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Home , Dwarf star, PG 1159 star, Pulsating white dwarf, White dwarf

A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society

This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions, American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected]. ©Sigma Xi, The Scientific Research Society and other rightsholders Dwarf

The remnants of -like stars, white dwarfs offer clues to the identity of dark and the age of our

Steven D. Kawaler and Michael Dahlstrom

ix billion years from now, someone these fascinating stars. Since they rep- with the naked eye. Obviously, some- Slooking up at the sky on a summer’s resent the final stage in the evolution of thing was different about these new day would not see the same bright Sun 98 percent of all stars, the study of objects. By 1914 the mystery was clear. we now see. In its place would be a tiny white dwarfs is very nearly the study For these stars to be so faint, they had orb—a “”—shining feebly of all stars. As the remains of once-bril- to be extremely small—about the same in a black sky. Whether anyone will be liant , white dwarfs can provide size as the , or just 1/100 the di- around to see such an alien sky is an- information about their earlier lives in ameter of the Sun. Their white-hot sur- other question: All life on Earth much the same way that human re- faces and small diameters provided a would have been obliterated when the mains provide information to forensic name for this new class of stars: white Sun entered its red-giant stage a bil- anthropologists. White dwarfs are also dwarfs. lion years earlier. The white dwarf convenient astrophysical laboratories White dwarfs were truly a puzzle. A will endure for many billions of years in which we can study matter at pres- with the of the Sun confined afterward as a small monument to our sures and temperatures that cannot be to the volume of the Earth must have . achieved in terrestrial laboratories. an enormous . How could such Our Sun may be billions of years Much of this information is revealed an object support itself against its own away from such a fate, but there are through complex vibrations created in ? What processes could make countless numbers of white dwarfs now the interiors of white dwarfs that can be such a star? Today we can answer these in our Galaxy. “Countless” is an apt term measured using a unique tool known as questions. in this case, since their total number is the Whole Earth Telescope. What as- During a star’s lifetime there are two not known—they are too small and too tronomers have learned about white forces fighting for control. The first is the dim to be easily seen. Indeed, white dwarfs has implications beyond our un- inward force of gravity, trying to com- dwarfs were only identified as a distinct derstanding of . Recent press the star to as small a point as pos- class of stars less than 100 years ago, a work shows that these stars can be used sible. Opposing gravity is the outward testimony to their relative obscurity. Al- to find the age of our Galaxy and may force of gas pressure provided by high most all of the catalogued white dwarfs even make up a large fraction of the temperatures inside the star. Although lie within the immediate solar neighbor- mysterious in the . energy is lost by radiation, the star main- hood, and nearly half of these can be tains its high temperature through nu- found within 75 light-years of our Sun. Strange Little Stars clear fusion as it burns into Although they are difficult to locate, In the year 1783, two years after dis- . These two forces balance each there are many reasons to care about covering the Uranus, British as- other precisely, creating a stable stellar tronomer became the structure—at least for a while. Steven Kawaler is professor of astrophysics in the first person to see a white . Eventually, the star’s central reserves Department of Physics and at Iowa On the evening of January 31, Herschel of hydrogen are exhausted. Fusion State University. A theorist in stellar evolution observed a star in his telescope named ceases at the center, but continues in a and pulsation, he has co-directed the Whole Earth 40 Eri B, which actually proved to be a thin shell surrounding the now pure Telescope since 1997. As time permits, he escapes pair of stars, one of which was a “faint, helium core. Within the core, the in- to the rhythms of the baseball (mostly as dusky star.” At the time he didn’t rec- ward force of gravity starts to win out a spectator these days). Michael Dahlstrom is an ognize it as being anything unusual. over the outward gas pressure, and the undergraduate student majoring in both The strangeness of Herschel’s star core collapses. The gravitational ener- biophysics and journalism at Iowa State did not become apparent for another gy released by the core, combined with University. He has been involved with the Whole 127 years. In 1910 re- the energy output of the burning shell, Earth Telescope since 1999. Michael enjoys observing and his neighbors through a vealed that 40 Eri B (and two other puffs the outer layers of the star to a small, four-inch telescope. Address for Kawaler: stars like it) had surfaces that were hot- huge radius with a low surface tem- Department of Physics and Astronomy, Iowa State ter than our Sun. But they were so perature (forming a star) and University, Ames, IA 50011. Internet: close to the Earth that, were they nor- briefly increases its energy output by a [email protected] mal stars, they would be easily visible thousand times.

