Solar Physics with Radio Observations, Proceedings of Nobeyama Symposium 1998, NRO Report 479

17 GHz Mode Coupling in the Solar Corona
Alejandro Lara,1 N. Gopalswamy,2 R. Pérez-Enrı́quez,1 and K. Shibasaki3
1Instituto de Geofı́sica UNAM, C. U. México D. F. 04510, México
The Catholic University of America, Washington DC 20064, USA3Nobeyama Radio Observatory, Nobeyama, Minamisaku, Nagano 384-1305, Japan
E-mail(AL): alara@tonatiuh.igeofcu.unam.mx
2Abstract
We studied the development of microwave polarization of a group of active regions for a period of
10 days during April, 1993 using data obtained by the Nobeyama radioheliograph. The observed sense ofpolarization at 17 GHz changed with the active region position on the solar disk. This change of polarization
can be explained by the mode coupling theory according to which a weak coupling between the ordinary andextraordinary electromagnetic modes takes place when the radiation crosses a region of transverse magnetic
ﬁeld and results in a polarization reversal. Since the strength of the mode coupling depends on the physicalparameters (and their gradients) of the quasi-transverse region, observations of polarization changes canbe used to obtain key values of the magnetic ﬁeld and ﬁeld gradient in the active region corona. Using theintensity and polarization images of active regions, we found that the coupling constant is typically > 103
corresponding to a weak coupling regime. We determined the mean value of the transition frequency to be∼ 5.3 × 1011 Hz, below which the weak coupling eﬀect is important. For all the active regions studied inthis paper, there seems to be a similarity in the position on the solar disk where the mode coupling eﬀects
become important. The polarization reversal always occurred when the active regions were farther than
the 500 arc sec mark from the disk center. Using this fact and extrapolated photospheric magnetic ﬁeld weare able to estimate heights of both the quasi-transverse layer and the source region. Assuming a value of∼ 70 G, we obtain a value of 2.2 × 104 km for the Q-T layer height.
Key words: Sun: active region, Sun: radio radiation

1.

Introduction

Active regions are produced by strong magnetic ﬁelds arising from the sub-photospheric layers into the corona.
The plasma trapped in such magnetic ﬁelds, called coronal arches, emits polarized radiation either by thermal
bremsstrahlung and/or by gyroresonance processes (low and high polarization level, respectively). When the emitted
radiation crosses a perpendicular magnetic ﬁeld layer it is possible, depending on the characteristics of the layer,
to have mode coupling, i.e., the ordinary and extraordinary modes going out of the quasi-transverse region canbe diﬀerent from the modes entering the layer. One typical manifestation of the mode coupling phenomena is thereversal of polarization when the modes cross the quasi-transverse layer.
The reversal of polarization has been known for many years, both during microwave bursts (Kakinuma 1958;
Tanaka and Kakinuma, 1959) and when active regions crossed the solar disk (Kundu and Alissandrakis, 1984).
Nevertheless, a detailed study of mode coupling using high resolution and long time observations is still lacking.
A clear understanding of the mode coupling process is essential for a proper interpretation of radio emission at allwavelengths (Gopalswamy et al. 1994).
In a recent work (Lara et al. 1998b) we studied the polarization evolution of a group of active regions observed
during 10 days of April 1993. We found polarization reversals when the ARs cross the solar disk, namely, when an
AR is near the solar limb their emited polarization is mostly unipolar with the polarization of the diskward sideof the AR. When the AR is near the center of the disk, inside the 30 deg of heliographic longitude, the observed
polarization is fully bipolar. In our period of study six regions presented similar polarization changes.
This behavior of the sense of polarization suggests that microwave emission originating on the limb side of theactive region encounters a transverse magnetic ﬁeld. The mode coupling theory predicts that the emission crossing
such a quasi-transverse magnetic ﬁeld layer reverses its sense of polarization if the coupling is weak.

