(Background above) When a prism is placed in the path of light captured by a telescope, the resulting photograph can look almost psychedelic. Each of the stars and other sources of radiation in the picture has its light split into its component colors, from red to violet. Here, in this strange image, we see a star-forming region (called the Carina nebula) containing many stars and much loose gas--all of whose light has been colorfully dispersed.
(Inset A) This is the same celestial object, now photographed without the prism. The result is the Carina nebula in its true color--mostly red, due to vast quantities of hydrogen gas spread across the 900-light-year-squared area of this photo.
(Inset B) Looking more carefully at spectra from individual stars, we often see two things: a colorful spectrum extending from red to violet, and a series of thin, dark lines across the spectrum. This is the spectrum of the brightest star in the sky, Sirius A.
(Inset C) This is the slightly different spectrum of Vega, the bright star in the constellation Lyra.
(Inset D) Examining spectra of stars even more closely, we find evermore dark lines. Here, in this spectrum of the star Arcturus, we can see many such lines in the yellow region alone. The tracing below records precise details about these lines that would be difficult or impossible to obtain just by looking at the spectrum. Spectra like these, which tell astronomers virtually all that we know about stars, are the subject of this chapter.
Studying this chapter will enable you to:
Describe the characteristics of continuous, emission, and absorption spectra, and the conditions under which each is produced.
Explain the relation between emission and absorption lines and what we can learn from these lines.
Discuss the observations that led scientists to conclude that light has particle as well as wave properties.
Specify the basic components of the atom and describe our modern conception of its structure.
Explain how electron transitions within atoms produce unique emission and absorption features in the spectra of those atoms.
Describe the general features of the spectra produced by molecules.
List and explain the kinds of information that can be obtained by analyzing the spectra of astronomical objects.
In the previous chapter, we saw how light behaves as a continuous wave, and how this description of electromagnetic radiation allows us to begin to decipher the information reaching us from the cosmos in the form of visible and invisible light. However, early in the twentieth century, it became clear that the wave theory of electromagnetic phenomena was incomplete--some aspects of light simply could not be explained purely in wave terms. When radiation interacts with matter on atomic scales, it does so not as a continuous wave, but in a jerky, discontinuous way--in fact, as a particle. This so-called "wave-particle duality" of light is even today not fully understood; nevertheless, it is an undeniable fact of nature. With this discovery, scientists quickly realized that atoms too must behave in a discontinuous way, and the stage was set for a scientific revolution that has affected virtually every area of modern life. In astronomy, the observational and theoretical techniques that enable researchers to determine the nature of distant atoms by the way they emit and absorb radiation are now the indispensable foundation of modern astrophysics.
Back In Chapter 3, we saw something of how astronomers can analyze electromagnetic radiation received from space to obtain information about distant objects. A vital step in this process is the formation of a spectrum--splitting the incoming radiation into its component wavelengths. But in reality, no cosmic object emits a perfect black-body spectrum like those discussed in Section 3.4. All spectra deviate from this idealized form--some by only a little, others by a lot. Far from invalidating our earlier studies, however, these deviations contain a wealth of detailed information about physical conditions in the source of the radiation. Because spectra are so important, let's examine in a little more detail how astronomers obtain and interpret them.
Simple studies of radiation spectra can be performed with an instrument known as a spectroscope. In its most basic form, this might consist of an opaque barrier with a slit in it (to define a beam of light), a prism (to split the beam into its component colors), and an eyepiece or screen (to allow the user to view the resulting spectrum). Figure 4.1 shows such an arrangement. The research instruments (called spectrographs, or spectrometers) used by professional astronomers are rather more complex, consisting of a telescope (to capture the radiation), a dispersing device (to spread it out into a spectrum), and a detector (to record the result). Despite their greater sophistication, their basic operation is conceptually similar to the simple spectroscope shown in the figure.
