Impact of non-uniform surface magnetic fields on stellar winds

Observations of active stars reveal highly non-uniform surface distributions of magnetic flux. Theoretical models considering magnetised stellar winds however often presume uniform surface magnetic fields, characterised by a single magnetic field strength. The present work investigates the impact of non-uniform surface magnetic field distributions on the stellar mass and angular momentum loss rates as well as on the effective Alfvénic radius of the wind. Assuming an axial symmetric and polytropic magnetised wind, the approach of Weber & Davis (1967) is extended to non-equatorial latitudes to quantify the impact of latitude-dependent magnetic field distributions over a large range of stellar rotation rates and thermal wind properties. Motivated by recent observational results, the analytically prescribed field patterns are dominated by magnetic flux concentrations at intermediate and high latitudes. The global stellar mass loss rates are found to be rather insensitive to non-uniformities of the surface magnetic field. Depending on the non-uniformity of the field distribution, the angular momentum loss rates deviate in contrast at all rotation rates between −60% and 10% from the Weber & Davis-values, and the effective Alfvénic radii up to about ±25%. These large variations albeit equal amounts of total magnetic flux indicate that a classification of stellar surface magnetic fields through a single field strength is insufficient, and that their non-uniformity has to be taken into account. The consequences for applications involving magnetised stellar winds are discussed in view of the rotational evolution of solar-like stars and of the observational determination of their mass loss rates using the terminal velocity and ram pressure of the wind. For rapidly rotating stars the latitudinal variation of the wind ram pressure is found to exceed, depending on the actual field distribution on the stellar surface, over two orders of magnitude. The assumption of a spherical symmetric wind geometry may therefore lead to a significant overor underestimation of the stellar mass loss rate.