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Physics LibreTexts

13.25 White Dwarfs

Different masses of stars face death in different ways. For stars like our Sun, the final stages of life include the formation of a planetary nebulae and a white dwarf — a star the size of the Earth with a density of 1 tone per cubic centimeter. That is star stuff 200,000 times denser than the Earth!

According to theory, stars that start their lives with masses from 0.1 times the mass of the Sun to a 8 to 10 solar masses will all die as white dwarfs. The upper limit on this mass range isn't well defined because different stars loose mass at different rates, and the true cut off is the "death" mass: white dwarfs are no larger than 1.4 solar masses. The outer atmospheres of stars that become white dwarfs bloat out as the star prepares to die, and they may shed outer layers during their red giant and asymptotic giant stages of life. Even though a lot of mass is lost, in many case most of the mass is still left behind in a dense and hot core. 

In 1844, the German astronomer Friedrich Bessel studied the motions of the brightest star in the sky, Sirius, and found that it was being perturbed back and forth by a faint, unseen star orbiting around it. This star was not glimpsed until 1862, when American telescope maker Alvan Clark detected it, almost lost in the glare of Sirius. In 1915, Mt. Wilson observer W. S. Adams discovered that the companion was hot and bluish-white, with properties that place it below the main sequence on the H-R diagram. It has about the mass of the Sun (determined from the binary orbit), but it has such a low luminosity that the total radiating surface cannot be much more than that of the Earth (determined by the Stefan-Boltzmann law). That such a small, dense star could exist was baffling, but so were stars in general in this era prior to the discovery of nuclear reactions. 

The theory that explains white dwarfs and other collapsed stars was developed between 1930 and 1931 by Subrahmanyan Chandrasekhar. Born in India, Chandrasekhar first began thinking about white dwarfs on the long boat voyage that took him to college in England. He theorized that if you turn of the nuclear power generation in the center of a star it will gravitationally collapse until its supported only by the force of particles against their neighbors. While he experienced prejudice many times in his life for his faith and his nationality, nothing was more hurtful to him than the scorn that many senior astronomers poured on his idea. He persevered and his ideas were eventually accepted by the community. Chandrasekhar received the Nobel Prize in physics in 1983. His calculations revealed a very strange state of matter. Chandrasekhar was not only a brilliant researcher but he was also a dedicated teacher and adviser, acting as the intellectual father to a whole generation of theoretical astrophysicists. 
Once no more energy is available to generate outward pressure, a star collapses until all its atoms are jammed together to make a very dense material. But what does jammed together"" really mean? At a white dwarfs high temperatures and densities, electrons move at almost the speed of light and matter loses its familiar properties. Stellar matter stops behaving like a perfect gas. In fact, it is no longer either gas, liquid, or solid, but a new form of matter composed of atomic nuclei held apart by a sea of electrons at extraordinary densities; a teaspoon full of white dwarf matter brought to Earth would weigh as much as an elephant. Although the interiors of white dwarfs may have densities of billions of kilograms per cubic meter, the outer layers of some may consist of ordinary matter — possibly hot gas at the surface and crystalline rocklike or glasslike solids in a crust 20 to 75 km deep (since many white dwarfs are made of carbon, they are structurally giant diamonds). At the base of these crusts, densities may be as high as 3 million kilograms per cubic meter. This high a density has only been achieved momentarily in laboratories on Earth.

At the microscopic level, positively charged atomic nuclei align themselves in orderly patterns, governed by the electrical forces that act between them. The electrons move freely through this crystalline lattice in the same way that electrons move through the copper lattice of a wire when an electric current flows. The quantum theory of matter says that no two particles can have exactly the same set of properties. This limitation means that electrons in close proximity experience a pressure that prevents the white dwarf from shrinking even further. This pressure is called degeneracy pressure, and the state of matter in a white dwarf is called a degenerate gas. The core of the Sun is destined to reach this strange state of matter in a bit more than 5 billion years. For low mass stars, this takes place in the degenerate helium core of the red giant phase instead of attaining a degenerate carbon core of the asymptotic giant phase. No matter which place in the HR diagram that a starts opts to become a white dwarf, it forms in the center of an expanding planetary nebulae.

Most white dwarfs have temperatures of 10,000 to 20,000 K, and the hottest exceed 100,000 K. However, these hot stars have low luminosity because they have such a small surface area. Their high temperatures are also very temporary. With such a large amount of stored heat and such a small surface area, white dwarfs take a long time to radiate enough energy to cool significantly. The oldest white dwarfs have cooled to temperatures under 4000 K and a luminosity less than 0.0001 times that of the Sun. To chill out to these temperatures, they needed to form at least 10 billion years ago! Some white dwarfs may be among the oldest stars we can observe. Over time, these stars will just keep cooling. Trillions of years from now, these cold stellar corpses will be dark objects.

White dwarfs cannot have more mass than 1.4 solar masses because the white dwarf structure becomes unstable at this point. If you tried to dump more mass on the surface of a 1.4 solar mass white dwarf, its gravity would become so strong that it would overcome the resistance of the electrons to denser packing. A still denser state of matter would arise. This critical mass is called the Chandrasekhar limit, and it applies only to the core mass of the star and not to the initial mass. Current data suggest that stars with initial masses from about 0.08 to about 8 to 10 solar masses evolve into white dwarfs. The more massive examples do so by developing strong stellar winds (like the solar wind) or eruptive explosions that blow off mass until they are below the Chandrasekhar limit. The Sun will probably blow off about 40% of its mass when it goes through its red giant stage about 5 billion years from now, collapsing into a white dwarf of about 0.6 times solar mass.

