MadSci Network: Physics

Re: Re: Cosmic Microwave Background Radiation

Date: Sat Apr 21 00:57:21 2012
Posted By: Vladimir Escalante-Ramirez,
Area of science: Physics
ID: 1333206178.Ph

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:

  1. Some pointing device for the horn and antenna.
  2. Two Styrofoam boxes, and a thermometer in each. The thermometers must be graded in Kelvin degrees and must be able to record temperatures down to 70 Kelvin. Fill one box with liquid nitrogen and leave the other empty. Beware of liquid nitrogen. It can freeze your finger instantly, and the container must always be kept in the open to prevent problems from possible leaks. I guess liquid nitrogen can be substituted with ice, but your measurement of the CMB will be more inaccurate.
  3. Two metal cones covered with rubber foam on the inside and a handle. The cones should be big enough to cover the horn antenna. One cone will be put inside the liquid nitrogen box (the "cold cone"), and the other inside the empty box (the "hot cone"). The rubber foam is supposed to work as a blackbody emitter. The cones will be used to calibrate the antenna.
  4. A large aluminum cone to direct the signal to the horn antenna. A cardboard cone covered with aluminum foil will do.

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:

  1. Point the antenna to the zenith.
  2. Record the liquid nitrogen or ice temperature with the thermometer (Tcold), and immediately cover the antenna with the cold cone (rubber foam towards the horn antenna) and measure the output power (Pcold). Tcold should be close to 77 Kelvin if you are using liquid nitrogen, or 273 Kelvin if you are using ice. Remove the cold cone. Record the empty box temperature (Thot), and immediately cover the antenna with the hot cone, and measure the output power (Phot).
  3. Remove the cones and point the horn antenna to a point in the sky, not too close to the horizon or a building, and really hold the antenna steady while measuring the output power (P). Record the angle z of the point from the zenith

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:

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)
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)
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.

Good luck!

Vladimir Escalante Ramírez
Center for Radio Astronomy and Astrophysics
National University of Mexico, Morelia, Mexico

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