White Dwarf Stars
White dwarfs are the remnants of small and medium mass stars that have died and left the Main
Sequence. Stars with a mass less than about 10 solar masses are destined to become white dwarfs. The Sun
will become a white dwarf in about 5 billion years time. Despite having a mass round about that of the Sun, a
white dwarf is only a little larger than the Earth and so is very dense!

The exact mass limit below which a star can become a white dwarf is not known exactly, because it varies
according to how much mass a star loses late in its life. The crucial point is that the mass of the remaining star
core must be below a maximum limit. This limit is called the
Chandrasekhar limit and is usually quoted as 1.44
solar masses (the exact limit depends upon the chemical composition of the core and is lower for say a core
comprising mostly iron than for a core comprising carbon and oxygen). If the core remnant has more mass than
the Chandraekhar limit then it will condense into either a
neutron star or a black hole.

When a star like the Sun is in old age it becomes a
red giant as it burns helium fuel and deposits carbon and
oxygen in its core. The Sun has insufficient mass for its core to ever become hot enough to burn carbon into
heavier elements (such as neon and magnesium). Remember that when a star burns fuel it is fusing the nuclei
of the atoms of an element together to make a heavier element, such as fusing hydrogen into helium, or helium
into carbon, oxygen and nitrogen, carbon into neon and magnesium, or silicon to iron, etc.

When the Sun builds up too much carbon and oxygen in its core, the core will contract under its own gravity,
since their is no burning in the core to generate the energy needed to oppose gravity. As the core contracts, so
the outer layers of the Sun will be blasted off into space, forming a planetary nebula. If the remaining core has
less than 1.44 solar masses, as it must do for the Sun since the Sun has only one solar mass to start with (!),
then the core will form a white dwarf.

In a white dwarf, the matter compresses to an enormous density (one cubic metre of material from a white dwarf
core weighs about one billion tonnes). The core is also very hot as it was once the active core of a star, but is
now exposed to outer space and will slowly cool over billions of years, as it no longer burns fuel by nuclear
fusion to generate heat. The material inside the white dwarf is rather like a very dense gaseous metal, initially,
with electrons tripped from the nuclei and nuclei vibrating due to their thermal energy. The thermal energy of
the ions initially prevents further contraction of the core, but as the white dwarf cools it
crsytallises (solidifies)
and somewhat resembles very hot and very dense solid metal with a high thermal and electrical conductivity.
When this happens, the white dwarf will contract slightly, until the electrons are squeezed together as tightly as
quantum mechanics will allow. At this point the gas of electrons which permeates the solid ion lattice becomes a
degenerate electron gas (which although extremely hot behaves as if it was cold). This is a purely (and
somewhat mysterious) quantum mechanical phenomenon, but the degeneracy pressure produced by these
tightly packed electrons stops the core from collapsing under its own gravity.

Eventually the white dwarf cools and dims, turning yellow, orange, red and finally ending as a cool
black dwarf.
This dead remnant is the most probable ultimate fate of the Sun. (Note a white dwarf that is yellow or red, or
any other hue, is still cooled a white dwarf so as not to confuse it with
Main Sequence stars of the yellow dwarf
and red dwarf varieties! Also do not confuse black dwarfs with brown dwarfs!).
Above: left - a newly formed white dwarf star is very hot and luminous. Right - peering beneath the thin
atmosphere we see the white dwarf crystallising. Often the magnetic field of the white dwarf is very strong
indeed, and this has resulted in the texture caused by alternating hot (bright) and cool (black) regions, in this
artistic impression..
Above: the white dwarf contracts slightly as it cools.
Above: as the white dwarf cools it dims and turns from white to yellow and then to red (left) and finally cools
completely to a black dwarf (right).
Structure of a white dwarf

A white dwarf has a thin atmosphere that emits light as heat left over from its birth is slowly radiated into space.
The atmosphere is mostly either hydrogen or helium. There are various models to account for this difference,
but they will not be discussed here as the subject is still very controversial. Beneath the atmosphere is a very
dense structure with a core predominantly of helium, if the parent star was of low mass, or carbon (C) and
oxygen (O), for a star initially about as massive as the Sun, or of oxygen (O), neon (Ne) and magnesium (Mg)
for stars between about 8 and 11 solar masses. Thus we talk about
helium white dwarfs and CO white
dwarfs
and ONeMg white dwarfs. Some calculations also predict that a narrow high mass limit may exist for a
white dwarf with a predominantly iron core (though since iron is only produced inside very massive stars, this
requires that the parent star lose massive amounts of mass in order to get below the Chandraekhar limit). Very
light stars possibly form white dwarfs with cores composed mostly of hydrogen - in a sense a brown dwarf turns
into a hydrogen-rich electron degenerate structure without ever losing mass as a planetary nebula, very small
stars just above the brown dwarf limit possibly retain much hydrogen (as well as helium) in their white dwarf
remnants.

More massive white dwarfs contract further and so, despite having more mass, are smaller in size! The
gravitational energy released by this contraction, increases the energy of the degenerate electrons and the
electrostatic repulsion between them. As the masses of a white dwarfs increase their electrons move faster and
faster and become more and more
relativistic (meaning their speeds are close to the speed of light). At the
Chandrasekhar limit the electrons move almost at the speed of light and are said to be
ultrarelativistic.
Ultrarelativistic particles  are a precarious means of support and the stellar remnant may collapse into a
neutron star or black hole or, in some circumstances, it may detonate and destroy itself in a
type Ia
supernova
explosion!