498 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. Hubble Heritage Team (AURA/STScI/NASA) Figure 1. Spectacular ejection of material from a dying star forms a planetary and leaves behind a feeble remnant, which will become a white dwarf (visible here in the center of the ring). Although some consider a white dwarf to be a dead star (since has ceased to provide energy within), it is hardly a quiet corpse. Changes in temperature and pressure within the white dwarf result in vibrational instabili- ties that resonate throughout the object, resulting in “starquakes.” Stellar seismologists have learned much about the structure and composi- tion of white dwarfs by continuously following their activity with a global network of telescopes, collectively known as the “Whole Earth Telescope.” Here a high-resolution image of the (M57) reveals details in the radial patterns sculpted in the gas and dust exhaled by the dying star. Our Sun will undergo a similar transformation in the course of its death throes about 5 billion years from now.

Soon, the compression of the core time (as an asymptotic giant-branch star). the center of the nebula is the collapsed generates enough to ignite the fu- As the core shrinks, some of its outer en- core—a newly formed white dwarf. sion of helium into , and the star velope breaks free and cools to become a To understand the of a returns to nearly normal dimensions. colorful (so called be- white dwarf’s collapse, imagine going Eventually, the central helium supply cause early astronomers confused these to the local bowling alley and finding also becomes exhausted and the dying structures with distant like the heaviest bowling ball they have. star succumbs to gravity again: The core Uranus; see “The Shapes of Planetary Take it in your hands and squeeze it collapses, shell burning resumes and the Nebulae,” American Scientist July–Au- until it is the size of this letter “o.” star becomes a red giant for a second gust 1996). Finally, glowing proudly at Compressing that much mass into

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 499 with permission only. Contact [email protected]. nearly pure nearly pure nearly pure exposed core of hydrogen surface neutral helium surface ionized helium surface carbon and helium shell

DA DB DO PG 1159

carbon and oxygen core

Figure 2. White dwarf varieties are defined by the elements that dominate their surfaces as revealed by their spectra (the continuum of light they emit). Nearly all white dwarfs are believed to contain a core of carbon and oxygen (blue). Three varieties—DA, DB and DO white dwarfs—have nearly pure surfaces of hydrogen or helium lying atop their cores, whereas PG 1159 stars appear to be partially exposed cores. White dwarfs may also have a mixture of elements on their surfaces, and are named accordingly. For example, DAB stars contain hydrogen and neutral helium, whereas DAO stars have hydrogen and ionized helium. such a small volume creates a very dinary gas pressure to resist. The only cannot share the same state. The gravi- dense vowel! This is the same degree force keeping the star from total de- ty of a white dwarf compresses the of compression a white dwarf faces struction is the behavior of . electrons to the point where they can- during its final . According to the Pauli exclusion prin- not be any closer. (This explanation At these high , the self- ciple, no two electrons can share the was first given in 1926 by the astro- gravity of the star is too strong for or- same quantum numbers and therefore physicist Ralph H. Fowler of the Uni- versity of Cambridge. It was later clar- 100 ified with numerical models by one of his students, Subrahmanyan Chan- drasekhar, who won a share of the 1983 for his efforts.) This degeneracy pressure stabi- 80 lizes the star at an incredibly high den- sity: one million times that of water. No arfs substance on Earth has a density any- dw where close. The densest terrestrial ma- 60 terial is pure iridium, with a density of white DA A 22.65 times that of water. Gold weighs in at merely 19.3, and is a light- weight at 7.9. non-D

of From this we can understand the 40 makeup of a typical white dwarf. Like the three layers of a melon, a white dwarf consists of an electron-degener- percentage ate core of carbon and oxygen, which is 20 surrounded by a thin rind of helium and an outer skin of hydrogen. Not all DB white dwarfs have the same structure, PG 1159 DO gap DB however. Subtle differences among white dwarfs show that a star may take 0 one of several possible evolutionary 100,000 65,000 40,000 28,000 15,000 10,000 6,000 paths as it runs out of nuclear fuel. temperature (, log scale) White Dwarf Flavors Spectroscopy reveals that most white Figure 3. Distribution of white dwarf varieties according to their temperatures reveals a mys- terious absence of non-DA stars around 40,000 kelvins, known as the “DB gap.” As their dwarfs have almost pure surfaces of ei- temperatures drop, DO white dwarfs are believed to become DB stars when the ionized heli- ther hydrogen or helium. This pro- um recombines with free electrons to form neutral helium. The absence of DO and DB stars vides a handy classification system that at the DB gap suggests an intermediate stage in which a DB star is masked as a DA star. The reflects the unusual surface composi- reason for the DB gap is not fully understood. tion of these stars. White dwarfs with

