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

Abstract

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 Alfvén 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.

Figures (10)

• Figure 1: Relation between the asymptotic expansion factor $f_\infty$ and solar wind velocity at $r=70 R_{\odot}$. Simulation results correspond to the colored symbols and the WS model correspond to black dotted line. The results are limited for the case with only $f_\infty$ and $B_{r,\rm{cb}}$ parameters changed from default values. Each color and marker in the plot corresponds to a single value of $B_{r,\rm{cb}}$.
• Figure 2: The line colors correspond to the same cases in the left and right panels. The upper and lower panels differ in the value of $r_{\rm{exp}}$ and $\sigma_{\rm{exp}}$, respectively: in the upper panels, $\sigma_{\rm{exp}}$ is fixed at $0.5R_\odot$, while in the lower panels, $r_{\rm{exp}}$ is fixed at $1.3R_\odot$. Left panels show the prescribed expansion factor profiles as a function of height from the photosphere $r/R_\odot-1$ (logarithmic scale). For reference, the transonic point in each simulation is indicated by a vertical dotted line. Right panels show the resulting solar wind speed profiles as a function of heliocentric distance $r$ (linear scale). In all cases presented here, the radial magnetic field strength at the coronal base, $B_{r,\rm{cb}}$, is fixed at $13$ G.
• Figure 3: The same as Figure \ref{['fig:exph_param']} but the cases differ in $g_{\rm{max}}$(top panels), $r_{\rm{max}}$(middle panels), $w$(bottom panels)
• Figure 4: Relation between wind velocity measured at $r=70 R_\odot$ and each feature candidate. Upper left: asymptotic expansion factor $f_{\infty}$. The wind speed predicted by the Wang-Sheeley model $v_{\rm{WS}}$ is indicated by the dotted line for comparison. Upper right: the quantity $f_{\infty}/B_{r,\rm{cb}}$, where $B_{r,\rm{cb}}$ is the radial magnetic field strength at the coronal base. Lower left: the quantity $f_{\rm{max}}/(B_{r,\rm{cb}}r_{\rm{half}}^2)$, where $f_{\rm{max}}$ is the maximum value of $f(r)$ and $r_{\rm{half}}$ is the radial distance at which $f(r)=f_{\rm{max}}/2$ for the first time. Lower right: integral value of $f(r)/B_{r,\rm{cb}}$ from coronal base to a certain height in atmosphere. Cases are divided into three groups: (1) monotonic expansion for fixed expansion height and scale($r_{\rm{exp}}$ & $\sigma_{\rm{exp}}$)(blue circles) (2) monotonic expansion for varied expansion height and scale(orange diamonds) (3) non-monotonic expansion, whose $g_{\rm{max}}$ is larger than $1$(green crosses).
• Figure 5: Relation between wind velocity $v_r$ at $r=70R_\odot$ and Alfvén wave energy flux per mass $F_A/\rho$ at the sonic point.