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[5.0] Fossil Stars (1): White Dwarfs

v3.2.1 / chapter 5 of 10 / 01 mar 14 / greg goebel / public domain

* After death, stars leave behind stellar "fossils" as gravestones of their existence. The most evident of these fossils, the small stars known as white dwarfs, have been known for over a century, and our knowledge of them continues to expand. By the middle of the 20th century, there were speculations that there might be much denser objects known as "neutron stars", or that stars might collapse forever into "singularities" folding space around themselves to form "a black hole in space". However, the astronomical community was reluctant to believe in such monstrous objects and persisted in dismissing them as fictions.

Sirius A & B from Hubble Space Telescope


[5.1] THE DISCOVERY OF WHITE DWARFS
[5.2] WHITE DWARFS AND ELECTRON DEGENERACY
[5.3] THE STRUCTURE AND EVOLUTION OF WHITE DWARFS
[5.4] WHITE DWARFS AND THE AGE OF THE UNIVERSE
[5.5] BEYOND WHITE DWARFS?

[5.1] THE DISCOVERY OF WHITE DWARFS

* The discovery by Alvan Graham Clark in 1862 of the dark companion of Sirius created a puzzle for astronomers. The companion, known as Sirius B or the Pup, had a thermal emission curve that indicated it was at a temperature of about 30,000 degrees Kelvin. However, Sirius B was about 10,000 times fainter than the primary, Sirius A. Since it was very bright per unit of surface area, the Pup had to be much smaller than Sirius A, with roughly the diameter of the Earth.

The faintness, of course, was one of the reasons that Sirius B took decades to find, even though astronomers knew roughly where to look. Sirius A was so much brighter than Sirius B that looking for the Pup was like looking for a lit match next to a searchlight beam. In fact, one of the main reasons that Sirius B was discovered in 1862 was because by that time it had moved relative to Sirius A so that its angular separation as seen from Earth was over three times greater than it had been when the search began in 1844.

Analysis of the orbit of the Sirius star system showed that the mass of the Pup was almost the same as that of our own Sun. That implied that Sirius B was thousands of times denser than lead, a conclusion that was about as uncomfortable as it was undeniable. As more white dwarfs were found, astronomers began to discover that although the Pup might be bizarre, it was hardly unique. White dwarfs are common in our Galaxy.

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[5.2] WHITE DWARFS AND ELECTRON DEGENERACY

* In his pioneering studies of astrophysics in the 1920s, Sir Arthur Stanley Eddington suggested that the high densities of white dwarfs were due to the complete ionization of the atoms in their interiors. With all the electrons stripped from all the nuclei, the nuclei could pack much more closely together, resulting in the extraordinary densities observed. However, the energetics involved in this process were puzzling and contradictory.

As mentioned previously, the Indian astrophysicist Subrahmanyan Chandrasekhar performed the pioneering studies in this field. In July 1930, the 19-year-old Chandrasekhar was on a sea voyage from Madras, India, to Southampton, England, and tinkered with physics to stave off boredom. Following work done by astrophysicist Ralph J. Fowler (1889:1944) in 1926, Chandrasekhar applied the latest discoveries in quantum mechanics to the interior of a white dwarf star and determined how it could have such enormous densities.

While a star is performing fusion reactions in its core, the outward pressure of the thermal motion of the particles in the star keeps it from collapse. When the star is depleted of materials that can support fusion reactions, it then collapses. In the case of big stars, this collapse leads to a catastrophic supernova explosion, while the collapse of smaller stars is much less violent. In either case, the star falls in on itself until halted by some obstacle.

Since the exhausted star can no longer produce fusion reactions, the only obstacle to collapse is "quantum-mechanical electron degeneracy". This is due to the "Pauli exclusion principle", a rule of quantum mechanics that dictates that no two electrons can have the same energy level in the same system. As the star shrinks into itself, the electrons arrange themselves in a fully occupied range of base level energy states that can accommodate no more electrons. This creates an "electron degeneracy pressure", completely independent of the electrical repulsion between electrons, that resists further contraction.

