White and Black Dwarfs

White dwarfs are stars of about one solar mass in the last stage of their lives. They have no more ways to generate energy, so they shine only because they are very hot. As they radiate their energy away, they cool and fade, becoming cold, dark black dwarfs.

Overview

White dwarfs are a unique class of stars. They have high surface temperatures, at least initially, and low luminosities. White dwarfs are very small—much smaller than stars in the energy-generating stages of their lives, with a diameter similar to that of Earth—but have a mass approximately the same as that of the sun, giving them average densities in the neighborhood of one billion kilograms per cubic meter.

The first white dwarf to be identified as such was discovered in 1862 by American astronomer and telescope maker Alvan Graham Clark. While testing the 18.5-inch refracting telescope he had made for Dearborn Observatory, Clark found that Sirius (Bayer designation Alpha Canis Majoris), the brightest-appearing star in the night sky, had a very faint companion, given the name Sirius B. In 1896, a similar but even fainter companion was discovered orbiting the star Procyon (Alpha Canis Minoris) and was given the name Procyon B. Then, in 1910, Harvard astronomers discovered that the faint star 40 Eridani B, part of the triple star system 40 Eridani (Omicron² Eridani), was in fact of spectral type A (white) rather than M (red), and thus was also a white dwarf—technically the first ever discovered, as it was first spotted by William Herschel in 1783. Shortly thereafter, Dutch American astronomer Adriaan van Maanen found a similar but still fainter single star (not a part of a binary system), which was subsequently named Van Maanen’s star (a.k.a. Van Maanen 2) in his honor.

During the mid-twentieth century, Willem Luyten of the University of Minnesota found several hundred of these white dwarf stars by looking for faint blue stars with large proper motions. The large proper motions showed that the stars were not very far away, so their faint appearance meant they really were intrinsically faint; the blue color showed they had hot surfaces, which, together with their faint luminosities, meant they were very small. Since then, even more white dwarfs have been found with improved detectors and observing techniques.

By the early 1900s, it was known that these stars were intrinsically very faint, very small, and incredibly dense. Most, but not all, had a bluish-white color, indicating a hot surface. Modern observations have refined these early findings. Sirius B has a surface temperature of about 24,000 kelvins, a luminosity about 0.020 times the sun’s, a radius of about 0.0084 times that of the sun (about 5,800 kilometers, or 3,600 miles—just 0.9 times the radius of the Earth), a mass of about 1.1 solar masses, and an average density of about 3 billion kilograms per cubic meter (about 3 million times the density of water). The white dwarf 40 Eridani B has a surface temperature of about 12,000 kelvins, a luminosity about 0.004 times the sun’s, a radius of about 0.014 solar radii (about 9,700 kilometers, or 6,050 miles), a mass of about 0.43 solar masses, and an average density of about 200 million kilograms per cubic meter (about 200,000 times the density of water).

The unusual properties of white dwarfs, especially their great densities, initially made many astronomers question whether such stars could really exist or whether there was something wrong with the observations or the analysis of them. The English astrophysicist Sir Arthur Stanley Eddington summed up the scientific community’s reactions thus: “The message of the companion of Sirius, when decoded, ran: ‘I am composed of material three thousand times denser than anything you’ve ever come across. A ton of my material would be a little nugget you could put in a matchbox.’ What reply could one make to something like that? Well, the reply most of us made in 1914 was, ‘Shut up; don’t talk nonsense.’”

The theoretical work to try to figure out this “nonsense” began with Eddington himself, who in 1924 suggested that the ultrahigh density of white dwarfs might be caused by their extremely high temperatures, which would totally ionize of the matter in them. The resulting bare nuclei and free electrons could be forced into a much smaller volume of space than un-ionized atoms surrounded by orbiting electrons could be packed.

In 1927, Ralph Howard Fowler used the newly developed Fermi-Dirac statistics (named for Enrico Fermi and Paul Dirac) and the Pauli exclusion principle (named for Wolfgang Pauli) from quantum mechanics to show that at the extreme densities within white dwarf stars, electrons are completely degenerate. This means that the electrons fill all the “cells” in combined momentum-position phase space up to some maximum momentum, with two and only two electrons in each “cell.” Unlike an ideal gas, which releases gravitational energy when it contracts, a sphere of degenerate electrons cannot shrink without an input of energy to increase the momentum of the electrons; shrinking reduces the position part of phase space, and this requires an increase in the momentum part of phase space. Consequently, without an input of energy, degenerate electrons behave collectively like an incompressible fluid.

