  Here we formulate and solve the 3D radiative transfer problem of the
polarization of the solar continuous radiation. Our approach takes into account
not only the anisotropy of the continuum radiation, but also the
symmetry-breaking effects caused by the horizontal atmospheric inhomogeneities
produced by the solar surface convection. Interestingly, our radiative transfer
modeling in a well-known 3D hydrodynamical model of the solar photosphere shows
remarkable agreement with the empirical data, significantly better than that
obtained via the use of 1D atmospheric models. Although this result confirms
that the above-mentioned 3D model was indeed a suitable choice for our
Hanle-effect estimation of the substantial amount of "hidden" magnetic energy
that is stored in the quiet solar photosphere, we have found however some small
discrepancies whose origin may be due to uncertainties in the empirical data
and/or in the thermal and density structure of the 3D model. For this reason,
we have paid some attention also to other (more familiar) observables, like the
center-limb variation of the continuum intensity, which we have calculated
taking into account the scattering contribution to the continuum source
function. The overall agreement with the observed center-limb variation turns
out to be impressive, but we find a hint that the model's temperature gradients
in the continuum forming layers could be slightly too steep, perhaps because
all current simulations of solar surface convection and magnetoconvection
compute the radiative flux divergence ignoring the fact that the effective
polarizability is not completely negligible, especially in the downward-moving
intergranular lane plasma.