Once the white dwarf is stabilized by electron degeneracy into a "fully degenerate" state, it can no longer contract. Since it cannot sustain fusion reactions, the white dwarf's energy is only due to the gravitational collapse that formed it. Chandrasekhar's insight into degeneracy pressure finally explained how white dwarfs could exist, and it was this work that persuaded the Nobel committee to award him the Nobel prize in physics in 1983, the prize being shared with Willy Fowler.

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[5.3] THE STRUCTURE AND EVOLUTION OF WHITE DWARFS

* Chandrasekhar's theoretical studies led to a better understanding of some of the characteristics of white dwarfs. The degenerate free electrons that permeate the white dwarf make the object an excellent thermal conductor, so the white dwarf is almost "isothermal" -- that is, its temperature almost uniform throughout its entire volume. The bare nuclei in this sea of electrons act as a close approximation of an ideal gas, providing a deep reservoir of kinetic energy in their random motions.

The material on the surface of the white dwarf is not degenerate. Although this layer is only about 50 kilometers thick, about 0.01% of the mass of the white dwarf, it still acts as an effective insulating layer. While the temperature at the bottom of the surface layer is about 10 million degrees Kelvin, it is a much "cooler" 10,000 degrees Kelvin at the surface, with the energy flow throttled by the diffusion of radiation through the surface layer and the vertical flow of heated material by convection through that layer. A white dwarf star, then, has a large supply of internal energy and an insulating surface layer that keeps the energy from radiating away rapidly. The result is that white dwarfs cool off very slowly through most of their lifetimes.

* When the 5.1 meter Hale telescope on Palomar Mountain, California, went into operation in 1948, astronomers were finally able to perform reasonable spectroscopic observations of white dwarfs. The result was another surprise: 80% percent of them showed an absorption spectrum of pure hydrogen, while most of the rest showed an absorption spectrum of pure helium.

The white dwarfs exhibiting pure hydrogen absorption spectra were designated type "DA", while those exhibiting pure helium absorption spectra were designated type "DB". In both cases, the surface layer was homogeneous to 1 part in 100,000. A small remainder had more complicated spectra and were designated type "DC", while a tiny handful had unclassifiable spectra.

The puzzling thing was that the stars the white dwarfs were derived from had no such purity of composition. The key to solving the puzzle was the intense gravity of the white dwarf, about 200,000 times that of Earth, which left light atoms on the surface while pulling down heavier atoms. A DA white dwarf still retains some hydrogen, and so has a surface layer of hydrogen with a sublayer of helium above the degenerate core. A DB white dwarf has lost nearly all of its hydrogen and so has a surface layer of helium.

The majority of white dwarfs that have been observed are isolated field stars, not part of binary systems. These isolated white dwarfs can be found by searching the sky for a faint blue star with a fast rate of motion across the sky. The blue color says that the object is hot, the fast motion hints that the object is nearby, and given these two facts the faintness suggests the object is small.

In many binary systems featuring a white dwarf and an active star, the white dwarf is draining mass off its active companion, a process that, as described earlier, leads to recurrent nova outbursts. There are also binary systems with two white dwarfs; one is known in which the two stars are approaching each other at about 2.5 centimeters every hour, with a collision likely in about a half-million years.

* A white dwarf is the endpoint of the evolution of an average star. After the star goes through its red giant phase and sheds a planetary nebula as it fades. The mass loss may end before all the outer hydrogen envelope is lost, and the ultimate result is a DA white dwarf. If all the hydrogen envelope is lost, the result is a DB white dwarf.

The white dwarf precursor forming at the center of the planetary nebula is known as a "planetary nebula nucleus (PNN)". A PNN with a mass of 0.6 Suns will evolve into a white dwarf in about 10,000 years, as the planetary nebula fades into space and all fusion reactions die out.

