Astronomy 302

Single-Dish Radio Observations of the Sun

Spring 2000

Introduction: Up to this point in this course, you have learned about basic concepts of radio astronomy in a laboratory setting. This week, we will put all of our new-found knowledge towards an observational challenge: characterization of a one-meter radio telescope, and measurement of the 4 GHz radio temperature of the Sun. In particular, we will cement the following concepts that you are already familiar with:

• Gaussian beam patterns: we will measure the ``field of view'', or beam width of the telescope.

• Source-beam coupling: When the object's angular displacement is smaller than the telescope beam width on the sky, the brightness of the object is ``diluted'' because the telescope beam is looking at blank sky in addition to the object.

• Sensitivity measurements: We will obtain an estimate of T$_{\rm RMS}$ from our observations. We can use these measurements to determine the sensitivity of our telescope.

• Concept of antenna ``brightness'' temperature: We will measure the radio brightness temperature of the Sun.

Experimental Apparatus:

Figure 1: The experimental setup, consisting of the 0.83 meter antenna, 4 GHz C-band feed horn and low-noise amplifier, total power box, integrator, and voltmeter.

1.

0.83-meter radio dish: Off-axis parabolic dish normally used by NRAO for site testing of future millimeter and submillimeter telescopes and interferometers.

2.

Feed horn, amplifier: ``C-band'' feed horn, commonly used for TV satellite dishes. The ``C-band'' is almost 1 GHz wide, centered approximately at a frequency of 4 GHz.

3.

Total Power Box: The output of the amplifier is transmitted via coaxial cable to a device which integrates the intensity of radio-wave radiation over the entire bandpass receivable by the feedhorn/amplifier system. The result is a single number that represents the relative total collected power.

4.

Integrator/Voltmeter: A low-pass RC filter (also known as an integrator) eliminates high-frequency noise; the circuit is essentially a frequency-sensitive voltage divider. At high frequencies the output behaves as if it is shorted to ground, while at low frequencies the output appears as an open circuit. The effective integration time of this circuit is $\tau = R C$ and the cutoff frequency where half of the power is removed is given by $f_c = 1/2\pi R C$. The time constant of the integrator/filter we will use is approximately one second.

Figure 2: Circuit diagram and sketchy frequency response of a low-pass filter.

Procedure:

This lab will be performed using the $\sim$ 0.83-meter radio telescope located on the roof adjacent to the 4'' James refractor. Follow the steps outlined below and write-up the lab using the same guidelines used in earlier lab reports. Show ALL work, analyze ALL data and discuss the other group's data thoroughly, as if it were your own.

1.

Owing to its proximity, the Sun is a bright radio source at most radio wavelengths. A reliable gauge of solar activity is the brightness, or flux of the Sun at a wavelength of 10.7 cm, or 2.8 GHz. A number of solar radio observatories report the daily average solar flux at this frequency. You can listen to WWV to get this information. WWV is a short-wave station, transmitting at 2.5, 5, 10, 15 and 20 MHz, that provides accurate time, solar flux, marine weather advisories, and GPS (Global Positioning System) status reports. You can learn more about WWV at http://www.boulder.nist.gov/timefreq/wwv/wwv.html

You can also get the average daily values by accessing the Web page at:

http://www.drao.nrc.ca/icarus/www/current_flux.shtml
http://www.drao.nrc.ca/icarus/www/archive.html

We will use this solar flux estimate to determine our telescope's temperature scale:

$$T_{\odot} = {S_\circ G\lambda^2\over 3.468}$$

where, $S_\circ=$ the solar flux in units of 10^-22 watts/m²Hz (SFU)

G = gain of telescope $= 4\pi/\Omega_A$, where $\Omega_A =$ beam solid angle

$\lambda =$ wavelength of observation

Derive the above expression using the Rayleigh-Jeans approximation ( $T= {{B\lambda^2}\over{2\,k}}$, where $B = S_\circ/\Omega_A$).

2.

First, point the telescope at the Sun until you see a peak in the output of the voltmeter and total power box. Note the location of the feed horn shadow on the dish; mark it at the ``peak'' if it has not been done for you. With the Sun ``peaked'' in the Gaussian beam ``field-of-view'', average about a minute of voltmeter readings. This is your ``on-source'' signal.

3.

Next, point the telescope well away from the Sun - to blank sky. Average about a minute of voltmeter readings. This is your mean ``off-source'' signal. Keep the individual readings; you will use them to estimate T$_{\rm SYS}$ later!

4.

Carefully move the telescope ``ahead'' (i.e. west) of the Sun's current position. Let the Sun drift through the beam, taking measurements at fixed intervals (e.g. every minute). Knowing how fast the Sun ``moves'' through the sky ( $4 / cos(\delta)$ minutes per degree moved, where $\delta$ is the declination of the Sun in the sky), estimate the size of the telescope's beam $\theta_{\rm beam}$ from your data. Now calculate the expected beam width of the antenna, at 4 GHz. How does the calculated value compare to the measured one? Why might they be different?

5.

Measure the gain of the antenna. Recall that the gain is defined as the fraction of sky that the antenna sees at once: $G = 4\pi/\Omega_A$. $\Omega_A$ is the beam solid angle, or approximately the number of ``square'' radians covered by the antenna beam. Assume that the beam has the projection of a circle on the sky and calculate $\Omega_A$, and therefore G. Compare the gain of this antenna with the gain of a length of wire, which has a gain of about 2 (an isotropic radiating antenna has a gain of identically 1).

6.

Before we go on to the next step, let's stop and understand this radio temperature of the Sun. To do so, we need to take account of one further fact. The area of the sky that our radio telescope gathers flux from is significantly larger than the Sun. This means that the temperature (intensity) we measure is that of the Sun, but smeared out over the area of the sky the radio telescope measures. The correction is just the relative areas of the Sun on the sky and the radio telescope's beam on the sky. Because the Sun's actual size is much smaller than the antenna beam-size, we are ``diluting'' the Sun's brightness temperature; in fact, this is called beam dilution:

Figure 3: An object with smaller source size than the beam will suffer from beam dilution - the measured beam temperature in this case will be 200K, not 1000K as naively anticipated.

To correct for the effects of beam dilution, the actual measured equivalent temperature is given by:

$$T_\odot = {T_{\rm observed}\over{\theta_\odot^2 /\theta_{\rm beam}^2}}$$

where $\theta_{\odot}$ is the apparent size of the Sun in degrees, also called the source size. Note that if the source size is comparable to the antenna beam width, $T_{\rm measured} \approx T_{\odot}$. Using the value for $\theta_{\rm beam}$ you measured above and assuming $\theta_{\odot} = 0.5^\circ$, calculate the actual equivalent temperature, $T_\odot$, of the radio emission from the Sun. Is it comparable to the thermal temperature of the Sun? If not, why might it be very different at these frequencies?

Using your value of $T_\odot$, compute a calibration factor for the receiver (i.e. degrees/volt).

7.

Reconsider your data, integrating on blank sky. Compute the 1 $\sigma$ (RMS) scatter in these values (use a spreadsheet, write a program, etc.), apply the calibration factor above, and determine an approximate value for T_RMS. Assuming a bandwidth of 100 MHz, compute how much on-source integration time it would take to reach a sensitivity of 1 Kelvin with this telescope.