Figure 4.1 Diagram of a simple spectroscope. A small slit in the mask on the left allows a narrow beam of light to pass. The light passes through a prism and is split up into its component colors. The resulting spectrum can be viewed through an eyepiece or simply projected onto a screen.
In many large instruments, the prism is replaced by a device called a diffraction grating, consisting of a sheet of transparent material with many closely spaced parallel lines ruled on it. The spaces between the lines act as many tiny openings, and light is diffracted as it passes through them. Because different wavelengths of electromagnetic radiation are diffracted by different amounts as they pass through a narrow gap (see Section 3.1), the effect of the grating is to split a beam of light into its component colors.
The spectra we encountered in Chapter 3 are examples of continuous spectra. A white-hot metal bar emits radiation of all wavelengths (mostly in the visible range). The distribution of the intensity of the various wavelengths is described by the black-body curve corresponding to the bar's temperature. Viewed through a spectroscope, the spectrum of the light from the bar would show the familiar rainbow of colors, from red to violet, without interruption, as presented in Figure 4.2(a). The light from an ordinary incandescent light bulb is another example of a continuous spectrum.
Figure 4.2 When passed through a slit and split up by a prism, light from a source of continuous radiation (a) gives rise to the familiar rainbow of colors. By contrast, the light from excited hydrogen gas (b) consists of a series of distinct spectral lines.
Not all spectra are continuous, however. For instance, if we took a glass jar containing pure hydrogen gas and passed an electrical discharge through it (a little like a lightning bolt arcing through Earth's atmosphere), the gas would begin to glow--that is, it would emit radiation. If we were to examine that radiation with our spectroscope, we would find that its spectrum consisted of only a few bright lines on an otherwise dark background, quite unlike the continuous spectrum described for the incandescent light bulb. Figure 4.2(b) shows this schematically. An actual photograph of the spectrum of hydrogen appears in the top panel of Figure 4.3. The light produced by the hydrogen in this experiment does not consist of all possible colors but instead includes only a few narrow, well-defined emission lines that resemble narrow "slices" of the continuous spectrum.
Figure 4.3 The emission spectra of some well-known elements.
After further experimentation, we would also find that although we could alter the intensity of the lines (for example, by changing the amount of hydrogen in the jar or the strength of the electrical discharge), we could not alter their color (in other words, their frequency or wavelength). The pattern of spectral emission lines is a property of the element hydrogen. Whenever we perform this experiment, the same characteristic colors for each gas result.
By the early nineteenth century, scientists had carried out similar experiments on many different gases. By vaporizing solids and liquids in a flame, they extended their inquiries to include materials that are not normally found in the gaseous state. Sometimes the pattern of lines was fairly simple, sometimes it was very complex. Always, though, it was unique. Even though the origin of the lines was a mystery, scientists quickly realized that the lines provided a one-of-a-kind "fingerprint" of the substance under investigation. Scientists could deduce the presence of a particular atom or molecule (a group of atoms held together by chemical bonds--see Section 4.4) solely through the study of the light it emitted.
Scientists have by now accumulated extensive catalogs of the specific wavelengths at which many different hot gases emit radiation. For gas of a given chemical composition, the particular pattern of the light it emits is known as its emission spectrum. Examples of the emission spectra of some common substances are shown in Figure 4.3.
When sunlight is split by a spectroscope, at first glance it appears to produce a continuous spectrum. This is what Isaac Newton must have seen over three centuries ago when he used a prism to view sunlight. However, closer scrutiny shows that the solar spectrum is actually interrupted by a large number of narrow dark lines, as shown in Figure 4.4. We now know that many of these lines are formed when intervening gases remove light from the Sun's otherwise continuous spectrum. These gases are present in the outer layers of the Sun or in Earth's atmosphere, and they absorb certain wavelengths, which then do not appear in the spectrum. The lines are called absorption lines.
Figure 4.4 This visible spectrum of the Sun shows hundreds of dark absorption lines superimposed on a bright continuous spectrum. Here, the scale extends from long wavelengths (red) at the upper left to short wavelengths (blue) at the lower right.