500 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. surfaces of hydrogen are called DA stars. White dwarfs that have pure he- lium atmospheres with strong neutral helium (He I) lines are named DB stars. If the helium white dwarf shows rela- DA PG 1159 DO tively strong lines of singly ionized he- lium (He II) it is called a DO star. As a temperatures DO star cools, the He II will recombine high with free electrons to form He I, even- tually changing the DO into a DB white dwarf. Although most white dwarfs show DO only hydrogen or helium on their sur- faces, there are a few with mixed spec- tra. They are named accordingly. Hy- drogen-covered white dwarfs with lines of He I are named DAB stars, whereas hydrogen stars with lines of DB DA DA He II are logically named DAO stars. gap? Some rare white dwarfs show evidence of carbon in their spectra (DQ stars) or other heavier elements (DZ stars). One of the most bizarre classes of white dwarf is the very hot, hydrogen- deficient PG 1159 stars. These are the hottest white dwarfs, with tempera- DB DB

tures as high as 170,000 kelvins. They temperatures have no hydrogen or He I lines, but do show weak He II lines and stronger low lines of ionized carbon and oxygen. PG 1159 stars appear to be the exposed in- ner core of a white dwarf. As a delight- Figure 4. Hot white dwarfs (top row) pass through one of several evolutionary paths (white arrows) as they cool with age. Some white dwarfs remain as DA stars throughout their exis- ful tongue twister, PG 1159 stars can tence (left column), whereas PG 1159 stars (middle column) may evolve through two or more also be classified as DOZQ stars! other white dwarf varieties. DO stars may evolve through the DB gap to become identifiable The flavor of a white dwarf is deter- DB stars (right column), but none has been observed within the gap. mined, in part, by the type of shell burning (hydrogen or helium) that dominated as it became a planetary nebula. If the star was burning hydro- gen, the white dwarf that resulted would probably be a hydrogen-rich volume

DA. If the parent star was burning he- unit lium, the most likely outcome would be a DO (and later, a DB) star. In rare per instances, a final burst of helium-gen- white dwarf erated nuclear energy occurs after the dwarfs “drop-off” planetary nebula has formed. This blast ejects the hydrogen and almost all white of the helium from the white dwarf, ex- of posing a PG 1159 star.

A very interesting phenomenon ap- number pears when we tally the actual num- bers of DA, DB, DO and PG 1159 stars according to the range of white dwarf relative temperatures. PG 1159 stars appear at bright of white dwarf dim the hot end, followed by the helium- rich DO stars. As the temperature de- Figure 5. White dwarfs become cooler and dimmer over time, allowing astronomers to esti- creases from 80,000 kelvins to 45,000 mate their age. Because the oldest white dwarfs must be the remnants of the Galaxy’s first stars, estimating their age provides astronomers with a tool to measure the age of the Milky kelvins, the hydrogen-rich DA stars in- Way. Here a rapid decrease in the numbers of very dim white dwarfs (a so-called “drop-off”) crease in number. Then suddenly, from suggests that the Galaxy is not sufficiently old to contain cooler (hence older) stellar rem- 45,000 kelvins to 27,000 kelvins, all he- nants. Current estimates based on the cooling rate of white dwarfs suggests that our Galaxy lium white dwarfs disappear, leaving is about 9 billion years old, an age consistent with independent estimates of the age of the only hydrogen DA stars. At tempera- universe (about 13 billion years old).