With high enough densities, the upper momentum states of degenerate electrons are relativistic; that is, the fastest electrons move at a speed that is a significant fraction of the speed of light. In the early 1930s, Subrahmanyan Chandrasekhar applied special relativity theory to derive an equation of state for relativistically degenerate electrons. The pressure of the degenerate electrons far exceeds the pressure of the nuclei, which still behave like an ideal gas. Thus it is degenerate electron pressure that balances gravity to maintain hydrostatic equilibrium in white dwarfs. Employing the degenerate electron equation of state and the condition of hydrostatic equilibrium, Chandrasekhar was able to compute models for the interior structure of white dwarfs of various masses. He found that the greater is the mass of a white dwarf, the smaller its size is and the greater its density is. This is shown in the data for Sirius B and 40 Eridani B; Sirius B is more massive, but smaller and denser, than 40 Eridani B. Chandrasekhar’s model implied that there is an upper mass limit for white dwarf stars, now called the Chandrasekhar limit, of about 1.4 solar masses. Although only a few white dwarfs in binary systems have had their masses measured directly, they are below and thus consistent with the Chandrasekhar upper mass limit. For his wide-ranging contributions to astrophysics throughout his career, of which his work on the physics of white dwarfs was just the beginning, Chandrasekhar was awarded the Nobel Prize in Physics in 1983.

The spectra of white dwarf stars are difficult to interpret. Their high surface gravity leads to pressure broadening of the absorption lines in their spectra, and in some cases (such as the white dwarf Wolf 489) the lines become so broad and shallow that they almost disappear into the continuous background spectrum. Some white-dwarf spectra display prominent hydrogen lines, others show strong helium lines, and still others have lines representing a mixture of hydrogen, magnesium, potassium, calcium, iron, or a combination of these elements. White dwarf spectra also show a very large Stark effect (named for Johannes Stark), caused by the presence of strong electrostatic fields that result from high densities and the accompanying degeneracy. The spectra of some white dwarfs indicate the presence of magnetic fields up to about 10 million times stronger than that of Earth.

Applications

Eddington realized that the large density and high surface gravity of white dwarfs provided a testing ground for a prediction of Albert Einstein’s theory of general relativity. According to general relativity, light emitted in the presence of a strong gravitational field (such as exists at the surface of a white dwarf) is redshifted; basically, photons of light lose energy climbing out of the strong gravitational field, thus lengthening their associated wavelengths. At Eddington’s request, Walter Sydney Adams at Mount Wilson Observatory attempted to measure this gravitational redshift in white dwarf spectra. His measurements were not accurate enough for a definitive confirmation, though they were consistent with the prediction of general relativity.

In 1954, using better instrumentation, D. M. Popper measured the wavelengths of the lines in the spectrum of 40 Eridani B with greater accuracy. He found that, after allowing for the Doppler shift of the spectral lines due to the star’s radial velocity, there was a residual wavelength increase of 0.0070 percent. Based on the mass and radius of this star, general relativity predicts its spectral lines should have their wavelengths increased by 0.0057 percent. (These percentage shifts mean that for a spectral line with a normal wavelength of 500 nanometers, general relativity predicts its wavelength should be increased by 0.029 nanometer, while Popper’s measurements corresponded to an increase of 0.035 nanometer—very good agreement considering the difficulty in accurately measuring the wavelengths of white dwarf spectral lines.) The confirmation of a prediction of general relativity through observation of a gravitational redshift in a white dwarf spectrum was a major achievement.

Context

All stars spend most of their energy-producing lives as main sequence stars, fusing hydrogen into helium in their cores. White dwarfs and black dwarfs now are understood as stars in the last stages in their lives, with less than about 8 solar masses when first formed. When stars with initial masses below about 8 solar masses exhaust the hydrogen in their cores, they expand to become red giants, eventually fusing helium into carbon and maybe oxygen in their cores. However, they are not massive enough to generate energy by any other nuclear fusion reactions. Strong stellar winds and thermal pulsations in their bloated atmospheres puff off their outer layers as expanding shells of gas called planetary nebulae (a term that has nothing to do with planets, but rather originated in the 1800s when, with the telescopes available then, these objects looked round, like planets, and fuzzy, like nebulae). The stars remaining at the centers of planetary nebulae are the former cores of red giants, exposed to view as the planetary nebulae expand and dissipate. These central stars of planetary nebulae are progenitors of white dwarfs.

