Simulations of stellar convection with CO5BOLD

Numerical Simulations of Stellar Convective Dynamos. I. The Model and Method

The observed surface angular velocity of main-sequence stars shows a sharp decrease at about spectral type F6. It is suggested that stars more massive than F6 cannot experience an appreciable angular-momentum loss because their convection zones cannot sustain a magnetic dynamo: without a magnetic field the angular-momentum loss is very small. The influence of rotation on the convective motions is essential for the existence of a solar-type dynamo. Rotation can influence these convective motions only if the typical convective time is larger than the rotation time. For main-sequence stars of different masses and chemical compositions the dimensionless parameter (convective velocity/sum's angular velocity times mixing length in the lower part of the convection zone) is evaluated. It is shown that this parameter increases very sharply for stars whose mass exceeds that defined by the relation log(star mass/solar mass) is of the order of 0.1. Thus even for large angular velocities, magnetic dynamos are not feasible if log(star mass/solar mass) appreciably exceeds 0.1.

On the angular momentum loss of late-type stars

The growth of linear, Boussinesq convective modes for a superadiabatic fluid in a planar
geometry with negligible thermal diffusion or molecular viscosity is analysed. Small and large
magnetic diffusivity limits are both considered. A finite amplitude theory is constructed by
assuming that non-linearities (e.g. shear instabilities) limit the flow amplitude, and the
dominant modes are assumed to be those which transport most heat. This leads to a unique
prescription for the average velocity, superadiabaticity and horizontal lengthscale as a
function of the imposed heat flux, rotation rate, large scale magnetic field and vertical
lengthscale. Simple analytical results are provided (in terms of the relevant dimensionless
numbers) which are as easy to apply as the conventional mixing length theory (MLT). The
conclusions are: (i) For no rotation or magnetic field, the model reproduces MLT except
that it predicts about an order of magnitude lower heat flux. (ii) Rotation alone or magnetic
field alone inhibits the convection. For a given heat flux, the convective velocity and
horizontal wavelength are reduced, and the temperature gradient increases. (iii) If R_0 ≾ 0.1,
where R_0 is the nominal Rossby number, then the combined effect of rotation and magnetic
field enhances the convection, and the maximum heat flux occurs at non-zero field. (iv) The
rotational inhibition of convection in rapidly rotating stars does not substantially modify
their static structure. (v) Convective velocities of around 0.02 cm/sec are predicted for the
Earth's core, consistent with geomagnetic secular variation timescales, provided the toroidal
field is less than about three times the poloidal field. (vi) In both the Earth and Jupiter, the
actual magnetic field is within an order of magnitude of the field which minimizes the
temperature gradient for a given heat flux.
Application of these results to stellar and planetary dynamos is briefly discussed and critically assessed.

Turbulent thermal convection in the presence of rotation and a magnetic field: A heuristic theory

The numerical solution of sixth-order boundary value problems by the modified decomposition method

Stellar convection theory. II - Single-mode study of the second convection zone in an A-type star

Anelastic Stellar Convection Theory Applied to A-type Stars.

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Stellar convection theory. II - Single-mode study of the second convection zone in an A-type star

Anelastic Stellar Convection Theory Applied to A-type Stars.