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Comparing stars

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# 2.3 The effect of interstellar gas

You have seen that the ISM has been studied through the radiation that the gas and dust absorb, emit and scatter. Figure 15 summarizes the differences between these three phenomena.

Let's first consider the three phenomena in relation to the gas. The gas scatters very little light and so we need only consider absorption and emission of radiation. You have already met absorption and emission of photons by atoms (which we shall call photoexcitation and photoemission, respectively). Atoms can also be excited by collisions between each other as the result of their random thermal motion (collisional excitation). For thermal motion, the average translational kinetic energy of an atom Ek is related to the temperature T of the gas via

where k is the Boltzmann constant. For a reasonable proportion of such collisions to be sufficiently energetic to excite an atom, Ek must be at least as large as the difference in energy between the excited and non-excited state, ε. So in order to obtain Ek ≥ ε we require

for collisional excitation to be important.

The most prominent lines from atoms in the interstellar medium are those of ionized calcium. Although these lines are also prominent in the spectra of stars of spectral class G and K due to ionized calcium in their atmospheres, the interstellar lines have very different characteristics. They are much narrower than the stellar spectral lines. Also, even though they are often much fainter than the stellar lines they are usually observable because their wavelengths are Doppler shifted due to the difference in radial velocity of the interstellar gas and the star itself. In spectroscopic binaries you can see the interstellar lines remaining at a fixed wavelength while the stellar lines move due to their orbital motion.

The processes of photoemission, photoexcitation and collisional excitation also operate in molecules, which are found in many parts of the ISM. Molecules are formed when atoms are bound together by chemical bonds. The electrons are 'shared' between the atoms (you could visualize this as an electron cloud surrounding the nuclei). The electrons in molecules occupy particular energy levels in a similar way to individual atoms (even though the electrons are 'shared'). Electronic transitions can take place leading to excitation, de-excitation and ionization of the molecule. The molecules also have discrete vibrational and rotational energy states and so can also undergo vibrational and rotational transitions. The vibrational energy states correspond to particular internuclear distances; when the distance becomes so large the atoms are no longer bound together, dissociation has occurred. A molecule can also rotate at different rates (and about different axes) resulting in discrete rotational energy states. At the molecular level, vibration and rotation, like electron energy, is quantized, contrary to our expectations from the large-scale world where we observe an apparently continuous range of these properties. Let's look at each of these in turn. The CO (carbon monoxide) molecule is a simple case that serves to introduce the important ideas.

Figure 15 Absorption, emission and scattering of radiation.

Figure 16 shows the electronic energy levels of the CO molecule. The levels above the lowest one correspond to the various excited states of just one of the 14 electrons that this molecule contains, in particular one of the outermost electrons, which are the least tightly bound and thus require less energy to excite them than the inner, more tightly bound electrons. For comparison, the electronic energy levels for atomic hydrogen are also shown. The excitation of a CO molecule from a lower electronic energy level to a higher one can happen through photoexcitation or through collisional excitation.

Figure 16 Electronic energy levels in CO and in H.

## Question 5

For the excitation of CO from its lowest electronic energy level to the one above it, calculate (a) the maximum photon wavelength for photoexcitation and (b) the minimum gas temperature for appreciable collisional excitation.

From Figure 16 we see that, for CO, the difference in energy ε between the lowest electronic level and the one above it is 5.94 eV (= 9.52 × 10−19 J).

ε corresponds to a photon wavelength given by

This is the maximum photon wavelength (minimum energy) for this excitation.

(b) From Equation 3, the minimum temperature is given by

So typically a temperature of at least 5 × 104K is required for the collisional excitation of this electronic state in CO molecules.

Thus, CO remains in its lowest electronic energy level unless it is exposed to photons at least as energetic as those in the near-UV region, or is at a temperature of order 105 K, or greater. These are the same sorts of criterion obtained for many atoms, and for many other molecules too, though in some atoms and molecules the lower electronic levels are not quite so widely spread.

Not all electronic excitations require such large energies. Thus, the higher electronic energy levels (Figure 16) are much more closely spaced, and excitations among them can be achieved by longer wavelength photons, and at lower temperatures.

A vibrational transition of CO is illustrated schematically in Figure 17, along with the lowest few vibrational energy levels for the case in which the molecule remains in the electronic state corresponding to the lowest electronic energy level. Note how much smaller are the gaps between the energy levels than is the case for the electronic transitions in Figure 16. This means that photoexcitation can take place at infrared (IR) wavelengths, and collisional excitation at temperatures down to the order of 103 K. These criteria are typical for vibrational transitions in molecules.

A rotational transition of CO is illustrated schematically in Figure 18, along with the lowest few rotational energy levels corresponding to the lowest energy electronic and vibrational states. The energy gaps are yet smaller, and photoexcitation can now be caused by microwaves, and collisional excitation occurs at temperatures down to the order of a frigid 10 K. Again, these criteria are typical, though many molecules have even smaller rotational energy gaps, and a few have much larger gaps.

A transition from a lower to a higher energy level can also involve some combination of electronic, vibrational and rotational energy changes, necessarily so in some cases.

Figure 17 Vibrational transitions and vibrational energy levels in CO. To the right are the vibrational states corresponding to the lowest two energy levels.
Figure 18 Rotational transitions, and rotational energy levels in CO. To the right are the rotational states corresponding to the lowest two energy levels.

Photoemission is the reverse process of photoexcitation, and so yields photons at wavelengths equal to those that would have caused photoexcitation between the two levels concerned.

Not all transitions involving photoexcitation and photoemission are equally probable, and so some spectral absorption and emission lines tend to be far weaker than others, and some are completely absent. Molecules consisting of two identical atoms, such as H2, have particularly weak vibrational and rotational lines.

We have examined the processes which can cause interstellar atoms and molecules to absorb or emit radiation; let's now see what happens to starlight passing through a cloud of interstellar gas. Figure 19 illustrates what is seen by observers when the cloud is in the line of sight to the star and when it is out of the line of sight. Note that the prominent absorption lines in the spectrum of the star arising from the stellar photosphere are seen by the observer in the line of sight (Figure 19b) together with the superimposed, generally narrower, interstellar lines.

Figure 19 The effect of interstellar gas on radiation from a star. (a) is the spectrum emitted from the star. Spectrum (b) is seen by an observer looking at the star through the gas cloud, while spectrum (c) is seen by an observer looking at the gas cloud against a star-less background.