As an application of the results derived in the previous sections, we
have calculated typical Stokes profiles of H
(
), and of the transitions 7-6
(
) and 12-8 (
) under
various conditions.
While H
has ever been of acknowledged importance in any studies of
solar and stellar atmospheres, infrared hydrogen lines, such as the 7-6
and the 12-8 transitions, have only recently been paid the due
attention as particularly suitable lines for electric fields measurement
in solar plasmas (e.g., Foukal et al. 1986; Moran & Foukal
1991; Foukal & Behr 1995; Casini 1996, CF96). In
addition, the 7-6 and the 12-8 transitions happen to be among the strongest lines
in the infrared spectrum of hydrogen between 8 and 
observed in
solar prominences (Zirker 1985; Foukal 1995), so our
choice is well justified.
In Fig. 1 (click here) we illustrate the slab geometry and the directions of the electric and magnetic fields with respect to the observer.
In Figs. 2 (click here), 3 (click here), and 4 (click here), we present our calculation of
the Stokes profiles of H
in the presence of 
and
(refer to the figure for illustration of the field
geometry), for five different values of the optical depth ranging from 
to 
, and for the three different forms of the source function
considered in this paper (also refer to the figures for illustration of the
source function parameters).
Figure 1: Geometry of the slab and of the electric and magnetic fields
with respect to the line-of-sight, 
.
The azimuth angles 
and
are measured from the reference direction
for positive Q
Figure 2: Calculated polarization profiles of the optically thick
H
in the presence of electric and magnetic fields and
thermal-Doppler broadening. A constant source function is assumed
Figure 3: Same as Fig. 2, but with a parabolic source function
Figure 4: Same as Fig. 2, but with a Gaussian source function
Figure 5: Calculated polarization profiles of the transition 7-6
in the presence of electric and magnetic fields and thermal-Doppler
broadening. A Gaussian source function is assumed
Figure 6: Calculated polarization profiles of the transition 12-8
in the presence of electric and magnetic fields and thermal-Doppler
broadening. A Gaussian source function is assumed
Figure 7: Calculated polarization profiles of the optically thick
H
in the presence of strong electric and magnetic fields and
thermal-Doppler broadening. A Gaussian source function is assumed
Figures 5 (click here) and 6 (click here) analogously show the calculated Stokes
profiles of the transitions 7-6 and 12-8 in the presence of 
and
, when the two fields are parallel to each other
and both perpendicular to the line-of-sight. The same range of optical
depths is considered. However, only the resultant profiles for the
Gaussian form of the source function are shown in this paper, since
the shapes of the profiles for the other two forms of the source
function do not differ noticeably from those given in Figs. 5 (click here) and
6 (click here).
The field intensities considered in the above calculations should be
in the range of the expected intensities of magnetic and electric fields
in prominences and post-flare loops, as suggested by present MHD models
of such coronal structures (e.g., Foukal & Hinata 1991; Foukal
& Behr 1995). However, the amount of linear polarization that we have
obtained for H
under such physical conditions (cf. Figs. 2 (click here),
3 (click here), and 4 (click here)) is much less than the one actually observed in
quiescent solar prominences, where it can attain 1% of the intensity level for
the integrated profiles (e.g., Leroy 1981). Our calculations then
show that the Zeeman effect in the presence of solar prominence magnetic fields
cannot actually be responsible for the observed linear polarization in
H
, which is rather due to the strong anisotropy of the incident
radiation field from the underlying photosphere. On the contrary, even
neglecting atomic polarization, a relevant linear polarization signature
due to the linear Stark effect is expected in infrared hydrogen lines
such as 7-6 and 12-8, for electric-field intensities as small as
(cf. Figs. 5 (click here) and 6 (click here)).
We also considered the calculation of the Stokes profiles of
H
in the presence of very strong fields (not attainable in the
solar atmosphere). Figure 7 (click here) shows such profiles calculated in the case
of a Gaussian source function, and for a wide range of optical depths.
This last figure illustrates very well the kind of frequency modulations of the polarized line profiles which can be expected because of the transport of radiation through an optically-thick medium embedded with electric and magnetic fields. Even more it stresses the urgent need for realistic radiative-transfer calculations of the Stokes profiles of (hydrogen) lines forming in the presence of external fields (possibly including non-LTE effects as well), in order to improve the present state of the diagnostics of simultaneous electric and magnetic fields in astrophysical plasmas.
This would likely increase our understanding of many processes (e.g., impact polarization from accelerated particles, current dissipation in neutral sheets, heating of corona, triggering of flares), occurring in solar magnetized plasmas, which are still lacking a definitive explanation, and in which electric fields should also play a primary role.