Dust formation, grain growth and evaporation under the influence of temperature fluctuations

V. Schirrmacher and U. Dirks

Astronomische Nachrichten, 324, Suppl. Issue 3, p. 128 (2003)

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Abstract:

The treatment of the astrophysical dust complex (i.e. dust formation, grain growth and evaporation) yields intrinsic memory effects, originating from the fact, that the evaporation of dust depends on the size distribution of dust particles, which again depends very sensibly on the exact growth history. The presence of such memory effects makes the investigation of the influence of thermodynamical fluctuations on the dust physics particulary interesting. For example, thermodynamic conditions which are not favourable for the formation of new dust in the deterministic case, might not necessarily be so hostile that dust - formed during a random temperature fluctuation - will reevaporate. As a consequence, dust might be present in situations, which under a strict deterministic treatment should be dust-free.

In this work, we have investigated the impact of temperature fluctuations on the formation and growth of astrophysical dust particles in a stationary stellar wind of a cool, evolved late type star. A subsequent application to less restrictive situations is in principle straight forward, and will be limited mainly by the available CPU-capacities.

In our approach (described in detail in Dirks, 2000), we follow a gas element on a deterministic trajectory of a given stationary wind of a star, i.e. no feedback effects to the wind structure (like acceleration by radiation pressure on dust, backwarming, etc.) are considered in this study. While, in the deterministic case, the hydro- and thermodynamical conditions of the wind are determined by velocity, density, and temperature structure - v(r), rho(r) and Tgas(r) - we regard the values of the density and the gas temperature as mean values and allow for stochastical fluctuations Theta(r) in the local gas temperature T(r) = Tmean(r) + Theta(r), which are coupled adiabatically to the local density rho(r) = T(r)/Tmean(r))(1/gamma-1). In practice, such fluctuations could be realised by acoustic waves originating from the star, the dissipation of shock waves or the
like.

The dust complex is treated using the dust moment method developed by Gail and Sedlmayr (1984) and Gauger (1990), which describes dust formation via a two step process of nucleation and subsequent grain growth. This leads to a set of differential equations for moments Ki(t) (i=0,1,2,...) of the particle size distribution function f(N,t). The advantage of this description is i) it is fast enough for the application to dynamical problems and ii) a detailed treatment of the evaporation process is included, which is crucial for our stochastic approach. Finally we arrive at a coupled system of Fokker-Planck equations for the dust moments Ki (i=0,1,2,3), which we have solved by standard numerical methods.

The results suggest that the inclusion of fluctuations does indeed facilitate the formation of circumstellar dust. The application to other astrophysical objects (e.g. non-stationary winds) is planned for the near future.

References:

Dirks, U., 2000, dissertation, TU Berlin,

Gail, H.-P., Keller, R., and Sedlmayr, E., 1984, A&A, Vol. 134, p. 320-332

Gauger, A., Gail, H.-P., and Sedlmayr, E., 1990, A&A, Vol. 235, p. 345-361