only in the hot, ionized or cool, molecular states with very rapid transitions between them. This is because in the non-irradiated model, or in the model with only direct irradiation and shadowing, the stagnation phase is absent.

Figure 7 displays the time-dependent disk evolution in the decay phase for the irradiated disk-instability model [*with both direct and indirect irradiation*]{}. The upper panel of figure 7 shows the evolution of the disk central temperature, $T_{\rm c}$. The squares denote the time at which the direct irradiation is terminated at a given radius as it falls into the shadow of interior regions. With irradiation, the evolution is much more complex, as illustrated in figure 7. At 14.2 d, the region at $\sim4\times10^{10}$ cm reaches the critical surface density for a thermal instability and begins the rapid cooling that characterizes the propagating cooling front of figure 6. The same transition is seen at $\sim2\times10^{10}$ cm after 41.6 d and at $\sim1\times10^{10}$ cm after 88 d. Rather than dropping directly to the cool state, however, these regions linger in an intermediate “metastable" stagnation state. This is obviously due to the effects of irradiation, since this behavior is absent in figure 6, the effects, however, 