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 501 with permission only. Contact [email protected]. A possible explanation lies in the chemical evolution of white dwarfs. Four processes can change the structure of a white dwarf: gravitational settling, hot , mass loss and subsurface convective mixing. Like the separation of oil and vine- gar, gravitational settling separates the high white dwarf’s constituents by atomic density surface cool cool weight. Under the intense gravity at surface wave the surface of a white dwarf (as much wave low low as 100,000 times stronger than at the density density surface Earth’s surface), heavier elements sink surface to the core, whereas lighter elements buoyancy wave wave float to the surface. This diffusion is high buoyancy density the dominant physical process in a high white dwarf, and it is responsible for density the ultra-pure surfaces we see with spectroscopy. Two of the processes oppose one an- other: accretion from the interstellar Figure 6. “Starquakes” on a white dwarf can be observed as periodic changes in the relative medium and the loss of mass. The inter- brightness of the star. Temperature changes within the white dwarf result in the vertical stellar medium is made mostly of hy- movement of dense material above its equilibrium point in the star. High-density material is drogen and helium, with trace amounts relatively hotter (and thus brighter) than low-density material, which results in variations in the amount of light emitted across the surface of the star. Since the changes in density are of heavier elements. These materials can restored by buoyancy (orange arrows), or gravity, these pulsations are known as “g-mode” fall onto the white dwarf, polluting an oscillations. The small vertical motions also generate larger, horizontal motions (surface otherwise pure surface. The opposite is waves) that propagate across the star. true of mass loss. The material near the surface of a white dwarf can drift off into space, exposing deeper material of tures cooler than 27,000 kelvins, the Such a linear scheme is a little too different composition. helium DB stars begin to appear and simple, however. Consider the “disap- Subsurface convection is the rapid dominate in numbers below 10,000 pearance” of helium white dwarfs be- and active mixing of the material in- kelvins. The decreasing surface tem- tween 45,000 and 27,000 kelvins. This side a star. As a white dwarf cools, con- peratures are indicative of a progres- mysterious observation is called the DB vection can mix material from below sive cooling, which suggests a general gap. Something strange is happening in into the surface layers. evolutionary sequence from PG 1159 the outer layers of helium white dwarfs These evolutionary processes act at stars to DO, then DA and then DB as they cool below 45,000 kelvins caus- different times in the cooling history of stars. ing the helium to disappear. a white dwarf, and the interplay be-

surface pulsation patterns

much warmer l=1 l=2 l=3 warmer m=1 m=1 m=1 l=2 little change m=0 cooler nodal planes n=2

Figure 7. Stellar pulsations (shading in the top three spheres at left) can be characterized by three harmonic components—l, m and n—that define nodal surfaces or planes, which mark a change in the phase of the vibrations. Thus a nodal surface corresponds to a region of the star where there is very little temperature change. The l component gives the number of nodal planes that slice through the star’s surface. The m component defines the number of these nodal planes that include the star’s axis. The n component identifies the number of nodes that lie in the radial dimension, concentrically layered inside the star (right). (Arrows signify the direction and size of the motion across the star).

