A&A 426, 329-331 (2004)
DOI: 10.1051/0004-6361:20047120
Research Note
K. R. Subramanian
Indian Institute of Astrophysics, Bangalore, 560 034, India
Received 22 January 2004 / Accepted 17 June 2004
Abstract
We present observations of the quiet Sun made at 34.5 MHz during the
solar minimum period June-July 1986 and May-June 1987 with the
Gauribidanur radio telescope and a grating array.
The brightness temperature of the quiet Sun varied from 1.0
105 K
to 4.5
105 K and the East-West diameter from 39 to 66 arcmin
during the above periods. Only a weak inverse correlation is found to exist
between the brightness temperature and the diameter of the quiet Sun
and it does not strongly support the scattering hypothesis used to
explain the low brightness temperature of the quiet Sun at decametric
wavelengths.
Key words: Sun: radio radiation - Sun: corona - radiation mechanisms: thermal - scattering
The continuum radio emission from the quiet Sun has been studied by
several groups. Aubier et al. (1971) observed the quiet Sun using the
Arecibo radio telescope and the brightness temperatures obtained by them
were 6
105 K, 5
105 K, and 3.8
105 K at 60, 36.9 and 29.6 MHz respectively. From the one-dimensional
scans of the Sun made using the Clark Lake radio telescope, Erickson
et al. (1977) obtained brightness temperatures of 2.3
105 K and
2.1
105 K respectively at 25.8 MHz and 30.9 MHz. Wang et al.
(1987) measured the brightness temperature of the quiet Sun
at 30.9 MHz as 1.5-2.0
105 K. Sastry et al. (1981, 1983)
reported that the brightness temperature of the quiet Sun at 34.5 MHz is
2
105 K. Thejappa & Kundu (1992) reported a brightness
temperature as low as 60 000 K from low frequency observations made
during the solar minimum years 1986-1987. All these observations
show that at frequencies
70 MHz the observed brightness
temperature is much less than 106 K, the coronal temperature.
The low brightness temperature of the quiet Sun is attributed by
Aubier et al. (1971), Riddle (1974), Thejappa & Kundu (1992) to the
the scattering of the radio waves by the coronal density inhomogenities.
The diameter of the quiet Sun at low frequencies was measured by Gergely
et al. (1985). The observed diameter of the radio Sun will be large
when scattering effects are introduced according to Aubier et al. (1971),
Thejappa & Kundu (1992). No study has been made of the relation between the
brightness temperature and the diameter of the quiet Sun at frequencies
below 38 MHz. We present here obervations of the integrated flux density,
brightness temperature and the East-West diameter of the quiet Sun at
34.5 MHz made during the minimum of the last solar cycle and discuss the
relation between them.
The observations presented here were made with a compound
grating interferometer with an East-West fan beam of 3 arcmin at 34.5 MHz.
It is the highest spatial resolution ever used to observe the quiet Sun at
this frequency. The array system consists of four grating units placed
at intervals of 1.4 km on an East-West baseline starting from the Western
end of the East-West array of the Gauribidanur radio telescope
(Sastry 1995). Each grating unit consists of 8 Yagi antennas combined
in a branched feeder system. The output of each of the grating units
was correlated with the output from the East-West array.
Observations of
the Sun were made during June-July 1986 and May-June 1987.
The spatial resolution for the first grating interferometer is 18 min of arc.
The data were integrated for 1 s for these observations. The minimum
detectable flux density is 20 Jy. Observations of the Sun were
made during the local meridian transit for about
15 min.
We have not observed any interferometer fringes due to the quiet Sun
beyond the first baseline, although fringes due to radio bursts
had been seen up to a baseline of 4.9 km. The quadrature outputs were
squared and added after phase calibration to obtain one-dimensional scans
of the Sun. Figure 1 shows a typical example of a such a scan for the first
grating interferometer.
![]() |
Figure 1: One dimensional scan of the quiet Sun obtained on June 6th, 1986 at 34.5 MHz. |
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One-dimensional scans of the Sun were calibrated using the radio
sources 3C 123, 3C 134 and 3C 144. Quiet Sun data with scintillation
free calibrators were available for 18 days. The Sun was very quiet
and no bursts were recorded in our data during the period of observations.
The assumed flux densities of the calibrators 3C 123, 3C 134 and 3C 144 are
616, 208 and 2527 Jy respectively. The integrated flux density of the
quiet Sun varied from 600 Jy to 3000 Jy. The error in the estimation of
the integrated flux density is 10
.
Gaussian fits were made
to the solar scans to determine their half widths. The diameter of the
radio Sun was computed using the relation
=
(Aubier et al. 1971), where
is the half power size of the source,
is the observed
half width of the scan and
is the half power beam width of the
first grating interferometer. The half width of the East-West brightness
distribution varied from 39 to 66 arcmin and agrees with the values
of the East-West diameter of the quiet Sun at these wavelengths
reported by Gergely et al. (1974), Thejappa & Kundu (1994).
The brightness temperatures were derived using the relation
/
(Aubier et al.
