Published online by Cambridge University Press: 03 August 2017
Since Landolt's discovery of the first ZZ Ceti star, the ranks of the compact pulsators have swollen to include planetary nebula nuclei, hot pre-white dwarf stars, hot and cool white dwarf stars, and possibly even neutron stars. The discovery of multi-periodic variations in these objects has helped to usher in a new era of rapid progress in the field of stellar seismology. For the compact stars this rapid progress is the result of a combination of four fortunate circumstances: their physical structure is relatively simple; typical amplitudes are small enough to be both readily observable and amenable to linear analysis; the wealth of observed periods in each object provides many independent clues to the underlying structure of the compact stars; and the periods are short enough that we can observe many cycles in a night, thereby completely resolving the period structure in many of these stars.
In this review I will discuss the current state of our understanding of these objects, with special emphasis on their distribution in the H-R diagram, range of pulsation properties, possible mode selection mechanisms, excitation of the pulsations, problems of convection, and particularly the measurement and interpretation of period changes. In addition to the results of recent research, I will review the techniques used to obtain them, pointing out both their strengths and weaknesses. I will close with a discussion of some of the important problems facing us in the study of these objects, and attempt to identify potentially fruitful directions for future research.