Connecting the Sun and the Solar Wind: The First 2.5 Dimensional Self-consistent MHD Simulation under the Alfv\'en Wave Scenario

The solar wind emanates from the hot and tenuous solar corona. Earlier studies using 1.5 dimensional simulations show that Alfv\'{e}n waves generated in the photosphere play an important role in coronal heating through the process of non-linear mode conversion. In order to understand the physics of coronal heating and solar wind acceleration together, it is important to consider the regions from photosphere to interplanetary space as a single system. We performed 2.5 dimensional, self-consistent magnetohydrodynamic simulations, covering from the photosphere to the interplanetary space for the first time. We carefully set up the grid points with spherical coordinate to treat the Alfv\'{e}n waves in the atmosphere with huge density contrast, and successfully simulate the solar wind streaming out from the hot solar corona as a result of the surface convective motion. The footpoint motion excites Alfv\'{e}n waves along an open magnetic flux tube, and these waves traveling upwards in the non-uniform medium undergo wave reflection, nonlinear mode conversion from Alfv\'{e}n mode to slow mode, and turbulent cascade. These processes leads to the dissipation of Alfv\'{e}n waves and acceleration of the solar wind. It is found that the shock heating by the dissipation of the slow mode wave plays a fundamental role in the coronal heating process whereas the turbulent cascade and shock heating drive the solar wind.