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Six billion years from now, someonelooking up at the sky on a summer’s

day would not see the same bright Sunwe now see. In its place would be a tinyorb—a “white dwarf”—shining feeblyin a black sky. Whether anyone will bearound to see such an alien sky is an-other question: All life on Earthwould have been obliterated when theSun entered its red-giant stage a bil-lion years earlier. The white dwarfwill endure for many billions of yearsafterward as a small monument to oursolar system.

Our Sun may be billions of yearsaway from such a fate, but there arecountless numbers of white dwarfs nowin our Galaxy. “Countless” is an apt termin this case, since their total number isnot known—they are too small and toodim to be easily seen. Indeed, whitedwarfs were only identified as a distinctclass of stars less than 100 years ago, atestimony to their relative obscurity. Al-most all of the catalogued white dwarfslie within the immediate solar neighbor-hood, and nearly half of these can befound within 75 light-years of our Sun.

Although they are difficult to locate,there are many reasons to care about

these fascinating stars. Since they rep-resent the final stage in the evolution of98 percent of all stars, the study ofwhite dwarfs is very nearly the studyof all stars. As the remains of once-bril-liant suns, white dwarfs can provideinformation about their earlier lives inmuch the same way that human re-mains provide information to forensicanthropologists. White dwarfs are alsoconvenient astrophysical laboratoriesin which we can study matter at pres-sures and temperatures that cannot beachieved in terrestrial laboratories.

Much of this information is revealedthrough complex vibrations created inthe interiors of white dwarfs that can bemeasured using a unique tool known asthe Whole Earth Telescope. What as-tronomers have learned about whitedwarfs has implications beyond our un-derstanding of stellar evolution. Recentwork shows that these stars can be usedto find the age of our Galaxy and mayeven make up a large fraction of themysterious dark matter in the universe.

Strange Little StarsIn the year 1783, two years after dis-covering the planet Uranus, British as-tronomer William Herschel became thefirst person to see a white dwarf star.On the evening of January 31, Herschelobserved a star in his telescope named40 Eri B, which actually proved to be apair of stars, one of which was a “faint,dusky star.” At the time he didn’t rec-ognize it as being anything unusual.

The strangeness of Herschel’s stardid not become apparent for another127 years. In 1910 spectroscopy re-vealed that 40 Eri B (and two otherstars like it) had surfaces that were hot-ter than our Sun. But they were soclose to the Earth that, were they nor-mal stars, they would be easily visible

with the naked eye. Obviously, some-thing was different about these newobjects. By 1914 the mystery was clear.For these stars to be so faint, they hadto be extremely small—about the samesize as the Earth, or just 1/100 the di-ameter of the Sun. Their white-hot sur-faces and small diameters provided aname for this new class of stars: whitedwarfs.

White dwarfs were truly a puzzle. Astar with the mass of the Sun confinedto the volume of the Earth must havean enormous density. How could suchan object support itself against its owngravity? What processes could makesuch a star? Today we can answer thesequestions.

During a star’s lifetime there are twoforces fighting for control. The first is theinward force of gravity, trying to com-press the star to as small a point as pos-sible. Opposing gravity is the outwardforce of gas pressure provided by hightemperatures inside the star. Althoughenergy is lost by radiation, the star main-tains its high temperature through nu-clear fusion as it burns hydrogen intohelium. These two forces balance eachother precisely, creating a stable stellarstructure—at least for a while.

Eventually, the star’s central reservesof hydrogen are exhausted. Fusionceases at the center, but continues in athin shell surrounding the now purehelium core. Within the core, the in-ward force of gravity starts to win outover the outward gas pressure, and thecore collapses. The gravitational ener-gy released by the core, combined withthe energy output of the burning shell,puffs the outer layers of the star to ahuge radius with a low surface tem-perature (forming a red giant star) andbriefly increases its energy output by athousand times.

