1 Introduction

Pulsating DA white dwarfs (WD) or ZZ Ceti stars have captured the attention of numerous researchers since the first star (HL Tau 76, Landolt 1968) belonging to this class was reported to exhibit multi-periodic luminosity variations (McGraw 1979). Over the last two decades, various studies have presented strong evidence that pulsating DA WDs represent an evolutionary stage in the cooling history of the majority, if not all, DA WDs. Rapid progress in the study of these pulsating stars has been possible thanks to the development of powerful theoretical tools paralleled by an increasing degree of sophistication in observational techniques. A major step towards the understanding of ZZ Ceti pulsations was given by Dolez & Vauclair (1981) and Winget et al. (1982) who independently demonstrated that models of ZZ Ceti stars have pulsationally unstables g-modes due to the $\kappa-\gamma$ mechanism. From then on, the asteroseismology of DA WDs has provided invaluable insights on their internal structure and evolution (Tassoul et al. 1990; Brassard et al. 1991, 1992a,b; Gautschy et al. 2001; Bradley 1996, 1998, 2001 amongst others).

An important aspect of pulsating WDs is related to the trapping properties. Mode trapping in compositionally stratified WDs has been invoked to explain the longstanding fact that all the modes expected from theoretical models are not actually observed in the ZZ Ceti stars (Winget et al. 1981; Brassard et al. 1992a). In this scenario, certain modes are characterized by local wavelengths that are comparable to the thickness of one of the compositional layer, particularly the hydrogen-rich envelope. The importance of trapped modes lies on the fact that they appear to be the most likely to be observed because they require low kinetic energies to reach observable amplitudes. More specifically, the amplitude of the eigenfunctions of modes trapped in the hydrogen envelope is small in the core, which causes such modes to have low oscillation kinetic energy as compared with adjacent modes. This behaviour manifests itself as local minima in kinetic energy versus period diagrams. In particular, trapped modes characterized by periods close to the thermal time-scale of the driving region will reach high enough amplitudes for them to be observed. This picture has been reinforced by non-adiabatic calculations (Dolez & Vauclair 1981; Winget et al. 1982). However, recent evidence seems to cast some doubts on the correlation between observed amplitudes and mode trapping. Indeed, recent seismological studies of ZZ Ceti stars (e.g. Bradley 1998) point to the fact that the observed periods having the largest amplitudes in the power spectrum do not correspond to trapped modes as predicted by the best fitting model.

The pulsation properties depend on the details of the WD modeling. This is particularly true regarding the abundance distribution at the chemical interfaces, mostly at the hydrogen-helium transition. In this connection, most of the existing calculations invoke diffusive equilibrium in the trace element approximation to assess the shape of the hydrogen-helium transition (Tassoul et al. 1990; Brassard et al. 1992a,b; Bradley 1996). However, equilibrium conditions may not be achieved at the base of massive hydrogen envelopes, even at the characteristic ages of ZZ Ceti stars (see Iben & MacDonald 1985). In view of these concerns, we have recently carried out new evolutionary calculations for DA WD stars which take fully into account time dependent element diffusion, nuclear burning and the history of the WD progenitor in a self-consistent way. The present letter is aimed at specifically exploring the trapping properties of such models.

Figure 1: Internal chemical profiles for hydrogen, helium, carbon and oxygen. The hydrogen-helium interface resulting from the predictions of non-equilibrium diffusion (diffusive equilibrium) are shown with solid line (thin dotted line) in the inset. The WD stellar mass is $0.563~M_{\odot}$ and the effective temperature is $\approx$12000 K.