The overall coronal structure is delineated by X-ray images and model
extrapolations from a photosphere level, but the precise value of the magnetic
field intensity is still required. It becomes clear that the microwave
observations are able to provide a tool for the measurements at coronal
altitudes up to 0.3Ro.
    There is no adequate method in use for the extended solar corona
like Zeeman vector magnetography for the solar photosphere and chromosphere.
The modern term "coronal magnetography" expresses the evaluations
of the strength of the magnetic field at a set of points in the solar corona
using the analysis of radio polarization observations. We prefer the microwave
measurements of the coronal magnetic field from the effect of the circular
polarization sign inversion. The inversion is a result of the magnetic field
line intersection by microwaves at the right
angle of 90°.
    Another way
of deriving the coronal magnetic field in a two-dimensional region
is to achieve a minimal difference between the calculated and the observed microwave
intensities. The spectro-polarimetric measurements of coronal magnetic field using
near-infrared Fe XIII
line are progressing as well.
§ 1. The polarization inversion and the depolarization strip
When the microwaves cross magnetic field lines at the right angle the sign
of circular polarization will change. This happens as long as the coronal
magnetic field is strong enough at the intersection points. The microwaves
within the short wavelength range do not respond on faint magnetic fields.
The longer the
wavelength of microwaves, the stronger they interfere with the transverse
coronal magnetic field. In such a manner the wavelength dependence of the
polarization inversion arises.
The arched structure of the bipolar solar active region gives
rise to an "inversion screen". Let us visualize the screen as an
approximately vertical surface bounded by the neutral line Bl = 0 on the
solar photosphere. A microwave source associated with the leading sunspot of an
active region is covered by the "inversion screen" when it is in the
western solar hemisphere. The polarization inversion in the source starts at
long cm wavelengths and thereafter goes down to the short ones.
    Both time and wavelength reguliarities of the polarization inversion could be
revealed by model simulations. It provides the simulated radio images of a solar active
region and the coronal region (surface) where the magnetic field lines of the active region are
perpendicular to the line of sight, so-called "inversion screen" (see
movie)).
During the polarization inversion within a sunspot-associated
microwave source the depolarization strip occurs. The depolarization
strip is the region of low circular polarization between the two oppositely
polarized parts of the source. (It is clearly seen in the figures of a right
column). The strip within the microwave source corresponds with the strength of
coronal field resulting in a low circular polarization at a given wavelength.
(The position of such a coronal field for the microwaves at 5.2 cm is marked by
red dots on the "inversion screen" in the upper row figures). The detection
of the depolarization strip while it travels across the microwaves source would
result in the inversion screen localization in the solar corona directly from radio
observations.
§ 2. The sensitivity of radio measurements
Most of the radio and optical measurements of the coronal magnetic field
either integrate along the line of sight or are rough estimates. Radio methods based on
the measurement of the circular polarization inversion are consedered to be the only
local measurements for the time being. The inversion results from the transformation
of the polarization state under a transverse propagation of microwaves. The drawback
of these measurements is due to the fact that the distance between the microwave source
and the coronal region where the transformation occurs (inversion screen) is difficult
to be determined and it depends on the coronal structure.
    The 2D coronal magnetogram is the result of the nonlinear conversion
of the radio map of a solar active region taken in the course of the
polarization inversion in the microwave source of the region. The
resolution of the magnetograms is determined by the angular resolution
of the radioheliograph in use. The sensitivity to the coronal magnetic field
is determined by the operational wavelength of radio observations. The accuracy
of the measurements is of the order of the accuracy of the polarizational radio
observations (1 - 10%).
Table. Radiotelescopes which are adequate for the coronal
magnetography
    The following steps of coronal magnetography are common :
- The inversion of the circular polarization is tested for a transverse propagation;
- The position and the shape of the coronal region of radio measurements (coronal
magnetography) are simulated with the help of the extrapolation of
the photospheric magnetic field;
- Finally, the position of the inversion screen in the corona is refined by
comparing the simulated inversion with the observed one.
§ 3. Coronal magnetic field above the sunspots
The inversion can manifest itself in a similar way in a complex,
non-bipolar active region (for example, the solar active region 7260). Both the
radio observations of bipolar active regions and model simulations reveal that
the microwave source associated with the following sunspots tends to invert the
polarization near the east solar limb. The microwave source of the leading
sunspot tends to invert the sign of circular polarization near the west limb.