498 American Scientist, Volume 88

White Dwarf Stars

The remnants of Sun-like stars, white dwarfs offer clues to the identityof dark matter and the age of our Galaxy

Steven D. Kawaler and Michael Dahlstrom

© 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

Steven Kawaler is professor of astrophysics in theDepartment of Physics and Astronomy at IowaState University. A theorist in stellar evolutionand pulsation, he has co-directed the Whole EarthTelescope since 1997. As time permits, he escapesto the rhythms of the baseball diamond (mostly asa spectator these days). Michael Dahlstrom is anundergraduate student majoring in bothbiophysics and journalism at Iowa StateUniversity. He has been involved with the WholeEarth Telescope since 1999. Michael enjoysobserving Jupiter and his neighbors through asmall, four-inch telescope. Address for Kawaler:Department of Physics and Astronomy, Iowa StateUniversity, Ames, IA 50011. Internet:[email protected]

Soon, the compression of the coregenerates enough heat to ignite the fu-sion of helium into carbon, and the starreturns to nearly normal dimensions.Eventually, the central helium supplyalso becomes exhausted and the dyingstar succumbs to gravity again: The corecollapses, shell burning resumes and thestar becomes a red giant for a second

time (as an asymptotic giant-branch star).As the core shrinks, some of its outer en-velope breaks free and cools to become acolorful planetary nebula (so called be-cause early astronomers confused thesestructures with distant planets likeUranus; see “The Shapes of PlanetaryNebulae,” American Scientist July–Au-gust 1996). Finally, glowing proudly at

the center of the nebula is the collapsedcore—a newly formed white dwarf.

To understand the magnitude of awhite dwarf’s collapse, imagine goingto the local bowling alley and findingthe heaviest bowling ball they have.Take it in your hands and squeeze ituntil it is the size of this letter “o.”Compressing that much mass into

2000 November–December 499© 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

Figure 1. Spectacular ejection of material from a dying star forms a planetary nebula and leaves behind a feeble remnant, which will become awhite dwarf (visible here in the center of the ring). Although some consider a white dwarf to be a dead star (since nuclear fusion has ceased toprovide 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 EarthTelescope.” Here a high-resolution image of the Ring Nebula (M57) reveals details in the radial patterns sculpted in the gas and dust exhaledby the dying star. Our Sun will undergo a similar transformation in the course of its death throes about 5 billion years from now.

Hubble Heritage Team (AURA/STScI/NASA)

such a small volume creates a verydense vowel! This is the same degreeof compression a white dwarf facesduring its final gravitational collapse.

At these high densities, the self-gravity of the star is too strong for or-

dinary gas pressure to resist. The onlyforce keeping the star from total de-struction is the behavior of electrons.According to the Pauli exclusion prin-ciple, no two electrons can share thesame quantum numbers and therefore

cannot share the same state. The gravi-ty of a white dwarf compresses theelectrons to the point where they can-not be any closer. (This explanationwas first given in 1926 by the astro-physicist Ralph H. Fowler of the Uni-versity of Cambridge. It was later clar-ified with numerical models by one ofhis students, Subrahmanyan Chan-drasekhar, who won a share of the 1983Nobel Prize in physics for his efforts.)This electron degeneracy pressure stabi-lizes the star at an incredibly high den-sity: one million times that of water. Nosubstance on Earth has a density any-where close. The densest terrestrial ma-terial is pure iridium, with a density of22.65 times that of water. Gold weighsin at merely 19.3, and iron is a light-weight at 7.9.

From this we can understand themakeup of a typical white dwarf. Likethe three layers of a melon, a whitedwarf consists of an electron-degener-ate core of carbon and oxygen, which issurrounded by a thin rind of heliumand an outer skin of hydrogen. Not allwhite dwarfs have the same structure,however. Subtle differences amongwhite dwarfs show that a star may takeone of several possible evolutionarypaths as it runs out of nuclear fuel.

White Dwarf FlavorsSpectroscopy reveals that most whitedwarfs have almost pure surfaces of ei-ther hydrogen or helium. This pro-vides a handy classification system thatreflects the unusual surface composi-tion of these stars. White dwarfs with

500 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

nearly pure hydrogen surface

heliumshell

DA DB

nearly pure neutral helium surface

carbon and oxygen core

DO

nearly pure ionized helium surface

exposed core ofcarbon and oxygen

PG 1159

Figure 2. White dwarf varieties are defined by the elements that dominate their surfaces as revealed by their spectra (the continuum of lightthey emit). Nearly all white dwarfs are believed to contain a core of carbon and oxygen (blue). Three varieties—DA, DB and DO whitedwarfs—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 hydrogenand neutral helium, whereas DAO stars have hydrogen and ionized helium.

