CIRCUMSTELLAR DUST SHELLS AROUND LONG-PERIOD VARIABLES .5. A CONSISTENT TIME-DEPENDENT MODEL FOR THE EXTREME CARBON STAR AFGL-3068

We present a consistent time-dependent model for the extreme carbon st ar AFGL 3068. The model includes a consistent treatment of the interac tions among hydrodynamics, thermodynamics, dust formation, and chemist ry. It is determined by the stellar parameters of the initial hydrosta tic model: stellar mass M = 1 M., stellar luminosity L* = 1.3 10(4) L o., stellar temperature T, = 2200 K, and carbon-to-oxygen abundance r atio epsilon(C)/epsilon(O) = 1.38. The pulsation of the star is simula ted by a piston approximation at the inner boundary where the velocity varies sinusoidally with a period of P = 696 d and an amplitude of De lta mu = 8 km s(-1). This model yields a time averaged outflow velocit y of 14.7 km s(-1) in good agreement with the rather well determined o bserved value and an average mass loss rate of 1.2 10(-4) M.yr(-1) whi ch is about a factor of 4 larger than the value usually derived from t he fitting of CO rotational lines profiles. Based on the atmospheric s tructure resulting from this hydrodynamic calculation, we have perform ed angle-and frequency-dependent continuum radiative transfer calculat ions, which yield the spectral energy distributions at different phase s of the pulsation cycle, synthetic light curves at different waveleng ths and synthetic brightness profiles of the dust shell model. The com puted energy distributions and the synthetic light curves are in good agreement with the observations of AFGL 3068. We derive a distance to AFGL 3068 of 1200 parsec. Furthermore, properties of the resulting gra in size distribution function are discussed. The dominant size of the grains formed in the circumstellar shell is found to be < a > similar to 0.1 mu m but grains with radii up to 0.7 mu m are also formed in su ch a quantity that they may contribute significantly to light scatteri ng in the near-infrared. We propose to perform high-resolution spatial observations of the circumstellar dust shell around AFGL 3068 which c ould be compared with the predictions of the model calculation.