What is a White
Dwarf?
The relative sizes
of Sirius B and the Earth
Imagine shrinking the sun by a factor of just over 100, to
a body the size of the earth. Since
the mass of the sun would remain unchanged the orbit of the earth and the
orbits of all the planets would be unaltered. The light emitted by the resulting midget sun, however,
would be reduced by over a factor of 10,000! The midday sun would be just a brilliant point of light
dimly illuminating the earth. All
the planets, even close-in Mercury, would quickly freeze. The laws of physics
dictate that such an icy solar system would contain, at its center a most
unusual object, distinctly different from all the familiar stars we see when we
stare up at the night sky.
Nature does not allow the unlimited compression of matter
to extreme densities without matter itself suffering dramatic and catastrophic
changes in its fundamental character. It came as a series of shocks to astronomers in the
early twentieth century that there might be types of matter that seemed to defy
description. The first of these shocks
involved the curious properties of the faint companion of Sirius. It slowly,
but unavoidably, dawned on astronomers and physicists that the tiny companion
of the brightest star in the sky must be a planet-sized star with the mass of the
sun. Elementary calculations
implied densities well over 50,000 grams per cubic centimeter, nearly 2000
times denser that the densest substances on earth! The questions
were unavoidable, how was such a state of matter possible and what would become
of such a star? A partial answer
came in 1926, in the form of the strange logic of quantum mechanics. Nature it seems can tolerate, and even
prefer, such extreme densities and conditions - if atoms themselves are
squeezed out of existence by the force of gravity. In such circumstances an entirely new type of star is
achieved, a white dwarf. A
second shock made it clear that the sky had to be full of these strange faint
minuscule stars. At the time, in
the 1920s and 1930s, it was far from clear how nature managed to make such
bizarre objects, but once formed they were destined to remain for eternity in
their extremely contracted and dense state.
So what were these bizarre objects and where did they come
from? We now know that they are
literally the corpses of dead stars that have reached their compact state after
a star's available nuclear fuel finally becomes exhausted. When nuclear energy finally fails, gravity
dominates and compresses what remains of the star to such an extent that
individual atoms are crushed out of existence. All that remains are disassociated, unrelated, individual
nuclei and their former electrons.
Densities now reach values of over 1 million grams per cubic centimeter.
The force that ultimately succeeds
in halting the gravitational contraction is due to a quantum mechanical
property of electrons. Called the Pauli
Exclusion Principle,
it forbids more than one electron from occupying the same quantum state. In atoms the Exclusion Principle directs
electrons to form orderly shells about the nucleus, resulting in the chemical
elements. Under the extreme
densities inside a white dwarf free electrons reconfigure themselves into a new
collective form of matter. No
longer associated with individual nuclei, electrons dissolve into a collective
'sea' of electrons. This produces
a 'pressure' that supports the star. The name given this situation is 'degenerate matter' from
the 'degenerate' electrons which produce it. (The 'degenerate' designation comes from a mathematical
tradition of describing the merging of separate solutions of an equation into a
single solution.)
Degenerate matter gives white dwarfs several unusual
characteristics. For example, the
more massive a white dwarf the smaller the resulting star. In the plot below the radii of white
dwarfs and normal (solar-like) stars are plotted as a function of mass. As expected, normal stars grow in
radius as mass increases. In
contrast the radii of white dwarfs (multiplied by 100 to keep them on the same
plot) shrink as mass increases.
The locations of Sirius A and B and the sun are shown on
the plot.
Another unique feature of white dwarfs is that these stars
have a maximum mass, the
'Chandrasekhar Limit' of 1.4 solar masses, named after S. Chandrasekhar, who in
1930 theoretically discovered this
property of white dwarfs, as a first year graduate student. Some five decades later, in 1983,
Chandrasekhar recieved the Nobel Prize in Physics for this and other
discoveries in stellar astrophysics.
Any white dwarf acquiring more mass than this limit will
catastrophically explode in what is called a type 1a supernova. These blasts can be detected all the
way across the Universe.
White dwarfs are thus examples of what have become known
as degenerate stars. After normal
stars, like the sun, white dwarfs form the second rung of a descending ladder
of compact stellar objects.
Neutron stars, with masses of about one and a half solar masses and sizes
of approximately 10 km, are the next rung. They are analogs of white dwarfs, but with neutrons
supplying degenerate pressure. On
the bottom rung of this ladder are black holes, objects so compressed that a
black hole the mass of the sun would have a 'radius' of just 3 km. The radius is not an actual radius in
the familiar sense, but the point at which gravity which becomes so intense (as
described by General Relativity) that it curves space to the extent that not
even light can escape.
The determining factor as to whether a white dwarf, a
neutron star or a black hole will be formed is the mass of the original
star. Approximately 98% of all
stars in our galaxy will eventually form white dwarfs, given enough time to
exhaust their nuclear fuel. In the
case of the sun this will occur in about 6 billion years and will produce a
0.55 solar mass white dwarf (the rest of the sun's mass will be shed into
interstellar space during the sun's red giant phase). If a star is more massive than about 8 or 10 solar masses it
will end its life as supernova, which may produce a neutron star. More massive stars yet , can produce
black holes.
White dwarfs like Sirius B live off their reservoirs of
internal energy; they spend hundreds of millions to billions of years slowly
cooling. For example, Sirius B
currently has a surface temperature of 25,000 K. It required about 123 million years for Sirius B to reach this
temperature, from the initial 100,000 K temperature it had when it was
formed. It will require further
billions of years to cool to a few thousand degrees Kelvin. White dwarfs are not completely made of degenerate matter,
only the core which has most of the mass, thin layers of helium and hydrogen
gas cover the surface. It is this
atmosphere of hydrogen or perhaps helium that we see when we study white
dwarfs.
White dwarfs continue to be at the forefront of modern astrophysics, from studies of the
history of our Milky Way Galaxy to methods used to probe the history of our
expanding universe and the nature of dark energy. There remain many things to be learned about white
dwarfs and from them.