@misc{Helling, author = {Helling, Christiane}, title = {Circuit of Dust in Substellar Atmopsheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7142}, number = {02-47}, abstract = {Substellar atmospheres are cool and dense enough that dust forms very efficiently. As soon as these particles are formed, they sizedependently precipitate due to the large gravity of the objects. Arriving in hot atmospheric layers, the dust evaporates and enriches the gas by those elements from which it has formed. The upper atmospheric layers are depleted by the same elements. Non-continuous and spatially inhomogeneous convective element replenishment, generating a turbulent fluid field, completes the circuit of dust. The formation of dust in substellar atmosphere is described by extending the classical theory of Gail\plus Sedlmayr for the case of different gas and dust velocities. Turbulence is modeled in different scale regimes which reveals turbulence as trigger for dust formation in hot environments. Both mechanisms cause the dust to be present in else wise dust-hostile region: precipitation transports the dust into hot regions, and turbulence allows the formation of dust in there.}, language = {en} } @misc{WoitkeHelling, author = {Woitke, Peter and Helling, Christiane}, title = {Dust in brown dwarfs II. The coupled problem of dust formation and sedimentation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7186}, number = {02-51}, abstract = {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.}, language = {en} } @misc{WoitkeHelling, author = {Woitke, Peter and Helling, Christiane}, title = {Formation and structure of quasi-static cloud-layers in brown dwarf atmospheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7338}, number = {03-11}, abstract = {In this paper, first solutions of the dust moment equations developed in [{\sl Woitke \& Helling 2002}] for the description of dust formation and precipitation in brown dwarf and giant gas planet atmospheres are presented. We consider the special case of a static brown dwarf atmosphere, where dust particles continuously nucleate from the gas phase, grow by the accretion of molecules, settle gravitationally and re-evaporate thermally. Applying a kinetic description of the relevant microphysical and chemical processes for TiO\$_2\$-grains, the model makes predictions about the large-scale stratification of dust in the atmosphere, the depletion of molecules from the gas phase, the supersaturation of the gas in the atmosphere as well as the mean size and the mass fraction of dust grains as function of depth. Our results suggest that the nucleation occu in the upper atmosphere where the gas is cool, strongly depleted, but nevertheless highly supersaturated (\$S\!\gg\!1\$). These particles settle gravitationally and populate the warmer layers below, where the in-situ formation (nucleation) is ineffective or even not possible. During their descent, the particles grow up to radii \$\approx\!0.3\,\mu{\rm m}\,...\,150\,\mu{\rm m}\$, depending gas around the cloud base. The particles finally sink into layers which are sufficiently hot to cause their thermal evaporation. Hence, an effective transport mechanism for condensable elements exi considered solid/liquid material. In the stationary case studied here, this downward directed element transport by precipitating dust grains is balanced by an upward directed flux of condensable elements from the deep interior of the star via convective mixing (no dust without mixing). We find a self-regulation mechanism which leads to an approximate phase equilibrium (\$S\!\approx\!1\$) around the cloud base. The mass fraction of dust present in the atmosphere results be to approximately given by the mass fraction of condensable elements in the gas being mixed up.}, language = {en} } @misc{HellingKleinWoitkeetal., author = {Helling, Christiane and Klein, Rupert and Woitke, Peter and Sedlmayr, Erwin}, title = {Dust formation in brown dwarf atmospheres under conditions of driven turbulence}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7294}, number = {03-07}, abstract = {Based on the knowledge gained from direct numerical simulations which are only possible in the microscale regime, a concept of driven turbulence is presented which allows to enter the mesoscopic scale regime. Here, dust formation under stochastic hydro- and thermodynamic conditions is studied: constructively superimposed stochastic waves initiate dust formation by the creation of singular nucleation events. It, hence, results a varying mean grain size and dust density in space and time. The newly formed dust changes the thermodynamic behavior from almost isotherm to adiabatic and chemically depletes the gas phase.}, language = {en} } @misc{HellingKleinWoitkeetal., author = {Helling, Christiane and Klein, Rupert and Woitke, Peter and Nowak, Ulrich and Sedlmayr, Erwin}, title = {Dust in Brown Dwarfs IV. Dust formation and driven turbulence on mesoscopic scales}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7555}, number = {03-33}, abstract = {Dust formation {in brown dwarf atmospheres} is studied by utilizing a model for driven turbulence in the mesoscopic scale regime. We apply a pseudo-spectral method where waves are created and superimposed {within} a {limited} wavenumber interval. The turbulent kinetic energy distribution follows the Kolmogoroff spectrum which is assumed to be the most likely value. Such superimposed, stochastic waves may occur in a convectively active environment. They cause nucleation fronts and nucleation events and thereby initiate the dust formation process which { continues until} all condensible material is consumed. Small disturbances {are found to} have a large impact on the dust forming system. An initially dust-hostile region, which may originally be optically thin, becomes optically thick in a patchy way showing considerable variations in the dust properties during the formation process. The dust appears in lanes and curls as a result of the interaction with waves, i.e. turbulence, which form larger and larger structures with time. Aiming on a physical understanding of the variability of brown dwarfs, related to structure formation in substellar atmospheres, we work out first necessary criteria for small-scale closure models to be applied in macroscopic simulations of dust forming astrophysical systems.}, language = {en} } @misc{HellingKleinSedlmayr, author = {Helling, Christiane and Klein, Rupert and Sedlmayr, Erwin}, title = {The multi-scale dust formation in substellar atmospheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7567}, number = {03-34}, abstract = {Substellar atmospheres are observed to be irregularly variable for which the formation of dust clouds is the most promising candidate explanation. The atmospheric gas is convectively unstable and, last but not least, colliding convective cells are seen as cause for a turbulent fluid field. Since dust formation depends on the local properties of the fluid, turbulence influences the dust formation process and may even allow the dust formation in an initially dust-hostile gas. A regime-wise investigation of dust forming substellar atmospheric situations reveals that the largest scales are determined by the interplay between gravitational settling and convective replenishment which results in a dust-stratified atmosphere. The regime of small scales is determined by the interaction of turbulent fluctuations. Resulting lane-like and curled dust distributions combine to larger and larger structures. We compile necessary criteria for a subgrid model in the frame of large scale simulations as result of our study on small scale turbulence in dust forming gases.}, language = {en} }