White Dwarfs

White dwarfs are stellar remnants of low to intermediate-mass stars. The name of these stars is related to the fact that they are relatively hot (or white in colour) and compact. Well over 90% of stars will end up as white dwarfs. However, since less-massive stars live longer than their more massive counterparts, most of them have not yet become white dwarfs, and therefore white dwarfs now only account for a few percent of the stars found in our galaxy. White dwarfs are compact objects with a typical radius on the order of 1% of the solar radius (or roughly equal to the Earth's radius) and they have an average density of roughly 106 g/cm3. This density is six orders of magnitude larger than the average density of the Sun. White dwarfs have relatively small luminosities because of their size and are found on the lower portion of the H-R diagram. The surface gravity of white dwarfs is several orders of magnitude larger than for typical main-sequence stars. This leads to large values of pressure at their surface and to wide atomic lines in their spectra. These large atomic line widths simplify the observational identification of white dwarfs.

Table-01 gives the fundamental parameters of the well-known white dwarf Sirius B. In reality, the star Sirius is a binary-star system. Sirius A is the star visible with the naked eye while Sirius B is its companion, which happens to be a white dwarf. Sirius B is too faint to be seen with the naked eye.

The internal pressure in white dwarfs is due to a degenerate electron gas. The equation of state of such a gas leads to a pressure that depends on the number density of the free electrons in the stellar plasma but that is independent of local temperature. Detailed calculations show that a white dwarf's radius decreases as a function of its mass. It is found that a white dwarf with a mass of approximately 1.43 M☉ has a radius that theoretically tends towards zero. This mass, which is called Chandrasekhar's limit, is the upper limit for the mass of white dwarfs. In the late stages of evolution of massive stars, if the degenerate core's mass reaches this value, it collapses and leads to the neutronization of matter where protons and electrons fuse to generate neutrons via the reaction

p + e- →n + ve

This process consequently produces a neutron star.

The core of white dwarfs is mostly formed of He or C and O. Stars with very low masses can only burn hydrogen since they cannot attain the central temperature needed for He burning. However, since the lifetime of stars with very low masses on the main sequence is larger than the age of the Universe, these stars are still on the main sequence at the present time and cannot account for white-dwarf cores made of helium. Another way of obtaining a white dwarf with helium core is via the evolution of a binary-star system. A star that has burned the hydrogen in its core and is in the process of becoming a red giant may have its outer shells stripped by the gravitational pull of its companion star. If this mass loss occurs before helium has started to fuse, it can stop further evolution of the star and leave a white dwarf made up mostly of helium. As mentioned previously, the evolution of binary systems can strongly modify the way stars in such a evolve. Meanwhile, the evolution of an intermediate-mass star such as the Sun, leaves behind a white dwarf with a core made mostly of C and O. Its outer layers may contain hydrogen and/or helium depending on the quantity of mass lost during its evolution.

White dwarfs are divided into spectral classes that are related to the composition of their outer layers (see table-02).

The system of classification of white dwarfs is symbolized by D (standing for degenerate) followed by the second letter that defines the spectral features. Contrarily to main-sequence stars classification that is directly related to Teff , the classification of white dwarfs are associated with their composition. Therefore, the Teff  range for certain spectral classes can overlap. Some white dwarfs pulsate and are therefore variable and in this case a V is added to their spectral class such as DAV stars (these stars are also called ZZ Ceti stars after the name of the first of this type of star discovered). Some white dwarfs also show hybrid spectral characteristics. For example, some have hydrogen-rich atmospheres but also show neutral helium lines in their spectra and are classified as DAB white dwarfs.

Magnetic fields are detected for a small portion (a few percent) of which dwarfs by the Zeeman of up to 109 G. These magnetic fields are enormous compared to the average field at the surface of the Sun (or the Earth) which is approximately one G, while it is on the order of a couple of kG in sunspots. It is believed that the magnetic fields in white dwarfs are remnants from the evolution of magnetic ApBp stars. Magnetic fields at the surface of ApBp stars can reach values of more than 10 kG. When the stellar core contracts to form such white dwarfs, the magnetic field lines follow the condensing plasma that intensifies the value of the magnetic field found in the original main-sequence stars.

Since white dwarfs have no thermonuclear energy source, they cool down with time. They will eventually be very faint objects commonly called black dwarfs. Theory predicts that these black dwarfs will ultimately crystallize. Since carbon predominates most of the black dwarfs, these objects are sometimes called the Universe's diamonds.