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a molecule can be in many different rotational states. Normally, interstellar molecules are studied by radio observations of rotational transitions within the same electronic state. The effect of the rotational energy levels is to split the optical electronic transition into several lines. For example, there are lines corresponding to a transition from a given rotational state of the ground electronic state to the same rotational state in the excited electronic state. The wavelengths of the various transitions are slightly different. In practice, two transitions are observed, one from the ground rotational state and the other from the first excited rotational state.

The relative strength of the two optical lines is equal to the ratio of the populations in the two rotational states (in the ground electronic state), n2/na. This is given by the Boltzmann equation as

n gi where g1 and g2 are the statistical weights of the two rotational levels, and E21 is the energy difference between the two rotational levels. The energy difference between the two levels in CN corresponds to the wavelength of 2.64 mm. If the CN is in a cloud of low density, there will be very few collisions with hydrogen to get molecules from the ground state to the next rotational state. (Collisions with electrons may also be important.) If there are no collisions, the CN can only get to the higher rotational state by absorbing radiation. If the CN is far from any star, the only radiation available is from the cosmic background. Under these circumstances, the populations will adjust themselves so the temperature in equation (21.6) is the temperature of the cosmic background radiation at 2.64 mm. (Of course, if the cosmic background radiation has a blackbody spectrum, its temperature at 2.64 mm should be the same as at any other wavelength.)

So, the CN sits in space, sampling the cosmic background radiation at a wavelength of 2.64 mm. This is a wavelength at which we could not directly measure the background temperature from the ground. The CN then modifies the light passing through the cloud. The relative intensity of these optical signals contains the information that the CN has collected on the cosmic background radiation. The optical signals easily penetrate the Earth's atmosphere. All we have to do is detect them and decode them. To decode them, we take the relative intensities as giving us n2/na. We then solve equation (21.6) for T. As a farther refinement, we can check to see if there is any excitation of the CN due to collisions by electrons or atoms or molecules in the cloud. If there were, then the T that we measure would be greater than the background temperature. But, if this were happening, there would be a weak emission line at 2.64 mm. By looking for such a line and not finding it, we can rule out significant colli-sional excitation of the CN.

The most careful application of these techniques gives a temperature of the cosmic background radiation at 2.64 mm of 2.80 K, with an uncertainty of about 1%. This agrees well with the best direct longer wavelength measurements, indicating that, as we approach the peak, the radiation keeps its blackbody nature. It is possible to study the next rotational transition up at 1.32 mm, giving the background temperature even closer to the peak. The lower level of the second rotational transition does not have much population, so this is a very difficult experiment. However, the results are consistent with the blackbody nature continuing to the peak. There is another use to the CN technique. If we can observe CN in distant objects, we will be seeing it as it was in the past, and so the cosmic background temperature will be higher, and the CN excitation temperature will be higher. This gives us a check on our theories of how the temperature of the universe varies with z.

There is an interesting aside to this story. When interstellar CN was discovered in the late 1930s, the people who observed it also observed both optical spectral lines. They noted that the relative amounts of absorption corresponded to a temperature of about 3 K, but did not attach any significance to

Diagram showing COBE satellite. [NASA Goddard Space Flight Center and the COBE Science Working Group]

Diagram showing COBE satellite. [NASA Goddard Space Flight Center and the COBE Science Working Group]

this. This shows us that, though many important discoveries in astronomy are made unexpectedly, simple luck is not enough. Confronted with the unexpected, the observer still must be able to recognize that something important is happening, and then be able to follow up the results.

The cosmic background radiation was considered so important that NASA decided to devote a whole satellite to its study. Thus, the Cosmic Background Explorer Satellite, or COBE, was launched in 1989. A diagram of the satellite is shown in Fig. 21.7. It carried instruments for making direct measurements of the radiation at wavelengths that were blocked by the atmosphere. The leader of the COBE team was John Mather of NASA's Goddard Spaceflight Center.

The COBE result for the spectrum is shown in Fig. 21.8. Measurements at many wavelengths are shown. Notice that the error bars are quite small. For comparison, we see the differences between observations and a 2.725 K blackbody. The agreement is spectacular. First, it is clear that the spectrum is truly that of a blackbody. The temperature of the background radiation has now been determined to better than 1%. There can be little doubt that this is the radiation predicted in 1948 by Alpher and Herman.

21.1.3 Isotropy of the cosmic background radiation

Earlier in this chapter, we said that the cosmic background radiation should appear the same no matter which way you look. That is, the radiation

Cosmic Microwave Background Spectrum

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