perc

enta

ge o

f non

-DA

whi

te d

war

fs

temperature (kelvins, log scale)

PG 1159 DO DBDBgap

DA

100,000 65,000 40,000 28,000 15,000 10,000 6,000

100

80

60

40

20

0

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 theirtemperatures drop, DO white dwarfs are believed to become DB stars when the ionized heli-um recombines with free electrons to form neutral helium. The absence of DO and DB starsat the DB gap suggests an intermediate stage in which a DB star is masked as a DA star. Thereason for the DB gap is not fully understood.

surfaces of hydrogen are called DAstars. White dwarfs that have pure he-lium atmospheres with strong neutralhelium (He I) lines are named DB stars.If the helium white dwarf shows rela-tively strong lines of singly ionized he-lium (He II) it is called a DO star. As aDO star cools, the He II will recombinewith free electrons to form He I, even-tually changing the DO into a DBwhite dwarf.

Although most white dwarfs showonly hydrogen or helium on their sur-faces, there are a few with mixed spec-tra. They are named accordingly. Hy-drogen-covered white dwarfs withlines of He I are named DAB stars,whereas hydrogen stars with lines ofHe II are logically named DAO stars.Some rare white dwarfs show evidenceof carbon in their spectra (DQ stars) orother heavier elements (DZ stars).

One of the most bizarre classes ofwhite dwarf is the very hot, hydrogen-deficient PG 1159 stars. These are thehottest white dwarfs, with tempera-tures as high as 170,000 kelvins. Theyhave no hydrogen or He I lines, but doshow weak He II lines and strongerlines of ionized carbon and oxygen. PG1159 stars appear to be the exposed in-ner core of a white dwarf. As a delight-ful tongue twister, PG 1159 stars canalso be classified as DOZQ stars!

The flavor of a white dwarf is deter-mined, in part, by the type of shellburning (hydrogen or helium) thatdominated as it became a planetarynebula. If the star was burning hydro-gen, the white dwarf that resultedwould probably be a hydrogen-richDA. If the parent star was burning he-lium, the most likely outcome wouldbe a DO (and later, a DB) star. In rareinstances, a final burst of helium-gen-erated nuclear energy occurs after theplanetary nebula has formed. Thisblast ejects the hydrogen and almost allof the helium from the white dwarf, ex-posing a PG 1159 star.

A very interesting phenomenon ap-pears when we tally the actual num-bers of DA, DB, DO and PG 1159 starsaccording to the range of white dwarftemperatures. PG 1159 stars appear atthe hot end, followed by the helium-rich DO stars. As the temperature de-creases from 80,000 kelvins to 45,000kelvins, the hydrogen-rich DA stars in-crease in number. Then suddenly, from45,000 kelvins to 27,000 kelvins, all he-lium white dwarfs disappear, leavingonly hydrogen DA stars. At tempera-


low

tem

pera

ture

shi

gh te

mpe

ratu

res

DA

DO

DOPG 1159

DA DA

DB DB

DBgap?

rela

tive

num

ber o

f whi

te d

war

fs p

er u

nit v

olum

e

luminosity of white dwarfbright dim

white dwarf“drop-off”

Figure 4. Hot white dwarfs (top row) pass through one of several evolutionary paths (whitearrows) as they cool with age. Some white dwarfs remain as DA stars throughout their exis-tence (left column), whereas PG 1159 stars (middle column) may evolve through two or moreother white dwarf varieties. DO stars may evolve through the DB gap to become identifiableDB stars (right column), but none has been observed within the gap.

Figure 5. White dwarfs become cooler and dimmer over time, allowing astronomers to esti-mate their age. Because the oldest white dwarfs must be the remnants of the Galaxy’s firststars, estimating their age provides astronomers with a tool to measure the age of the MilkyWay. Here a rapid decrease in the numbers of very dim white dwarfs (a so-called “drop-off”)suggests that the Galaxy is not sufficiently old to contain cooler (hence older) stellar rem-nants. Current estimates based on the cooling rate of white dwarfs suggests that our Galaxyis about 9 billion years old, an age consistent with independent estimates of the age of theuniverse (about 13 billion years old).

