On Convection in Stellar Atmospheres
Abstract
Summary. Three nonlocal theories of stellar convection are discussed. Two of these, due to Ulrich and Spiegel, predict convective fluxes widely different from those predicted by local mixing-length theory. With the aid of differential equations for the vertical velocity, excess temperature, and excess energy of fluctuations in turbulent convective layers, the importance of radiative and turbulent exchange is discussed. It is found that the amount of radiative cooling effectively determines the importance of convective flux relative to radiative flux, and that the turbulent dilution of kinetic energy determines the convective velocities. A parametrization of the rate of turbulent dilution in terms of a mixing length allows local mixing-length theory expressions for the convective flux to be obtained in the limit of slowly varying conditions. A local approximation for the ratio between excess energy and vertical velocity is found to give expressions for the convective flux in close agreement with expressions given previously by Parsons. The numerical investigation applies powerful difference equation methods to radiative transfer; this is used to construct an iterative Newton-Raphson procedure producing realistic fluxconstant models including nonlocal convection. By comparing models with different convection theories and by analysing the importance of radiative cooling, it is concluded that the first two theories noted above overestimate the importance of convection in the visible layers of giants and solar type stars. A quantitative measure of the importance of the convective flux in the visible layers is introduced, and it is concluded that this quantity is small in main sequence stars and in giants whose effective temperatures exceed approximately 5000 K and 4000 K, respectively. Key words: stellar atmospheres - convection - non-local effects - F-, G- and K-stars
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- June 1974
- Bibcode:
- 1974A&A....32..407N