2013ApJ...762...67P

In this paper, we consider the variability of the luminosity of a compact object (CO) powered by the accretion of an extremely inhomogeneous (clumpy) stream of matter. The accretion of a single clump results in an X-ray flare; we adopt a simple model for the response of the CO to its arrival, and derive a stochastic differential equation (SDE) for the accretion-powered luminosity L(t). We set the SDE in the equivalent form of an equation for the flare luminosity distribution (FLD) and discuss its solution in the stationary case. We apply our formalism to the analysis of the FLDs of supergiant fast X-ray transients (SFXTs), a peculiar sub-class of high-mass X-ray binary (HMXB) systems. We compare our theoretical FLDs to the distributions observed in the SFXTs IGR J16479-4514, IGR J17544-2619, and XTE J1739-302. Despite its simplicity, our model agrees well with the observed distributions and allows us to predict some properties of the stellar wind. Finally, we discuss how our model may explain the difference between the broad FLDs of SFXTs and the much narrower FLDs of persistent HMXBs.