4.4 Spectral-Line Analysis

Astronomers apply the laws of spectroscopy in analyzing radiation from beyond Earth. A nearby star or a distant galaxy takes the place of the lightbulb in our previous examples. An interstellar 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.

A SPECTROSCOPIC THERMOMETER

Stars are very hot, especially deep down in their cores, where the temperature is measured in millions of kelvins. Because of the heat, atoms are fully ionized. Electrons travel freely through the gas, unbound to any nucleus, and the spectrum of radiation is continuous. However, at the relatively cool stellar surface some atoms retain a few, or even most, of their orbital electrons. As discussed previously, by matching the spectral lines we see with the laboratory spectra of known atoms, ions, and molecules, we can determine a star’s chemical composition.

The strength of a spectral line (brightness or darkness, depending on whether the line is seen in emission or absorption) depends in part on the number of atoms giving rise to the line—the more atoms there are to emit or absorb photons of the appropriate frequency, the stronger the line. But line strength also depends on the temperature of the gas containing the atoms, because temperature determines how many 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—then the only transitions that could occur would be the Lyman series (see More Precisely 4-1), 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 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 5800 K (as we saw in Chapter 3), few hydrogen atoms have electrons in any excited state. (Sec. 3.4) Hence, in the Sun, visible hydrogen lines are quite 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.

Spectroscopists have developed mathematical formulae that relate the number of emitted or absorbed photons to the energy levels of the atoms involved and the temperature of the gas. 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. These temperature measurements are generally much more accurate than crude estimates based on the radiation laws and the assumption of blackbody emission. (Sec. 3.4)

THE DOPPLER EFFECT AND LINE BROADENING

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 usual 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. (Sec. 3.5) They thus allow astronomers to measure how fast the source of the radiation is moving along the line of sight from the observer (its radial velocity). For example, suppose the 486.1 nm H line of hydrogen in the spectrum of a distant galaxy is received on Earth at a wavelength of 485 nm—blueshifted to a shorter wavelength. We can compute the galaxy’s line-of-sight velocity relative to Earth by using the Doppler equation presented in Section 3.5. We find that

so the recession velocity is (485/486.1 - 1) c = –680 km/s. In other words, the galaxy is approaching us at a speed of 680 km/s.
Figure 4.15 Line Profile By tracing the changing brightness across a typical emission line (a) and expanding the scale, we obtain a graph of its intensity versus wavelength (b).

The structure of the lines themselves reveals still more information. At first glance the emission lines shown earlier may seem uniformly bright, but more careful study shows that this is in fact not the case. As illustrated in Figure 4.15, the line brightness is greatest at the center and falls off toward either side. We stressed earlier that photons are emitted and absorbed at very precise energies, or frequencies. Why then 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. For definiteness, Figure 4.15 and subsequent figures refer to emission lines, but the ideas apply equally well to absorption features.

Several physical mechanisms can broaden spectral lines. The most important again involve the Doppler effect. Imagine a hot gas cloud containing individual atoms in random thermal motion in every possible direction, as illustrated in Figure 4.16(a). If an atom happens to be moving away from us as it emits a photon, that photon is redshifted by the Doppler effect—we do not record it at the precise wavelength predicted by atomic physics, but rather at a slightly longer wavelength. The extent of this redshift is proportional to the atom’s instantaneous velocity away from the detector. Similarly, if the atom is moving toward us at the instant of emission, its light is blueshifted. In short, because of thermal motion within the gas, emission and absorption lines are observed at frequencies slightly different from those we would expect if all atoms in the cloud were motionless.

Figure 4.16 Thermal Broadening Atoms moving randomly (a) produce broadened spectral lines (b) as their individual redshifted and blueshifted emission lines merge in our detector. The hotter the gas, the greater the degree of thermal broadening.
Most atoms in a typical cloud have small thermal velocities, so in most cases the line is Doppler-shifted just a little. Only a few atoms have large shifts. As a result, the center of a spectral line is much more pronounced than its “wings,” producing a bell-shaped spectral feature like that shown in Figure 4.16(b). Thus, even if all atoms emitted and absorbed photons at only one precise wavelength, the effect of their thermal motion would be to smear the line out over a range of wavelengths. The hotter the gas, the larger the spread of Doppler motions and the greater the width of the line. (More Precisely 3-1) By measuring a line’s width, astronomers can estimate the temperature of the gas producing it.

Rotation produces a similar effect. Consider an astronomical object (a planet, a star, or even an entire galaxy) oriented so that we see it spinning, as sketched in Figure 4.17. 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. Very often, the object under study is so small or far away that our equipment cannot distinguish, or resolve, different parts from one another—all the emitted light is blended together in our detector, producing a net broadening of the observed spectral lines. (If we could resolve the object, of course, we would be able to distinguish the redshifted and blueshifted sides and measure the rotation rate directly.) Note that this broadening has nothing to do with the temperature of the gas producing the lines, and is generally superimposed on the thermal broadening just discussed. The faster the object spins, the more rotational broadening we see.

Figure 4.17 Rotational Broadening 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 broadened lines. The more rapid the rotation, the greater the broadening.

Yet another mechanism that can cause line broadening is gas turbulence, which exists when the gas in an interstellar 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 also causes Doppler shifts of spectral lines, but lines from different parts of the cloud are shifted more or less randomly. Just as in the case of rotation, if our equipment is unable to resolve the cloud, a net broadening of its observed spectral lines results. The faster the internal motion, the greater the broadening observed. Remember that, again, the internal motion has nothing to do with the temperature of the gas.

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, “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.

Finally, magnetic fields can also broaden spectral lines, via a process called the Zeeman effect. The electrons and nuclei within atoms behave as tiny spinning magnets, and the basic emission and absorption rules of atomic physics change slightly whenever atoms are immersed in a magnetic field, as is the case in many stars to greater or lesser extents. The result is a slight “splitting” of a spectral line, which blurs into an overall line broadening. Generally, the stronger the magnetic field, the more pronounced the spectral-line broadening.

Additional analysis is usually required to determine the precise cause of line broadening. For example, if we know the temperature of the emitting gas by other means (perhaps by comparing intensities of different spectral lines, as discussed earlier), then we can calculate how much of the broadening is due to thermal motion. In addition, it is often possible to distinguish between the various broadening mechanisms described here by studying the detailed shapes of the lines.

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.


Concept Check

Why is it so important for astronomers to analyze spectral lines in detail?