Astron. Astrophys. 337, 149-177 (1998)

Hydrodynamical models and synthetic spectra of circumstellar dust shells around AGB stars

II. Time-dependent simulations

Matthias Steffen ^{1, 2}, Ryszard Szczerba ³ and Detlef Schönberner <sup>4

1</sup> Astrophysikalisches Institut Potsdam, D-14482 Potsdam, Germany (MSteffen@aip.de)
² Institut für Astronomie und Astrophysik der Universität Kiel, D-24098 Kiel, Germany (Steffen@astrophysik.uni-kiel.de)
³ Nicolaus Copernicus Astronomical Center, PL-87-100 Torun, Poland (Szczerba@ncac.torun.pl)
⁴ Astrophysikalisches Institut Potsdam, D-14482 Potsdam, Germany (Deschoenberner@aip.de)

Received 19 February 1998 / Accepted 19 May 1998

Abstract

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 numerical 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 and a final mass , but for different assumptions concerning the composition of the dust grains: amorphous carbon or "astronomical" 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 100 µm 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 100 µm surface brightness distributions showing the time-evolution of 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 fixed velocity 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 simply translate into a correspondingly narrow, high-density shell moving through the circumstellar envelope. Rather, the signature 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 mechanism producing thin shells of enhanced gas density in the outer regions of carbon-rich AGB shells: interaction of winds of different speed and density.

Key words: stars: AGB and post-AGB circumstellar matter stars: Mass loss dust, extinction hydrodynamics radiative transfer

Send offprint requests to: Matthias Steffen

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Contents

• 1. Introduction
• 2. Time-dependent hydrodynamical model calculations
  • 2.1. Equations of radiation hydrodynamics
  • 2.2. Dust opacities
  • 2.3. Initial condition, radial grid
  • 2.4. Controlling the grid motion
  • 2.5. Boundary conditions
• 3. Stellar evolution with mass loss
• 4. Results of the numerical simulations
  • 4.1. Time evolution of a circumstellar shell with amorphous carbon dust - a paradigmatic overview
    • 4.1.1. From the initial model through the `first' thermal pulse
    • 4.1.2. Further evolution
    • 4.1.3. End of the AGB evolution
    • 4.1.4. Summarizing the dynamical evolution of the shell
  • 4.2. Model calculations for a shell with silicate dust
  • 4.3. Variation of emergent spectrum and surface brightness distribution during a thermal pulse cycle
    • 4.3.1. Model fluxes for carbon stars
    • 4.3.2. Model fluxes for oxygen stars
• 5. Comparison with observations
  • 5.1. The distribution of AGB stars in the IRAS two-color diagrams
    • 5.1.1. Comparison for carbon stars
    • 5.1.2. Comparison for oxygen stars
    • 5.1.3. The influence of f_cond
  • 5.2. The spectral energy distribution of S Scuti
  • 5.3. The detached dust shell of Y CVn
  • 5.4. Transition to the post-AGB phase: IRAS 17437+5003
• 6. Concluding remarks
• Acknowledgements
• References

© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998
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