A calibration of the mixing-length for solar-type stars based on hydrodynamical simulations - I. Methodical aspects and results for solar metallicity

Based on detailed 2D numerical radiation hydrodynamics (RHD) calculations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of solar-type stars. The RHD models provide information about the convective efficiency in the supe...

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Bibliographic Details
Published inarXiv.org
Main Authors H -G Ludwig, Freytag, B, Steffen, M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.03.1999
Subjects
Abundance
Astronomical models
Calibration
Compressibility
Computational fluid dynamics
Computer simulation
Convection cooling
Darkening
Dynamic structural analysis
Fluid flow
Helium
Hydrodynamics
Metallicity
Parameters
Stellar structure
Surface layers
Temperature dependence
Time compression
Time dependence
Yttrium
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Summary:Based on detailed 2D numerical radiation hydrodynamics (RHD) calculations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of solar-type stars. The RHD models provide information about the convective efficiency in the superadiabatic region at the top of convective envelopes and predict the asymptotic value of the entropy of the deep, adiabatically stratified layers. This information is translated into an effective mixing-length parameter alpha suitable to construct standard stellar structure models. We validate the approach by a detailed comparison to helioseismic data. The grid of RHD models for solar metallicity comprises 58 simulation runs with a helium abundance of Y=0.28 in the range of effective temperatures 4300K < Teff < 7100K and gravities 2.54 < logg < 4.74. We find a moderate, nevertheless significant variation of alpha between about 1.3 for F-dwarfs and 1.75 for K-subgiants with a dominant dependence on Teff. In the close neighbourhood of the Sun we find a plateau where alpha remains almost constant. The internal accuracy of the calibration of alpha is estimated to be +/- 0.05 with a possible systematic bias towards lower values. An analogous calibration of the convection theory of Canuto & Mazzitelli gives a different temperature dependence but a similar variation of the free parameter. For the first time, values for the gravity-darkening exponent beta are derived independently of mixing-length theory: beta=0.07...0.10. We show that our findings are consistent with constraints from stellar stability considerations and provide compact fitting formulae for the calibrations.
ISSN:2331-8422