Early stages in a star's life:
A star radiates energy into space because it is hot. The energy lost into interstellar space is replenished by fusion. When fusion stops, the lost energy is no longer replaced, and the temperature and pressure within the star drop.
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.
Consider what happens to a giant star which
runs out of fuel.
The core collapses and heats up: It becomes a white dwarf with a
surface temperature of T = 100,000 Kelvin, or more.
The outer envelope, heated by the core, is ejected: A giant with
a mass M = 1 Msun will eject 0.4 Msun of
gas into outer space, leaving a 0.6 Msun white dwarf
behind.
The ejected outer envelope forms an emission nebula surrounding the white dwarf. An emission nebula of this sort (ejected gas which is being excited by a hot white dwarf) is called a planetary nebula. This confusing name goes back to the 18th century; viewed through a small telescope, the fuzzy disk of a planetary nebula looks a bit like the fuzzy disk of a planet like Uranus.
The above picture is of the Ring Nebula, a
planetary nebula in the constellation Lyra. Click on the image
for a higher-resolution version. The blue light in the center of
the nebula is emitted by ionized helium. In the cooler outer
regions of the nebula, the dominant sources of emission are
neutral hydrogen and oxygen. The central hot white dwarf is
visible as a point of light in the center of the nebula.
(Image credit: N. Lame and R. Pogge [OSU])
Measuring the Doppler shifts of planetary nebulae reveals that they are expanding. A typical middle-aged planetary nebula will be about 10,000 A.U. across. A planetary nebula will last for about 50,000 years before fading into invisibility.
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.
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 T decreases and 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? Next Lecture
