THE ACCRETION DISK LIMIT-CYCLE MECHANISM IN THE BLACK-HOLE X-RAY BINARIES - TOWARD AN UNDERSTANDING OF THE SYSTEMATIC EFFECTS

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 m odel described in detail by Cannizzo, Chen, and Livio with parameters appropriate for a system such as A0620-00. We investigate (1) the effe ct of the grid spacing, utilizing a logarithmic radial spacing Delta r proportional to r in addition to the spacing Delta r proportional to r(1/2), (2) the dependence of the local flow speed of gas within the h ot 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 funct ion of the triggering location for the instability, (4) the long-term light curves of outbursts taken from trials in which complete cycles o f quiescence and outburst are followed, both including and excluding t he effect of evaporation or removal of matter from the inner edge of t he disk, and (5) the strength of the self-irradiation of the outer par ts 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 simi lar or equal to 20 grid points using the logarithmic spacing produce d ecay timescales that are artificially slow by factors of similar to 2- 3 and slower than exponential; (2) the deviation from steady state wit hin 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 f ront, the flow speed is similar to alpha c(s)(h/r), whereas at the int erface between the transition front and the cold disk, the flow speed is similar to alpha(s); (3) the outburst-triggering location must be g reater than or similar to 100r(inner) for the rise time of the resulti ng outburst to be as short as is observed in the standard, bright syst ems; (4) the longterm light curves using the standard model produce fr equent outbursts that are triggered near the inner disk edge and that have slow rise times, and the long-term light curves calculated assumi ng evaporation of matter from the inner disk exhibit outbursts with lo nger recurrence times and somewhat (but not significantly) shorter ris e times; and (5) for a system with parameters relevant to A0620-00, ou r ''standard'' system, irradiation is not a dynamically significant ef fect, in accord with recent results of van Paradijs.