The rms-flux relation in accreting objects: not a simple “volume control”

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