Astronomy & Astrophysics

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Issue		A&A Volume 395, Number 1, November III 2002
Page(s)		99 - 115
Section		Formation, structure and evolution of stars
DOI		10.1051/0004-6361:20021153

A&A 395, 99-115 (2002)
DOI: 10.1051/0004-6361:20021153

Numerical simulations of surface convection in a late M-dwarf

H.-G. Ludwig^{1, 2}, F. Allard² and P. H. Hauschildt^{3, 2}

¹ Lund Observatory, Box 43, 22100 Lund, Sweden
e-mail: hgl@astro.lu.se
² C.R.A.L., École Normale Supérieure, 69365 Lyon Cedex 7, France
³ Dept. of Physics and Astronomy & Center for Simulational Physics, University of Georgia, Athens, GA 30602-2451, Greece

(Received 17 January 2002 / Accepted 1 August 2002)

Abstract
Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf ( $\ensuremath{T_{{\rm eff}}}\approx 2800\rm\,K$ , $\ensuremath{\log g} =5.0$ , solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of $\approx$ $100\rm\,s$ , and a horizontal scale of $80\rm\,km$ ; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square vertical velocities reach 240 $\rm\,m\,s^$ at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmospheres. A mixing-length parameter of $\ensuremath{\alpha_{{\rm MLT}}} ~=$ 2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope ( $\ensuremath{\alpha_{{\rm MLT}}} ~=$ 1.5), or when matching the vertical velocity ( $\ensuremath{\alpha_{{\rm MLT}}} ~=$ 3.5). The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.

Key words: convection -- hydrodynamics -- radiative transfer -- stars: atmospheres -- stars: late-type

Offprint request: H.-G. Ludwig, hgl@astro.lu.se

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