The English astronomer William Wollaston first noticed the solar absorption lines in 1802. They were studied in greater detail about 10 years later by the German physicist Joseph Fraunhofer, who measured and cataloged over 600 of them. They are now referred to collectively as Fraunhofer lines. Although the Sun is by far the easiest star to study, and so has the most extensive set of observed absorption lines, similar lines are now known to exist in the spectra of all stars.
At around the same time as the solar absorption lines were discovered, scientists found that absorption lines could also be produced in the laboratory by passing a beam of light from a continuous source through a cool gas, as shown in Figure 4.5. They quickly observed an intriguing connection between emission and absorption lines: The absorption lines associated with a given gas occur at precisely the same wavelengths as the emission lines produced when the gas is heated. Thus, if the emission lines form a unique fingerprint, so do the absorption lines.
Figure 4.5 (a) A hot light bulb produces a continuous emission spectrum. (b) When some cool gas is placed between the bulb and the detector, the resulting emission spectrum is crossed by a series of dark absorption lines. These lines are formed when the intervening gas absorbs certain wavelengths (colors) from the original beam. The absorption lines appear at precisely the same wavelengths as the emission lines that would be produced if the gas were heated to high temperatures.
As an example, consider the element sodium, whose emission spectrum appears in Figure 4.3. When sodium vapor is heated or energized in some other way, it emits almost all of its radiation at just two particular wavelengths in the visible range. The two characteristic yellow lines, with wavelengths of 589.0 nm and 589.6 nm, are clearly visible.
Now compare that result with what happens when a continuous spectrum is passed through some relatively cool sodium vapor. Two sharp, dark absorption lines appear in the spectrum at precisely the same wavelengths as the two lines that were emitted by hot sodium. The emission and absorption spectra of sodium are compared in Figure 4.6. The two spectra are shown to the same scale, clearly illustrating the relation between emission and absorption features.
Figure 4.6 (a) The characteristic emission lines of sodium. The two bright lines in the center appear in the yellow part of the spectrum. (b) The absorption spectrum of sodium. The two dark lines appear at exactly the same wavelengths as the bright lines in the sodium emission spectrum.
Back The analysis of the ways in which matter emits and absorbs radiation is called spectroscopy. One early spectroscopist, the German physicist Gustav Kirchhoff, summarized the observed relationships between the three types of spectra--continuous, emission line, and absorption line--in 1859. He listed three spectroscopic rules, now known as Kirchhoff's laws, governing the formation of spectra:
Figure 4.7 illustrates Kirchhoff's laws and the relationship between absorption and emission lines. When viewed directly, the light source, a hot solid (the filament of the bulb), has a continuous (black-body) spectrum. When viewed through a cloud of cool hydrogen gas, a series of dark absorption lines appear at wavelengths characteristic of hydrogen. The lines appear because the light at those wavelengths is absorbed by the hydrogen. As we will see later in this chapter, the absorbed energy is subsequently reradiated into space, but in all directions, not just the original direction of the beam. Consequently, when the cloud is viewed from the side against an otherwise dark background, a series of faint emission lines is seen. These lines contain the energy lost by the forward beam. If the gas were heated to incandescence, it would produce stronger emission lines at precisely the same wavelengths.
Figure 4.7 A source of continuous radiation, here represented by a light bulb, is used to illustrate Kirchhoff's laws of spectroscopy. (a) The unimpeded beam shows the familiar continuous spectrum of colors. (b) When viewed through a cloud of hydrogen gas, a series of dark hydrogen absorption lines appears in the continuous spectrum. These lines are formed when the gas absorbs some of the bulb's radiation and reemits it in random directions. Since most of the reemitted radiation does not go through the slit, the effect is to remove the absorbed radiation from the light that reaches the screen at left. (c) When the gas is viewed from the side, a fainter hydrogen emission spectrum is seen, consisting of reemitted radiation. The absorption lines in (b) and the emission lines in (c) thus have the same wavelengths. (If the gas were heated to incandescence, it would produce stronger emission lines at the same wavelengths.)
