Two-dimensional numerical simulations on the origin of network magnetic field in the solar quiet region

The magnetic network is one of the most characteristic horizontal structures observed in the lower-atmospheric (UV and IR) emission of the sun. The horizontal advection by the horizontal flow of supergranulation is often perceived to form the magnetic network. However, the origin of supergranulation itself remains unsolved for over 50 years. We newly develop a radiative magneto-hydrodynamic simulation code for the realistic calculation of the solar surface magneto-convection to show the formation process of the magnetic network and supergranulation. When the magnetic field strength is moderate, no supergranular peak is found in the kinetic energy spectrum. However, the magnetic energy spectrum has an clear peak at the scale of the magnetic network. The horizontal structure of this magnetic network has a correlation with the horizontal flow at a depth of about 3 Mm. When the magnetic field becomes sufficiently strong, the back reaction from the magnetic network to the supergranular convection occurs and the supergranular spectral peak appears in the kinetic energy spectrum.