tokens: for density ρ , velocity , the specific entropy S , and the magnetic vector potential are given by where P is the pressure with , which is defined up to some additive constant, c p and c v are the specific heats at constant pressure and density, respectively, T is the temperature with being the ideal gas equation of state, K is the thermal diffusivity, ν is the kinematic viscosity, η is the magnetic diffusivity, is the magnetic field with b 0 being the imposed field, and is the current density that was already defined in the introduction. We adopt a polytropic stratification with background temperature , so T = 0 at z = 0. We fix d and choose to set the degree of stratification. The smaller the , the stronger the stratification, i.e., the stronger the temperature contrast. In the following we choose , so the temperature changes by a factor of 10; see Hurlburt et al. ( 1984 ) for a similar setup. We choose to be either negative or positive, corresponding to the northern or southern hemispheres, respectively. A vertical magnetic field is imposed and tangled by this velocity field. The simulation setup is similar to that of Hurlburt Toomre ( 1988 ), except they did not include rotation, which makes our present simulations therefore closer to those of Brandenburg et al. ( 1990 ), which did include rotation. In the following, we denote by the density at . Some of the parameters are listed in Table 3 . The imposed magnetic field points in the z direction and is given by , where is the thermal equipartition field strength. We use in all cases. The Rayleigh number is defined as , where and are density and the specific entropy of the hydrostatic solution in the middle of the domain. Table 3 Parameters for Convection Simulations Cross sections of , , and near the surface are shown in Figure 10 for the results of such a simulation. One sees cyclonic convection in the northern hemisphere as viewed from the top, so all converging inflows attain a counterclockwise swirl, and all diverging outflows have a clockwise swirl. A similar appearance is also attained by the magnetic field. If we viewed this pattern from beneath, we would see a mirror image of the original pattern and therefore the opposite sign of the B polarization. The consequence of this can be seen in Figure 11 , where we plot and for north (red) and south (blue) for Runs A and B, whose parameters are summarized in Table 3 . There is now a systematic EB correlation, so is positive in the north and negative in the south; see Table 4 . This is very promising and agrees with our intuition. Figure 10. Magnetic field vectors and the line-of-sight component (color-coded; left) as well as E -mode (middle) and B -mode polarization (right) in rotating convection viewed from the top onto the convecting layer. Figure 11. (top) and (bottom) for convection simulations corresponding to the northern (red) and southern (blue) hemispheres for Runs A (thin lines) and B (thick lines). The gray shades indicate
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