They are the compressed former cores of their parent stars. A white dwarf of the sun's mass is the size of the earth. With no more nuclear heat source, the white dwarf simply cools off, a process that takes many millions of years. Through most of the white dwarf, the pressure of degenerate electrons supports the material against gravity, but near the surface the electrons become less degenerate and the ions become important. The ions are also important in setting the specific heat and thus the rate at which the white dwarf can cool.
White dwarfs are also sometimes pulsationally unstable.
Pulsation is a process that is sensitive to specific heats, and indeed white dwarfs are often in several pulsation modes simultaneously. Figure 3 illustrates the importance of improved opacity and equations of state on the understanding of stellar evolution. The figure shows the effects of opacity on Cepheid pulsations. Until the early 1990s, there remained a discrepancy between the predicted mass of pulsating Cepheid stars and observation. The results of the comparison indicate that the new opacities resolve the discrepancy, putting the observations and the theory in agreement.