© 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

tures cooler than 27,000 kelvins, thehelium DB stars begin to appear anddominate in numbers below 10,000kelvins. The decreasing surface tem-peratures are indicative of a progres-sive cooling, which suggests a generalevolutionary sequence from PG 1159stars to DO, then DA and then DBstars.

Such a linear scheme is a little toosimple, however. Consider the “disap-pearance” of helium white dwarfs be-tween 45,000 and 27,000 kelvins. Thismysterious observation is called the DBgap. Something strange is happening inthe outer layers of helium white dwarfsas they cool below 45,000 kelvins caus-ing the helium to disappear.

A possible explanation lies in thechemical evolution of white dwarfs.Four processes can change the structureof a white dwarf: gravitational settling,interstellar medium accretion, massloss and subsurface convective mixing.

Like the separation of oil and vine-gar, gravitational settling separates thewhite dwarf’s constituents by atomicweight. Under the intense gravity atthe surface of a white dwarf (as muchas 100,000 times stronger than at theEarth’s surface), heavier elements sinkto the core, whereas lighter elementsfloat to the surface. This diffusion isthe dominant physical process in awhite dwarf, and it is responsible forthe ultra-pure surfaces we see withspectroscopy.

Two of the processes oppose one an-other: accretion from the interstellarmedium and the loss of mass. The inter-stellar medium is made mostly of hy-drogen and helium, with trace amountsof heavier elements. These materials canfall onto the white dwarf, polluting anotherwise pure surface. The opposite istrue of mass loss. The material near thesurface of a white dwarf can drift offinto space, exposing deeper material ofdifferent composition.

Subsurface convection is the rapidand active mixing of the material in-side a star. As a white dwarf cools, con-vection can mix material from belowinto the surface layers.

These evolutionary processes act atdifferent times in the cooling history ofa white dwarf, and the interplay be-

502 American Scientist, Volume 88

cool cool

hot

high

dens

ity

low

density

highdensity

lowdensity

high

density

surface wave

surface wave

surface

wave

surface

wave

buoyancy

buoyancy

Figure 6. “Starquakes” on a white dwarf can be observed as periodic changes in the relativebrightness of the star. Temperature changes within the white dwarf result in the verticalmovement of dense material above its equilibrium point in the star. High-density material isrelatively hotter (and thus brighter) than low-density material, which results in variations inthe amount of light emitted across the surface of the star. Since the changes in density arerestored by buoyancy (orange arrows), or gravity, these pulsations are known as “g-mode”oscillations. The small vertical motions also generate larger, horizontal motions (surfacewaves) that propagate across the star.

nodal planes

l=1m=1

l=2m=1

surface pulsation patterns

l=2m=0 n=2

much warmerwarmerlittle changecooler

l=3m=1

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

tween them offers one possible expla-nation for the DB gap. The picture be-gins with a white dwarf that has a heli-um surface with some trace amounts ofhydrogen: a helium-rich DO whitedwarf. As it cools towards the hot endof the DB gap, hydrogen (being lighterthan helium) floats to the surface viagravitational settling. By 45,000 kelvinsthe atmosphere has become almostpure hydrogen, masking the star as aDA white dwarf. Further cooling drivessubsurface convection, mixing the com-ponents of the star and bringing heli-um back to the surface. The star wouldnow be classified as a DB white dwarf.

Though this logical scheme explainsthe DB gap nicely, it only serves as anoutline that must be filled in with com-putational models of white dwarf evo-lution. Efforts to model the evolution ofwhite dwarfs by Ben Dehner, then ofIowa State University, and one of us(SK) have successfully reproducedsome features of the observed stars.However, no single, self-consistentcomputational model has been able tosatisfy all of the observed constraints.A complete explanation of the DB gapremains elusive.

Cooling With AgeEverything we know about whitedwarfs comes from the energy they ra-diate into space. But where does thisenergy come from if white dwarfsceased burning their nuclear fuel longago? In 1952, British astrophysicistLeon Mestel showed that this energy isthe leftover heat from the star’s days offusion that leaks slowly into space.

