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Two-dimensional MHD models of solar magnetogranulation. Dynamics of magnetic elements

We present the results of a statistical analysis of the Doppler shifts and the asymmetry parameters of V profiles of the Fe I 630.25 nm line produced by 2D MHD simulations of solar granulation. The realism of the simulations tested using the magnetic ratio of Fe I 524.71 and 525.02 nm lines. The Stokes spectra were synthesized in snapshots with a mixed polarity field having a mean magnetic flux density of 0.2 mT and mean unsigned field strength of 35 mT. We found that downflows with a velocity of 0.5 km/s predominate, on the average, in areas with some network magnetic elements at the disk center. In separate strong fluxtubes the average velocity is equal to 3 km/s and the maximum velocity is 9 km/s. In weak diffuse magnetic fields upflows dominate. Their average velocity is 0.5 km/s and maximal one is 3 km/s. The V-profile asymmetry depends on the spatial resolution. The V profiles synthesized with high spatial resolution (35 km) have average amplitude and area asymmetries -1%, 1%, respectively. The asymmetry scatter is \pm70% for weak profiles and \pm10% for strong ones. The profiles with low spatial resolution (700 km) have average amplitude and area asymmetries 3%, -2\%, respectively. Low spatial resolution is a reason why the amplitude asymmetry is always positive and greater than the area asymmetry in V profiles observed. We found weak correlation between the asymmetry of V profiles and velocity. Upflows cause negative asymmetry, on the average, and downflows cause positive asymmetry. We examined center-to-limb variations of vertical velocity in magnetic elements. Beginning from cos theta = 0.9, the average velocity abruptly increases from 0.5 to 2 km/s and then slightly varies closer to the limb. We found nonlinear oscillations of vertical velocity with power peaks in the 5-minute and 3-minute bands.