502 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. tween them offers one possible expla- 0.2 nation for the DB gap. The picture be- gins with a white dwarf that has a heli- 0.1 um surface with some trace amounts of hydrogen: a helium-rich DO white 0 dwarf. As it cools towards the hot end of the DB gap, hydrogen (being lighter (relative change) than helium) floats to the surface via pulsation amplitude –0.1 gravitational settling. By 45,000 kelvins the atmosphere has become almost 0 1 2 3 4 5 6 7 pure hydrogen, masking the star as a time (hours) DA white dwarf. Further cooling drives subsurface convection, mixing the com- Figure 8. Light curve from a pulsating DA white dwarf shows the relative change in the ponents of the star and bringing heli- amplitude of the star’s pulsations over the course of about seven hours. The pulsation ampli- tude temporarily drops to nearly zero (at about 3.75 hours) as simultaneous pulsation modes um back to the surface. The star would of slightly different periods cancel each other by destructive interference. This star pulsates now be classified as a DB white dwarf. in more than 10 independent modes. Some pulsating white dwarfs show hundreds of sepa- Though this logical scheme explains rate periodicities. Distinguishing these modes is one of the challenges faced by stellar seis- the DB gap nicely, it only serves as an mologists (see Figure 9). outline that must be filled in with com- putational models of white dwarf evo- Mestel’s model likens a white dwarf two processes complicate the behavior lution. Efforts to model the evolution of to a heated piece of iron that is placed in of real white dwarfs. white dwarfs by Ben Dehner, then of a cool environment. Such a chunk of The first is emission. Neu- Iowa State University, and one of us iron would cool rapidly when exposed trinos are tiny, almost massless particles (SK) have successfully reproduced to the outside air unless it was sur- that are formed inside the white dwarf. some features of the observed stars. rounded by some sort of insulating blan- As the are released into space, However, no single, self-consistent ket. In , such as is they take a little bit of energy with them. computational model has been able to found in the core of all white dwarfs, the Early in the white dwarf’s life, there are satisfy all of the observed constraints. electrons are so close together that some so many neutrinos escaping into space A complete explanation of the DB gap are “free to roam,” resulting in a materi- that the white dwarf radiates more en- remains elusive. al that is similar in thermal properties to ergy through these particles than a terrestrial . This means that just through normal photon luminosity. Cooling With Age like the exposed iron, the cores of white Thus neutrinos increase the cooling rate Everything we know about white dwarfs would cool very rapidly. How- over that outlined by Mestel. dwarfs comes from the energy they ra- ever, the nondegenerate outer layers of The other effect is . In diate into space. But where does this the star do not act like . They trap a fully ionized medium, such as a energy come from if white dwarfs the heat and act as an insulating blan- white dwarf, a cloud of electrons com- ceased burning their nuclear fuel long ket. It therefore takes a long time for a pletely cancels the charge of the posi- ago? In 1952, British astrophysicist white dwarf to lose all of its stored heat, tive ions, creating a neutral star. But at showed that this energy is allowing it to glow for billions of years. the cooler end of a white dwarf’s life, the leftover heat from the star’s days of Mestel’s theory is a good approxi- the density increases and the charge fusion that leaks slowly into space. mation of how a white dwarf cools, but cancellation become imperfect. As the

5,192 microhertz

5,192 intensity 8,424 microhertz power 8,424 8,787

time frequency (microhertz) 8,787 microhertz white dwarf light curve power spectrum 3 components

Figure 9. Complex light curve (left) from a white dwarf can be decomposed into its single-period components (middle), allowing scientists to characterize the frequency and the strength of the individual pulsation modes (right). The individual frequencies are very sensitive to vari- ous properties of the white dwarf—including its mass and temperature, its rate of rotation and the depth of the transitions between its layers (for example, from hydrogen to helium to carbon and oxygen).

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 503 with permission only. Contact [email protected]. Haute-Provence Iowa Beijing

McDonald La Palma

Mauna Kea Kavalur

Itajuba Siding Spring Cerro Tololo Sutherland

Mt. John

Figure 10. The Whole Earth Telescope, consisting of many observers across the globe, allows astronomers to obtain a continuous light curve from a white dwarf 24 hours a day. Since the whole cycle of a white dwarf’s oscillation may take several weeks or months to complete, this approach is crucial to understanding a white dwarf’s properties. (A typical observing-run configuration is shown here.) The data from the individual telescopes are usually collected and analyzed at the Telescope’s control center at Iowa State University, where the astronomers are fueled by high-density jelly beans and hot pizza. interactions between ions strengthen, is 9.3 ± 1.5 billion years. This is consistent impossible to probe until the tech- the mutual Coulomb repulsion be- with the Hubble age estimate of 12 bil- niques of stellar seismology were ap- comes strong enough to lock the star lion to 14 billion years for the universe. plied to white dwarfs. into a giant crystal. As the star crystal- The precise age of the Galaxy based lizes it releases latent heat, providing on the cooling of white dwarfs de- Leukonanoseismology an additional energy source that slows pends on computational models that Nearly everything we have learned the cooling process compared to Mes- include Mestel’s effects, neutrinos, about white dwarfs, and all stars in tel’s model. Once the bulk of the star is crystallization and other details. One fact, is based on the light that comes crystalline, heat can travel through the of these important factors is the com- from their surfaces. This light not only star more easily and the white dwarf position of the white dwarf’s interior. contains information about the white cools faster. The cooling rate depends on the mean dwarf’s chemistry, but in certain in- The cooling rate of a white dwarf is atomic weight of the core, as well as stances it also encodes information proportional to its temperature (hotter the thickness of the “insulating blan- about the star’s interior. This “inside white dwarfs cool faster). Therefore, one kets” of hydrogen and helium. These information” is contained in complex, would expect to see more white dwarfs regions lie well below the observable but well-ordered, pulsations that are at the cooler end of the spectrum be- surface of white dwarfs and were once caused by disturbances or quakes cause their cooling rate has slowed down. This is indeed the case. However, there is an abrupt and steep drop-off in the numbers of white dwarfs at very hydrogen hydrogen cool temperatures that cannot easily be hydrogen explained as a cooling effect. helium helium helium This drop-off is a result of the finite time that white dwarfs have had to cool. carbon carbon The time it takes for a white dwarf to cool carbon below this temperature must be almost and oxygen as long as the age of the original ancient mixture star, and therefore a measure of how long oxygen ago stars first formed in the Galaxy. Thus oxygen the temperature of this drop-off is a direct measure of the age of the Galaxy. From Figure 11. Separation of the oxygen and carbon in a white dwarf’s core may include a process current studies, the best estimate of the in which oxygen “snow” falls through the carbon toward the center of the star. The question age of the disk of the Galaxy is now being addressed by scientists using the Whole Earth Telescope.

