Forward modeling of the Mg 12.32 μm line from a 3D magnetohydrodynamic model of an enhanced network

The Mg I 12 mu m lines, 12.22 and 12.32 mu m, represent a pair of emission lines, and their line cores originate around the temperature minimum region. These lines exhibit the highest ratio of Zeeman to Doppler broadening in the infrared solar spectrum, making them crucial for accurately investigating the solar magnetic field. We synthesized the Mg 12.32 mu m Stokes profiles from a 3D magnetohydrodynamic (MHD) model and studied the validity of different methods for extracting the magnetic field. The observational profiles at different spatial resolution were simulated, which are helpful for the design of future solar telescopes with large apertures. We used a 3D MHD simulation model for an enhanced network computed using the Bifrost code. We performed nonlocal thermal equilibrium calculations for Stokes profiles of the Mg 12.32 mu m line using the Rybicki-Hummer code. From the simulation we determined the average formation height of the Mg 12.32 mu m line to be around 450 km. The various solar features have different formation heights, and the variance of formation height in magnetic concentration regions is about 160 km. The wavelength-integrated method is proven effective in calibrating the integrated Stokes profiles to obtain the longitudinal ($B_l$) and horizontal ($B_H$) field components for weak magnetic fields; the $B_l$ is below 300 G. Furthermore, the weak field approximation was found to be valid only for estimating magnetic fields with $B_l$ below 150 G. The Stokes I profiles clearly show Zeeman triple splitting around the magnetic flux concentration with a grid resolution of 48 km. We determined that a resolution of $0.97^ $, equivalent to the diffraction limit of a telescope with a diameter of 3.2 m, was necessary to detect the Zeeman splitting for the simulated snapshot. Our results from this 3D MHD model are valuable for interpreting data from the Accurate Infrared Magnetic Field Measurements of the Sun (AIMS) telescope and designing future solar infrared telescopes.