Mestel’s model likens a white dwarfto a heated piece of iron that is placed ina cool environment. Such a chunk ofiron would cool rapidly when exposedto the outside air unless it was sur-rounded by some sort of insulating blan-ket. In degenerate matter, such as isfound in the core of all white dwarfs, theelectrons are so close together that someare “free to roam,” resulting in a materi-al that is similar in thermal properties toa terrestrial metal. This means that justlike the exposed iron, the cores of whitedwarfs would cool very rapidly. How-ever, the nondegenerate outer layers ofthe star do not act like metals. They trapthe heat and act as an insulating blan-ket. It therefore takes a long time for awhite dwarf to lose all of its stored heat,allowing it to glow for billions of years.

Mestel’s theory is a good approxi-mation of how a white dwarf cools, but

two processes complicate the behaviorof real white dwarfs.

The first is neutrino emission. Neu-trinos are tiny, almost massless particlesthat are formed inside the white dwarf.As the neutrinos are released into space,they take a little bit of energy with them.Early in the white dwarf’s life, there areso many neutrinos escaping into spacethat the white dwarf radiates more en-ergy through these particles thanthrough normal photon luminosity.Thus neutrinos increase the cooling rateover that outlined by Mestel.

The other effect is crystallization. Ina fully ionized medium, such as awhite dwarf, a cloud of electrons com-pletely cancels the charge of the posi-tive ions, creating a neutral star. But atthe cooler end of a white dwarf’s life,the density increases and the chargecancellation become imperfect. As the


Figure 8. Light curve from a pulsating DA white dwarf shows the relative change in theamplitude 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 modesof slightly different periods cancel each other by destructive interference. This star pulsatesin more than 10 independent modes. Some pulsating white dwarfs show hundreds of sepa-rate periodicities. Distinguishing these modes is one of the challenges faced by stellar seis-mologists (see Figure 9).

Figure 9. Complex light curve (left) from a white dwarf can be decomposed into its single-period components (middle), allowing scientists tocharacterize 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).

0.2

0.1

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–0.1puls

atio

n am

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(rel

ativ

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)

time (hours)0 1 2 3 4 5 6 7

inte

nsity

time

white dwarf light curve3 components

pow

er

frequency(microhertz)

power spectrum

5,1928,424

8,787

5,192 microhertz

8,424 microhertz

8,787 microhertz

interactions between ions strengthen,the mutual Coulomb repulsion be-comes strong enough to lock the starinto a giant crystal. As the star crystal-lizes it releases latent heat, providingan additional energy source that slowsthe cooling process compared to Mes-tel’s model. Once the bulk of the star iscrystalline, heat can travel through thestar more easily and the white dwarfcools faster.

The cooling rate of a white dwarf isproportional to its temperature (hotterwhite dwarfs cool faster). Therefore, onewould expect to see more white dwarfsat the cooler end of the spectrum be-cause their cooling rate has sloweddown. This is indeed the case. However,there is an abrupt and steep drop-off inthe numbers of white dwarfs at verycool temperatures that cannot easily beexplained as a cooling effect.

This drop-off is a result of the finitetime that white dwarfs have had to cool.The time it takes for a white dwarf to coolbelow this temperature must be almostas long as the age of the original ancientstar, and therefore a measure of how longago stars first formed in the Galaxy. Thusthe temperature of this drop-off is a directmeasure of the age of the Galaxy. Fromcurrent studies, the best estimate of theage of the disk of the Milky Way Galaxy

is 9.3 ± 1.5 billion years. This is consistentwith the Hubble age estimate of 12 bil-lion to 14 billion years for the universe.

The precise age of the Galaxy basedon the cooling of white dwarfs de-pends on computational models thatinclude Mestel’s effects, neutrinos,crystallization and other details. Oneof these important factors is the com-position of the white dwarf’s interior.The cooling rate depends on the meanatomic weight of the core, as well asthe thickness of the “insulating blan-kets” of hydrogen and helium. Theseregions lie well below the observablesurface of white dwarfs and were once

impossible to probe until the tech-niques of stellar seismology were ap-plied to white dwarfs.

