Dynamical models of dust-filled planetary nebulae

Far infrared observations of planetary nebulae, and other ionized nebulae, in the ten to twenty micron wavelength region, have disclosed the existence of large infrared excesses in the spectra of these objects. The most commonly accepted explanation for this infrared radiation involves the presence of dust grains of sub-micron size, which absorb visible and ultraviolet radiation efficiently and reradiate thermally at temperatures of one to two hundred degrees Kelvin. Even relatively small amounts of dust are sufficient to absorb all of the hydrogen Lyman-alpha photons, and these are usually assumed to provide the major source of heating for the grains. In order to test this hypothesis in detail, and to study the effects of these grains on the dynamics and evolution of the nebula, a series of computer models of planetary nebulae have been constructed. These models have been carried out for nebulae of 0.15 and 0.5 solar masses, containing ''normal'', one-tenth, and ten times normal dust amounts. A variety of initial conditions were used, including both uniform and non-uniform initial density and velocity, and the effects of varying the stellar luminosity were also considered. The hydrodynamics of the gas were calculated using the Richtmyer-von Neumann pseudoviscosity method. In all of the models studied, the dust moved little relative to the gas. Contrary to expectations, the Lyman-alpha radiation was not the dominant source of grain heating. The expansion velocity increased with time, but considerably more slowly in the high-mass than in the low-mass case. The observed mass, calculated from the luminosity and radius, decreased strongly once complete ionization was achieved, so that real nebulae might have two or three times the mass suggested by observations, the discrepancy being accounted for by unobservable gas in the low-density tail