At first, the white dwarf is very hot, with a surface temperature of more than 100,000 degrees Kelvin, and much hotter in its interior. It is so hot that any trace of hydrogen left in its interior is quickly fused into helium, and then helium is converted to carbon and oxygen. The interior of a typical white dwarf is mostly composed of carbon and oxygen nuclei, though white dwarfs formed by smaller stars may be mostly helium and those formed by bigger stars may be formed of oxygen, neon, and magnesium.

In the early phase of its existence, the internal processes of a white dwarf generate large numbers of neutrinos. Neutrinos hardly interact with matter and flood out of the interior of the white dwarf, draining it of energy and allowing it to cool rapidly. About 10 million years after its formation, the interior of a white dwarf cools to about 30,000 degrees Kelvin and the star stops radiating neutrinos, with cooling slowing down dramatically. At first, most of the white dwarf's energy is lost by radiation, but as the white dwarf cools further, convection processes come into play, mixing the surface hydrogen layer with the lower helium layer. Eventually, helium may predominate, turning a DA white dwarf into a DB white dwarf.

A white dwarf loses most of its energy a billion years after its formation. During the long cooling period, the degenerate core continues to grow at the expense of the outer layer. Once the energy has effectively been dissipated, the white dwarf then starts to "crystallize". The bare nuclei in the core of the object link up into a symmetrical lattice, and the crystallization then expands outward. The transformation from a fluid to a crystal releases energy and slows down the cooling for a short time. Once the interior becomes heavily crystallized, however, thermal conductivity increases and the white dwarf's cooling proceeds more rapidly. The white dwarf becomes a fading cinder, the only remnant of a once brilliant star, and eventually fades to a dim black dwarf.

* Interestingly, the route to the black-dwarf state includes a detour. While it might be, and long was, assumed that a white dwarf would grow dimmer and redder as it cools until it goes completely dark, research studies performed in the late 1990s showed that once it goes below 4,500 degrees Kelvin, it suddenly turns blue. The blue light is emitted by a "nonthermal process". Molecular hydrogen in the white dwarf's cooling atmosphere absorbs the red light from the star itself and re-emits it at shorter, bluer wavelengths. Sky surveys performed after the publication of this research in fact showed up many faint blue objects that had been previously ignored.

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[5.4] WHITE DWARFS AND THE AGE OF THE UNIVERSE

* One of the reasons astronomers find white dwarf stars interesting is that they provide a key to obtaining the age of the Universe. As already described, a white dwarf is the fossil remnant of a star that has exhausted its nuclear fuel, lost most of its mass in a planetary nebula, and cooled down to a dim cinder. A plot of all the observed white dwarfs by their temperatures shows that as white dwarfs grow cooler, their numbers increase until the temperature of 3,500 degrees Kelvin is reached. Below that temperature, there are none. The reason for this is because the Galaxy is not old enough to have allowed even the oldest white dwarfs to cool off any more than that. This means that if we know how long it takes a white dwarf to cool off, we can use that knowledge to estimate the age of our Galaxy, and in turn at least set a limit on the age of the Universe itself.

As discussed later, the primary way of estimating the age of the Universe is through measurements of its expansion rate, derived from the redshifts of distant galaxies and various means of determining the distance to nearby galaxies for calibration. Using the cooling rate of white dwarfs as a stepping stone to the age of the Universe is an entirely independent approach, useful as a reality crosscheck.

Observations by the Hubble Space Telescope announced in 2002 of the globular star cluster M4, orbiting our own Milky Way Galaxy, managed to identify white dwarfs that were estimated to be from 12 billion to 13 billion years old. Modern cosmological studies indicate that the Universe is about 14 billion years old. Assuming that the white dwarfs observed in the Hubble survey were among the first stars created in the Universe, less than a billion years after the birth of the Universe in the "Big Bang", and incorporated into globular clusters, then their apparent age gives an age of the Universe consistent with estimates using other methods.

* There is, of course, the problem of determining if astronomers really do know the actual cooling rate of white dwarfs. Theoretical studies on the cooling rate have been assisted by observations of the vibrations of white dwarfs.