LeukonanoseismologyNearly everything we have learnedabout white dwarfs, and all stars infact, is based on the light that comesfrom their surfaces. This light not onlycontains information about the whitedwarf’s chemistry, but in certain in-stances it also encodes informationabout the star’s interior. This “insideinformation” is contained in complex,but well-ordered, pulsations that arecaused by disturbances or quakes


Mauna Kea

McDonald

Itajuba

Cerro Tololo

Haute-Provence

La Palma

Sutherland

Kavalur

Siding Spring

Mt. John

BeijingIowa

carbonand

oxygenmixture

oxygen

carbon

oxygen

carbon

hydrogen hydrogen hydrogen

heliumheliumhelium

Figure 11. Separation of the oxygen and carbon in a white dwarf’s core may include a processin which oxygen “snow” falls through the carbon toward the center of the star. The questionis now being addressed by scientists using the Whole Earth Telescope.

Figure 10. The Whole Earth Telescope, consisting of many observers across the globe, allows astronomers to obtain a continuous light curvefrom 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, thisapproach is crucial to understanding a white dwarf’s properties. (A typical observing-run configuration is shown here.) The data from theindividual telescopes are usually collected and analyzed at the Telescope’s control center at Iowa State University, where the astronomers arefueled by high-density jelly beans and hot pizza.

within the star. Much as earthquakescan be used to probe the interior of theEarth, “starquakes” reflect the internalconditions of a star.

Asteroseismologists have been ableto discern distinct classes of stellar pul-sations. Stars like our Sun appear to bedominated by pulsations that travelthrough its interior by means of pres-sure waves, or “p-mode” oscillations.The p-mode oscillations are caused bychanges in the temperature of theSun’s outer layers, which cause the ma-terial to absorb heat, expand, and thencool and contract again. These expan-sions and contractions generate sound(pressure) waves of assorted frequen-cies that travel to various extentsthroughout the Sun, depending ontheir wavelength and the Sun’s inter-nal structure. By “listening” to thesesolar oscillations, helioseismologistshave learned much about the Sun’s in-terior (see “Sounds of the Sun,” Ameri-can Scientist, January–February 1994).

By contrast, white dwarf pulsationsare dominated by buoyancy (gravita-tional) waves, or “g-mode” oscilla-tions. (These buoyancy waves shouldnot be confused with the “gravitationalwaves” predicted by general relativi-ty.) As the temperature or pressurechanges within a white dwarf, stellarmaterial of a particular density movestemporarily above its equilibriumpoint in the star but is then restoredback down again by its relative buoy-ancy. These small vertical movementsgenerate larger, horizontal motionswithin the white dwarf. Their propa-gation through the star is determinedby their wavelength and the star’s in-terior structure. When these oscilla-tions reach the white dwarf’s surface,they produce areas of higher densityand temperature. Where the tempera-ture is locally higher, the surface of thestar is brighter. This change in thewhite dwarf’s luminosity can be ob-served with sensitive photometers onthe Earth. Such measurements allowaccurate determinations of the star’smass, rotation rate, cooling and con-traction rate, compositional stratifica-tion and magnetic-field strength.

Aside from their oscillations, pulsat-ing white dwarfs look like “normal”white dwarfs. From this we concludethat all white dwarfs either have beenor will be pulsators for some fraction oftheir lives. By studying the pulsatorswe get a snapshot that should apply toall white dwarfs.

Examples of pulsating white dwarfscan be found among the DA, DB andPG 1159 categories. Each flavor of whitedwarf pulsates only when its surfacetemperature lies in a relatively narrowrange: DA stars pulsate between 13,000and 11,000 kelvins, DB stars pulsate be-tween 27,000 and 25,000 kelvins andthe PG 1159 stars pulsate between140,000 and 80,000 kelvins.

All three classes of pulsating whitedwarfs oscillate with periods rangingbetween 100 and 1,000 seconds, whichmeans they undergo several oscilla-tions per hour. This makes them fun toobserve—they actually do somethingwhile we watch. It’s been said that as-teroseismology makes stellar evolutiona spectator sport!

The changes in the white dwarf’s lu-minosity over time are recorded to pro-duce a “light curve.” The job of the as-teroseismologist is to break up the lightcurve into its many single-period com-ponents. In other words, we must sep-arate the individual g-modes from amixture of hundreds of g-modes allpulsating at the same time. An equiva-lent effort would be to identify thesound of an individual violinist duringa symphony performance, when mostare playing similar parts.