504 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. within the star. Much as earthquakes Examples of pulsating white dwarfs can be used to probe the interior of the can be found among the DA, DB and Earth, “starquakes” reflect the internal PG 1159 categories. Each flavor of white conditions of a star. dwarf pulsates only when its surface Asteroseismologists have been able temperature lies in a relatively narrow to discern distinct classes of stellar pul- range: DA stars pulsate between 13,000 sations. Stars like our Sun appear to be and 11,000 kelvins, DB stars pulsate be- dominated by pulsations that travel tween 27,000 and 25,000 kelvins and through its interior by means of pres- the PG 1159 stars pulsate between sure waves, or “p-mode” oscillations. 140,000 and 80,000 kelvins. The p-mode oscillations are caused by All three classes of pulsating white changes in the temperature of the dwarfs oscillate with periods ranging Sun’s outer layers, which cause the ma- between 100 and 1,000 seconds, which terial to absorb heat, expand, and then means they undergo several oscilla- cool and contract again. These expan- tions per hour. This makes them fun to sions and contractions generate sound observe—they actually do something (pressure) waves of assorted frequen- while we watch. It’s been said that as- cies that travel to various extents teroseismology makes stellar evolution throughout the Sun, depending on a spectator sport! their wavelength and the Sun’s inter- The changes in the white dwarf’s lu- nal structure. By “listening” to these minosity over time are recorded to pro- solar oscillations, helioseismologists duce a “light curve.” The job of the as- have learned much about the Sun’s in- teroseismologist is to break up the light terior (see “Sounds of the Sun,” Ameri- curve into its many single-period com- can Scientist, January–February 1994). ponents. In other words, we must sep- By contrast, white dwarf pulsations arate the individual g-modes from a are dominated by buoyancy (gravita- mixture of hundreds of g-modes all tional) waves, or “g-mode” oscilla- pulsating at the same time. An equiva- Figure 12. Crystal structure of carbon in a tions. (These buoyancy waves should lent effort would be to identify the white dwarf (top) is unlike any carbon struc- not be confused with the “gravitational sound of an individual violinist during ture found on the Earth, including diamond waves” predicted by general relativi- a symphony performance, when most (bottom). It is a “nuclear crystal” consisting ty.) As the temperature or pressure are playing similar parts. of bare carbon nuclei (orange balls) which changes within a white dwarf, stellar Fortunately stars have a limited are held in position by their mutual repul- material of a particular density moves number of available “normal modes” sion. In contrast, diamond is an “electronic crystal” in which the carbon (blue temporarily above its equilibrium of oscillation. Each component of the balls) are held together by electron shells point in the star but is then restored oscillation is made up of two angular that form attracting bonds. The unit cell (the back down again by its relative buoy- components known as “spherical har- simplest repeating pattern) of the white- ancy. These small vertical movements monics” and one radial component. dwarf carbon crystal is about 100 times generate larger, horizontal motions They are characterized by three inte- smaller than the diamond’s unit cell. within the white dwarf. Their propa- gers: l, m and n. The l value signifies the gation through the star is determined number of nodal lines on the surface of many qualities of a white dwarf using by their wavelength and the star’s in- the star that separate variations of op- simple pulsation theory. However, good terior structure. When these oscilla- posite phase. The m value denotes the results can come only from good data. tions reach the white dwarf’s surface, number of these nodal lines that pass they produce areas of higher density through the poles. The n value gives The Whole Earth Telescope and temperature. Where the tempera- the number of nodal surfaces between The most challenging aspect of white ture is locally higher, the surface of the the surface of the star and its center. dwarf seismology is not the faintness star is brighter. This change in the Each oscillation mode (a given value of of the stars or the low amplitude of the white dwarf’s luminosity can be ob- l, m and n) has a specific frequency. variations in the signal, it is observing served with sensitive photometers on Once the individual frequencies are the pulsating star continuously for as the Earth. Such measurements allow known, we can compare these to theo- long as needed to see the whole pat- accurate determinations of the star’s retical models to determine the star’s tern of the oscillation. The period of mass, rotation rate, cooling and con- properties. The frequencies are very each individual oscillation is usually traction rate, compositional stratifica- sensitive to the mass and temperature only a few minutes long, but because tion and magnetic-field strength. of the star, the rate of rotation and the the signal from a pulsating white Aside from their oscillations, pulsat- depth below the surface of the transi- dwarf is made up of many different ing white dwarfs look like “normal” tions from hydrogen to helium to car- modes, the overall pattern of the pulsa- white dwarfs. From this we conclude bon and oxygen. By varying these pa- tion can take much longer before it re- that all white dwarfs either have been rameters in a model to reproduce the peats. Because modes “beat” against or will be pulsators for some fraction of observed pulsation frequencies, we can one another, they create a cycle from their lives. By studying the pulsators probe the depths of the star. constructive to destructive interference we get a snapshot that should apply to This is the power of stellar seismolo- on a frequency that is the difference be- all white dwarfs. gy. One can learn a great deal about tween the individual oscillation fre-

