  Before using 3D MHD simulations of the solar photosphere in the determination
of elemental abundances, one has to ensure that the correct amount of magnetic
flux is present in the simulations. The presence of magnetic flux modifies the
thermal structure of the solar photosphere, which affects abundance
determinations and the solar spectral irradiance. We compare the polarization
signals in disk-center observations of the solar photosphere in quiet-Sun
regions with those in Stokes spectra computed on the basis of 3D MHD
simulations having average magnetic flux densities of about 20, 56, 112 and 224
G. This approach allows us to find the simulation run that best matches the
observations. The observations were taken with the Hinode SP, TIP, POLIS and
the GFPI, respectively. We determine characteristic quantities of full Stokes
profiles in a few photospheric spectral lines in the visible (630 nm) and
near-infrared (1083 and 1565 nm). We find that the appearance of abnormal
granulation in intensity maps of degraded simulations can be traced back to an
initially regular granulation pattern with numerous bright points in the
intergranular lanes before the spatial degradation. The linear polarization
signals in the simulations are almost exclusively related to canopies of strong
magnetic flux concentrations and not to transient events of magnetic flux
emergence. We find that the average vertical magnetic flux density in the
simulation should be less than 50 G to reproduce the observed polarization
signals in the quiet Sun internetwork. A value of about 35 G gives the best
match across the SP, TIP, POLIS and GFPI observations.
