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Astron. Astrophys. 337, 962-965 (1998)

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1. Introduction

The question whether accretion discs can be in a state of self-organised criticality (SOC) (Bak et al. 1988, Kadanoff et al. 1989) was raised explicitly by Mineshige et al. (1994), and strongly implicitly by Bak et al. (1988). Young & Scargle (1996) have raised the related question of transient chaos in accretion systems. A distinctive feature of SOC is flickering energy transport with no characteristic lengthscale or time separation, displaying a [FORMULA] power spectrum; in this context, [FORMULA] is shorthand for inverse power law frequency dependence with unspecified index. In SOC systems, for which mathematical sandpiles (Bak et al. 1988, Kadanoff et al. 1989) provide a paradigm, global transport occurs as a result of self-organised avalanches which are triggered locally when the accretion of sand leads to a critical gradient being exceeded at a given point. This causes local redistribution of sand, which may lead to the critical gradient being exceeded at neighbouring points, resulting in further redistribution and, cumulatively, to a global avalanche. Following the avalanche, the system returns to a subcritical configuration; accretion then continues until it again creates a local excess gradient, triggering a further avalanche. In the SOC-sandpile paradigm, it is helpful to note that the word "critical" is being used in two senses: the sandpile has a critical gradient, redistribution being triggered wherever this gradient is exceeded; and the self-organised global avalanches which emerge from the integrated effects of local redistribution may be scale-free, in which case they are linked to the generic field of critical phenomena.

In mathematical models and also some experimental realisations (Nagel 1992, Feder 1995, Frette et al. 1996, Christensen et al. 1996), avalanche statistics display scale-free [FORMULA] characteristics. SOC sandpile algorithms are extremely simple and possess the attraction of any successful reduced system: it becomes unnecessary to attempt to model the detailed, and perhaps insuperably complex, microphysics of transport in the real system. Such an approach has been applied to the statistics of solar X-ray bursts (Lu & Hamilton 1991; for a recent treatment, see MacKinnon & Macpherson 1997 and references therein) and to transport phenomena in magnetically confined plasmas (Newman et al. 1996, Carreras et al. 1996, Dendy & Helander 1997, 1998). It is clearly of interest to establish whether, in certain circumstances, the detailed modelling of astrophysical accretion flows could be substituted by a simple SOC sandpile paradigm. This is a highly cross-disciplinary question. In the present paper, we aim to carry forward the debate in two ways: by identifying in greater detail the classes of accretion flow where SOC might play a role; and by examining theoretical arguments that we believe point clearly towards SOC in some accretion flows.

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© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998