White Dwarfs and Supernovae Part I
A star is a celestial body of hot gas that radiates energy derived from thermonuclear reactions in its interior. These bodies of hot gas are self-luminous spheres that shine by generating their own energy and radiating it off into space.
The stuff that fuels the stars to generate this energy is the stuff they are made of -- hydrogen, helium, carbon, etc. -- which they burn by converting these elements into heavier elements. "Burning" in this context does not refer to the kind of burning we are familiar with, such as the burning of wood or coal, which is chemical burning. It refers to nuclear burning, in which the nuclei of atoms fuse into nuclei of heavier atoms.
In the star's hot interior there is a conversion of hydrogen to helium and the helium accumulates at its center. When the helium core reaches a certain size, the star starts to change in size and temperature dramatically. It expands enormously and its surface becomes cooler. In other words, it leaves the main sequence and moves in the red giant direction. The more massive the star then the quicker it will reach this point.
Despite its temperature the expanded giant releases more heat because of its larger surface area. This change in the helium core after it has reached a certain size, precipitating it's expansion into a red giant, is explained by the British Astronomer Fred Hoyle as due to a contraction of this helium core giving rise to higher temperatures where the helium nuclei fuse into carbon nuclei and therefore liberate more energy. According to Hoyle the new carbon core heats up further, and more complicated atoms, such as oxygen and neon begin to form. While this is happening, the star is contracting and getting hotter again and beginning to move back towards the main sequence. By now the star has begun to acquire a series of layers, like an onion. It has an oxygen-neon core, then a layer of carbon, then one of helium and the whole is enveloped in a skin of still unconverted hydrogen.
However in comparison to its long life as a hydrogen consumer, the star is on a quick descent through its remaining fuels. Its life is now limited since the energy produced by helium fusion and beyond is about one-twentieth of that produced by hydrogen fusion. In a comparatively short time, the energy required to keep the star expanded against the strong pull of its own gravitational field begins to fall short, and the star contracts ever more swiftly. It contracts not only back to what have been the size of a normal star, but even beyond that-----into a WHITE DWARF.
Probably all stars with initial masses up to about eight solar masses finally end up as white dwarfs. Stars with more than about 8 solar masses explode as type 2 supernovae after a lifetime of only a few million years and become neutron stars or black holes. 90 percent of all stars finally become white dwarfs when their nuclear energy generation has ceased.
When the radius and masses of white dwarfs such as Sirius B were first computed, astronomers were flabbergasted. Stars with masses comparable to that of the Sun were scrunched down into a volume comparable to that of the Earth. What is the source of the pressure which keeps white dwarfs from collapsing under their own strong gravitational force?
A white dwarf is supported by a different type of pressure (not dependent on the temperature of the white dwarf): electron degeneracy pressure.
White dwarfs are very small (R = 0.01 Rsun) compared to a main sequence star, even though they have masses which are comparable to that of a main sequence star. Thus, white dwarfs must be very dense compared to an everyday main sequence star. The density of a white dwarf is approximately 3 MILLION grams / cm3.
That's 3 tons per cubic centimeter. A teaspoonful of white dwarf stuff would be as massive as an elephant.
Under the extreme conditions which prevail within a white dwarf, the laws of quantum mechanics become important. Quantum mechanics is nothing more than the study of how subatomic particles (such as electrons, protons, and neutrons) behave. Subatomic particles do not always obey the same laws as large objects. Hence, the laws of quantum mechanics sometimes seem contrary to common sense.
One rule of quantum mechanics (known as the Pauli exclusion principle) is this:
Two identical electrons, located in the same region of space, cannot have the same energy. In a dense white dwarf, where the electrons are packed close together, all the low energy levels in a given region are full. Some of the electrons are forced to occupy high energy levels. This means that the electrons in a white dwarf form a degenerate gas. (In the language of quantum mechanics, a degenerate object is one in which all the low energy levels are fully occupied.
In a degenerate object such as a white dwarf, the fast-moving high-energy electrons provide a pressure which is independent of temperature. Even as the temperature of a white dwarf falls toward absolute zero, the Pauli exclusion principle demands that the high-energy electrons keep moving at the same speed. Hence, the pressure exerted by the electrons remains constant as the temperature falls.
During the contraction the outermost layers of the star may be left behind or even blown off because of the heat developed by the contraction. The white dwarf is then surrounded by an expanding shell of gas that appear as a "smoke ring" or "donut" of gas. These are the PLANETARY NEBULAE because the smoke surrounds the star like a planetary orbit made visible. Eventually the ring of smoke expands and thins out invisibly, and we have white dwarfs such as Sirus B with no signs of any surrounding nebulosity. After the planetary nebula fades, the white dwarf will still be visible. White dwarfs shine because they are hot; although a white dwarf has no internal power source, it takes billions of years for a white dwarf to cool down. Thermal energy in the interior of a white dwarf is carried to the surface by conduction, then radiated away.
White dwarfs form in this way rather quietly and such quiet "death" lies in the future for stars like our sun and smaller ones. Also, white dwarfs, if undisturbed, have an indefinitely prolonged life, or a kind of long rigor mortis, in which they slowly cool until, eventually, they are no longer hot enough to glow (many billions of years in the future) and then continue for further billions and billions of years as BLACK DWARFS.
As the temperature T of the white dwarf's surface decreases, the radius R remains constant. (Remember the electron degeneracy pressure which supports a white dwarf is not dependent on T; thus, hydrostatic equilibrium is maintained even as the white dwarf cools.) Since temperature (T) decreases and Radius (R) is constant, the luminosity L decreases. The oldest, coldest white dwarfs have L = 0.0001 Lsun and T = 5000 Kelvin. In the future, the eventual fate of a white dwarf will be to become a black dwarf (not to be confused with a black hole). A black dwarf is an extremely cold compact object supported by electron degeneracy pressure.
There is an UPPER LIMIT to the permitted mass of a white dwarf. White dwarfs with larger masses have smaller radii. The pressure within a white dwarf depends only on density, not on temperature; to maintain the tremendous pressures required to support a massive white dwarf, the white dwarf must have a very great density. At a mass of M = 1.4 Msun (a mass known as the Chandrasekhar limit, after the man who discovered it), the radius of the white dwarf is squeezed down to nothing, and the density shoots up to infinity. In practical terms, this means that a white dwarf more massive than 1.4 solar masses doesn't have an electron degeneracy pressure large enough to maintain hydrostatic equilibrium.
You can't have a stable white dwarf more massive than 1.4 Msun.
Supergiant stars, and massive giant stars, lose matter into space at a rapid rate. It is possible for massive stars to slim down to below the Chandrasekhar limit by the time they collapse into white dwarfs. A star with a main sequence mass of 6 Msun, for instance, will lose about 4.6 Msun into outer space, and will end as a 1.4 Msun white dwarf. Stars which are more massive than about 6 Msun during their main sequence lives will NOT be able to lose enough mass to become white dwarfs. (Parenthetic note: the amount of mass lost by a star is somewhat uncertain. Some calculations indicate that stars as massive as 9 Msun may be able to reduce themselves to the Chandrasekhar limit.) What happens to stars which are too massive to become white dwarfs? See Part 2