Abstract
The origin of global magnetic fields in celestial bodies is generally ascribed to dynamo action by fluid motions in their electrically conducting interiors. Some objects โ e.g. closeโin extraโsolar planets or the moons of some giant planets โ are embedded in ambient magnetic fields which modify the generation of the internal field in these bodies. Recently, the feedback of the magnetospheric field by ChapmanโFerraro currents in the magnetopause onto the interior dynamo has been proposed to explain the observed weakness of the intrinsic magnetic field of planet Mercury. We study a simplified meanโfield dynamo model which allows us to analytically address various issues like positive and negative feedback situations, stationary versus timeโdependent solutions, and the stability of weak and strong field branches. We discuss the influence of the response function on the solutions when the external field depends on the strength of the intrinsic field like in the situation of the feedback dynamo of Mercury. We find that the feedback mechanism works only for a narrow range of dynamo numbers in the case of Mercury which makes him unique in our solar system. We conclude with some implications for extraโsolar planets (ยฉ 2011 WILEYโVCH Verlag GmbH & Co. KGaA, Weinheim)