Solar winds along curved magnetic field lines

Context. Both remote-sensing measurements using the interplanetary scintillation (IPS) technique and in-situ measurements by the Ulysses spacecraft show a bimodal structure for the solar wind at solar minimum conditions. At present it still remains to address why the fast wind is fast and the slow wind is slow. While a robust empirical correlation exists between the coronal expansion rate f(c) of the flow tubes and the speeds v measured in situ, a more detailed data analysis suggests that v depends on more than just f(c). Aims. We examine whether the non-radial shape of field lines, which naturally accompanies any non-radial expansion, could be an additional geometrical factor. Methods. We solved the transport equations incorporating the heating from turbulent Alfven waves for an electron-proton solar wind along curved field lines given by an analytical magnetic field model, which is representative of a solar minimum corona. Results. The field line shape is found to influence the solar wind parameters substantially, reducing the asymptotic speed by up to similar to 130 km s(-1) or by similar to 28% in relative terms, compared with the case where the field line curvature is neglected. This effect was interpreted in the general framework of energy addition in the solar wind: compared to the straight case, the field line curvature enhances the effective energy deposition to the subsonic flow, which results in a higher proton flux and a lower terminal proton speed. Conclusions. Our computations suggest that the field line curvature could be a geometrical factor which, in addition to the tube expansion, substantially influences the solar wind speed. Furthermore, although the field line curvature is unlikely to affect the polar fast solar wind at solar minima, it does help make the wind at low latitudes slow, which in turn helps better reproduce the Ulysses measurements.