As a white dwarf cools, vibrations can arise with a period from 100 seconds to several hours, due to spasmodic releases of energy through the dwarf's outer layer that cause the entire star to oscillate. These vibrations, which appear as small variations in brightness, give clues to the internal processes of the dwarf, just as seismic waves give clues to the internal structure of the Earth. Understanding the internal structure of a white dwarf means obtaining a better estimate for its cooling rate.

The patterns of oscillation can be complicated, with different oscillatory modes and frequencies overlaying each other. Fourier analysis can be used to break the composite oscillation down into its spectrum, or graph of individual frequency components, but mapping the composite oscillation can take a day or more.

Such "asteroseismology" requires extended observations from a set of networked telescopes around the world. An international network of telescopes, known as the "Whole Earth Telescope", was set up in the 1990s and now can provide effectively continuous observations for extended periods of time, with data collected at a central location using electronic mail. Now satellites, such as the French COROT spacecraft, launched in 2006, are getting in on the asteroseismology act as well. The process of studying white dwarfs through asteroseismology is still evolving, but practitioners feel assured that they will be able to obtain much more precise data on the structure and evolution of white dwarfs.

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[5.5] BEYOND WHITE DWARFS?

* When Chandrasekhar published his analysis of the underlying mechanisms of white dwarfs in 1930, there was an implication that bothered many of his contemporaries. Chandrasekhar determined that if a white dwarf has a mass of more than 1.44 Suns, electron degeneracy pressure would not be able to halt its collapse. This limit, known as the "Chandrasekhar limit", was discussed earlier.

The mass limit was not a problem in itself. What was troublesome was that once the limit was exceeded, nothing could halt stellar collapse, and the collapse would never end. Eddington found this result distasteful, saying that "there should be a law of Nature to prevent a star from behaving in this absurd way." He strongly attacked Chandrasekhar's work; Chandrasekhar was young and impressionable and the attacks were painful, but he was encouraged by others such as the Danish physicist Niels Bohr to stand his ground.

Still, nobody knew exactly what to make of the idea that a star could collapse forever; although Chandrasekhar's advocates believed his mass limit was correct, they generally felt that "a miracle would happen" and get rid of the excess mass, conveniently eliminating the problem of indefinite collapse. That was not a completely ridiculous idea, since as discussed earlier old stars tend to shed mass, but nobody came up with any convincing reason to think they had to shed all their excess mass.

* Chandrasekhar was not the first to consider the possibility of superdense objects. Einstein's theory of General Relativity, published in 1916, stated that mass distorted space and time in its surroundings. The German astronomer Karl Schwarzchild (1873:1916) used the equations of General Relativity to perform an analysis of how a star distorts space and time in its vicinity, and while doing so had discovered something odd. Schwarzchild found that for any given mass, there was a certain radius where time was compressed down to zero while the spatial dimensions stretched to infinity. This "Schwarzchild radius" is very small, about three kilometers for a star with the mass of our Sun.

Schwarzchild felt that the matter was academic. Chandrasekhar's analysis of white dwarfs lay in the future, and by the physics available to him Schwarzchild could see no way a star could become so compressed; he died of an illness while serving on the Eastern Front in the Kaiser's army, and that was the end of his thoughts on the matter. Albert Einstein was more uncomfortable with the Schwarzchild radius and its implications, but the matter still did not seem very important. Einstein didn't get around to dealing with it until 1939, when he published a paper in the physics press where he attempted to prove that a mass could not be compressed to its Schwarzchild radius.

Surprisingly enough, the basic idea of such a "dark star" had been proposed in 1783, over a century earlier, by a British "natural philosopher" named John Michell (1724:1793). At that time, the general consensus, following the thinking of the towering English physicist Isaac Newton (1643:1727), was that light was a particle phenomenon. It was known to travel at 300,000 kilometers per second, and Michell did some figuring on how dense an object had to be before it had a gravitational escape velocity of 300,000 kilometers per second, determining that it would be about a diameter of 6 kilometers for a mass the size of the Sun. Such an object would be forever dark, unable to emit light and trapping all light that fell onto it.

