  The chromosphere of the quiet Sun is an important stellar atmospheric region
whose thermal and magnetic structure we need to decipher for unlocking new
discoveries in solar and stellar physics. To this end, we must identify and
exploit observables sensitive to weak magnetic fields (B<100 G) and to the
presence of cool and hot gas in the bulk of the solar chromosphere. Here we
report on an investigation of the Hanle effect in two semi-empirical models of
the quiet solar atmosphere with different chromospheric thermal structures. Our
study reveals that scattering polarization in the Ca II IR triplet has thermal
and magnetic sensitivities potentially of great diagnostic value. The linear
polarization in the 8498 A line shows a strong sensitivity to inclined magnetic
fields with strengths between 0.001 and 10 G, while the emergent linear
polarization in the 8542 A and 8662 A lines is mainly sensitive to magnetic
fields with strengths between 0.001 and 0.1 G. The reason for this is that the
scattering polarization of the 8542 A and 8662 A lines, unlike the 8498 A line,
is controlled mainly by the Hanle effect in their (metastable) lower levels.
Therefore, in regions with magnetic strengths sensibly larger than 1 G, their
Stokes Q and U profiles are sensitive only to the orientation of the magnetic
field vector. We also find that for given magnetic field configurations the
sign of the Q/I and U/I profiles of the 8542 A and 8662 A lines is the same in
both atmospheric models, while the sign of the linear polarization profile of
the 8498 A line turns out to be very sensitive to the thermal structure of the
lower chromosphere. We suggest that spectropolarimetric observations providing
information on the relative scattering polarization amplitudes of the Ca II IR
triplet will be very useful to improve our empirical understanding of the
thermal and magnetic structure of the quiet chromosphere.
