Blowing up warped disks in 3D

Three-dimensional AMR simulations of point-symmetric nebulae

¹ Sterrewacht Leiden, PO Box 9513, 2300 RA, Leiden, The Netherlands e-mail: rijkhorst@strw.leidenuniv.nl
² ASTRON, PO Box 2, 7990 AA Dwingeloo, The Netherlands

Received: 7 September 2004
Accepted: 22 August 2005

Abstract

The Generalized Interacting Stellar Winds model has been very successful in explaining observed cylindrical and bipolar shapes of planetary nebulae. However, many nebulae have a multipolar or point-symmetric shape. Previous two-dimensional calculations showed that these seemingly enigmatic forms can be reproduced by a two-wind model in which the confining disk is warped, as is expected to occur in irradiated disks. In this paper we present the extension to fully three-dimensional Adaptive Mesh Refinement simulations using the publicly available hydrodynamics package Flash. We briefly describe the mechanism leading to a radiation driven warped disk, and give an equation for its shape. We derive time scales related to the disk and compare them to the radiative cooling time scale of the gas, thereby determining the relevant part of parameter space. By comparing two-dimensional calculations including realistic radiative cooling through a cooling curve, with ones employing a low value for the adiabatic index γ, we show that the latter, computationally less expensive approach, is a valid approximation for treating cooling in our nebulae. The results of the fully three-dimensional wind-disk simulations show our mechanism to be capable of producing a plethora of multipolar (and quadrupolar) morphologies, which can explain the observed shape of a number of (proto-)planetary nebulae.