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The Horizontal Internetwork Magnetic Field: Numerical Simulations in Comparison to Observations with Hinode**

Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe i 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where, depending on the initial state or the boundary condition, it surpasses the vertical component by a factor of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean horizontal field component that is 1.6 or 4.3 times stronger than the vertical component, depending on the initial state or the boundary condition. This is a consequence of both the intrinsically stronger flux density of and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, whereas the Poynting flux is negative in the convectively unstable layer below it.

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