Aspherical two-wind configurations

Summary

Abstract

Planetary nebulae (PN) are bubbles blown by a tenuous, fast stellar wind into a dense, slow, fossil red giant envelope (RGE). This interactingwinds model is quite complete in spherical geometry (Castor et al. 1975, Weaver et al. 1977, Kwok 1982, Lamers 1983, Kahn 1983). New developments in this sector will be treated by others in this volume. Therefore, my aim is to present some critical remarks which are mainly relevant to aspherical interacting winds and in particular cylindrical ones.

Analytical beginnings

Balick (1987, 1988) suggested that the interacting-winds model for planetary nebulae, if generalized to two dimensions, might explain the morphologies of nearly all PNs. He supposed that the fossil red giant envelope (RGE) is cylindrically symmetric and that the density is higher at the equator than at the poles. The PN morphology and its evolution is then purely a consequence of the mass distribution in the RGE and the properties of the fast stellar wind.

Analytical models for aspherical PNs have been quite successful in describing the propagation of the outer shock of a two-wind configuration. One uses either a snowplow-type approximation (Kahn & West 1985, Soker & Livio 1989) or a generalization of the work of Kompaneets (1960; Balick et al. 1987, Icke 1988, Icke et al. 1989), in which the wind is supposed to generate a uniform pressure inside the expanding bubble. The method is easy to apply and shows the generic features of the outer shocks clearly. It works as follows.