Meridional flow and differential rotation by gravity darkening in fast rotating solar-type stars

An explanation is presented for the rather strong total surface differential rotation of the observed very young solar-type stars like AB Dor and PZ Tel. Due to its rapid rotation, a non-uniform energy flux leaves the stellar core so that the outer convection zone is non-uniformly heated from below. Due to this "gravity darkening" of the equator, a meridional flow is created owing equatorwards at the surface and thus accelerating the equatorial rotation. The effect linearly grows with the normalized pole-equator difference, epsilon, of the heat-flux at the bottom of the convection zone. A rotation rate of about 9 h leads to epsilon = 0.1 for a solar-type star. In this case the resulting equator-pole differences of the angular velocity at the stellar surface, deltaOmega, varies from unobservable 0.005 day(-1) to the (desired) value of 0.03 day(-1) when the dimensionless diffusivity factors c(nu) and c(chi) vary between 1 and 0.1 (standard value c(nu) similar or equal to c(chi) similar or equal to 0.3, see Table 1). In all cases the related temperature differences between pole and equator at the surface are unobservably small. The (clockwise) meridional circulation which we obtain flows opposite to the (counterclockwise) circulation appearing as a byproduct in the Lambda-theory of the non-uniform rotation in outer convection zones. The consequences of this situation for those dynamo theories of stellar activity are discussed that work with the meridional circulation as the dominant magnetic-advection effect in latitude to produce the solar-like form of the butterfly diagram.