By the late nineteenth century, spectroscopists had developed a formidable arsenal of techniques for interpreting the radiation received from space. Once astronomers knew that spectral lines were indicators of chemical composition, they set about identifying the observed lines in the solar spectrum. Almost all of the lines in light from extraterrestrial sources could be attributed to known elements (for example, many of the Fraunhofer lines in sunlight are associated with the element iron). However, some new lines also appeared in the solar spectrum. In 1868, astronomers realized that those lines must correspond to a previously unknown element. It was given the name helium, after the Greek word helios, meaning "Sun." Only in 1895, almost three decades after its detection in sunlight, was helium discovered on Earth. (A laboratory spectrum of helium is part of Figure 4.3.)
For all the information that nineteenth-century astronomers could glean from observations of stellar spectra, they still lacked a theory explaining how the spectra themselves arose. Despite their sophisticated spectroscopic equipment, they knew scarcely any more about the physics of stars than did Galileo or Newton. To understand how spectroscopy can be used to extract detailed information about astronomical objects from the light they emit, we must delve more deeply into the processes that produce line spectra.
Back By the start of the twentieth century, experimental physicists had accumulated evidence that light sometimes behaves in a manner that simply cannot be explained by the wave theory. As we have just seen, the production of absorption and emission lines involves only certain very specific frequencies or wavelengths (colors) of light. This would not be expected if light behaved like a continuous wave and matter always obeyed the laws of Newtonian mechanics. Other experiments conducted around the same time strengthened the conclusion that the notion of radiation as a wave was incomplete. It became clear that, when light interacts with matter on very small scales, it does so not in a continuous way but in a discontinuous, stepwise manner. The challenge was to find an explanation for this unexpected behavior. The eventual solution revolutionized our view of nature and now forms the foundation not just for physics and astronomy, but for virtually all of modern science.
Albert Einstein provided a major breakthrough in 1905. He realized that it was possible to explain a number of puzzling experimental results (especially the photoelectric effect--see the More Precisely feature below) by assuming that light travels as individual packets of electromagnetic energy, now called photons. In this way, Einstein revised the entire theory of electromagnetic radiation, showing that although it sometimes behaves as a wave, at other times it acts as a stream of particles.
Further, Einstein was able to quantify the relationship between the two aspects of light's double nature. He found that the energy carried by a photon is proportional to the frequency of the radiation:
photon energy radiation frequency.
Thus, for example, a "red" photon with a frequency of 4 × 1014 Hz (corresponding to a wavelength of approximately 750 nm, or 7500 ) has 4/7 the energy of a "blue" photon with a frequency of 7 × 1014 Hz (and a wavelength 400 nm, or 4000 ).
The realization that light can behave both as a wave and as a particle is another example of the scientific method at work. Despite the enormous success of the wave theory of radiation in the nineteenth century, the experimental evidence led scientists to the inevitable conclusion that the theory was incomplete--it had to be modified to allow for the fact that light exhibits particle characteristics. In addition to bringing about the birth of a whole new branch of physics--now known as quantum mechanics--this new theory radically changed the way physicists view light and all other forms of radiation.
Environmental conditions ultimately determine which description best fits the behavior of electromagnetic radiation--a wave or a stream of particles. As a general rule of thumb, in the macroscopic realm of everyday experience, radiation is more usefully described as a wave, while in the microscopic domain of atoms, it is best characterized as a series of particles. Many people are confused by the idea that light can behave in two such different ways. To be truthful, modern physicists don't yet fully understand why nature displays this wave-particle duality. Nevertheless, there is irrefutable experimental evidence for both of these aspects of radiation.
