Although they are tiny in size, white dwarfs have played a great role in astronomy. These compact stars are very different from familiar objects like our sun. They also pose a seemingly endless series of puzzles, whose solutions provide new insights into many areas of physics and astronomy. To unravel a wide variety of phenomena such as cataclysmic variables (novae, dwarf novae), planetary nebulae, and some types of supernova, we have to understand white dwarfs. These stars may even hold clues to one of the most fundamental questions of all- how old is the universe?
White dwarfs come in a variety of types ranging from hot to luminous to cool and dim. Some are among the faintest of all stars, but paradoxically their study began with that of Sirius, the brightest star in our night sky. The Dog star is a slightly scaled-up version of the Sun, with about twice the mass and 25 times the luminosity. It is an unremarkable object comfortably fusing enough hydrogen into helium in its core to supply the energy radiated from the surface and to provide the thermal pressure needed to balance the inward force of gravity. Sirius appears bright to us because it is so close, less than 9 light-years away.
In the last century Sirius attracted the attention of Friedrich W. Bessel. By carefully measuring the Dog star, position from 1834-1844, he found irregularities in its motion across the sky. He attributed this behavior to the influence of an unseen companion.
Despite many efforts the proposed attendant escaped visual detection until 1862. In that year, Alvan Graham Clark, the 3 telescope maker, was testing the objective lens of a new 18.5-inch refractor when he unexpectedly spotted the elusive companion, now known as Sirius B, or the Pup.
Today, it is clear why the detection was so long delayed. In 18844, when the search began, Sirius B was only 3 arc seconds from the primary star, but by 1862 the separation between the pair had reached 9.5 arc seconds. This made the discovery much easier. Also hindering the detection was the tremendous brightness difference between the two companions, the Pup being 10,000 times fainter than Sirius itself.
The white color of Sirius B shows a high surface temperature of about 30,000 Kelvin. Although the name “white dwarf” applies well to a star like the Pup, some members of the class are much cooler and have very different colors.
The origins of white dwarf stars are examined in order to understand their surface compositions and evolution. A star runs out of fuel at its center at the end of its main-sequence phase. While the outer part of the star expands enormously, hydrogen continues to burn in a narrow shell surrounding the now pure helium core. As it becomes a red giant, its luminosity increases and its temperature falls. The core helium eventually gets hot enough to fuse into oxygen and carbon. If the mass of the star is between 2 and 8 Suns, helium ignition occurs quietly and evolution continues with a helium-burning shell. This star lies on the horizontal branch on the H-R diagram.
Helium and hydrogen continue to burn in relatively thin shells surrounding a now degenerate core of oxygen and carbon, when the new fuel in the core is in turn exhausted. While this is happening, the outer envelope swells even more, until it extends out to several times the Earth-Sun distance. The star is now on the asymptotic giant branch.
The mass of the core increases and the star gets brighter as the hydrogen and helium burning shells eat their outward from the center. The star moves upward on the H-R diagram and becomes a red super-giant. During this phase, two significant processes occur. First, the rarified outer envelope starts to evaporate. Second, the3 hydrogen-burning shell consumes material faster than the helium burning one does; resulting in a configuration that is unstable. This instability leads to rapid increases in luminosity-”flashes”-each time the mass of a newly formed helium deposited on the inner shell exceeds some critical value.
In some way, the steady mass loss plus the possible influence of the flashing helium shell remove much of the extended hydrogen envelope in only a few tens of thousands of years. The star, reduced to some 20% of its initial mass, evolves quickly and moves rapidly to the left across the top of the H-R diagram. Ultraviolet light emitted from the increasingly hot star causes the ejected material to glow, forming a planetary nebula, the birth pang of many white dwarfs. Mass loss may continue until helium-rich material is exposed to the surface, so whether the remnant becomes a DA or DB white dwarf depends a lot on what happens at this stage.
What remains of the expose core of the asymptotic giant branch star is called a planetary nebula nucleus, or PNN. Typically, one mass of 0.6 Sun evolves across the H-R diagram in only 10,000 years. As the shell-burning energy sources die out, the star’s luminosity drops, and it rounds the “knee” of its evolutionary track. As the planetary nebula disperses, the hot, degenerate remnant emerges from its cocoon and settles down as a cooling white dwarf.
