The observed center-to-limb variation (CLV) of the scattering polarization in
different lines of the Second Solar Spectrum can be used to constrain the
height variation of various atmospheric parameters, in particular the magnetic
fields via the Hanle effect. Here we attempt to model non-magnetic CLV
observations of the Q/I profiles of the Ca I 4227 A line recorded with the
ZIMPOL-3 at IRSOL. For modeling, we use the polarized radiative transfer with
partial frequency redistribution with a number of realistic 1-D model
atmospheres. We find that all the standard FAL model atmospheres, used by us,
fail to simultaneously fit the observed (I, Q/I) at all the limb distances
(μ). However, an attempt is made to find a single model which can provide a
fit at least to the CLV of the observed Q/I instead of a simultaneous fit to
the (I, Q/I) at all μ. To this end we construct a new 1-D model by
combining two of the standard models after modifying their temperature
structures in the appropriate height ranges. This new combined model closely
reproduces the observed Q/I at all the μ, but fails to reproduce the
observed rest intensity at different μ. Hence we find that no single 1-D
model atmosphere succeeds in providing a good representation of the real Sun.
This failure of 1-D models does not however cause an impediment to the magnetic
field diagnostic potential of the Ca I 4227 A line. To demonstrate this we
deduce the field strength at various μ positions without invoking the use
of radiative transfer.Comment: 20 pages, 10 figures, Accepted for publication in Ap