Critical temperature and accretion rate of outbursts in long-period dwarf novae

Dwarf nova outbursts are nonlinear phenomena, and a time-dependent disk model is necessary to account for observations in detail. However, it is also necessary to elaborate a simpler steady-state fit to interpret observations. To know in what condition the outburst is initiated, understanding of the dwarf nova outburst is important. The parameterized, steady-state fitting formulae are suggested by Smak (Acta Astron. 52, 429 (2002); ibid 60, 83 (2010)) for the critical disk temperature and mass accretion rate above which the disk becomes thermally unstable. The fits give a single-valued temperature and accretion rate and are radius-independent whereas the observations show that the outbursts are radius-dependent phenomena of the ionizaton propagating in the disk. The fits have been tested to account for the observed outbursts only for systems with orbital periods shorter than a half day. Therefore, we examine the fits for orbital period as long as 2 days and compare the fits to the time-dependent model of a long-period dwarf nova GK Per. The fits are not much different from the time-dependent result for the critical temperature. However, the fits for the critical mass accretion rate above which the disk enters the hot state overestimate the time-dependent model for a long-period system like GK Per. The critical mass accretion rate in the intermediate state is consistent with that from the time-dependent disk model. However, the fit value should be treated as a maximum possible value below which the disk maintains the intermediate state, which is consistent with an interpretation for the observations of the Z Cam stars.