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The current theory of circumstellar envelope (CSE) dynamics of evolved stars consists of three phases: 1) gas is levitated from the star by pulsations and/or by radiation pressure on molecules, 2) at an appropriate height above the star, grain nucleation and growth occurs, 3) radiation pressure on grains, which are momentum coupled to the gas, drive the CSE away from the star at velocities around 10 km/s. Previous studies of CSE dynamics and dust formation have taken a piece-meal approach, treating each problem separately, even though they are intimately related. In particular, studies of grain formation have generally assumed that a steady state outflow already exists. Likewise, studies of hydrodynamics in CSE's have assumed an oversimplified or ad hoc model of grain formation. No one has self-consistently solved the grain formation problem involving the hydrodynamics of a multi-fluid gas-grain mixture.
In this work, we have solved the grain formation problem with hydrodynamics in spherical envelopes around carbon stars. This method requires the calculation of relevant quantities for carbon clusters up to the equivalent size of large PAHs, as well as the calculation of mean grain properties. In addition, the velocity of each component of the mixture is calculated, keeping track of both radiation and drag forces. The hydrodynamics equations are efficiently solved via Glimm's method. The grain formation problem is handled using a kinetic theory plus moment equations method. Our results indicate that grain formation occurs at higher supersaturation ratios than expected from classical nucleation theory, resulting in a larger final grain size. Furthermore, the final grain size is very dependent on the velocity structure of different cluster components. Model results will show the time evolution of the CSE, including the velocity structure, distributions and densities of the gas and grain components as well as observational consequences of the results.
This research has been partially supported by the U.S. Air Force and NASA.
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