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 505 with permission only. Contact [email protected]. PG 1159-035 and GD 358, showing that the stratified outer layer evolved pre- cisely as described by the theory of grav- itational settling in white dwarf stars. One of the most exciting observa- tions made by the WET team is of an extremely massive DA white dwarf, BPM 37093. BPM 37093 is so large that the carbon and oxygen in its core is ex- pected to be completely crystallized. BPM 37093 provides a test bed for the- ories of how crystallization occurs. Does the oxygen crystallize first and “snow” down to the core, or does it re- main suspended in the carbon? If the former is true, this process would in- crease the cooling time, thereby adding roughly one billion years to the esti- I c

S mated age of the galaxy. Theory also T S

/ predicts that the crystal structure of A R

U carbon under white dwarf conditions A

d is very different from anything seen in n a

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a Earthly carbon. These issues and more i b

m are now being addressed. u l o C h s i White Dwarfs and Dark Matter t i r B When astronomers measure the rota- f o y t tion of our Galaxy they find that there i s r e is 10 times more matter than can be ac- v i n

U counted for in the stars, nebulae and ( r e other visible matter. This unknown h c i R

and mysterious mass is called dark . H

, matter, and it appears to make up be- A S

A tween 90 and 99 percent of the entire N universe. The distribution of galactic Figure 13. White dwarf stars must be relatively close to the Earth for astronomers to dark matter is presumed to be in a observe them with optical telescopes because of their faintness. These white dwarfs spherical region called the dark halo (arrows) lie within the M4, which is situated about 7,000 light-years away extending far beyond the visible disk within the halo of the Milky Way. Many other “invisible” white dwarfs are believed to of the Milky Way. reside in the galactic halo and may constitute a large fraction of the so-called missing Just what dark matter is composed “dark matter” in the Galaxy. of is unknown. Much of it should be ordinary matter, and it must be dark, quencies. Since there are many possible eral points across the globe. As the sub- meaning too faint to detect, yet wide- modes, these beats are quite complex, ject star is setting for one observer, the spread. One effort to identify the dark and it may take weeks or months for next site to the West can continue the matter, assuming it is in the form of the overall cycle to repeat. observation, and so on around the stellar-mass objects, is known as the A single telescope cannot observe globe. Data from each site in the net- MACHO (Massive Compact Halo Ob- such a pulsating star for an entire beat work are sent by Internet to the control ject) survey, led by Charles Alcock, for- cycle because the Earth gets in the way center (usually at Iowa State Universi- merly of the Lawrence Livermore Na- at starset, and the Sun gets in the way ty) where they are reduced and exam- tional Laboratory, and others. As these at sunrise. Data from a single site have ined by the local scientists. The WET is massive dark objects (or MACHOs) periodic interruptions corresponding a powerful instrument, which has ob- drift through space, they should come to the daylight hours, and these breaks tained data of extremely high quality between Earth and a more distant star. can hide important features of the on several pulsating white dwarfs. When this happens, the gravity of the star’s spectrum. An early success of the WET came MACHO will cause the light from the To solve this problem, observations with observations of PG 1159-035 back distant star to brighten in a pre- must be conducted 24 hours a day. in 1989. Results from these observations dictable way (using the theory of This requires coordinated observations gave us a precise mass and rotation rate gravitational lensing, a consequence at telescopes all over the world. Such for the star, and revealed that it was lay- of Einstein’s theory of general relativ- observations are obtained for pulsating ered as theory predicted. Later observa- ity). By observing this change in the white dwarfs by using the Whole Earth tions of a pulsating DB white dwarf, GD brightness of the star, the MACHO Telescope, or WET. WET scientists 358, showed that it too was stratified. project can determine the mass of the track the pulsations of stars from sev- Computational models were able to link intervening object.

