Radiative shock overstability of finite-sized objects

We investigate the radiative shock overstability for finite-sized objects. We follow the analysis of Chevalier & Imamura (1982), but we take into account the transverse flow of material out of the potshock region. The mass loss from the postshock region stabilizes the flow. As a rough estimate, the shock radiative instability takes place when the shock wave position with no radiative cooling (only mass loss present) is larger than the shock position with no mass loss (only radiative cooling present). For typical conditions of planetary nebulae we find that in order for the shock radiative overstability to occur, the nebular radius should be R approximately less than 10(exp 19) n(sub a)(exp -1) cm, where n(sub alpha) is the total number density of the interstellar medium (in units of cm(exp -3). We give several examples of interacting planetary nebulae in light of this condition.