Nobody knew if there was any limit on stellar density at the time, but within a generation Newton's particulate view of light began to fall out of fashion, and the notion of dark stars was lost until Schwarzchild brought it up again, using more advanced and correct physics. It didn't exactly take the world by storm the second time around, either; nobody took Schwarzchild's idea very seriously.

* However, other studies had been and were being performed on superdense objects and their properties. In 1932, British physicist James Chadwick (1891:1974) discovered the neutron, which opened the door to some interesting possibilities. A few scientists, particularly the Bulgarian-Swiss-American astronomer Fritz Zwicky (1898:1974) of the California Institute of Technology and Soviet physicist Lev D. Landau (1908:1968), speculated that neutrons could be the key to stars far more dense than white dwarfs.

If a collapsing star were put under extreme pressure, they suggested, electrons could be forced into protons to form neutrons, creating a densely packed sphere a few kilometers across but with stellar mass. This sphere would resist further compression, and so at least up to a certain mass a star exceeding the Chandrasekhar limit would not collapse forever. Zwicky and Walter Baade very astutely suggested further this pressure could be caused by supernova explosions, creating what is now known as a "neutron star".

However, Zwicky was an astronomer dabbling in the domain of physicists, and many of them regarded him, justly or not, as an arrogant, obnoxious loudmouth. One colleague with little liking for Zwicky called him a "borderline psychotic". Zwicky and Baade had a strong working relationship until Zwicky accused Baade of being a "Nazi" during World War II, and the result was that those organizing conferences of astronomers had to remember to try to avoid putting the two men in the same room together. Physicists pointedly snubbed his work on neutron stars, and in fact his analysis had a number of technical errors.

Landau took a different approach to the concept, wondering if a normal star might actually have a compressed "neutron core" that generated the star's energy by the continued accumulation of mass, instead of fusion reactions. Landau was highly respected by the physics community, and the prominent American physicist J. Robert Oppenheimer (1904:1967) led several of his students, most prominently Hartland S. Snyder (1913:1962), to research the concept of the neutron core, resulting in a series of papers on the matter that were published in 1938 and 1939. Ironically, their research showed that Landau's idea of a neutron core wasn't realistic: once a star formed a neutron core, the rest of the star would quickly collapse into the core. Nobody wanted to admit it, but it looked like Zwicky might be right after all.

One of the interesting questions they considered was an upper mass limit for neutron stars, similar to the Chandrasekhar limit for white dwarfs, above which the neutron star would collapse indefinitely. Snyder, working from suggestions by Oppenheimer, performed an analysis based on General Relativity of what would happen if the neutron star collapsed and fell through its Schwarzchild radius.

The mass would tend to collapse without limit, forming a "singularity". If an observer was watching a clock on the surface of the collapsing star that emitted a pulse of light at regular intervals, the pulses would become redder and the pulse interval would become longer, since time would slow down in the increasing gravity field. At the Schwarzchild radius, the pulse interval of the clock would become infinite, as would the wavelength of the redshifted light. In other terms, once the clock reached the Schwarzchild radius, light could no longer escape from it; nothing could escape from it. Oppenheimer and Snyder concluded that a singularity "tends to close itself off from any communication with a distant observer; only its gravitational field persists."

The concept of a singularity, a superdense object from which no light could escape, was a theoretical curiosity at the time, and the theoretical model created by Oppenheimer and Snyder was so full of simplifying assumptions to make calculations easier that there was plenty of room for skepticism. World War II put the matter on the back burner for over a decade. Oppenheimer went on to the Manhattan Project to help develop the atomic bomb. In 1947, he became director of the Institute of Advanced Studies at Princeton University, where Albert Einstein was a professor. There is no record of any discussions between them of the fate of collapsing stars, and in fact Oppenheimer, worn out by responsibilities, controversies, and personal problems, had lost interest in the matter.

In the postwar period, astronomers did search for neutron stars. A target of particular interest was the Crab Nebula, the remains of the 1054 CE Type II supernova. Although optical astronomers found a compact object at the core of the nebula, there was no way at the time for them to determine exactly what it was.

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