506 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. A startling conclusion of the a significant fraction of the dark halo Kawaler, S. D. 1996. White Dwarf Stars. In Stellar MACHO survey was that the dark ob- comes from the , a Remnants: the 25th Saas Fee Advanced Course, pp. 1–95, ed. G. Meynet and M. Mayor. Berlin: jects typically had near 0.5 solar long-exposure survey by the Hubble Springer. masses. Had these objects been ordi- Space Telescope. The northern part of Kawaler, S. D., and P. A. Bradley. 1994. Precision nary stars, they would have been de- the Hubble Deep Field reveals several of the pre-white dwarf star tected long ago by their own light. Their very faint stellar sources, whose color PG 1159-035. Astrophysical Journal 420:415. relative mass and dimness leaves open and extreme faintness are consistent Montgomery, M. H., and D. E. Winget. 1999. The only one possibility: They could only be with distant white dwarf stars. If these effect of crystallization on the pulsations of white dwarf stars. Astrophysical Journal white dwarf stars. The MACHO scien- results hold up, white dwarf stars may 526:976. tists estimate that up to 50 percent of the provide a solution to the riddle of the Nather, R. E., D. E. Winget, J. C. Clemens, C. J. mass of the dark halo is in the form of dark matter in our galaxy. In addition Hansen and B. P. Hine. 1990. The whole earth old white dwarfs! If this interpretation to illuminating our understanding of telescope—A new astronomical instrument. is correct, not only are white dwarfs the Sun’s ultimate evolutionary fate, Astrophysical Journal 361:309. common, but they also outnumber or- white dwarfs may be very important on Unglaub, K., and I. Bues. 2000. The chemical evo- dinary stars five to one. a galactic or even cosmological scale. lution of hot white dwarfs in the presence of diffusion and mass loss. Astronomy and Astro- Another interpretation, by American physics 359:1042. astronomers Geza Gyuk and Evalyn Bibliography Winget, D. E., and R. E. Nather. 1992. Taking Gates, suggests that these white dwarfs Dehner, B. T., and S. D. Kawaler. 1995. Thick to the pulse of white dwarfs. Sky and Telescope may lie not in a spherical halo, but in a thin: The evolutionary connection between April: 374. thick disk surrounding the galaxy. If so, PG 1159 stars and the thin helium-enveloped GD 358. Astrophysical then only four percent of the dark Journal (Letters) 445:L141. halo’s mass needs to be made of white Gyuk, G., and E. Gates. 1999. Large Magellanic dwarfs. This scenario requires the exis- Cloud microlensing and very thick discs. tence of an entirely new population of Monthly Notices of the Royal Astronomical Soci- stars in our galaxy to make up the re- ety 304:281. mainder of the dark matter. O’Brien, M. S., and S. D. Kawaler. 2000. The pre- dicted signature of neutrino emission in ob- Further evidence supporting the the- servations of pulsating pre-white dwarf stars. ory that ancient white dwarfs make up Astrophysical Journal 539:372.

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 507 with permission only. Contact [email protected].