Fortunately stars have a limitednumber of available “normal modes”of oscillation. Each component of theoscillation is made up of two angularcomponents known as “spherical har-monics” and one radial component.They are characterized by three inte-gers: l, m and n. The l value signifies thenumber of nodal lines on the surface ofthe star that separate variations of op-posite phase. The m value denotes thenumber of these nodal lines that passthrough the poles. The n value givesthe number of nodal surfaces betweenthe surface of the star and its center.Each oscillation mode (a given value ofl, m and n) has a specific frequency.

Once the individual frequencies areknown, we can compare these to theo-retical models to determine the star’sproperties. The frequencies are verysensitive to the mass and temperatureof the star, the rate of rotation and thedepth below the surface of the transi-tions from hydrogen to helium to car-bon and oxygen. By varying these pa-rameters in a model to reproduce theobserved pulsation frequencies, we canprobe the depths of the star.

This is the power of stellar seismolo-gy. One can learn a great deal about

many qualities of a white dwarf usingsimple pulsation theory. However, goodresults can come only from good data.

The Whole Earth TelescopeThe most challenging aspect of whitedwarf seismology is not the faintnessof the stars or the low amplitude of thevariations in the signal, it is observingthe pulsating star continuously for aslong as needed to see the whole pat-tern of the oscillation. The period ofeach individual oscillation is usuallyonly a few minutes long, but becausethe signal from a pulsating whitedwarf is made up of many differentmodes, the overall pattern of the pulsa-tion can take much longer before it re-peats. Because modes “beat” againstone another, they create a cycle fromconstructive to destructive interferenceon a frequency that is the difference be-tween the individual oscillation fre-


Figure 12. Crystal structure of carbon in awhite dwarf (top) is unlike any carbon struc-ture found on the Earth, including diamond(bottom). It is a “nuclear crystal” consistingof bare carbon nuclei (orange balls) whichare held in position by their mutual repul-sion. In contrast, diamond is an “electroniccrystal” in which the carbon atoms (blueballs) are held together by electron shellsthat form attracting bonds. The unit cell (thesimplest repeating pattern) of the white-dwarf carbon crystal is about 100 timessmaller than the diamond’s unit cell.

quencies. Since there are many possiblemodes, these beats are quite complex,and it may take weeks or months forthe overall cycle to repeat.

A single telescope cannot observesuch a pulsating star for an entire beatcycle because the Earth gets in the wayat starset, and the Sun gets in the wayat sunrise. Data from a single site haveperiodic interruptions correspondingto the daylight hours, and these breakscan hide important features of thestar’s spectrum.

To solve this problem, observationsmust be conducted 24 hours a day.This requires coordinated observationsat telescopes all over the world. Suchobservations are obtained for pulsatingwhite dwarfs by using the Whole EarthTelescope, or WET. WET scientiststrack the pulsations of stars from sev-

eral points across the globe. As the sub-ject star is setting for one observer, thenext site to the West can continue theobservation, and so on around theglobe. Data from each site in the net-work are sent by Internet to the controlcenter (usually at Iowa State Universi-ty) where they are reduced and exam-ined by the local scientists. The WET isa powerful instrument, which has ob-tained data of extremely high qualityon several pulsating white dwarfs.

An early success of the WET camewith observations of PG 1159-035 backin 1989. Results from these observationsgave us a precise mass and rotation ratefor the star, and revealed that it was lay-ered as theory predicted. Later observa-tions of a pulsating DB white dwarf, GD358, showed that it too was stratified.Computational models were able to link

PG 1159-035 and GD 358, showing thatthe 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 anextremely massive DA white dwarf,BPM 37093. BPM 37093 is so large thatthe 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 theformer is true, this process would in-crease the cooling time, thereby addingroughly one billion years to the esti-mated age of the galaxy. Theory alsopredicts that the crystal structure ofcarbon under white dwarf conditionsis very different from anything seen inEarthly carbon. These issues and moreare now being addressed.

White Dwarfs and Dark MatterWhen astronomers measure the rota-tion of our Galaxy they find that thereis 10 times more matter than can be ac-counted for in the stars, nebulae andother visible matter. This unknownand mysterious mass is called darkmatter, and it appears to make up be-tween 90 and 99 percent of the entireuniverse. The distribution of galacticdark matter is presumed to be in aspherical region called the dark haloextending far beyond the visible diskof the Milky Way.