While the nuclei of planetary nebulae are thought to be major contributors to the white-dwarf population of the galaxy, other evolutionary paths are also important for single stars. One example is the class of so-called hot subdwarfs that occupies a region of the H-R diagram between the PNN’s and the white dwarfs. While the evolutionary status of these stars is still uncertain, astronomers think that they, too, are direct ancestors of white dwarfs.
Sirius B’s low luminosity was the first major puzzle involving white dwarf, for it had to be smaller than earth for it to be so hot yet so faint. The situation became even more bizarre when the orbital motion of the components showed that the mass of the Pup was slightly greater than that of the sun!
This seemed so paradoxical in the 1920’s that the anthrophysicist Sir Arthur Eddington argued that such a star could not exist. The observed properties imply enormous densities. If the atoms in the deep interiors of white dwarfs were completely ionized, that is, striped of all their electrons, the physics of that day indicated that the resulting mixture of nuclei and electrons could reach a lower energy state by recombining. This led to a problem. Eddington didn’t see how a star, which once had got into this compressed condition was ever going to get out of it. As far as they knew, the close packing of matter is only possible so long as the temperature is great enough to ionize the material. When the star cools down and regains the normal density associated with solids, it must expand and do work against gravity. The star will need energy in order to cool.
The physical structure of white-dwarf interiors remained a mystery until unraveled by Ralph H. Fowler in 1926 and S. Chandrasekhar in the early 1930’s. The quantum revolution that transformed physics at the same time made their work possible. They showed that the enormous pressure created by the intense gravity in the star does indeed crush the interior atoms. Thereby embedding the atomic nuclei in a sea of free electrons.
Thermal energy can’t balance the crushing force of gravity inside a white dwarf alone. Instead, the star is supported by a quantum-mechanical effect known as electron degeneracy pressure; at high densities the free electrons can’t be squeezed into the same energy state. In this way the star’s equilibrium is maintained independently of the thermal energy. Once a star reaches this fully degenerated state, its further evolution consists mostly of a gradual cooling, with no significant change in size.
In 1948, Jesse L. Greenstein and collaborators used the 200-inch telescope to study white dwarfs. Their exteriors presented another puzzle.
The spectra of the stars showed that their surface compositions are essentially pure- usually a single element is present. About 80% of all white dwarfs (the DA variety) display only hydrogen absorption lines in their spectra. The rest show only helium features and are called type DB. Type DC have no identifiable lines at all, and others have more complex spectra.
Evry Schatzman suggested an explanation for this puzzling result. He explained that white dwarfs are very different from the main-sequence stars from which they descended. In particular, their small sizes and large masses imply surface gravities almost 10,000 times that of the Sun and 200,000 times that of the earth. This intense gravity leads to a layered arrangement of material within the star; heavy constituents sink while light atoms such as hydrogen are left at the surface.
Gravitational settling purifies the outer layers of white dwarfs far beyond the satisfaction that already exists because of prior stellar evolution In principle, this explains why most stars like this show unusually pure spectra of helium and hydrogen, with no more than one part in 100,000 of other elements. Below the surface, this phenomenon reinforces the body’s layercake structure, with hydrogen (where present) and helium shells overlaying a core of heavier elements.
The most studied white dwarfs are single, or “field” stars. They provide a homogeneous sample that allows us to place them in the context of stellar evolution theory. They are easily recognizable by looking for faint blue stars moving fast across the sky. Such a combination generally indicates a relatively nearby object. The technique was successfully demonstrated by William J. Luyten, Henry L. Giclas, and others. Studies of large samples of field white dwarfs, mostly by Volker Weidemann and collaborators, have found a surprising distribution of masses for these stars. They lie in a very narrow range, most falling between 0.5 and 0.7 Sun.
White dwarfs are also found in more exotic settings, such as binary and multiple systems. In many of these cases, mass is being transferred from the companion to an accretion disk around the white dwarf, as in novae and other cataclysmic variables. Recently, systems containing a pair of white dwarfs, with one shedding material onto the other, have been invoked by some astronomers to explain the formation of some neutron stars and Type I supernovae.