Back To explain the formation of spectral lines, we must understand not just the nature of light, but also something of the structure of atoms--the microscopic building blocks from which all matter is constructed. Let us start with the simplest atom of all--hydrogen. A hydrogen atom consists of an electron, with a negative electrical charge, orbiting a proton, which carries a positive charge. The proton forms the central nucleus (plural: nuclei) of the atom. The hydrogen atom as a whole is electrically neutral. The equal and opposite charges of the proton and the orbiting electron produce an electrical attraction that binds them together within the atom.
How does this picture of the hydrogen atom relate to the characteristic emission and absorption lines associated with hydrogen gas? If an atom emits some energy in the form of radiation, that energy has to come from somewhere within the atom. Similarly, if energy is absorbed, it must cause some internal change. It is reasonable (and correct) to suppose that the energy emitted or absorbed by the atom is associated with changes in the motion of the orbiting electron.
The first theory of the atom to provide an explanation of hydrogen's observed spectral lines was propounded by the Danish physicist Niels Bohr. This theory is now known simply as the Bohr model of the atom. Its essential features are as follows. First, there is a state of lowest energy--the ground state--which represents the "normal" condition of the electron as it orbits the nucleus. Second, there is a maximum energy that the electron can have and still be part of the atom. Beyond that energy, the electron is no longer bound to the nucleus, and the atom is said to be ionized. (An ion is an atom that has either lost or gained electrons.) Third, and most important (and also least intuitive), between those two energy levels, the electron can exist only in certain sharply defined energy states, sometimes referred to as orbitals. The orbital energies are said to be quantized. This description of the atom contrasts sharply with the predictions of Newtonian mechanics, which would permit orbits at any energy, not just at certain specific values. The rules of quantum mechanics are far removed from everyday experience.
In Bohr's model, each electron orbital was pictured as having a specific radius, much like a planetary orbit in the solar system, as shown in Figure 4.8. However, the modern view is not so simple. Although each orbital does have a precise energy, the electron is now envisioned as being smeared out in an "electron cloud" surrounding the nucleus, as illustrated in Figure 4.9. It is common to speak of the mean (average) distance from the cloud to the nucleus as the "radius" of the electron's orbit. When a hydrogen atom is in its ground state, the radius of the orbit is about 0.05 nm (0.5 ). As the orbital energy increases, the radius increases, too. For the sake of clarity in the diagrams that follow, we will represent electron orbitals by solid lines, but bear in mind always that Figure 4.9 is a more accurate depiction of reality.
Figure 4.8 An early conception of the hydrogen atom pictured its electron orbiting the central proton in a well-defined orbit, rather like a planet orbiting the Sun. Two electron orbits of different energies are shown. The left-hand figure represents the ground state, the right-hand figure an excited state.
Figure 4.9 The modern view of the hydrogen atom sees the electron as a "cloud" surrounding the nucleus. The same two energy states are shown as in Figure 4.8.
Atoms do not always remain in their ground states. An atom is said to be in an excited state when an electron occupies an orbital at a greater than normal distance from its parent nucleus. An atom in such an excited state has a greater than normal amount of energy. The excited state with the lowest energy (that is, the one closest in energy to the ground state) is conventionally called the first excited state, that with the second-lowest energy the second excited state, and so on.
How can atoms become excited? Generally, in one of two ways: They can become radiatively excited by absorbing some light energy from a source of electromagnetic radiation, or they can become collisionally excited by colliding with another particle--an atom or a free electron, for example. However, the electron cannot stay "out of place" in this higher orbital forever--the ground state is the only level where it can remain indefinitely. After about 10-8 s, it returns to its normal ground state.
Here now is the crucial point that links atoms to radiation and allows us to interpret atomic spectra. Because electrons may exist only in orbitals having specific energies, atoms can absorb only specific amounts of energy as their electrons are boosted into excited states. Likewise, they can emit only specific amounts of energy as their electrons fall back to lower energy states. Thus, the amount of light energy absorbed or emitted in these processes must correspond precisely to the energy difference between two orbitals. The quantized nature of the atom's energy levels requires that light must be absorbed and emitted in the form of little "packets" of electromagnetic radiation, each carrying a very specific amount of energy--that is, in the form of photons.
