2. Some sites of interest
It was noted by Bak et al. (1988) that flickering signals with power spectra have been observed for the X-ray variability of active galactic nuclei (AGNs), specifically: 0.05-2keV X-rays from the Seyfert galaxy NGC4051 (Lawrence et al 1987) and 2-7keV X-rays from the Seyfert galaxy NGC5506 (McHardy & Czerny 1987), and for 10-140 keV X-rays from the massive compact binary Cyg X-1 (Nolan et al. 1981). Similar spectra for X-ray variability from binary accreting systems were noted by Mineshige et al. (1994) (neutron stars, Makashima 1988) and by Geertsema & Achterberg (1992) (cataclysmic variables and dwarf novae, Wade & Ward 1985). While we believe this list can be extended, as we discuss below, it is also important to be more specific about where, in these diverse systems, SOC might be occurring.
Perhaps the simplest case is presented by a paradigmatic AGN. Let us take for this the standard picture of a massive black hole fed by a cascade of structures: the accretion disc, the molecular torus and on a larger scale the galactic disc and its barred or spiral structure, which together generate a clumpy and irregular transfer of gas and stars. This irregular mass transfer could be analogous to the random and discrete feeding of a sandpile with grains of sand near its apex. It is believed that, at least in thin discs, the residence time of matter in the disc is much longer than the free-fall time, at radius R:
where is the thickness of the disc, and is the well-known viscosity parameter. The condition , which is implicit in most accretion disc models, appears to be necessary, at least in principle, for the validity of a sandpile-type approach to mass transfer within the disc.
Thus if the accretion disc, like the sandpile, is in a state of SOC, there would be no clear link between the pattern of accretion from the torus and the pattern of avalanches leading to mass transfer across the disc, over its inner edge, and onto the black hole, giving rise to the X-ray signal. The latter would automatically display flicker. On larger space and timescales relating to our own Galaxy, even steady gas inflow from the Galactic bar could also result in avalanches to the inner regions, and these avalanches could give rise to episodes of AGN activity during an otherwise quiescent phase, with a duty cycle of a few percent, as inferred on statistical grounds for other AGNs (Mezger et al., 1996). The sandpile-SOC paradigm thus provides a candidate framework for summing up the consequences of the complex and intricate physics that relates the largescale dynamics of the Galactic disc to the activity of its central black hole.
Cataclysmic variables, and in particular dwarf novae, present further opportunities for SOC. First, the flow of matter from the secondary across the inner Lagrangian point could itself be an avalanching process governed by SOC. In this case, if the radiation source was a hot spot where the accreting mass flow reached the outer edge of an accretion disc, it would flicker with statistics. Steady mass flow from the secondary would also be compatible with a SOC signal, however, provided the latter originated from SOC mass transfers from the accretion disc (or accretion column in the strongly magnetised regime) to the white dwarf. Either regime appears possible in principle, both for dwarf novae and in the wider context of binary accreting systems. In dwarf novae, it is pointed out by van Amerongen et al. (1990) and Lasota et al. (1995) that outbursts are due to suddenly increased accretion towards the white dwarf, but that it is unclear whether the instability resides in mass transfer from the secondary to the accretion disc, or across the accretion disc and onto the white dwarf. We note that, observationally, flickering is more often strong during the quiescent phase of dwarf novae than during major eruptions (Wade & Ward 1985). Questions relating to the location of unstable flows in soft X-ray transients (Lasota et al. 1996) are similar to those in dwarf novae. For the wind-fed X-ray binary pulsar GX301-2, a model has been proposed (Orlandini & Morfill 1992) involving "noisy" accretion of blobs of matter formed by magnetohydrodynamical (MHD) instability at the magnetospheric radius, and not caused by inhomogeneities present in the stellar wind from the optical companion. This approach is somewhat reminiscent of that of Baan (1977), where accreted matter accumulates at the magnetopause of a rotating neutron star until an interchange instability is triggered, after which the released matter generates an X-ray burst. Baan (1977) suggested that, since most of the time between bursts is a refilling time, an approximately linear relation should exist between burst energy and the subsequent quiescent interval. However, in a SOC model where randomly arising local instability is sufficient to trigger a global avalanche, there would be no such correlation. This appears to be a key observational discriminant for the possible presence of SOC in a given accreting system. We also note that, from the theoretical point of view, Frank et al. 1992 have pointed out that a local instability in a given annulus of the disc can only trigger large-scale instability accross the disc if parameters in neighbouring annuli are such that the effect of this instability in these annuli can in turn trigger local instability there. This amounts to a prescription for a sandpile-type approach, and hence for the possibility of SOC.
It seems clear from the foregoing that there is good observational and interpretative motivation for testing for SOC in a broad range of accreting astrophysical systems, encompassing flickering AGNs and certain distinct locations within a variety of binary objects. Firm identification of SOC would yield information on the global consequences of the smaller-scale physics of the accretion process, while short-circuiting the need for detailed modelling. Let us now turn to theoretical arguments for expecting SOC.
© European Southern Observatory (ESO) 1998
Online publication: August 27, 1998