Astronomers apply the laws of spectroscopy in analyzing radiation from beyond the Earth. A nearby star or a distant galaxy takes the place of the light bulb in our previous examples. A galactic cloud or a stellar (or even planetary) atmosphere plays the role of the intervening cool gas. And a spectrograph attached to a telescope replaces our simple prism and detector. We began our study of electromagnetic radiation by stating that virtually all we know about planets, stars, and galaxies is gleaned from studies of the light we receive from them, and we have presented some of the ways in which that knowledge is obtained. Here we describe a few of the ways in which the properties of emitters and absorbers can be determined by careful analysis of radiation received on (or near) Earth. We will encounter other important examples as our study of the cosmos unfolds.
Stars are very hot, especially deep down in their cores, where the temperature is measured in millions of kelvins. Because of the heat, the atoms are ionized, and the spectrum of radiation is continuous. However, at the relatively cool surface of a star, some atoms retain a few, or even most, of their orbital electrons. By matching the spectral lines we see with the laboratory spectra of known atoms, ions, and molecules, we can determine the chemical composition of the star.
As we have already seen, literally thousands of dark absorption lines cover the Sun's visible spectrum; nearly 800 of them are produced by variously excited atoms and ions of just one element: iron. Atoms of a single element, such as iron, can yield many lines for two reasons. First, the 26 electrons of a normal iron atom can make an enormous number of different transitions among energy levels. Second, many iron atoms are ionized, with some of their 26 electrons stripped away. Because the removal of electrons alters an atom's electromagnetic structure, the energy levels of ionized iron are quite different from those of neutral iron. Each new level of ionization introduces a whole new set of spectral lines. Besides iron, many other elements, also in different stages of excitation and ionization, absorb photons at visible wavelengths. When we observe the entire Sun, all these atoms and ions absorb simultaneously to yield the rich spectrum we see.
The spectra of many atoms and ions are well known from laboratory measurements. Often, however, a familiar pattern of lines appears, but the lines are displaced from their expected locations. In other words, a set of spectral lines may be recognized as belonging to a particular element, except that they are all offset—blueshifted or redshifted—by the same amount from their normal wavelengths. Such shifts are produced by the Doppler effect; they thus allow astronomers to find out how fast the source of the radiation is moving along the line of sight from the observer (its radial velocity). 
(Sec. 3.5)
Still more information can be obtained from detailed study of the lines themselves. Because the intensity of a line is proportional to the number of photons emitted or absorbed by the atoms, the intensity of a particular line depends in part on the number of atoms giving rise to the line. The more atoms present to emit or absorb the photons corresponding to a given line, the stronger (brighter or darker, depending on whether it is seen in emission or absorption) that line is.
But intensity also depends on the temperature of the atoms—that is, the temperature of the entire gas of which the atoms are members—because temperature determines what fraction of the atoms at any instant are in the right orbital to undergo any particular transition. Consider the absorption of radiation by hydrogen atoms in an interstellar gas cloud or in the outer atmosphere of a star. If all the hydrogen were in its ground state—as it would be if the temperature were relatively low—the only transitions that could occur would be the Lyman series (see More Precisely 4-2), resulting in absorption lines in the ultraviolet portion of the spectrum. Thus, astronomers would observe no visible hydrogen absorption lines (for example, the Balmer series) in the spectrum of this object, not because there was no hydrogen, but because there would be no hydrogen atoms in the first excited state (as is required to produce visible absorption features).
The spectrum of our own Sun is a case in point. Because the temperature of the Sun's atmosphere is a relatively cool 6000 K (as we saw in Chapter 3), few hydrogen atoms have electrons in any excited state. (Sec. 3.4.1) Hence, in the Sun, visible hydrogen lines are relatively weak—that is, of low intensity compared with the same lines in many other stars—even though hydrogen is by far the most abundant element there.
As the temperature rises, atoms move faster and faster. More and more energy becomes available in the form of collisions, and more and more electrons are boosted into an excited state. At any instant, then, some atoms are temporarily in an excited state and so are capable of absorbing at visible or longer wavelengths. As the number of atoms in the first excited state increases, lines in the Balmer series become more and more evident in the spectrum. Eventually, a temperature is reached at which most of the atoms are in the first excited state, simply because of their frequent, energetic collisions with other atoms in the gas. At this point the Balmer lines are at their strongest (and the Lyman lines are much weaker).
At even higher temperatures, most atoms are kicked beyond the first excited state into higher-energy orbitals, and new series of absorption lines are seen, while the strength of the Balmer series declines again. Eventually, the temperature becomes so high that most hydrogen is ionized, and no spectral lines are seen at all.
Over the years, astronomers have developed mathematical formulas that relate the number of emitted or absorbed photons to the temperature of the atoms as well as to their number. Once an object's spectrum is measured, astronomers can interpret it by matching the observed intensities of the spectral lines with those predicted by the formulas. In this way, astronomers can refine their measurements of both the composition and the temperature of the gas producing the lines.
