Are Pulsations a Useful Probe of the Structure of the Outer Layers of White Dwarfs ?

Abstract

The most fundamental aspect of white dwarf seismology is the determination of the gravity-mode (g-mode) period structures of models of isolated pulsating white dwarfs. These stars show multiperiodic luminosity variations which result from the superposition of excited pulsation modes. Among the many oscillation modes available in the very rich nonradial g-mode spectra of white dwarfs, the observed modes are selectively chosen by a filtering mechanism. Although the period evolution is strongly tied to the core temperature evolution in a white dwarf, the period structure remains largely specified by the mechanical properties of the star. The most basic structural feature of a white dwarf is its highly degenerate interior, which leads to nearly isothermal and nearly isentropic stratifications in the core region containing more than 99% of the mass of the star. In particular, because the density gradient is almost adiabatic throughout the interior of a white dwarf, the Brünt-Väisälä frequency (see below) is very small there and low-order g-modes cannot propagate. As a result, g-modes are essentially envelope modes in white dwarfs, with large amplitudes occuring only in the non-degenerate outer layers. One can thus expect that g-modes in white dwarfs are extremely sensitive to envelope properties such as compositional stratification and partial ionization mechanisms. Compositional stratification is, in fact, the second structural feature of a white dwarf model which has strong effects on the period structure. Indeed, trapped modes result when a resonance or near-resonance occurs between the local g-mode radial wavelength and the thickness of one of the composition layers. This results in a period structure which strongly bears the signature of compositional stratification in the outer layers. Thus, it has been widely accepted that white dwarf pulsations probe primarily the outer layers of these stars. This point of view has been borne out by detailed pulsation calculations carried out by several independant groups (see Winget 1987 and references therein).