THE SHAPING OF PLANETARY-NEBULAE - ASYMMETRY IN THE EXTERNAL WIND

We have modeled planetary nebulae (PNs) in the context of the interact ing stellar winds model. If the two interacting winds have constant pr operties, the velocity of the PN shell tends toward a constant with ti me and the shape becomes self-similar. Additionally, if the velocity o f the fast wind is much higher than the expansion velocity of the shel l, the interior of the hot shocked bubble becomes isobaric. Using semi -analytical methods, complemented by hydrodynamic simulations, we have calculated the shapes of PNs in the self-similar stage. An asymmetric density profile is assumed for the slow outer wind. The asymmetry is modeled using different functions, which depend on the degree of asymm etry and the steepness of the density profile in the angular direction . We include the effects of the ambient wind velocity, which has not r eceived much attention since the work of Kahn & West (1985). The fact that typical PN velocities (10-40 km s(-1)) are only marginally greate r than typical red giant wind velocities (5-20 km s(-1)) indicates tha t this is an important parameter. The morphological appearance is a co nsequence of the density contrast, steepness of the density profile an d velocity of the ambient medium; classification of PNs purely on the basis of the first two factors may be misleading. Moderate values of t he density contrast result in a cusp at the equator. A higher density contrast coupled with a low velocity for the external medium gives ris e to extremely bipolar nebulae. For large density contrasts and a sign ificant value of the slow wind velocity, the surface density maximum o f the shell shifts away from the equator, giving rise to peanut-shaped structures with pronounced equatorial bulges. If the external wind ve locity is small compared to the expansion velocity of the nebula, the PNs tend to be more bipolar, even with a moderate density contrast. If the PN velocity is close to that of the external wind, the shape is r elatively spherical. However, a velocity asymmetry in the external win d can lead to a bipolar shape if the equatorial velocity is sufficient ly low. Our numerical simulations show that asymmetric PN shells are c orrugated because of Kelvin-Helmholtz instabilities. They also indicat e that several doubling times are needed to approach the self-similar state. A ratio of interior sound speed to shell velocity greater than or similar to 10 is found to yield nebulae whose shapes match those gi ven by the isobaric approximation.