The Accretion Disk Limit Cycle Mechanism in the Black Hole X‐Ray Binaries: Toward an Understanding of the Systematic Effects

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Abstract
We examine in detail several aspects of the physics of accretion disks that are of possible relevance to the outburst mechanism of the black hole X-ray transients. We adopt the one-dimensional, time-dependent model described in detail by Cannizzo, Chen, and Livio with parameters appropriate for a system such as A0620-00. We investigate (1) the effect of the grid spacing, utilizing a logarithmic radial spacing Δr ∝ r in addition to the spacing Δr ∝ r1/2, (2) the dependence of the local flow speed of gas within the hot part of the disk on radius and time during the time of the cooling wave propagation, (3) the shape of the outburst light curve as a function of the triggering location for the instability, (4) the long-term light curves of outbursts taken from trials in which complete cycles of quiescence and outburst are followed, both including and excluding the effect of evaporation or removal of matter from the inner edge of the disk, and (5) the strength of the self-irradiation of the outer parts of the disk by the X-rays from the inner disk. Our primary findings in each of these areas are that (1) low-resolution runs taking N 20 grid points using the logarithmic spacing produce decay timescales that are artificially slow by factors of ~2-3 and slower than exponential; (2) the deviation from steady state within the outer part of the inner hot disk appears to be in accord with the discussion given in Vishniac and Wheeler—far from the transition front, the flow speed is ~αcs(h/r), whereas at the interface between the transition front and the cold disk, the flow speed is ~αcs; (3) the outburst-triggering location must be 100rinner for the rise time of the resulting outburst to be as short as is observed in the standard, bright systems; (4) the long-term light curves using the standard model produce frequent outbursts that are triggered near the inner disk edge and that have slow rise times, and the long-term light curves calculated assuming evaporation of matter from the inner disk exhibit outbursts with longer recurrence times and somewhat (but not significantly) shorter rise times; and (5) for a system with parameters relevant to A0620-00, our "standard" system, irradiation is not a dynamically significant effect, in accord with recent results of van Paradijs.
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