Cosmic Microwave Background

The cosmic microwave background (CMB) is a key prediction of the hot Big Bang model, and the most important observation that discriminates between the Big Bang and the Steady State models. So it is an interesting historical anomaly that this prediction was not put forward and tested by the inventors of either theory, and that the first observers of the CMB were completely unaware of its cosmological significance.

The CMB has the spectrum of a blackbody. A blackbody spectrum is produced by an isothermal, opaque and non-reflecting object. Usually a cavity with a small hole is used in the laboratory to make an opaque and non-reflective object. Radiation that enters the cavity through the hole will have to bounce off many walls before it returns to the outside, so even if the walls are only somewhat dark, the hole will appear to be completely black. The diagram at right shows such a cavity, with the blue incoming ray being absorbed completely while the red rays show the outgoing thermal radiation. A simple gedanken experiment shows that the spectrum emitted by a blackbody can only depend on its temperature T. The proof first assumes that two blackbodies have different spectra and then shows that this leads to a contradiction. Let two blackbodies A & B, both at temperature T, radiate different spectra. Then use a filter and aperture stops to allow them to transfer heat only by radiation in a given passband. Then the radiation of A is entirely absorbed by B, and the radiation of B is entirely absorbed by A. Thus if their spectra are different, there would be a net transfer of heat between A & B, but their temperatures are the same. Since heat transfer between objects of the same temperature does not occur, the spectra must be identical. The choice of filter passband was arbitrary, so the spectra must be identical at all frequencies. This universal blackbody spectrum was clearly a very important topic in physics at the end of the 19th century, and Planck was studying blackbody radiation when he introduced the idea of quanta, and defined the quantum of action h which we now know as Planck's constant. Because of the universality of the blackbody spectrum, we can convert any spectral measurement into a brightness temperature at the measured wavelength. The unique character of a blackbody spectrum is that the brightness temperature of a blackbody is the same at all wavelengths. When talking about the CMB scientists always use the Kelvin scale of temperature, which is just like the Celsius scale except the zero point is absolute zero instead of the freezing point of water at Tice = 273.15 K.

The graph above shows the measured brightness temperature TB of the CMB at many different wavelengths. Clearly TB = 2.725 K is consistent with all the data within the statistical scatter expected for the stated errors.

In order to make a blackbody spectrum, an object as to be opaque, non-reflective and isothermal. Thus a star, which is opaque, does not produce a blackbody spectrum because we can see both cooler outer layers and hotter deeper layers. But even though the temperature of the Universe changes as it evolves, with TCMB = To (1+z), the Universe looks isothermal because the redshifting of radiation makes the warmer but redshifted distant Universe appear to have exactly the same temperature as the Universe today.

The FIRAS instrument on COBE had a large conical horn for collecting the cosmic microwave background. There was only a small hole in the end of the horn to let the radiation into the instrument. But FIRAS also carried a microwave absorber, the external calibrator or XCAL, that could be inserted into the horn like a trumpet mute, and heaters that could make the whole horn+plus absorber cavity isothermal. When the XCAL was in the horn FIRAS observed a very good blackbody cavity, but when the XCAL was out FIRAS observed the CMB. No signifcant difference could be seen. The CMB is very close to a blackbody with temperature 2.725 K. The FIRAS results are shown below in units of intensity (power per unit area per unit frequency per unit solid angle) vs. frequency and/or wavelength.

Eric Adelberger would like me to point out that the fundamental FIRAS measurement is the residual plot at the bottom. This is what FIRAS actually measured: the difference between the CMB and the best fitting blackbody. The plot at top shows this residual added to the theoretical blackbody spectrum at the best fitting XCAL temperature, based on the function derived by Planck in 1900. The three curves in the bottom correspond to three fairly likely non-blackbody spectra: the grey curve shows a body with a reflectivity of 100 parts per million instead of zero, and the red and blue curves show the effect of hot electrons adding an excess 60 parts per million of energy to the CMB either before (blue) or after (red) 1000 years after the Big Bang. These curves show the maximum distortions allowed by the FIRAS data.


The first observations of the CMB were made by McKellar using interstellar molecules in 1940. The image at right shows a spectrum of the star zeta Oph taken in 1940 which shows the weak R(1) line from rotationally excited CN. The significance of these data was not realized at the time, and there is even a line in the 1950 book Spectra of Diatomic Molecules by the Nobel-prize winning physicist Gerhard Herzberg, noting the 2.3 K rotational temperature of the cyanogen molecule (CN) in interstellar space but stating that it had "only a very restricted meaning." We now know that this molecule is primarily excited by the CMB implying a brightness temperature of To = 2.729 +/- 0.027 K at a wavelength of 2.64 mm ( Roth, Meyer & Hawkins 1993).