An atom therefore absorbs and emits radiation
at the same characteristic wavelengths, which are determined by the
atom's own internal structure. The basic process of absorption and
emission of photons by a hydrogen atom are illustrated schematically in
Figure 4.10(a). In the example shown here, where a hydrogen atom makes
transitions between the ground state and the first excited state, the
photon energy happens to correspond to an ultraviolet photon, of
wavelength 121.6 nm (1216
Classical Hydrogen Atom I
Classical Hydrogen Atom II
Figure 4.10 (a) Diagram of a photon being absorbed by a hydrogen atom (left), causing the momentary excitation of that atom (center) into its first excited state. Eventually, the atom returns to its ground state, accompanied by the emission of a photon of the same energy as the original photon (right). (b) Absorption of a photon might also boost the atom into a higher excited state, from which there may be several possible paths back to the ground state. (The sharp lines used for the orbitals here and in similar figures that follow are intended merely as a schematic representation of the electron energy levels, and are not meant to be taken literally. In actuality, electron orbitals are "clouds," as shown in Figure 4.9. As ultraviolet photons from a hot star pass through surrounding hydrogen gas, many are absorbed by the gas, boosting its atoms into excited states. Electrons in the second excited state can fall to the first excited state on their way back to the ground state (the upper path in part b). This transition produces radiation in the visible region of the spectrum--the 656.3 nm red glow that is characteristic of excited hydrogen gas. The object shown in the inset, designated NGC 2440, is an emission nebula: an interstellar cloud consisting largely of hydrogen gas excited by an extremely hot star (the white dot in the center).
Absorption can also boost an electron into higher excited states. From such a state, the electron may return to the ground state via several alternate paths. Thus, the absorption of a single high-energy photon may lead to the subsequent emission of two or more lower-energy photons as the atom returns to its ground state. For example, as illustrated in Figure 4.10(b), a hydrogen atom can be boosted from the ground state past the first excited state, all the way up into the second excited state. As before, the electron returns rapidly to the ground state, but this time it can do so in two possible ways:
Absorption of additional energy could boost the electron to even higher orbitals within the atom. As the excited electron cascaded back down to the ground state, the atom could emit many photons, each with a different energy and hence a different wavelength. The resulting spectrum would therefore show many spectral lines. In a sample of heated hydrogen gas, at any instant, atoms are found in many different excited states. The complete emission spectrum therefore consists of wavelengths corresponding to all possible transitions between those states and states of lower energy. The visible hydrogen spectrum shown earlier (in Figure 4.3) is the result. In the case of hydrogen, it so happens that transitions from higher states back to the first excited state are the ones corresponding to spectral lines in the visible range. As we have just seen, transitions ending at the ground state produce ultraviolet photons. The energy levels and the spectrum of hydrogen are discussed in more detail in the next More Precisely feature.
Back To appreciate further how spectral lines are produced, let's reconsider our earlier discussion of emission and absorption lines in terms of the model just presented. In Figure 4.7, a beam of continuous radiation shines through a cloud of hydrogen gas. The beam contains photons of all energies, but most of them cannot interact with the gas--the gas can absorb only those photons having precisely the right energy to cause a change in an electron's orbit from one state to another (an electronic transition). All other photons in the beam--with energies that cannot produce a transition--do not interact with the gas at all, but pass through it unhindered. Those photons that do have the right energy excite the gas and are removed from the beam.
The excited atoms return rapidly to their original states, each emitting one or more photons in the process. We might think, then, that although some photons from the beam are absorbed by the intervening cool gas, they would quickly be replaced by reemitted photons, so we would never observe the effects of absorption. This is not the case, however, for two important reasons. First, although the photons not absorbed by the intervening gas follow a clear path to the detector, the reemitted photons can leave in any direction. Thus, many of the photons are absorbed and reemitted at other angles, and so are effectively lost from the original beam. Second, as we have just seen, electrons can cascade back to the ground state, emitting several lower-energy photons instead of a single photon equal in energy to the one originally absorbed. The net result of these two processes is that the original energy is channeled into photons of many different colors, moving in many different directions.
