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We perform radiative magnetohydrodynamic calculations for the solar quietregion to investigate the dependence of statistical flow on magnetic propertiesand the three-dimensional (3D) structure of magnetic patches in the presence oflarge-scale flow that mimics differential rotation. It has been confirmed thatstrong magnetic field patches move faster in the longitudinal direction at thesolar surface. Consequently, strong magnetic patches penetrate deeper into thesolar interior. The motion of the deep-rooted magnetic patches is influenced bythe faster differential rotation in the deeper layer. In this study, we performrealistic radiative magnetohydrodynamic calculations using R2D2 code tovalidate that stronger patches have deeper roots. We also add large-scale flowto mimic the differential rotation. The magnetic patches are automaticallydetected and tracked, and we evaluate the depth of 30,000 magnetic patches. Thevelocities of 2.9 million magnetic patches are then measured at thephotosphere. We obtain the dependence of these values on the magneticproperties, such as field strength and flux. Our results confirm that strongmagnetic patches tend to show deeper roots and faster movement, and we compareour results with observations using the point spread function of instruments atthe Hinode and Solar Dynamics Observatory (SDO). Our result is quantitativelyconsistent with previous observational results of the SDO.

Relationship between magnetic field properties and statistical flow using numerical simulation and magnetic feature tracking on solar photosphere