Interstellar molecules and the sea of microwave radiation

We come now to methods of detecting the sea of microwave radiation, the CMBR, and we begin with interstellar molecules that serve as "thermometers." This provided a measure of the temperature of the radiation some two dozen years before its presence was recognized.

25 In the language of thermal physics, Tolman (1931) had shown that the homogeneous and isotropic expansion of a universe filled with free thermal radiation is a reversible process: it conserves entropy. Tolman remarked that a bounce might be violent enough to be irreversible, producing entropy. Dicke gave an explicit example. Tolman's result follows in a free gas of particles with energy proportional to a power of momentum, as in photons or nonrelativistic particles, though the cooling rates as the universe expands are different. A rapid transition from a relativistic to nonrelativistic gas is irreversible. Yakubov (1964) computed the resulting entropy production in Zel'dovich's cold big bang model.

The function of a species of interstellar molecule as a thermometer follows from some results from quantum physics. The energy of an isolated object such as an atom or molecule has discrete - quantized - allowed values: it has a ground level with energy E0, a first excited level with energy E1, a second level at E2, and so on. The energy levels of an object as large as a person would be fantastically closely spaced if we were able to truly isolate someone, but it can't be done: we interact - exchange energy - too strongly with our environment. The effect of the quantization of energy is clear and distinct on the much smaller scale of atoms and molecules, however.

In a dilute gas of molecules bathed in blackbody radiation at temperature T, absorption and emission of the thermal radiation causes the ratio of numbers of molecules in the first excited energy level and the ground level to relax to the value given by the equation a = e-(Ei-E0)/kT (3.13)

This has the same form as equation (3.10) for the thermal equilibrium ratio of numbers of neutrons to protons in the early universe, but here applied at much lower energies and temperatures and much later in the history of the expanding universe. Because the energy levels might be labeled by the spin angular momentum quantum number, this expression is said to give the spin temperature corresponding to a measured ratio n1/n0.26

The ratio n1/n0 for a species of molecules in interstellar space can be measured by comparing the strength of absorption of light from a background star by the molecules in the two energy levels. Starlight photons may be absorbed by a molecule in its ground level, with energy E0, leaving the molecule in some highly excited level, with energy E*. The photon has to supply the energy difference, E* — E0. From Planck's condition E = hv we see that this absorption produces an absorption line at frequency va = (E* — E0)/h in the spectrum of light from the star. A starlight photon with the lower frequency vb = (E* — E1)/h can be absorbed by a molecule in the first excited level, E1, which again leaves the molecule at energy E*. This produces a second absorption line, at frequency vb. The ratio of the amount of absorption at the two frequencies is a measure of the value of n1/n0. Since the energy difference E1 — E0 is known, equation (3.13) gives us a temperature. Thus, we have a thermometer.

There is the problem that the spin temperature measured by the ratio n1/n0 is determined not only by the effective temperature of electromagnetic

26 It is conventional to use this spin temperature as a measure of the ratio ni/no even when the ratio is determined by energy exchanges that are not at all close to thermal equilibrium.

radiation bathing the molecules, but also by the interstellar particles that are colliding with the molecules we are studying and knocking them from one energy level to another. In effect the molecules are coupled to two heat reservoirs, radiation and interstellar particles, at different temperatures. The molecule cyanogen (CN, a carbon atom bound to a nitrogen atom) in interstellar space has two useful properties. First, it recovers quickly from collisions with particles. That means interstellar particles have relatively little effect on n\/n0: this thermometer is more sensitive to the temperature of the radiation than to the temperature of the interstellar matter. Second, the CN energy levels are well spaced for the measurement of radiation temperatures near that of the CMBR. The energy difference E\ — E0 for CN corresponds to the microwave wavelength 2.6 mm, which you can see is close to the peak of the spectrum in Figure 2.2. The spin temperature of interstellar CN thus provides a very convenient thermometer for the CMBR.

McKellar (1941) used equation (3.13) to translate observations of absorption of starlight by interstellar CN molecules in the two lowest levels to the spin temperature:

With hindsight, the inference we would draw is that interstellar CN molecules are bathed in radiation at about this temperature. But that was not suggested by McKellar or by Adams (1941), who made the measurements. Herzberg (1950) comments that this temperature "has of course only a very restricted meaning." The restriction he had in mind likely is that, as we have said, the excited levels of CN might be populated by particle collisions rather than radiation.

Astronomers are accustomed to dealing with complex situations that require them to remember and evaluate the possible significance of many curious things. In the early 1960s some knew that the observed excitation of CN by interstellar particles would require a curiously large collision rate. And after the proposed identification of the CMBR astronomers were quick to remember McKellar's spin temperature and recognize its possible relation to the hot big bang cosmology. How that happened is one of the threads running through the essays.

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