Dust-driven mass loss from carbon stars as a function of stellar parameters

II. Effects of grain size on wind properties

¹ DARK Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100, Copenhagen Ø, Denmark
e-mail: mattsson@dark-cosmology.dk
² Dept. Physics and Astronomy, Div. of Astronomy and Space Physics, Uppsala University, Box 516, 751 20 Uppsala, Sweden

Received: 11 August 2010
Accepted: 6 July 2011

Abstract

Context. It is well established that the winds of carbon-rich AGB stars (carbon stars) can be driven by radiation pressure on grains of amorphous carbon and collisional transfer of momentum to the gas. This has been demonstrated convincingly by different numerical wind models that include time-dependent dust formation. To simplify the treatment of dust opacities, radiative cross sections are usually computed using the assumption that the dust grains are small compared to wavelengths around the stellar flux maximum. Considering the typical grain sizes that result from these models, however, the applicability of this small-particle limit (SPL) seems questionable.

Aims. We explore grain size effects on wind properties of carbon stars, using a generalized description of radiative cross sections valid for particles of arbitrary sizes. The purpose of the study is to investigate under which circumstances the SPL may give acceptable results, and to quantify the possible errors that may occur when the SPL does not hold.

Methods. The time-dependent description of grain growth in our detailed radiation-hydrodynamical models gives information about dust particle radii in every layer at every instant of time. Theses grain radii are used for computing opacities and determining the radiative acceleration of the dust-gas mixture. From the large number of models presented in the first paper of this series (based on SPL dust opacities) we selected two samples, i.e., a group of models with strong, well-developed outflows that are probably representative of the majority of wind-forming models, and another group, close to thresholds in stellar parameter space for dust-driven winds, which are referred to as critical cases.

Results. We show that in the critical cases the effect of the generalized description of dust opacities can be significant, resulting in more intense mass loss and higher wind velocities compared to models using SPL opacities. For well-developed winds, however, grain size effects on mass-loss rates and wind velocities are found to be small. Both groups of models tend towards lower degrees of dust condensation compared to corresponding SPL models, owing to a self-regulating feedback between grain growth and radiative acceleration. Consequently, the “dust-loss rates” are lower in the models with the generalized treatment of grain opacities.

Conclusions. We conclude that our previous results on mass-loss rates obtained with SPL opacities are reliable within a wide region of stellar parameter space, except for critical cases close to thresholds of dust-driven outflows where SPL models will tend to underestimate the mass-loss rates and wind velocities.