Stellar statistics reveal that most main sequence stars are less massive than the Sun. Therefore most stars will end their lives as white dwarfs. In the classic Pink Floyd song "Shine On, You Crazy Diamond," a dying star is a metaphor for the brilliant but troubled life of one of the founding members of the group. With its crystalline carbon core, a white dwarf does resemble a massive diamond in some ways. However, each of these celestial gems is destined to lose its luster and eventually fade from view.

Astropedia Image
White dwarf stars. Click here for original source URL.

", electrons move at almost the speed of light and matter loses its familiar properties. Stellar matter stops behaving like a perfect gas. In fact, it is no longer either gas, liquid, or solid, but a new form of matter composed of atomic nuclei held apart by a sea of electrons at extraordinary densities; a teaspoon full of white dwarf matter brought to Earth would weigh as much as an elephant. Although the interiors of white dwarfs may have densities of billions of kilograms per cubic meter, the outer layers of some may consist of ordinary matter — possibly hot gas at the surface and crystalline rocklike or glasslike solids in a crust 20 to 75 km deep (since many white dwarfs are made of carbon, they are structurally giant diamonds). At the base of these crusts, densities may be as high as 3 million kilograms per cubic meter. This high a density has only been achieved momentarily in laboratories on Earth.

 

Astropedia Image
W. S. Adams. Click here for original source URL.

Astropedia Image
Alvan Clark. Click here for original source URL.

Astropedia Image
This Hubble Space Telescope image shows Sirius A, the brightest star in our nighttime sky, along with its faint, tiny stellar companion, Sirius B. Astronomers overexposed the image of Sirius A [at centre] so that the dim Sirius B [tiny dot at lower left] could be seen. The cross-shaped diffraction spikes and concentric rings around Sirius A, and the small ring around Sirius B, are artifacts produced within the telescope's imaging system. The two stars revolve around each other every 50 years. Sirius A, only 8.6 light-years from Earth, is the fifth closest star system known. Click here for original source URL.

Astropedia Image
Friedrich Bessel. Click here for original source URL.

Astropedia Image
Hertzsprung-Russell diagram. Click here for original source URL.

At the microscopic level, positively charged atomic nuclei align themselves in orderly patterns, governed by the electrical forces that act between them. The electrons move freely through this crystalline lattice in the same way that electrons move through the copper lattice of a wire when an electric current flows. The quantum theory of matter says that no two particles can have exactly the same set of properties. This limitation means that electrons in close proximity experience a pressure that prevents the white dwarf from shrinking even further. This pressure is called degeneracy pressure, and the state of matter in a white dwarf is called a degenerate gas. The core of the Sun is destined to reach this strange state of matter in a bit more than 5 billion years. For low mass stars, this takes place in the degenerate helium core of the red giant phase instead of attaining a degenerate carbon core of the asymptotic giant phase. No matter which place in the HR diagram that a starts opts to become a white dwarf, it forms in the center of an expanding planetary nebulae.

Astropedia Image
Subrahmanyan Chandrasekhar. Click here for original source URL.

Most white dwarfs have temperatures of 10,000 to 20,000 K, and the hottest exceed 100,000 K. However, these hot stars have low luminosity because they have such a small surface area. Their high temperatures are also very temporary. With such a large amount of stored heat and such a small surface area, white dwarfs take a long time to radiate enough energy to cool significantly. The oldest white dwarfs have cooled to temperatures under 4000 K and a luminosity less than 0.0001 times that of the Sun. To chill out to these temperatures, they needed to form at least 10 billion years ago! Some white dwarfs may be among the oldest stars we can observe. Over time, these stars will just keep cooling. Trillions of years from now, these cold stellar corpses will be dark objects.

White dwarfs cannot have more mass than 1.4 solar masses because the white dwarf structure becomes unstable at this point. If you tried to dump more mass on the surface of a 1.4 solar mass white dwarf, its gravity would become so strong that it would overcome the resistance of the electrons to denser packing. A still denser state of matter would arise. This critical mass is called the Chandrasekhar limit, and it applies only to the core mass of the star and not to the initial mass. Current data suggest that stars with initial masses from about 0.08 to about 8 to 10 solar masses evolve into white dwarfs. The more massive examples do so by developing strong stellar winds (like the solar wind) or eruptive explosions that blow off mass until they are below the Chandrasekhar limit. The Sun will probably blow off about 40% of its mass when it goes through its red giant stage about 5 billion years from now," collapsing into a white dwarf of about 0.6 times solar mass.

Stellar statistics reveal that most main sequence stars are less massive than the Sun. Therefore most stars will end their lives as white dwarfs. In the classic Pink Floyd song ""Shine On", You Crazy Diamond," a dying star is a metaphor for the brilliant but troubled life of one of the founding members of the group. With its crystalline carbon core, a white dwarf does resemble a massive diamond in some ways. However, each of these celestial gems is destined to lose its luster and eventually fade from view.