|MadSci Network: Physics|
Yes, it is possible to measure the cosmic microwave background (CMB) radiation with a small horn antenna and modern electronics, or thus said a colleague of mine. Measuring a background signal is always difficult because you need to extract any other signal above the CMB and then be able to discern the small residual signal from the electronic noise of the apparatus. I am assuming that you have a microwave antenna with the necessary electronics to measure its output power. Your receiver should be set up near the peak emission of the CMB around 176 GHz. A large horn over the antenna is necessary. I am going to explain a procedure for a project currently being done at the Harvard astronomy department. It is a design by John Kovac from the Harvard-Smithsonian Center for Astrophysics, in Cambridge, Massachusetts.
The basic idea is to scan the sky at four or five points and calculate the antenna temperature (TA). TA is just a measurement of the signal power at the antenna receiver. If the temperature of the atmosphere, Tatm is constant at all points in the sky, the following formula should approximately hold for points not too close to the horizon:
TA = TCMB + C Tatm sec(z)where TCMB is the value of the temperature of the cosmic microwave background radiation that we are seeking. C is the value of a constant and z is the angle in the sky measured from the zenith (the highest point in the sky) and sec(z) is the secant of angle z, which is equal to 1 over cosine of z. If you graph the measured values of TA at different angles z versus sec(z), you should get a straight line with a slope CTatm. We don't need to know the value of CTatm. TCMB is given by the intersection of the line with the vertical axis of the graph. This is the easy part, that is, the theory.
The difficult part is to measure TA. To do that you need the following:
The following picture shows the apparatus at the Harvard astronomy department roof with the corresponding numbers in the list above. The arrow points to the horn antenna.
The measurement procedure is as follows:
Repeat steps 2 and 3 above at four or five different angles z in the sky. The output power of the antenna is given by the formula:
P=g(TA+Tsys)where Tsys is the system temperature, also known as Nyquist temperature. It comes from oscillating currents in the electronics. g is the conversion factor between power and temperature. We need to measure Tsys and g to get TA at each z. Use the following formulae to get g, Tsys and TA at each z:
g=(Thot-Tcold)/ (Phot-Pcold)Now graph the values of TA versus the corresponding values of sec(z)=1/cos(z). Try to fit a straight line to the points on the graph. The point of intersection of the line with the vertical axis should be the CMB temperature. Don't be surprised if you don't get a value close to 3 Kelvin. This is a home experiment after all! You can get a recent account of how the original detection of the CMB was done by Robert Wilson himself in "History of the Discovery of the Cosmic Microwave Background Radiation," Physica Scripta, Vol. 21, pp. 599-605 (1980). You'll notice that Penzias and Wilson used liquid helium instead of liquid nitrogen among many other devices to get a more accurate result.
Y = Phot/Pcold (this is the Y-factor)
Tsys=(Thot-YTcold)/ (Y-1) (this is the Y-factor method to get Tsys)
TA=P/g-Tsys (here's where we subtract the system noise temperature from the output signal)
Vladimir Escalante Ramírez
Center for Radio Astronomy and Astrophysics
National University of Mexico, Morelia, Mexico
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