Investigation of white dwarfs provide important constraints on the theory of stellar evolution. E.g. the existence of white dwarfs in young stellar clusters (with turn-off masses of about 5 solar masses ) show that massive stars must loose the bulk of their matter during their lifetime until they become a white dwarf with about 1.15 solar masses. The majority of white dwarfs have masses of about 0.6 solar masses and stems from progenitors with about 2 solar masses. The mass-loss processes during the stellar evolution is not well understood; the largest quantity is lost on the asymptotic giant branch (AGB) when the energy in a star is produced by alternating ignitions of a hydrogen and helium burning shell ("thermal pulses") in the interior. At the end of this phase about 0.1-0.3 solar mases are lost when the outer layers are blown away; this matter subsequently becomes visible as a planetary nebula. The nebula emits light since it is ionized by the hot (typically 50-200 kK) remnant. This central star of a planetary nebula is the direct progenitor of a white dwarf. After about 30000 years the nebula becomes invisible and the white dwarf cools down before they eventually become invisible. The coolest white dwarfs known have an age of about 9-10 billion years; the existence of these stars is a measure for the age of the disc of our galaxy.
With the exception of very cool objects the equation of state in the atmospheres of white dwarfs is the one for an ideal gas. For a white dwarf with an effective temperature of 25000K the particle densities and the temperatures range from 10^15-10^17 cm^-3 and 15-50 kK, respectively.
The chemical composition of white dwarfs is rather peculiar compared to main sequence stars: Normally only one element shows up in the optical spectra. The reason for this almost mono-elemental composition has been known for a long time. In 1949 Schatzman has shown that the huge gravitational acceleration (typically 10^8 cm sec^-2) together with the electric field leads to a downward diffusion of the heavier elements on time scales which are rather short compared to the evolutionary time scale.
The stars with spectral type DA are defined by the fact that their optical spectra exhibit the Balmer lines of hydrogen only. About 80% of all known white dwarfs belong to this class. Nearly all atmospheres of the non-DAs are dominated by helium. Depending on the effective temperature He II (spectral type DO, 45-120000K) or HeI (type DB, 11-28000K) lines are the strongest. On the cool end of the cooling sequence (below 11000K) the high energy needed to excite spectral lines leads to a continuous spectrum in the optical (type DC). In some stars with helium atmospheres, lines of carbon (type DQ) or other metals (Ca, Mg, Fe: spectral type DZ) show up in the spectra, probably due to accretion from the interstellar medium.
While many details and physical processes in the atmospheres of white dwarfs are well understood, the most obvious observational fact, namely that the white dwarfs are basically divided into two major groups --- the DAs and the non-DAs ---, is still unexplained. One possible explanation is that the spectral type is determined by the pre-white dwarf evolution. It has been suggested that the exact phase, when the star leaves the AGB, or a late thermal pulse in a post-AGB star determines whether significant amounts of hydrogen are left over in the atmosphere or not.
It is, however, very certain that transitions between the DA and the non-DA sequence must occur: between 28000K and 45000K not a single non-DA star exists. Since there is no physical process known by which the effective temperature of a DO with 45000K should jump down to 28000K the DO stars must become hydrogen rich at about 45kK for some, yet unknown reason.