1971) where S is the integrated flux density of the quiet Sun in Janksy,
is the wavelength of observation in meters,
and
are the East-West and North-South diameter of the quiet Sun
in arcminutes. To determine the North-South diameter of the quiet Sun
an ellipticity of 0.82 is used as shown in the observations of Thejappa
& Kundu (1992) at 38.5 MHz. The calculated brightness temperature of
the quiet Sun at 34.5 MHz varied from 1
105 K to 4. 5
105 K. Figure 2 shows the scatter plot of the East-West diameter of the quiet Sun against the brightness temperature, and the least square fit. The inverse linear correlation coefficient is -0.34.
![]() |
Figure 2: Scatter plot of East-West diameter vs brightness temperature of the quiet Sun at 34.5 MHz. |
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At decameter wavelengths the radio emisssion of the Sun originates
in the outer corona. The observed brightness temperature
is related
to the kinetic temperature
by the relation
=
where
is the optical depth. The integrated optical depth along
any direction can be computed using Ray-Tracing methods (Smerd 1950;
Bracewell & Preston 1956).The Sun was quiet with no active regions
during the period of the observations, which indicates that the variation
of
is due to the entire Sun. We have computed the integrated optical
depths and turning points at 34.5 MHz for different density enhancement factors
(.01 to 1.0) for a 106 K spherically symmetric corona and
Newkirk's density model (Newkirk 1961) with different density gradients
. The density model in this case is given by
=
4.2
104
,
where
is measured in solar
radii. A corona without any magnetic field is also assumed. Figure 3
shows the variation of the optical depth for different density enhancement factors
and density gradients. We find that the optical depth is a slowly varying
function of
.
The computed optical depth in the direction of the
center of the Sun is
1.5 for
of 1.0 for the
4.32.
The brightness temperature for this optical depth should be of the order of
0.8 to
K. For the brightness temperature to be
0.1
106 K, the optical depth should decrease to
0.1.
To get such an optical depth, the density has to be decreased by a factor
of more than 100. But in this case the turning point is
for
= 4.32 as can be seen from Fig. 4. This turning point
is much smaller than the observed diameter of the radio Sun at 34.5 MHz.
![]() |
Figure 3: Variation of optical depth at 34.5 MHz with density enhancement factor. The solid curve is for density gradient 3.32, the dotted one for 4.32 and the dashed one for 5.32. |
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![]() |
Figure 4: Variation of turning point in solar radii at 34.5 MHz with the density enhancement factor. The solid curve is for density gradient 3.32 and the dotted one for 4.32 and the dashed one for 5.32. |
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It was first pointed out by Aubier et al. (1971) that the low brightness temperature of the quiet Sun at decameter wavelengths cannot be explained by generally accepted density models. They introduced the effect of scattering on the radio emission of the quiet by coronal density inhomogenities. The effect of scattering is to raise the height of reflection of the rays above the plasma level leading to a larger diameter of the radio Sun. Since most of the contribution to the optical depth comes from the region close to the plasma level, the optical depth is reduced leading to a lower brightness temperature. Therefore one expects a strong inverse correlation between the brightness temperature and the diameter of the quiet Sun at decameter wavelengths if scattering plays an important role.
The weak inverse correlation between the brightness temperature
and the diameter of the quiet Sun at 34.5 MHz observed by us does not strongly
support the scattering hypothesis. The effect of scattering is given
by the scattering parameter
/h where h is the
scale height of inhomogenities and
is the
rms relative density fluctuation (
/
). Subramanian &
Sastry (1988) noted that the scattering with
= 0.2
and h = 5
(where
is the solar radius)
cannot reduce the brightness temperature below 200 000 K. According to
McMullin & Helfer (1977), increasing
from 2 (
/
= 0.01) to 12 (
/
0.024) will increase the diameter of the
Sun by about 75%. The density fluctuation of 0.1 used by Thejappa & Kundu
(1992) then will lead to a large diameter of the Sun. Rms density fluctuation
values
0.4 lead to nearly the same brightness temperature at different
frequencies (Fig. 7a in Thejappa & Kundu 1992). The observed size and
directivity of Type I radio bursts do not support scattering effects according to Mclean & Melrose (1985). How ever, if the radiation comes from only a small
fraction of the area of the apparent source described by a filling factor f,
then the actual brightness temperaure is larger
by 1/f. Our observations imply a filling factor of 0.1 to 0.5. This small
filling factor implies that the source should be uniform and of low
brightness or consist of speckles. High resolution observations of the quiet
Sun at 75 MHz with VLA or at 50 MHz with GMRT will be able to detect the
existence of such substructures. Multi frequency observations of the quiet
Sun in the band 40-150 MHz with the Gauribidanur radio heliograph
(Ramesh et al. 1998) will enable us to study the relation between the
brightness temperature and the size of the quiet Sun at several
low frequencies to understand the effect of scattering of the radio emission of the
quiet Sun at decametric wavelengths.
Acknowledgements
I would like to thank Dr. Ch. V. Sastry for many useful discussions. I also like to thank N. NanjeGowda, G. N. Rajasekara, A. T. Abdul Hameed and H. Aswathappa for maintaining the antenna, receiver system and collection of data.