  The Sun is the only star where we can resolve the intricate magnetism that
all convective stars harbor. Yet, more than 99% of its visible surface along
the solar cycle (the so-called quiet Sun) is filled with a tangled, unresolved
magnetism. These "hidden" fields are thought to store enough magnetic energy to
play a role in the heating of the Sun's outer atmosphere, but its field
strength is still not constrained. Previous investigations based on the Hanle
effect in atomic lines claim a strong magnetization of about 100 G, while the
same effect in molecules show a factor of 10 weaker fields. The discrepancy
disappears if the magnetic field strength of the hidden is not homogeneous in
the solar surface. In this letter, we prove using magnetohydrodynamical
simulations that it is possible to infer the average field strength of the
hidden quiet Sun magnetic fields using multi-line inversions of intensity
profiles in the Zeeman regime. Using this technique with 15 spectral lines in
the 1.5 $\mu$m spectral range, we reveal that the spatial distribution of the
hidden field is strongly correlated with convection motions, and that the
average magnetization is about 46 G. Reconciling our findings with the Hanle
ones is not obvious and will require future work on both sides, since it
implies an increase of the field strength with height, something that is
physically questionable.
