An exact analytic treatment of propagating mass accretion rate fluctuations in X-ray binaries

TL;DR

This paper derives exact analytical formulas for the power and lag spectra in the propagating fluctuations model of X-ray binary variability, enabling precise theoretical predictions and fitting to observational data.

Contribution

It provides the first exact analytic expressions for the power and lag spectra in the propagating fluctuations model, improving upon previous simulation-based approaches.

Findings

Derived exact formulas for power spectrum and lag spectrum.

Successfully fitted the model to observational data from XTE J1550-564.

Enhanced the theoretical framework for analyzing X-ray variability.

Abstract

Many statistical properties of the aperiodic variability observed in X-ray radiation from accreting compact objects can be naturally explained by the propagating fluctuations model. This considers variations in mass accretion rate to be stirred up throughout the accretion flow. Variations from the outer regions of the accretion flow will propagate towards the central object, modulating the variations from the inner regions and eventually modulating the radiation, giving rise to the observed linear RMS-flux relation and also Fourier frequency dependent time lags. Previous treatments of this model have relied on computationally intensive Monte Carlo simulations which can only yield an estimate of statistical properties such as the power spectrum. Here, we find exact and analytic expressions for the power spectrum and lag spectrum predicted by the same model. We use our calculation to fit the model of Ingram & Done (2012) to a power spectrum of XTE J1550-564. The result we present here will apply to any treatment of the propagating fluctuations model and thus provides a very powerful tool for future theoretical modelling.