A LIVELY OLD AGE
Some very interesting physics controls the evolution of hot, new-formed white dwarfs. For most of their lives these degenerate objects cool by radiating away the kinetic energy of the bare nuclei they contain. However, another mechanism is active at an early stage, when copious numbers of neutrinos are produced deep in their interiors. These bizarre elementary particles barely interact with matter and escape from the star immediately, carrying away energy as they go. Theoretical estimates indicate that neutrino cooling dominates the evolution of a white dwarf for the first few million years.
If we could measure the rate at which hot white dwarfs cool, we would also be measuring the rate at which they lose energy by neutrino emission. Fortunately, these stars are also hot, with surface temperatures in excess of 100,000′K, that they evolve rapidly. This swift development provides us with a fleeting opportunity to watch these stars age in just a few years.
The rate of contraction and cooling of hot white dwarfs has been measured, thanks to a lucky break-several of them are variable and pulsate regularly. The pulsation periods are sensitive to conditions deep inside the star, and change with variations of the interior structure. Observations of the rate of period change for one such object, PG 1159-035, confirm that the star is cooling as predicted and have brought the study of stellar evolution into the realm of spectator sports (SandT: June,85 page 493)
About 10 million years after its formation, a white dwarf has faded to one-tenth the Sun’s luminosity and its surface temperature has fallen to some 30,000′K, though there are many just slightly hotter and cooler. This mystery is still unexplained.
During the warm stages of a white dwarf’s evolution, after neutrino cooling has subsided, radiation is transported outward by photons of light. However, as the star cools, convection begins in its outer portions, which are well mixed as a result. As the temperature falls further, the convection layer extends deeper into the interior. This behavior explains why the relative number of non-hydrogen white dwarfs increases dramatically at temperatures below about 10,000′K. At this temperature the convective layer penetrates below the surface hydrogen layer to the pure helium underneath, mixing the two. Thus a cool DA dwarf will eventually turn into a DB.
However, there is a limit to the depth of the convection zone, for the lowering temperatures also cause an increase in the size of the region of degenerate electrons. Eventually the two boundaries meet. Because energy transport by the electrons is so efficient, the base of the convection zone retreats toward the surface as the degeneracy boundary moves outward.
Theory indicates that it takes a white dwarf over a billion years to cool up to a barely warm ball of degenerate gas. Calculations indicate that at this stage the star undergoes one final remarkable change-it begins to crystallize.
Throughout its evolution up to this point, the star has remained a ball of gas. Art first it was a nearly ideal gas, and while later the electrons became degenerate, the bare nuclei (ions) still moved around freely. However, as the white dwarf cooled, each ion began to feel the electrical, or Coulomb, forces of its neighbors. At first the kinetic energy of the ions was large enough that this effect was confined to their nearest neighbors, producing short-range order (typical of liquids) in the material. Matter in this phase is described as a Coulomb liquid.
Eventually, however, the energies of the ions become so small that the electric forces dominate over increasing distances. More and more nuclei are bound together in a symmetric solid lattice-a crystal. This freezing out of the material is caused by the lowering temperature, but is aided by the high pressure that squeezes the nuclei together. Thus crystallization begins at the center of the white dwarf and marches inexorably outward.
This dramatic change of state has an important effect on the star’s final stages of evolution. First, the shift from liquid to solid releases energy, called the latent heat of crystallization, which is familiar in processes such as the freezing of water. This change of phase briefly slows the temperature drop. However, once a significant portion of its interior has crystallized, a white dwarf cools much more rapidly than before.
Since the time for a white dwarf to cool to the crystallization stage is estimated to be about the same as the age of our galaxy, we might date the first epoch of star formation in the Milky Way by finding the system’s coolest white dwarf. In other words, there should be a “cut-off” in faint white dwarfs caused by the limited time these oldest stars have had to cool. James W. Liebert and collaborators have conclusively shown that there are a few, if any, white dwarfs with luminosities much less than about 0.0001 that of the Sun.
To translate this into our galaxy’s age, we must ensure that our understanding of the basic physics involved in the cooling of white dwarfs is correct. This is where the pulsating specimens are most valuable. By determining the actual rates of evolution for stars all along the “cooling track” and comparing these observations with theory, we can calibrate our models of white dwarf cooling. Then we can compare the number of observed cool white dwarfs with the theoretical predictions to give us an absolute determination of the time of the first epoch of star formation. White dwarfs will thus enable us to read the history of the Milky Way as frozen in its oldest stars.