The Accretion Disk Limit Cycle Model: Toward an Understanding of the Long-Term Behavior of SS Cygni

We present detailed computations of the limit cycle model for dwarf nova outbursts with application to SS Cygni, the best studied dwarf nova. We examine how secular changes in the input parameters of the model affect the properties associated with the outbursts. For input parameters which reproduce the observed outburst recurrence times and outburst durations for SS Cyg, our time-dependent, accretion disk instability code generates light curves in which one or more short outbursts tend to be sandwiched between two long outbursts. We find that the relative frequency of long versus short outbursts can be influenced by changes in the accretion disk viscosity and mass transfer rate. By forming moving averages taken from the long-term AAVSO light curve of SS Cyg, we find a strong correlation between the recurrence time for outbursts tc and the ratio of the number of long outbursts N(L) to the number of short outbursts N(S) occurring in a given time interval. This can be accounted for in the model in several ways. Changes in the radius of the inner edge of the disk produce correlated changes in tc and N(L)/N(S), as do slow variations in either αcold or αhot -- the accretion disk viscosity parameters in quiescence and outburst. In this latter scenario, there must be a fundamental asymmetry between the two alphas in the sense that both quantities cannot be varying in step with each other i.e., one must remain fixed while the other varies. Finally, variations in the mass transfer rate MṡT cannot directly account for the observed long-term changes in the light curve of SS Cyg as was postulated by Hempelmann & Kurths and by Cannizzo & Mattei.