HYDRODYNAMICAL MODELS AND SYNTHETIC SPECTRA OF CIRCUMSTELLAR DUST SHELLS AROUND AGE STARS - II - TIME-DEPENDENT SIMULATIONS

We have employed time-dependent two-component hydrodynamics/radiative transfer calculations to investigate the structure, dynamics and emerg ent spectral energy distribution of dusty circumstellar shells around carbon and oxygen stars in the final stages of their AGB evolution. Th ese internally consistent, physical models describe a stellar wind dri ven by radiation pressure on dust grains and subsequent momentum trans fer to the gas component via collisions. Detailed stellar evolution ca lculations, with a prescribed mass loss rate that is a function of the fundamental stellar parameters, have been used as a time-dependent in ner boundary condition for the numerical solution of the coupled equat ions of hydrodynamics and frequency-dependent radiative transfer gover ning the structure and temporal evolution of the circumstellar dust/ga s shell. The calculations are based on one particular evolutionary tra ck for an initial stellar mass M-i = 3.0 M. and a final mass M-f = 0.6 05 M., but for different assumptions concerning the composition of the dust grains: amorphous carbon or ''astronomical'' silicates. Using ou r hydrodynamics code to simulate the dynamical response of the circums tellar wind shell to the evolutionary changes of the stellar parameter s, we find that the large temporal variations of stellar luminosity an d mass loss rate associated with the final thermal pulses near the end of the AGB evolution lead to characteristic, time-dependent signature s in the density structure and emergent energy distribution of the cir cumstellar dust shell. We present the resulting ''loops'' in the IRAS two-color-diagram, which we find to extend to regions quite remote fro m the simple color-color relation defined by steady state models. Thes e time-dependent hydrodynamical models explain the existence of carbon and oxygen stars with excess emission near lambda 60 and 100 mu m as a natural consequence of the sharp decrease of the mass loss rate foll owing a thermal pulse, leading to the development of a detached dust s hell. As an illustration, we present a series of synthetic spectra and corresponding 100 mu m surface brightness distributions showing the t ime-evolution of the circumstellar dust emission during a thermal puls e cycle, both for a carbon-rich and an oxygen-rich dust shell. We demo nstrate that it is unrealistic to assume a fixed velocity profile whic h is independent of mass loss rate: to a first approximation, the gas velocity is a bimodal function of the mass loss rate. A short event of high mass loss does not sim ply translate into a correspondingly narr ow, high-density shell moving through the circumstellar envelope. Rath er, the signature of a short mass loss peak broadens due to velocity g radients as it moves towards the outer regions of the wind. Hence, thi s is hardly a viable scenario to explain the existence of very thin mo lecular shells that have recently been detected around some carbon sta rs. Our simulations suggest a more promising mechanism producing thin shells of enhanced gas density in the outer regions of carbon-rich AGE shells: interaction of winds of different speed and density.