Observations of the Sun


Joachim Köppen Strasbourg 2010


Observations of the Sun are quite important, not only because of the Sun, but also to measure important parameters of the telescope itself. At the frequency of 11 GHz the Sun emits a continuum radiation produced by the hot gas which makes up the Sun. However, at radio frequencies the emission does not come from the photosphere that we observe in the visible wavelength range, but from the hotter layers above the photosphere: at 11 GHz we look at the bottom of the Transition Layer between the Chromosphere and the Corona where the temperature starts to rise.

The other aspect is about the telescope: Since the empty sky provides radio wave emission only at negligible intensity, the signal that we measure is essentially the background noise from our receiver. Comparing the solar signal with that of the sky we obtain a measure of the sensitivity of our instrument: The larger the ratio of the solar and sky signals is, more sensitive is the system. We express this more quantitatively as the System Temperature.

The third aspect is also technical: We can determine the width of the antenna pattern, i.e. the Half-Power Beam Width (HPBW) which describes also the angular resolution possible with the antenna. This is done by letting the Sun - which we use as a source with a constant signal - pass through the antenna beam, and measure the time it takes. With the knowledge of the Earth rotation's angular velocity we convert the time interval into an angle, the HPBW.

Observational procedure

Important note: Because the positioning system of this telescope has only a limited accuracy and stability, good observations require the your presence during the observing run, because you have to manually optimize the pointing of the antenna to your source.

After starting up the system, described here, we recommend to follow this sequence:


Analysis

Let's suppose that we use Microsoft Excel to do the interpretation of the data. Then we recommend to follow this sequence:

To complete the analysis, we need to determine the HPBW of our antenna. If you have been able to obtain a full drift scan, you could simply take the last plot and look up the times when the relative power was one half of the maximum value. If you did a half dift scan, and you are sure that you started exactly at the maximum signal, you could also look up the time that passed between the maximum and one half of the maximum value, then double this time. But the neatest way is to match a simple model to your curve:


More about our results

Below we show one of our first drift scans with proper flux calibration. As described above, and in the Data Reduction, the raw data is corrected for the background and calibrated. The calibration measurement on the Holiday Inn hotel provides a temperature of about 300 K, hence the antenna temperature is 210 K.

To interpret our data, we need to understand how the measurements are related to the physical quantities (see Fundamental Concepts for the explanation of the technical terms):

What happens during calibration? Because the calibrator emits thermal radiation, the true temperature of the source is equal to the brightness temperature

T_B_cal = T_cal
So the intensity is
I = 2 k T_cal /l
Since the calibrator fills the entire beam of the antenna, the solid angle is
W = W_ant = l/A
which gives a flux
F = I * W = 2 k T_cal / A
and a received power
P = F * A / 2 = k T_cal
Hence the antenna temperature is:
T_ant_cal = T_B_cal = T_cal

Now let us consider what happens during the observation of the Sun: Again, the approximation of solar radiation by thermal emission of a certain temperature T_sun implies its equqlity with the brightness temperature

T_B_sun = T_sun
So the intensity is
I_sun = 2 k T_sun /l
But since the Sun's diameter of 0.5 deg is smaller than the antenna's HPBW of 3 deg (for the present state of our dish), the solid angle is that of the source
W = W_sun
which gives a received power
P = I_sun * W_sun * A / 2 = k T_sun * W_sun / W_ant
since we made use of W = W_ant = l/A. Hence the antenna temperature is:
T_ant_sun = T_sun * W_sun / W_ant

This determines our procedure:

From the full drift scan shown on the right hand side of the above overview plot, we reduced the data which included taking into account the time changes of background and calibration levels, and we obtained the reduced data shown below:

The HPBW is determined as 3.75, the solar antenna temperature of 210 K, and with a ratio of the solid angles of 56.3 the solar temperature is 11800 K. This is the temperature of the bottom of the corona, where the plasma is sufficiently transparent to let the 11 GHz radio waves escape. The value is in excellent agreement with literature data.


In the course of time, we became certain that our instrument did not perform as closely to the prototype as one could have expected. It turned out that the arm carrying the LNB had been bent upwards, as the telescope once got thrown over by strong wind gusts, and hence the dish was out of focus. Once the LNB arm had been straightened, the instrument performance came close to that of the prototype. For instance, the Sun has now a maximum signal of about 8 dB over the background level and the antenna beam is as narrow as expected. A full drift scan of the Sun is shown here, along with the flux calibrations:

The HPBW now is only 1.5, the solar antenna temperature 1035 K, and with a ratio of the solid angles of 9.3 the solar temperature is 9650 K. However, further observations did give higher temperatures, but also different values for the HPBW. Also, it is interesting to notice a small asymmetry of the antenna pattern ...


During our next observational campaign in 2008, Aikaterini Panopoulou conducted a careful study, measuring the peak solar signal many times, and under various weather conditions:

dayweathertemperature
14 Jan 08sunny, partly cloudy10261
30 Jan 08cloudy10897
1 Feb 08very cloudy+windy10516
2 feb 08sunny, partly cloudy11607
4 feb 08cloudy10501
19 feb 08sunny10820
29 Feb 08very cloudy+windy10692
On the whole, she does not find any relation of the deduced solar temperatures with the local weather condition - although she never had the chance to observe the sun when it was raining or snowing! So we can say that we can measure the solar temperature reliably and at practically all times.


To capture the real peak may not be so easy: As explained above, we first search manually for the position with the highest signal. Because of the fluctuations of the signal, this requires some patience. Also, if we move the antenna a bit in one direction, then back in the other direction, this does not mean that we have returned exactly to the first position ... In the above figure we tried to capture the solar passage many times, after each passage searching again for the maximum signal and then going a bit to the right (and a bit downwards) to capture the sun again. As can be seen, while the absolute maximum is indeed just below +48.0 dBV, several observations missed the sun by as much as 0.5 dB! An error of that size results in an error of 1600 K or about 15 percent in temperature!


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last update: May 2013 J.Köppen