Proposal of a Novel Physical Parameter Characterizing Solar Wind Speed in a Wave-Driven Model

Empirical solar wind speed models play an important role in enabling space weather forecasting with low computational cost. Among these, one model called WS model is based on the asymptotic expansion factor. However, it is known that it fails in the case of pseudostreamers. In this study, as a first step toward constructing a solar wind speed empirical model based on physical parameters, we investigated the effect of the radial profile of flux-tube shape on the solar wind speed using one-dimensional numerical simulations. In the simulations, ad hoc Alfv\'en waves are injected from the photosphere at $r=R_\odot$ as the energy source, and the MHD equations are solved out to the interplanetary space at $r=70R_\odot$ to reproduce solar wind acceleration. As a result, even when the coronal base magnetic field and the asymptotic expansion factor are fixed, the final solar wind speed varies by approximately 300 km s$^{-1}$ depending on changes in the expansion height or non-monotonic expansion. Additionally, across all simulations performed, a better correlation is found with the quantities that reflect the information about the radial profile of flux-tube shape than the asymptotic expansion factor. Our results suggest that, as a physical characteristic parameter of the solar wind speed, an operation that can account for the expansion factor throughout the corona is necessary.