Energy injection via flux emergence on the Sun depending on the geometric shape of magnetic field

Flux emergence is a complicated process involving flow and magnetic field, which provides a way of injecting magnetic energy into the solar atmosphere. We show that energy injection via this complicated process is characterized by a physical quantity called the emergence velocity, which is determined by the spatial relationship between the flow velocity and magnetic field vectors. By using this quantity, we demonstrate that the geometric shape of magnetic field might play an important role in the energy injection via flux emergence.