Hydrodynamical models and synthetic spectra of circumstellar dust shells around AGB stars II. Time-dependent simulations

We have employed time-dependent two-component hydrodynamics/radiative transfer calculations to investigate the structure, dynamics and emergent spectral energy distribution of dusty circumstellar shells around carbon and oxygen stars in the final stages of their AGB evolution. These internally consistent, physical models describe a stellar wind driven by radiation pressure on dust grains and subsequent momentum transfer to the gas component via collisions. Detailed stellar evolution calculations, with a prescribed mass loss rate that is a function of the fundamental stellar parameters, have been used as a time-dependent inner boundary condition for the numer- ical solution of the coupled equations of hydrodynamics and frequency-dependent radiative transfer governing the structure and temporal evolution of the circumstellar dust/gas shell. The calculations are based on one particular evolutionary track for an initial stellar mass Mi =3 . 0 M⊙ and a final mass Mf =0 . 605 M⊙, but for different assumptions concerning the composition of the dust grains: amorphous carbon or "astro- nomical" silicates. Using our hydrodynamics code to simulate the dynamical response of the circumstellar wind shell to the evolutionary changes of the stellar parameters, we find that the large temporal variations of stellar luminosity and mass loss rate associated with the final thermal pulses near the end of the AGB evolution lead to characteristic, time-dependent signatures in the density structure and emergent energy distribution of the circumstellar dust shell. We present the resulting "loops" in the IRAS two-color-diagram, which we find to extend to regions quite remote from the simple color-color relation defined by steady state models. These time-dependent hydrodynamical models explain the existence of carbon and oxygen stars with excess emission near � 60 and 100µm as a natural consequence of the sharp decrease of the mass loss rate following a thermal pulse, leading to the development of a detached dust shell. As an illustration, we present a series of synthetic spectra and corresponding 100µm surface brightness distributions showing the time-evolution of Send offprint requests to: Matthias Steffen the circumstellar dust emission during a thermal pulse cycle, both for a carbon-rich and an oxygen-rich dust shell. We demonstrate that it is unrealistic to assume a fi xed ve- locity profile which 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 narrow, high-density shell moving through the circumstellar envelope. Rather, the signa- ture of a short mass loss peak broadens due to velocity gradients as it moves towards the outer regions of the wind. Hence, this is hardly a viable scenario to explain the existence of very thin molecular shells that have recently been detected around some carbon stars. Our simulations suggest a more promising mecha- nism producing thin shells of enhanced gas density in the outer regions of carbon-rich AGB shells: interaction of winds of dif- ferent speed and density.