Testing the flux tube expansion factor Solar wind speed relation with Solar Orbiter data

Context. The properties of the solar wind measured in situ in the heliosphere are largely controlled by energy deposition in the solar corona, which is in turn closely related to the properties of the coronal magnetic field. Previous studies have shown that long-duration and large-scale magnetic structures show an inverse relation between the solar wind velocity measured in situ near 1 au and the expansion factor of the magnetic flux tubes in the solar atmosphere. Aims. The advent of the Solar Orbiter mission offers a new opportunity to analyse the relation between solar wind properties measured in situ in the inner heliosphere and the coronal magnetic field. We exploit this new data in conjunction with models of the coronal magnetic field and the solar wind to evaluate the flux expansion factor and speed relation. Methods. We use a Parker-like solar wind model, the "isopoly" model presented in previous works, to describe the motion of the solar wind plasma in the radial direction and model the tangential plasma motion due to solar rotation with the Weber and Davis equations. Both radial and tangential velocities are used to compute the plasma trajectory and streamline from Solar Orbiter location sunward to the solar 'source surface' at r(ss). We then employed a potential field source surface (PFSS) model to reconstruct the coronal magnetic field below r(ss) to connect wind parcels mapped back to the photosphere. Results. We found a statistically weak anti-correlation between the in situ bulk velocity and the coronal expansion factor, for about 1.5 years of solar data. Classification of the data by source latitude reveals different levels of anticorrelation, which is typically higher when Solar Orbiter magnetically connects to high latitude structures than when it connects to low latitude structures. We show the existence of a fast solar wind that originates in strong magnetic field regions at low latitudes and undergoes large expansion factor. We provide evidence that such winds become supersonic during the super-radial expansion (below r(ss)) and are theoretically governed by a positive v-f correlation. We find that faster winds exhibit, on average, a flux tube expansion at a larger radius than slower winds. Conclusions. An anticorrelation between solar wind speed and expansion factor is present for solar winds originating in high latitude structures in solar minimum activity, typically associated with coronal hole-like structures, but this cannot be generalized to lower latitude sources. We have found extended time intervals of fast solar wind associated with both large expansion factors and strong photospheric magnetic fields. Therefore, the value of the expansion factor alone cannot be used to predict the solar wind speed. Other parameters, such as the height at which the expansion gradient is the strongest, must also be taken into account.