Flux-tube geometry and solar wind speed during an activity cycle

International audienceContext. The solar wind speed at 1 AU shows cyclic variations in latitude and in time which reflect the evolution of the global background magnetic field during the activity cycle. It is commonly accepted that the terminal (asymptotic) wind speed in a given magnetic flux-tube is generally anti-correlated with its total expansion ratio, which motivated the definition of widely used semi-empirical scaling laws relating one to the other. In practice, such scaling laws require ad hoc corrections (especially for the slow wind in the vicinities of streamer/coronal hole boundaries) and empirical fits to in situ spacecraft data. A predictive law based solely on physical principles is still missing. Aims: We test whether the flux-tube expansion is the controlling factor of the wind speed at all phases of the cycle and at all latitudes (close to and far from streamer boundaries) using a very large sample of wind-carrying open magnetic flux-tubes. We furthermore search for additional physical parameters based on the geometry of the coronal magnetic field which have an influence on the terminal wind flow speed. Methods: We use numerical magneto-hydrodynamical simulations of the corona and wind coupled to a dynamo model to determine the properties of the coronal magnetic field and of the wind velocity (as a function of time and latitude) during a whole 11-yr activity cycle. These simulations provide a large statistical ensemble of open flux-tubes which we analyse conjointly in order to identify relations of dependence between the wind speed and geometrical parameters of the flux-tubes which are valid globally (for all latitudes and moments of the cycle). Results: Our study confirms that the terminal (asymptotic) speed of the solar wind depends very strongly on the geometry of the open magnetic flux-tubes through which it flows. The total flux-tube expansion is more clearly anti-correlated with the wind speed for fast rather than for slow wind flows, and effectively controls the locations of these flows during solar minima. Overall, the actual asymptotic wind speeds attained - especially those of the slow wind - are also strongly dependent on field-line inclination and magnetic field amplitude at the foot-points. We suggest ways of including these parameters in future predictive scaling laws for the solar wind speed