Distribution of starspots on cool stars A Model Based On the Dynamics of Magnetic Flux Tubes

Abstract

A theoretical study of storage, instability and rise of magnetic flux tubes in the outer convection zone of a cool star is presented. Special emphasis is laid on their emergence latitudes at the surface of magnetically active stars. We apply the ‘solar paradigm’ and assume toroidal magnetic flux tubes to be stored in force equilibrium within the overshoot layer underneath the convection zone. A non-axisymmetric (undulatory) instability leads to the formation of flux loops, which rise through the convection zone and emerge at the surface to form bipolar magnetic regions and starspots. Our approach combines the analytical determination of the linear stability properties of flux tubes with numerical simulations of the nonlinear evolution of the instability and the rise of magnetic flux tubes through the convection zone. It is found that for sufficiently rapidly rotating stars the magnetic flux emerges at high latitudes since the Coriolis force leads to a poleward deflection of rising flux loops. The latitude distribution of the emerging flux is determined for a number of stellar models along the evolutionary sequence of a star with one solar mass, from the pre-main sequence evolution up to the giant phase. Rapid rotation and deep convection zones favour flux emergence in high latitudes. Starspots right at the stellar (rotational) poles form either directly by flux eruption from small stellar cores (as for T Tauri stars or giants) or by a poleward slip of the sub-surface part of the flux tube after flux emergence in mid latitudes. The latter process explains the simultaneous existence of polar spots and spots at intermediate latitudes as observed on some stars.