  When observed in quiet regions close to the solar limb, many strong resonance
lines show conspicuous linear polarization signals, produced by scattering
processes, with extended wing lobes. Recent studies indicate that, contrary to
what was previously believed, the wing lobes are sensitive to the presence of
relatively weak longitudinal magnetic fields through magneto-optical (MO)
effects. We theoretically investigate the sensitivity of the scattering
polarization wings of the Ca I 4227 {\AA} line to the MO effects, and we
explore its diagnostic potential for inferring information on the longitudinal
component of the photospheric magnetic field. We calculate the intensity and
polarization profiles of the Ca I 4227 {\AA} line by numerically solving the
problem of the generation and transfer of polarized radiation under non-local
thermodynamic equilibrium conditions in one-dimensional semi-empirical models
of the solar atmosphere, taking into account the joint action of the Hanle,
Zeeman, and MO effects. We consider volume-filling magnetic fields as well as
magnetic fields occupying a fraction of the resolution element. In contrast to
the circular polarization signals produced by the Zeeman effect, we find that
the linear polarization angle in the scattering polarization wings of Ca I 4227
presents a clear sensitivity, through MO effects, not only to the flux of the
photospheric magnetic field, but also to the fraction of the resolution element
that the magnetic field occupies. We identify the linear polarization angle in
the wings of strong resonance lines as a valuable observable for diagnosing
unresolved magnetic fields. Used in combination with observables that encode
information on the magnetic flux and other properties of the observed
atmospheric region, it can provide constraints on the filling factor of the
magnetic field.