As a result the coronal magnetic fields are evaluated above corresponding
sunspots (see the plot).
It is worth noting
that each bipolar pair within an active region can be shown as containing an
"inversion screen". Two sunspots or a sunspot-flocculus pair with the
opposite magnetic polarities create the screen in the solar corona. In this
manner the multiple polarization inversions through the microwave wavelength
range arise. The sunspot - associated source in the active region 7154 is
"occulted" by the inversion screens at least twice.
(Strictly speaking, it was fourfold rather than twofold inversion.) The
multiple inversions seem to be a promising way for the coronal magnetography
simultaneously at a number of coronal heights.
The topological properties of the inversion screens are
intriguing. Indeed, all coronal neutral points and neutral current sheets are
to be found on an inversion screen for any direction to the observer; the
magnetic structure in the vicinity of neutral points is inclined to produce
a double polarization inversion. The coronal structure, responsible for the
multiple inversions, could be a hierarchy of coronal arches of different sizes.
§ 4. Coronal magnetogram
The distinctive properties of the technique are a high accuracy
(~ 10%), local values of the measured coronal magnetic field (not
integrated more then ~ 10³ km along the line of sight), and
the absence of dependence on the assumption of the emission mechanism.
    The polarization inversion at microwaves is not rare to supply enough data
for the magnetography: the inversion manifests itself in more than a half
of bipolar active regions. The distribution of the strength of the coronal
magnetic field is of decisive importance in the research of the plasma flow
and radiative processes, the magnetic field involvement in a solar flare, and
the MHD oscillations of magnetic loops.
The solar flare models suggest that the magnetic structural
peculiarities may be of utmost importance to understand the nature of flares. The radio
observations produce evidence that the peculiarities manifest themselves as
nonthermal microwave sources and current sheets. The points of interest are the
region above the photosphere neutral line Bl = 0, the vicinity of a
neutral point, and the magnetic separator. The topological regions mentioned above are to be
placed on the "inversion screen" for any line of sight
and could be revealed by the coronal magnetography. The analyses of the
structural links and the changes in the magnetic skeleton will give the
direction of further research of the physical processes at work behind the
evolution of the magnetic field.
Searching new relations between the position and the intensity
of an explosive event on the Sun and solar plasma conditions, especially in the
vicinity of the key topological regions (peculiarities), may be the objective
of solar coronal magnetography.
The enlarged coronal magnetograms of about 2' x 2' to be obtained for the polarization
inversion in the microwave sources associated with a solar plage (see results of
model simulations in the movie 1 ).
The real SSRT radio observations of the polarization inversion in an active solar
region are presented in the
movie 2.
Solar coronal magnetography references
Reviews and references therein:
- "Magnetic Field Diagnostics in the Low Corona from Microwave
Circular Polarization Inversion", Alissandrakis C.E.,-
NRO Report 479, "Solar Physics with Radio Observations", Proc. of the
Nobeyama Symp., Kiyosato, Japan, Oct.27-30, 1998, ed. by T. Bastian,
N.Gopalswamy, K.Shibasaki, 1999, p.53-58.
- "Physics of the Solar Active Regions from Radio Observations", Gelfreikh G.B.,-
NRO Report 479, "Solar Physics with Radio Observations", Proc. of the
Nobeyama Symp., Kiyosato, Japan, Oct.27-30, 1998, ed. by T. Bastian,
N.Gopalswamy, K.Shibasaki, 1999, p.41-51.
Descriptions of the techniques:
- "Coronal magnetography of an active region from
microwave polarization inversion", Ryabov B.I., Pilyeva N.A., Alissandrakis C.E.,
Shibasaki K., Bogod V.M.,
Garaimov V.I., and Gelfreikh G.B.,- Solar Physics, 1999, v.185, N1, p.157-175.
- "Coronal magnetography of a solar active region using coordinate SERTS and VLA observations",
Brosius J. W., Davila J. M., Thomas R. J., and White S. M.,- Ap. J., 1997, v.488, p.488.
Last update February 1, 2002