In the light of recent significant progress on both the observational and theoretical fronts, we review the status of white dwarf stars as cosmochronometers. These objects represent the end products of stellar evolution for the vast majority of stars and, as such, can be used to constrain the ages of various populations of evolved stars in the Galaxy. For example, the oldest white dwarfs in the solar neighborhood (the remnants of the very first generation of intermediate-mass stars in the Galactic disk) are still visible and can be used, in conjunction with cooling theory, to estimate the age of the disk. More recent observations suggest the tantalizing possibility that a population of very old white dwarfs inhabits the Galactic halo. Such a population may contribute significantly to baryonic "dark" matter in the Milky Way and may be used to obtain an independent estimate of the age of the halo. In addition, white dwarf cosmochronology is likely to play a very significant role in the coming era of giant 8-10 m telescopes when faint white dwarf populations should be routinely discovered and studied in open and globular clusters.

We present a detailed analysis of 108 helium-line (DB) white dwarfs based on model atmosphere fits to high signal-to-noise optical spectroscopy. We derive a mean mass of 0.67 M ⊙ for our sample, with a dispersion of only 0.09 M ⊙ . White dwarfs also showing hydrogen lines, the DBA stars, comprise 44% of our sample, and their mass distribution appears similar to that of DB stars. As in our previous investigation, we find no evidence for the existence of low-mass (M < 0.5 M ⊙ ) DB white dwarfs. We derive a luminosity function based on a subset of DB white dwarfs identified in the Palomar-Green survey. We show that 20% of all white dwarfs in the temperature range of interest are DB stars, although the fraction drops to half this value above T eff ∼ 20, 000 K. We also show that the persistence of DB stars with no hydrogen features at low temperatures is difficult to reconcile with a scenario involving accretion from the interstellar medium, often invoked to account for the observed hydrogen abundances in DBA stars. We present evidence for the existence of two different evolutionary channels that produce DB white dwarfs: the standard model where DA stars are transformed into DB stars through the convective dilution of a thin hydrogen layer, and a second channel where DB stars retain a helium-atmosphere throughout their evolution. We finally demonstrate that the instability strip of pulsating V777 Her white dwarfs contains no nonvariables, if the hydrogen content of these stars is properly accounted for.

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We present a summary of what is currently known about the three distinct families of isolated pulsating white dwarfs. These are the GW Vir stars (He/C/O-atmosphere stars with T eff ≃ 120; 000 K), the V777 Her stars (He-atmosphere, T eff ≃ 25; 000 K), and the ZZ Ceti stars (H-atmosphere, T eff ≃ 12; 000 K), all showing multiperiodic luminosity variations caused by low-order and low-degree g-mode instabilities. We also provide, in an Appendix, a very brief overview of the newly found evidence in favor of the existence of a fourth category of oscillating white dwarfs bearing strong similarities with these families of pulsators. We begin our survey with a short historical introduction, followed by a general discussion of pulsating white dwarfs as compact pulsators. We then discuss the class properties of these objects, including an updated census. We next focus on the instability domains for each family of pulsators in the log g À T eff diagram, and present their time-averaged properties in more detail. This is followed by a section on excitation physics, i.e., the causes of the pulsational instabilities, with emphasis on the common properties of the different types of pulsator. We then discuss the time-dependent properties of the pulsating white dwarfs featuring, among other things, a brief "picture tour" across the ZZ Ceti instability strip. We next review the methods used to infer or constrain the angular geometry of a pulsation mode in a white dwarf. These include multicolor photometry and time-resolved spectroscopy, the exploitation of the nonlinear features in the observed light curves, and rotational splitting. We also consider basic adiabatic asteroseismology starting with a discussion of the reaction of the period spectrum to variations of model parameters. We next review the various asteroseismological inferences that have so far been claimed for white dwarfs. We also discuss the potential of exploiting the rates of period change. We finally provide some concluding remarks, including a list with several suggestions for future progress in the field.

We present new calculations that strongly reinforce the idea-originally proposed by Charpinet et al.-that pulsation modes are driven through an opacity bump due to a local enhancement of the iron abundance in the envelopes of sdB stars. Our improved models incorporate nonuniform iron abundance distributions obtained through the condition of diffusive equilibrium between gravitational settling and radiative levitation. They also include special Rosseland opacity tables that take into account the large variations of the iron abundance about the cosmic value that are predicted by equilibrium radiative levitation theory. For representative models with M ϭ 0.48 M J and log g ϭ 5.8, we find strong instabilities for low-order radial and nonradial ( p and f) pulsation modes in the range 36,500 K ? T eff ? 29,000 K. The four pulsating sdB stars currently known all have effective temperatures in that range. In addition, one of our models with T eff ϭ 34,000 K has a band of unstable modes with periods in the range 116 -195 s, in excellent agreement with those of the known pulsators. We therefore claim that our proposed iron bump mechanism provides a natural explanation for the instabilities found in the newly discovered class of pulsating sdB stars.