Interestingly, the dense crystallised core of a carbon rich white dwarf has been likened to a huge diamond the
size of the Earth, since diamond is crystalline carbon!
White dwarf structure
Above: a model of the internal structure of a white dwarf star with a mass of about 1 solar mass (one
times the Sun's mass). The density in the core is estimated to range from about 10^8 g/cm^3 to 10^13
g/cm^3, depending on mass, being greater for more massive white dwarfs. The density drops rapidly
towards the surface of the white dwarf. The white dwarf is surrounded by a small non-degenerate
atmosphere some 1-10 km thick, with a density of about 100 to 1000 g/cm^3. The core temperature
is initially around 10^10 degrees (K), at which temperatures any remaining hydrogen will be burnt to
helium by nuclear fusion, but white dwarfs gradually cool and their luminosity is predicted to drop
tenfold every 10 billion years, until the cold black dwarf stage is reached. A typical ball-park white
dwarf surface temperature is given as 10 000 degrees. The degenerate electron gas makes an
excellent thermal conductor, such that heat is transported easily throughout the core by
conduction and evenly distributes itself, resulting in a core at uniform temperature (an
isothermal
core
). The temperature drops rapidly in the outermost third of the white dwarf as heat is being
radiated to the atmosphere. In the atmosphere, heat is transported largely by turbulent
convection
until the
photosphere is reached, from where light and heat are radiated into space. This convection
is greatest in less massive white dwarfs, such that in the smallest, the convection zone may be so
deep as to possibly extend part-way into the degenerate layers of the star.
Some estimates put the mean core density of a very light white dwarf (say 0.2 solar masses) at below 10^6
g/cm^3 at which the electrons are non-relativistic (though still degenerate). Such a light white dwarf is most likely
to be a helium white dwarf (although the correlation between initial main sequence stellar mass and final white
dwarf mass is not necessarily predictable, since stars can lose an uncertain amount of mass prior to becoming
white dwarfs). In a white dwarf of about 0.4 solar masses and above, such as perhaps a typical carbon or iron
white dwarf, the core density exceeds 10^6 g/cm^3 at which the electrons become relativistic.

Very hot and newly born white dwarfs, with temperatures above 10^10 K are expected to radiate most of their
thermal energy by another mechanism - neutrino radiation. The weak force (which dominates certain reactions
involving leptons like neutrinos and electrons) becomes important at these high temperatures and thermal
energy is converted into neutrinos. Neutrinos are almost massless particles that travel at about the speed of light
and they can also pass through even very dense matter easily, only occasionally bumping into atoms, and so
they radiate away as if the star was transparent to them, carrying away the thermal energy (
neutrino cooling).
When temperatures drop below about 10^10 K the conduction/convection/radiation heat transport mechanism
becomes dominant.

Despite their initial high temperatures, the small size of white dwarfs (with a diameter of about 10 000 km) means
that they are faint, with luminosities only one thousandth that of the Sun. Studying white dwarfs that are
components of binary star systems enables their mass to be accurately determined. For example, Sirius B is a
white dwarf of 1.05 solar masses, and 40 Eri B, a white dwarf of 0.45 solar masses. These are all below the
estimated Chandrasekhar mass (which is about 1.2 solar masses, 1.44 for a helium white dwarf, 1.1 for an iron
white dwarf). A massive white dwarf might contain elemental layers, with a carbon/oxygen core (carbon-12 and
oxygen-16 isotopes) with a helium (helium-4) envelope and possibly a hydrogen crust or atmosphere (if any
hydrogen survives the initial high temperatures without burning to helium).
Degenerate stars

In a white dwarf the energy of the electrons is much greater than the energy of the ions, and in the core the
ions crystallise, due to the immense pressure whilst the energetic electrons support the star against
gravitational collapse. The high pressures keep the material ionised, even in a black dwarf at zero degrees
Kelvin! In a
neutron star, the matter is also degenerate, but the pressures and densities are much greater and
electrons and protons are squeezed together into neutrons (electron capture) and so the electrons can no
longer support the star and instead the star is supported by degenerate neutron pressure.

In the degenerate matter of a white dwarf, the electrons are squeezed so close together that
Heisenberg's
Uncertainty Principle
prevents further collapse as the immense gravitational field tries to collapse the star.
This principle says that there is a limit to how accurately the momentum and position of a particle can be known,
confining one or the other of this pair of values to a narrow range, increases the uncertainty or range of the
other value. As the immense pressures confine the motion, and hence momentum, of the electrons, there
spatial position becomes more uncertain and they spread out and so are kept apart by a purely
quantum-mechanical phenomenon which halts further gravitational collapse. Another way of looking at this is
Pauli's Exclusion Principle, which states that two or more particles called fermions cannot coexist in the same
space with the same quantum numbers (quantum numbers are parameters describing the energy and
momentum of the particle and in quantum mechanics only certain values of energy are allowed) that is with the
same values of energy and momentum.
Electrons are fermions, and in a white dwarf, the electrons are
pressed together into the lowest available energy levels, so that many electrons close together have the same
energy and momentum, but the exclusion principle forbids them from occupying the same space, so they
cannot be squeezed together any more.
Degenerate means having the same energies. In normal,
non-degenerate gases, thermal energy excites the particles to a variety of higher energy levels, such that few
particles have the same energy. Since this thermal excitation is prevented by the immense pressures in
degenerate matter, degenerate matter is said to be cold (there is no thermal excitation). In reality, the gas is
never a perfect degenerate gas as there is always a small amount (say 10%) of thermal excitation - no matter
can ever be perfectly cold.

The degenerate electrons supply almost all of the pressure that supports the white dwarf against gravity. These
electrons have
very high thermal conductivity. The ions contain most of the star's mass and its store of
thermal energy.
White Dwarf, Pov-Ray model
young white dwarf
white dwarf surface
white dwarf contracting
white dwarf contracting 2
very old and very cool white dwarf star
black dwarf