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The fact that the change of polarization occurs at almost the same heliographic longitude (∼ ±30 deg) for all
regions can be understood if the height of the quasi-transverse layer is similar in all the active regions studied. In
other words, the geometrical structure (at least the altitude) of the active regions is similar.
In this work, we use the observed mode coupling and extrapolated (photospheric) magnetic ﬁeld to estimate theheight of both the 17 GHz emitting arches and the quasi-transverse layer in active regions.
2.

Data

The microwave data used in this work were obtained by the Nobeyama Radio Heliograph (NoRH) in Japan, asolar dedicated radio interferometer operating at 17 GHz (1.76 cm) with a bandwidth of 33.6 MHz. The NoRHimages the Sun in both right (R) and left (L) circular polarizations and has a ﬁeld of view of 40’ with a spatial
resolution of ∼ 10 arc sec (Nakajima et al., 1994).
For the 1993 April 17 - 28 period, nine R and L maps per day were used to obtain the daily total intensity
R−L(I = R+L2 ) and circular polarization (V =2 ) maps. From these I and V maps, we determine the characteristicsof the mode coupling process.
We complete our data set with soft X-ray solar images from the Yohkoh Soft X-ray Telescope and magnetogramsfrom the Solar Vacuum Tower Telescope at Kitt Peak.
3.

Mode Coupling

According to the mode coupling theory (Cohen 1960; Zheleznyakov 1996) the conditions of the quasi-transverse
region in the path of the radio emission are described by the coupling parameter:G⊥ =3πωp2 ωB(1)

8cω| dαdl |where ωp is the plasma frequency, ωB is the electron gyro-frequency, ω is the observing frequency, α is the angle
between the magnetic ﬁeld and the direction of propagation, c is the speed of light and l is the coordinate along theray path.
When G⊥  1 the coupling is weak, the ordinary and extraordinary modes are conserved during passage throughthe quasi-transverse layer. However, since the direction of the magnetic ﬁeld changes, the sense of polarization of
the two modes is reversed. On the other hand, when G⊥  1 the coupling is strong and the modes are interchanged,with no change in sense of polarization.
The critical frequency at which the coupling constant changes from weak to strong (G⊥ = 1) is given by:ωt =π 2 e5 N B 3
2m4 c4 | dα|dl1/4(2)Where N and B are the electron density and the magnetic ﬁeld in the quasi-transverse region, e and m are thecharge and mass of the electron.
Then, for a given region (N and B known) we know at which frequencies the mode coupling is weak (ω  ωt ) orstrong (ω  ωt ). Using the mode coupling theory, it is thus possible to identify the transition frequency and hence
obtain the limiting values for the density and magnetic ﬁeld in the quasi-transverse layer.
In order to calculate the coupling constant and the transition frequency (Lara et al. 1998b), we use the computed
magnetic ﬁeld necessary to produce the observed degree of polarization at both maximum I (BI ) and V (BV ) andthe density computed using Yohkoh/SXT images (assuming thermal free-free emission, Lara et al. 1998a). Also, we
assume that the gradient of the angle between the magnetic ﬁeld and the ray path is approximately equal to theinverse of half of the active region size. We can estimate an upper limit to the magnetic ﬁeld scale length as thedistance that an active region crosses between the two positions that cause polarization inversion which is 1.3 × 1010
cm.
Then, using equation (1) we obtained a mean value of 1.3 × 106 for G⊥ (BV ) and 1.0 × 105 for G⊥(BI ). In either
case, G⊥  1 and the mode coupling must be weak. Also, we get mean values of ωt (BV ) ∼ 5.3 × 1011 Hz andωt (BI ) ∼ 2.0 × 1011 Hz. Comparing these values with the observing frequency (ω ∼ 1.1 × 1010 Hz) we can establishthat the mode coupling should be weak.

