uttley 2006; Ingram & van der Klis 2013; Scaringi 2014; Cowperthwaite & Reynolds 2014; Hogg & Reynolds 2016). We show that it is not, and that this was, already discussed and ruled out by UMV05
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