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Dust in brown dwarfs II. The coupled problem of dust formation and sedimentation

Please always quote using this URN: urn:nbn:de:0297-zib-7186
  • In this paper, we quantify and discuss the physical and surface chemical processes leading to the formation, temporal evolution and sedimentation of dust grains in brown dwarf and giant gas planet atmospheres: nucleation, growth, evaporation and gravitational settling. Considering dust particles of arbitrary sizes in the different hydrodynamical regimes (free molecular flow, laminar flow, turbulent flow), we evaluate the equilibrium drift velocities (final fall speeds) and the growth rates of the particles due to accretion of molecules. We show that a depth-dependent maximum size of the order of $a_{\rm max}\!\approx\!1\,\mu{\rm m\,(upper\ regions)} \ldots 100\,\mu{\rm m\,(lower\ regions)}$ exists, which depends on the condensate and the stellar parameters, beyond which gravitational settling is faster than growth. Larger particles can probably not be formed and sustained in brown dwarf atmospheres. We furthermore argue that the acceleration towards equilibrium drift is always very fast and that the temperature increase of the grains due to the release of latent heat during the growth process is negligible. Based on these findings, we formulate the problem of dust formation coupled to the local element depletion/enrichment of the gas in brown dwarf atmospheres by means of a system of partial differential equations. These equations state an extension of the moment method developed by Gail\plus Sedlmayr\,(1988) with an additional advective term to account for the effect of size-dependent drift velocities of the grains. A dimensionless analysis of the new equations reveals a hierarchy of nucleation $\to$ growth $\to$ drift $\to$ evaporation, which characterises the life cycle of dust grains in brown dwarf atmospheres. The developed moment equations can be included into hydrodynamics or classical stellar atmosphere models. Applications of this description will be presented in a forthcoming paper of this series.

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Metadaten
Author:Peter Woitke, Christiane Helling
Document Type:ZIB-Report
Tag:brown dwarfs; dust formation; precipitation
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R30 Inverse problems
85-XX ASTRONOMY AND ASTROPHYSICS (For celestial mechanics, see 70F15) / 85Axx Astronomy and astrophysics (For celestial mechanics, see 70F15) / 85A20 Planetary atmospheres
Date of first Publication:2002/12/19
Series (Serial Number):ZIB-Report (02-51)
ZIB-Reportnumber:02-51
Published in:Appeared in: Astronomy & Astrophysics 399 (2003) 207-313
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