17 GHz Mode Coupling in the Solar Corona
4.

85

Q-T layer structure

In order to obtain a three dimensional view of the active region, we use the Sakurai (1982) code to extrapolate thephotospheric magnetic ﬁeld of AR7477 when it was near the center of the disk on 1993 April 22. Figure 1. shows aview perpendicular to the line of sight of the magnetic ﬁeld lines. The color code of magnetic lines is as follows:

Fig. 1.. In gray scale are the photospheric magnetic (bottom) field and 17 GHz total flux (top) of AR7477 on April 22, 1993. Extrapolatedmagnetic lines are over-plotted (see text for the color code)• purple: 17 GHz emitting loops. Using the observed degree of polarization we computed the source magneticﬁeld; the purple lines represent magnetic ﬁeld intensity from 250 to 850 G.
• red: mode coupling layer for a speciﬁc value of magnetic ﬁelds. Assuming a magnetic ﬁeld between 60 and 80
G, and an angle greater than 40 degrees between the magnetic lines and the vertical direction, we determined
the quasi-transverse layer on the extrapolated lines.
• blue: magnetic lines that can produce quasi-transverse layers. Lines with an angle greater than 40 degrees with

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the vertical are perpendicular to the ray path when the active region is outside of the 30 deg of heliographic
longitude range. These lines could cause an inversion of polarization, even though the magnetic ﬁeld strength
is low.

• black. The black dashed lines represent the “light cone” where mode coupling is not observed. This constrains
the height of the Q-T layer.
In gray scale are the photospheric magnetic ﬁeld (bottom) and the observed total ﬂux at 17 GHz (top). Figure 2.
is a view parallel to the line of sight of the system. It is interesting to note the correspondence between the mostprobable emitting loops (purple) and the 17 GHz source. This correspondence shows that the method to deduce themagnetic ﬁeld from the observed degree of polarization is a good approximation.

Fig. 2.. Top view of fig. 1.. Scales are in arc sec and solar north is to the top.

From the extrapolated magnetic ﬁeld lines, we can compute the height of the mode coupling layer and the emitting
loops. In Fig. 3. (left) we present a histogram plot of the height of the quasi-transverse layer. There is a well deﬁned
peak around 2.2 × 104 km. The height of the emitting loops is very low, ∼ 900 km, although the distribution
correspond well to the transition zone - low corona height levels, up to ∼ 6 × 103 km (Fig. 3. right).
5.

Conclusions

In this work we analyzed the change of observed circular polarization of microwave emission from several active
regions when they crossed the solar disk. Our main results are:Using the computed magnetic ﬁeld necessary to produce the observed degree of polarization, the density obtained
from SXT/YOHKOH images and half of the size of each active region as the magnetic ﬁeld scale length, we foundthat the coupling constant is typically > 103 .
In the same way, we found that the transition frequency is ∼ 3 × 1011 Hz. The observing (angular) frequency ofω ∼ 1.1 × 1010 is smaller than the transition frequency and hence weak mode coupling operates.

17 GHz Mode Coupling in the Solar Corona87Fig. 3.. Computed heights for both the Q-T layer (left) and 17 GHz source region.

Most active regions have similar behavior of polarization reversal. The reversal typically occurs when the region
reaches ±500 arc sec mark from the central meridian (approximately 30 deg of heliographic longitude).
This result means that most of the active regions during our study period seem to have similar geometricalstructures, principally the altitude.
Extrapolating photospheric magnetic ﬁeld we found:• For a magnetic ﬁeld of ∼ 70 G, the height of the quasi-transverse layer is between ∼ 1 and 3 × 104 km. The
peak of the distribution is near 2 × 104 km.
• The height of the radio emitting magnetic loops is in the 0.9 to 6 × 103 km range and the peak seems to be low∼ 900 km.
In this preliminary work, we also show that the observed polarization of the AR microwave radiation can be used
to deduce the magnetic and geometric structure of the low-coronal emitting loops.
This work was supported in part by CONACyT project No.25744-T. Part of this work was done when AL visited
the Catholic University of America in 1998. NG was supported by NASA grant NAG-5-6139. The Nobeyama
radioheliograph was supported by the Ministry of Education, Science, Sports and Culture of Japan.
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