▪ Abstract  We review the state of observational and theoretical studies of the shaping of planetary nebulae (PNe) and protoplanetary nebulae (pPNe). In the past decade, high-resolution studies of PNe have revealed a bewildering array of morphologies with elaborate symmetries. Recent imaging studies of pPNe exhibit an even richer array of shapes. The variety of shapes, sometimes multiaxial symmetries, carefully arranged systems of low-ionization knots and jets, and the often Hubble-flow kinematics of PNe and pPNe indicate that there remains much to understand about the last stages of stellar evolution. In many cases, the basic symmetries and shapes of these objects develop on extremely short timescales, seemingly at the end of AGB evolution when the mode of mass loss abruptly and radically changes. No single explanation fits all of the observations. The shaping process may be related to external torques of a close or merging binary companion or the emergence of magnetic fields embedded in dense outflowing stellar winds. We suspect that a number of shaping processes may operate with different strengths and at different stages of the evolution of any individual object.

A description is given for preserving ∇ · B = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, Total Variation Diminishing (TVD) scheme and the Strang-type operator splitting for multi-dimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is calculated by interpolating the values from grid interfaces. The advective fluxes on grid edges for the magnetic field evolution are calculated from the upwind fluxes at grid interfaces. Then, the magnetic field can be maintained with ∇ · B = 0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analytic solutions or with numerical solutions from the code using an explicit divergence-cleaning method. Also the robustness is shown through tests involving realistic astrophysical problems.

The explosive BN/KL outflow emerging from OMC1 behind the Orion Nebula may have been powered by the dynamical decay of a non-hierarchical multiple system ∼500 years ago that ejected the massive stars I, BN, and source n, with velocities of about 10 to 30 km s −1 . New proper motion measurements of H 2 features show that within the errors of measurement, the outflow originated from the site of stellar ejection. Combined with published data, these measurements indicate an outflow age of ∼500 years, similar to the time since stellar ejection. The total kinetic energy of the ejected stars and the outflow is about 2 to 6 × 10 47 ergs. It is proposed that the gravitational potential energy released by the formation of a short-period binary, most likely source I, resulted in stellar ejection and powered the outflow. A scenario is presented for the formation of a compact, non-hierarchical multiple star system, its decay into an ejected binary and two high-velocity stars, and launch of the outflow. Three mechanisms may have contributed to the explosion in the gas: (i) Unbinding of the circumcluster envelope following stellar ejection, (ii) disruption of circumstellar disks and high-speed expulsion of the resulting debris during the final stellar encounter, and (iii) the release of stored magnetic energy. Plausible proto-stellar disk end envelope properties can produce the observed outflow mass, velocity, and kinetic energy distributions. The ejected stars may have acquired new disks by fallback or Bondi-Hoyle accretion with axes roughly orthogonal to their velocities. The expulsion of gas and stars from OMC1 may have been driven by stellar interactions.

We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit nite di erence method on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. The constraint of a divergence-free eld is enforced exactly by calculating a correction via a gauge transformation in each time step.Results from two-dimensional shock tube tests show that the code captures correctly discontinuities in all three MHD waves families as well as contact discontinuities. The numerical viscosities and resistivity in the code, which are useful in order to understand simulations involving turbulent ows, are estimated through the decay of two-dimensional linear waves. Finally, the robustness of the code in two-dimensions is demonstrated through calculations of the Kelvin-Helmholtz instability and the Orszag-Tang vortex.

The origin, evolution and role of magnetic fields in the production and shaping of protoplanetary nebulae (PPNe) and planetary nebulae (PNe) are a subject of active research. Most PNe and PPNe are axisymmetric with many exhibiting highly collimated outflows; however, it is important to understand whether such structures can be generated by isolated stars or require the presence of a binary companion. Towards this end, we study a dynamical, large-scale α − interface dynamo operating in a 3.0 M Asymptotic Giant Branch (AGB) star in both an isolated setting and a setting in which a low-mass companion is embedded inside the envelope. The back reaction of the fields on the shear is included and differential rotation and rotation deplete via turbulent dissipation and Poynting flux. For the isolated star, the shear must be resupplied in order to sufficiently sustain the dynamo. Furthermore, we investigate the energy requirements that convection must satisfy to accomplish this by analogy to the Sun. For the common envelope case, a robust dynamo results, unbinding the envelope under a range of conditions. Two qualitatively different types of explosion may arise: (i) magnetically induced, possibly resulting in collimated bipolar outflows and (ii) thermally induced from turbulent dissipation, possibly resulting in quasi-spherical outflows. A range of models is presented for a variety of companion masses.