A detector looking through the cloud at the source of the radiation (a star, say) records a continuous spectrum, except at those precise wavelengths where photons have been subtracted from the beam. The dark absorption lines thus produced are characteristic of the intervening gas. They are direct indicators of the energy differences between atomic orbitals. The regions of bright emission surrounding the dark lines is unchanged by the intervening cloud. It is produced by those photons in the beam that passed through the gas without being absorbed.
A detector looking at the cloud from the side records the energy that is reemitted from the cloud after absorption within the gas. Again, the spectrum is characteristic of the gas, not of the original beam. An example is shown in the inset of Figure 4.10, where the (mainly ultraviolet) radiation from a young, hot star excites the surrounding cool hydrogen gas out of which the star recently formed. The gas emits a characteristic red glow at a wavelength of precisely 656.3 nm--the wavelength corresponding to transitions from the second to the first excited states of hydrogen.
Absorption and emission spectra are created by the same atomic processes. They correspond to the same atomic transitions. They contain the same information about the composition of the cloud. In the lab, we can move our detector and can measure both. In astronomy, we are not able to change our vantage point--the type of spectrum we see depends on our chance location with respect to both the source and the cloud.
All hydrogen atoms have basically the same structure--a single electron orbiting a single proton--but, of course, there are many other kinds of atoms, each kind having a unique internal structure. The number of protons in the nucleus of an atom determines the element that it represents. That is, just as all hydrogen atoms have a single proton, all oxygen atoms have 8 protons, all iron atoms have 26 protons, and so on.
The next simplest element after hydrogen is helium. The central nucleus of the most common form of helium is made up of two protons and two neutrons (another kind of elementary particle having a mass slightly larger than that of a proton but having no electrical charge at all). About this nucleus orbit two electrons. As with hydrogen and all other atoms, the "normal" condition for helium is to be electrically neutral, with the negative charge of the orbiting electrons exactly canceling the positive charge of the nucleus (Figure 4.11).
Figure 4.11 A helium atom in its normal, ground state. Two electrons occupy the lowest-energy orbital around a nucleus containing two protons and two neutrons.
More complex atoms contain more protons (and neutrons) in the nucleus and have correspondingly more orbiting electrons. For example, an atom of carbon, shown in Figure 4.12, consists of six electrons orbiting a nucleus containing six protons and six neutrons. As we progress to heavier and heavier elements, the number of orbiting electrons increases, and the number of possible electronic transitions rises rapidly. The result is that very complicated spectra can be produced. The complexity of atomic spectra generally reflects the complexity of the atoms themselves. A good example is the element iron, which contributes several hundred of the Fraunhofer absorption lines seen in the solar spectrum. The many possible transitions of its 26 orbiting electrons yield an extremely rich line spectrum (see Figure 4.4). Even very heavy elements, such as gold (with 79 orbiting electrons) and lead (with 82) have been observed in some astrophysical settings.
Figure 4.12 A carbon atom in its normal, ground state. Six electrons orbit a six-proton, six-neutron nucleus, two in an inner orbital, the other four at a greater distance from the center.
The complex transitions among the various orbitals are unique to each element. Consequently, as electrons in a given atom return to lower orbitals from higher-energy states, or absorb radiation and jump to excited states, the photons that emitted or absorbed carry energies characteristic of that element--and only that element. This fact explains the power of spectroscopy. Even though many different kinds of atoms might be mixed together in a gas, spectroscopy enables us to study one kind of atom to the exclusion of all others simply by focusing on specific wavelengths of radiation. Thus, for example, a cool intervening gas cloud containing many elements will produce a very complicated absorption spectrum in the light received from a background continuous source. Nevertheless, by identifying the (superimposed) absorption spectra of many different atoms, we can determine the cloud's composition. Figure 4.13 shows an actual spectrum observed coming from a cosmic object, with some spectral lines labeled.