Just what dark matter is composedof is unknown. Much of it should beordinary matter, and it must be dark,meaning too faint to detect, yet wide-spread. One effort to identify the darkmatter, assuming it is in the form ofstellar-mass objects, is known as theMACHO (Massive Compact Halo Ob-ject) survey, led by Charles Alcock, for-merly of the Lawrence Livermore Na-tional Laboratory, and others. As thesemassive dark objects (or MACHOs)drift through space, they should comebetween Earth and a more distant star.When this happens, the gravity of theMACHO will cause the light from thedistant star to brighten in a pre-dictable way (using the theory ofgravitational lensing, a consequenceof Einstein’s theory of general relativ-ity). By observing this change in thebrightness of the star, the MACHOproject can determine the mass of theintervening object.


Figure 13. White dwarf stars must be relatively close to the Earth for astronomers toobserve them with optical telescopes because of their faintness. These white dwarfs(arrows) lie within the globular cluster M4, which is situated about 7,000 light-years awaywithin the halo of the Milky Way. Many other “invisible” white dwarfs are believed toreside in the galactic halo and may constitute a large fraction of the so-called missing“dark matter” in the Galaxy.

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A startling conclusion of theMACHO survey was that the dark ob-jects typically had masses near 0.5 solarmasses. Had these objects been ordi-nary stars, they would have been de-tected long ago by their own light. Theirrelative mass and dimness leaves openonly one possibility: They could only bewhite dwarf stars. The MACHO scien-tists estimate that up to 50 percent of themass of the dark halo is in the form ofold white dwarfs! If this interpretationis correct, not only are white dwarfscommon, but they also outnumber or-dinary stars five to one.

Another interpretation, by Americanastronomers Geza Gyuk and EvalynGates, suggests that these white dwarfsmay lie not in a spherical halo, but in athick disk surrounding the galaxy. If so,then only four percent of the darkhalo’s mass needs to be made of whitedwarfs. This scenario requires the exis-tence of an entirely new population ofstars in our galaxy to make up the re-mainder of the dark matter.

Further evidence supporting the the-ory that ancient white dwarfs make up

a significant fraction of the dark halocomes from the Hubble Deep Field, along-exposure survey by the HubbleSpace Telescope. The northern part ofthe Hubble Deep Field reveals severalvery faint stellar sources, whose colorand extreme faintness are consistentwith distant white dwarf stars. If theseresults hold up, white dwarf stars mayprovide a solution to the riddle of thedark matter in our galaxy. In additionto illuminating our understanding ofthe Sun’s ultimate evolutionary fate,white dwarfs may be very important ona galactic or even cosmological scale.

BibliographyDehner, B. T., and S. D. Kawaler. 1995. Thick to

thin: The evolutionary connection betweenPG 1159 stars and the thin helium-envelopedpulsating white dwarf GD 358. AstrophysicalJournal (Letters) 445:L141.

Gyuk, G., and E. Gates. 1999. Large MagellanicCloud microlensing and very thick discs.Monthly Notices of the Royal Astronomical Soci-ety 304:281.

O’Brien, M. S., and S. D. Kawaler. 2000. The pre-dicted signature of neutrino emission in ob-servations of pulsating pre-white dwarf stars.Astrophysical Journal 539:372.

Kawaler, S. D. 1996. White Dwarf Stars. In StellarRemnants: the 25th Saas Fee Advanced Course,pp. 1–95, ed. G. Meynet and M. Mayor. Berlin:Springer.

Kawaler, S. D., and P. A. Bradley. 1994. Precisionasteroseismology of the pre-white dwarf starPG 1159-035. Astrophysical Journal 420:415.

Montgomery, M. H., and D. E. Winget. 1999. Theeffect of crystallization on the pulsations ofwhite dwarf stars. Astrophysical Journal526:976.

Nather, R. E., D. E. Winget, J. C. Clemens, C. J.Hansen and B. P. Hine. 1990. The whole earthtelescope—A new astronomical instrument.Astrophysical Journal 361:309.

Unglaub, K., and I. Bues. 2000. The chemical evo-lution of hot white dwarfs in the presence ofdiffusion and mass loss. Astronomy and Astro-physics 359:1042.

Winget, D. E., and R. E. Nather. 1992. Takingthe pulse of white dwarfs. Sky and TelescopeApril: 374.


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