Later Robert Dicke made measurements that could have discovered the CMB. He measured the brightness temperature of the sky as a function of the elevation angle. As his antenna pointed closer to the horizon the brightness temperature went up and became closer to the air temperature. Dicke used a low sidelobe flared horn, and he invented a rapidly switching differential radiometer for this work, now known as a Dicke radiometer, that switched between the sky and an ambient temperature (300 K) load. Using this data Dicke determined the absorption of the atmosphere at 1 to 1.5 cm wavelength and showed that this microwave "K band" could be used for radar. The short wavelength allowed radars to fit inside fighter planes and greatly aided the Allied war effort in WW II. Dicke was not interested in the temperature of the sky outside the atmosphere but in 1946 Dicke et al. published an upper limit on the brightness temperature of the sky: Tsky < 20 K. By using a room temperature load Dicke had a large difference signal at the zenith, and a few percent uncertainty in his absolute gain calibration generated a several Kelvin uncertainty in the sky temperature.

The plot on the left above is the actual data from Figure 3 of the Dicke et al. (1946), although I had to do a fit to find the baseline that was subtracted. As you can see, the extrapolation to 100% transmission is large because of the water vapor absorption and the chopped signal at 100% transmission is large so the gain uncertainty shown in blue leads to a large uncertainty in Tsky. On the right is a hypothetical experiment that could have been done in 1945 with a cold reference at a wavelength not on the water vapor line. If Dicke had used a low temperature load and had observed from a mountaintop instead of Florida, he would have detected the CMB. Ironically, the paper by Gamow describing the hot Big Bang occurs in the same volume of the Physical Review. A later paper by Alpher, Bethe & Gamow describing the hot Big Bang is one of the classic jokes in physics: Gamow added Bethe's name to this paper just to make it sound like alpha, beta, gamma. Bethe actually didn't do any work on it.

A further irony is that one person did make the connection between McKellar's 2.3 K and the Universe, and that was Fred Hoyle in a 1950 review (1950, Observatory, 70, 194-195) of a book by Gamow and Critchfield (1949, "Theory of Atomic Nucleus and Nuclear Energy-Sources"). Hoyle was one of the three inventors of the Steady State model which was the main competitor to Gamow's Big Bang model. Hoyle wrote: "[the Big Bang model] would lead to a temperature of the radiation at present maintained throughout the whole of space much greater than McKellar's determination for some regions within the Galaxy." The appendix with Gamow's cosmological model gives values from which To = 11 K can be computed, which certainly is larger than the observation of 2.3 K. But Hoyle did not consider Alpher and Herman's paper (1949, Phys. Rev., 75, 1089-1095) which gave two versions of the Big Bang, one with To = 1 K and one with To = 5 K. Thus the uncertainties in the cosmological parameters easily allowed for McKellar's CN data to be a confirmation of the Big Bang instead of a refutation of it. But none of the participants in this debate ever looked further into the interstellar CN data, and thus the CMB remained undiscovered until 1965. In fact Gamow seemed to conspicuously ignore this discrepancy, and gives To = 50 K in his book "Creation of the Universe" (1955, 1961).

Penzias & Wilson were studying the radiation collected by a large horn antenna in New Jersey when they found an excess radiation at 7.35 cm wavelength that was equivalent to a 3.5 +/- 1 K blackbody. Their horn had low sidelobes, and Penzias & Wilson switched against a low temperature reference load. They did not know what this excess meant, but spoke to Bernie Burke of MIT, who knew that Dicke was now leading a group planning to measure the CMB. Ironically Dicke had forgotten about his old upper limit, but he knew how to do the measurement. But before his group could finish building their instrument, Dicke got a call from Penzias & Wilson. After hearing about their data, Dicke said: "Boys, we've been scooped." Papers by Penzias & Wilson and by Dicke, Peebles, Roll & Wilkinson describing these results appeared in the 1965 Astrophysical Journal. Wilkinson went on to measure the CMB at a large number of wavelengths and always found the same brightness temperature over a wide range of wavelengths.

Claims that Le Roux measured the CMB in the 1950's are incorrect. Le Roux used an ordinary parabolic dish, which is not designed for very low sidelobes, and used the horizon as an absolute temperature reference. He also observed at 900 MHz where the galactic foreground is very bright. While Le Roux's unpublished thesis gives Tsky = 3 +/- 1 K, the first published version (Denisse, Lequeux & Le Roux, 1957, Comptes Rendus, 244, 3033) gives Tsky < 3 K. Both of these results are incorrect because the galactic foreground makes the minimum temperature of the sky > 4 K at this frequency. A more complete published version gives Tsky < 20 K ("une vingtaine"). This is a more reasonable assessment of the precision of these data.

Tutorial: Part 1 | Part 2 | Part 3 | Part 4
FAQ | Age | Distances | Bibliography | Relativity

Ned Wright's home page

© 2007-2009 Edward L. Wright. Last modified on 24 Oct 2009