Figure 4.13 The visible spectrum of the hot gases in a nearby star-forming region known as the Omega nebula (M17). Shining by the light of several very hot stars, the nebula produces a complex spectrum of bright and dark lines (bottom), also shown here as an intensity trace from red to blue (center).
Spectral lines occur throughout the entire electromagnetic spectrum. Usually, electron transitions among the lowest orbitals of the lightest elements (such as hydrogen and helium) produce visible and ultraviolet spectral lines. Transitions among very highly excited states of hydrogen and other elements can produce spectral lines in the infrared and radio parts of the electromagnetic spectrum. Conditions on Earth make it all but impossible to detect these radio and infrared features in the laboratory, but they can be routinely observed coming from space. Electron transitions among lower energy levels in heavier, more complex elements produce X-ray spectral lines. These lines have been observed in the laboratory; some of them are also observed in stars and other cosmic objects.
Back A molecule is a tightly bound group of atoms held together by interactions between their orbiting electrons--interactions that we call chemical bonds. Much like atoms, molecules can exist only in certain well-defined energy states, and again like atoms, molecules produce emission or absorption spectral lines when they make a transition from one state to another. Because molecules are more complex than individual atoms, the rules of molecular physics are also much more complex. Nevertheless, as with atomic spectral lines, painstaking experimental work over many decades has determined the precise frequencies (or wavelengths) at which millions of molecules emit and absorb radiation. In addition to the lines resulting from electron transitions, lines are produced by molecules because of two other kinds of changes not possible in atoms: molecules can rotate, and they can vibrate. Figure 4.14 illustrates these basic molecular motions. Molecules rotate and vibrate in specific ways. Only certain spins and vibrations are allowed by the rules of molecular physics. When a molecule changes its rotational state or its vibrational state, a photon is emitted or absorbed. Spectral lines characteristic of the specific kind of molecule result. These lines are molecular fingerprints, just like their atomic counterparts, enabling researchers to identify and study one kind of molecule to the exclusion of all others.
Figure 4.14 Molecules can change in three ways while emitting or absorbing electromagnetic radiation. Sketched here is the molecule carbon monoxide (CO) experiencing (a) a change in electron arrangement, in which an electron in the outermost orbital of the oxygen atom drops to a lower-energy state, (b) a change in rotational state, and (c) a change in vibrational state.
As a rule of thumb, we can say that
Molecular lines usually bear little resemblance to the spectral lines associated with their component atoms. For example, Figure 4.15(a) shows the emission spectrum of the simplest molecule known--molecular hydrogen. Notice how different it is from the spectrum of atomic hydrogen shown in part (b) of the figure.
Figure 4.15 (a) The spectrum of molecular hydrogen. Notice how it differs from the spectrum of the simpler atomic hydrogen (b).
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.
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 and molecules, the chemical composition of the star can be determined.
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 might 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, discussed in Section 3.6. They thus allow astronomers to find out how fast the source of the radiation is moving along the line of sight to the observer (its radial velocity).
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 the More Precisely feature below), 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 is 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. Hence, in the Sun, visible hydrogen lines are relatively weak--that is, of low intensity compared to 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. It takes a little time--about 10 nanoseconds (10-8 s), typically--for the electrons to fall back to the ground 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 where 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 (while 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.
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 against wavelength (b).
Several physical mechanisms can broaden spectral lines. The most important of these involve the Doppler effect. 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. According to our previous discussion of the Doppler effect, the extent of this red shift is proportional to the velocity away from the detector. Similarly, if the atom is moving toward us, its light is received at a shorter wavelength and so is blueshifted.
Figure 4.17 Atoms moving around 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.
Actually, 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 together 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 contained in 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 the means by which astronomers obtain the data they need in their quest to understand the cosmos.