To become white dwarfs, stars must lose enough of their original mass during the last stages of their lives—whether by strong stellar winds, planetary nebulae, or some other mechanism—that their final mass is less than the Chandrasekhar limit of 1.4 solar masses. Stars with initial masses below about 0.25 to 0.5 of a solar mass are not massive enough to ignite helium fusion in their cores and probably will never become red giants or planetary nebulae; instead they may progress slowly from the main sequence directly to the white dwarf stage, taking perhaps hundreds of billions to trillions of years to do so.

White dwarf stars can no longer generate energy through any nuclear fusion process. They cannot release gravitational energy by contracting because their electrons are degenerate. They shine only because they are very hot, with central temperatures perhaps as high as 100 million kelvins initially. As they shine, they radiate their energy away, slowly cooling and fading, like an ember plucked from a fire. At the initial high temperatures, the atomic nuclei in white dwarfs behave like an ideal gas, but as the stars cool, the nuclei “freeze” into a regular lattice-like pattern, similar to a giant crystal, through which the degenerate electrons move freely. The white dwarfs, now essentially solid, continue to cool and grow fainter, eventually becoming cold, dark black dwarfs. This is the fate that awaits Earth's sun several billion years in the future.

However, this may not be the end for all white dwarfs. If a white dwarf is a member of a close binary system with a red giant companion, gas (mostly hydrogen) can be transferred from the red giant onto the white dwarf. The hydrogen that accumulates on the white dwarf’s surface may be heated sufficiently to fuse explosively into helium. A shell of hot gas is blasted into space, becoming as much as 100,000 times brighter than the white dwarf itself. This explosive outburst is called a nova. Since the process can repeat over and over again, novae can recur for decades or even centuries.

If the white dwarf in a close binary system is already almost at the Chandrasekhar limit (the maximum mass a white dwarf can have), any additional matter transferred from the companion can push the white dwarf over the mass limit. If this happens, the white dwarf collapses on itself and heats up to about a billion kelvins. The high temperature initiates a series of nuclear fusion reactions that blow the star apart as a Type Ia supernova. (A Type II supernova is produced by a massive supergiant that explodes once it develops an iron core that collapses.) Because Type Ia supernovae all are produced in the same way by essentially identical objects (white dwarfs gaining enough mass to exceed the Chandrasekhar limit), they reach approximately the same peak luminosity, nearly 10 billion solar luminosities, making them reliable “standard candles.” Since their peak luminosity is so high, they can be used as standard candles to determine the distances of galaxies billions of light-years away.

In 2015 the National Aeronautics and Space Administration (NASA) discovered evidence using the Chandra X-Ray Observatory and other telescopes that showed that a white dwarf star may have destroyed a planet that came too close in orbit. This event occurred at the center of the globular cluster NGC 6388. These instruments detected x-rays close to the center of the cluster but determined that it was not a black hole. Further evidence collected suggested that the source of the x-rays was a former planet. Although Earthbound astronomers have had difficulty detection planets orbiting white dwarf stars, the James Web Space Telescope, launched by NASA in 2021, could be a notable aid in finding such planets. The orbiting telescope is capable of seeing evidence of the infrared heat signature given off by the planets in the spectrography of the white dwarf.

In 2018, astrophysicist Noemi Giammichele of the Institut de Recherche en Astrophysique et Planétologie (Institute of Research in Astrophysics and Planetology) and colleagues reported that, using data from NASA's Kepler space telescope and a series of computer simulations, they had mapped the interior of a white dwarf—KIC 08626021, in the Cygnus constellation—for the first time ever. Their research revealed the core of the white dwarf to consist of about 86 percent oxygen, 15 percent more than previous calculations had indicated. If further research shows this greater-than-expected oxygen content to be a trend among other white dwarfs, it could have significant implications for scientists' understanding of stellar evolution.

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