Consider an emission line, such as the one shown in Figure 4.16(a). (The discussion that follows holds equally well for absorption features.) The line seems uniformly bright, but more careful study shows that its brightness is greatest at the center and tapers off toward either side, as illustrated in Figure 4.16(b). We stressed earlier that photons are emitted and absorbed at very precise wavelengths. Why aren't spectral lines extremely narrow, occurring only at specific wavelengths? This line broadening is not the result of some inadequacy of our experimental apparatus. It is caused by the environment in which the emission or absorption occurs, which often changes our perception of a photon's energy, and it tells us a lot about the physical state of the gas involved.
Figure 4.16 By tracing the changing brightness across a typical emission line (a) and expanding the scale, we obtain a graph of its intensity plotted versus wavelength (b).
Several physical mechanisms can broaden spectral lines. The most important of these involve the Doppler effect. (Sec. 3.5) To understand how the Doppler effect can broaden a spectral line, imagine a hot gas cloud. Individual atoms are in random, chaotic motion. The hotter the gas, the faster the random thermal motions of the atoms, as illustrated in Figure 4.17(a). If a photon is emitted by an atom in motion, the wavelength of the detected photon is changed by the Doppler effect. For example, if an atom is moving away from our eye or from our detector while in the process of emitting a photon, that photon is redshifted. The photon is not recorded at the precise wavelength predicted by atomic physics but rather at a slightly longer wavelength. The extent of this redshift is proportional to the velocity away from the detector. Similarly, if the atom is moving toward us, its light is blueshifted.
Figure 4.17 Atoms moving randomly (a) produce broadened spectral lines (b) as their individual redshifted and blueshifted emission lines merge in our detector.
In a cloud of gas, atoms are in constant thermal motion. Some atoms move toward us, some away from us. Still others are moving transverse to our line of sight and are unaffected by the Doppler effect (at least, from our perspective). Throughout the whole cloud, atoms move in every possible direction. The result is that many atoms emit or absorb photons at slightly different wavelengths than would normally be the case if all the atoms were motionless. Most atoms in a typical cloud have very small thermal velocities. As a result, most atoms emit or absorb radiation that is Doppler-shifted only a little, and very few atoms have large shifts. So, the center of any spectral line is much more pronounced than either of its "wings." The result is a bell-shaped spectral feature like that in Figure 4.17(b). Thus, even if all atoms emitted and absorbed photons at only one specific wavelength, the effect of their thermal motion would be to smear the line out over a small range of wavelengths. The hotter the gas, the larger the spread of Doppler motions and the greater the width of the line. By measuring a line's width, astronomers can estimate the temperature of the gas producing it.
Unfortunately, the situation is not so simple. Several other physical mechanisms can also produce line broadening. One such mechanism is gas turbulence, which exists when the gas in a cloud is not at rest or flowing smoothly but instead is seething and churning in eddies and vortices of many sizes. Motion of this type causes Doppler-shifting of spectral lines, but lines from different parts of the cloud are shifted more or less randomly. Very often, the cloud is so small or far away that our equipment cannot distinguish, or resolve, different parts from one another—the light from the entire cloud is blended together in our detector. When averaged over the whole cloud, the net effect appears rather similar to the thermal broadening just discussed. However, it has nothing to do with the temperature of the gas.
Rotation produces a similar effect. Consider a star or a gas cloud oriented so that we see it spinning. Photons emitted from the side spinning toward us are blueshifted by the Doppler effect. Photons emitted from the side spinning away from us are redshifted. As with turbulence, if our equipment is unable to resolve the object, a net broadening of its observed spectral lines results, as illustrated in Figure 4.18. Like the effect of turbulence, line broadening due to rotation has nothing to do with the temperature of the gas producing the lines.
Figure 4.18 The rotation of a star can cause spectral line broadening. Since most stars are unresolved, light rays from all parts of the star merge to produce wide lines.
Other broadening mechanisms do not depend on the Doppler effect at all. For example, if electrons are moving between orbitals while their parent atom is colliding with another atom, the energy of the emitted or absorbed photons changes slightly, thus "blurring" the spectral lines. This mechanism occurs most often in dense gases, where collisions are most frequent. It is usually referred to as collisional broadening. The amount of broadening increases as the density of the emitting or absorbing gas rises. Yet another cause of spectral-line broadening is magnetism. The electrons and nuclei within atoms behave as tiny, spinning magnets. As a result, the basic emission and absorption rules of atomic physics change slightly whenever atoms are immersed in a magnetic field, as is found in many stars to a greater or lesser degree. Generally, the greater the magnetic field, the more pronounced the spectral-line broadening.
Given sufficiently sensitive equipment, there is almost no end to the wealth of data that can be obtained from starlight. Table 4.1 lists some basic measurable properties of an incoming beam of radiation, and indicates what sort of information can be obtained from them. It is important to realize, however, that deciphering the extent to which each of the factors just described influences a spectrum can be a very difficult task. Typically, the spectra of many elements are superimposed on one another, and several competing physical effects are occurring simultaneously, each modifying the spectrum in its own way. The challenge facing astronomers is to unravel the extent to which each mechanism contributes to spectral-line profiles and so obtain meaningful information about the source of the lines. In the next chapter we will discuss some of the means by which astronomers obtain the data they need in their quest to understand the cosmos.
