We extend the model of King et al. (2004) for variability in black holeaccretion discs, by taking proper account of the thermal properties of thedisc. Because the degree of variability in the King et al. (2004) model dependssensitively on the ratio of disc thickness to radius, H/R, it is important tofollow the time-dependence of the local disc structure as the variabilityproceeds. In common with previous authors, we develop a one-zone model for thelocal disc structure. We agree that radial heat advection plays an importantrole in determining the inner disc structure, and also find limit-cyclebehaviour. When the stochastic magnetic dynamo model of King et al. (2004) isadded to these models, we find similar variability behaviour to before. We are now better placed to put physical constraints on model parameters. Inparticular, we find that in order to be consistent with the low degree ofvariability seen in the thermal disc component of black hole binaries, we needto limit the energy density of the poloidal field that can be produced by localdynamo cells in the disc to less than a few percent of the energy density ofthe dynamo field within the disc itself.
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