ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O B-CelestialObject O O O O O O O O O O O O O
tokens: region (see panel a of Fig. 8 ). This chemical interface induces a bump in at (panel a of Fig. 9 ). This interface also affects the shape of the Lamb frequency. In the case of white dwarfs with carbon-oxygen cores, the internal chemical structure is substantially more complex than in the case of the helium-core white dwarf models (see panels b, c, and d in Fig. 8 ). This results in a much more complex form of the run , as can be seen in panels b, c, and d of Fig. 9 . Indeed, in these cases, the Brunt-Väisälä frequency is characterized by additional maxima induced by the presence of the C/O-He and C/O chemical interfaces. Fig. 9 Propagation diagrams, the spatial run of the logarithm of the squared Brunt-Väisälä and Lamb frequencies (Unno et al. 1989 ), corresponding to the white dwarfs models shown in Fig. 8 for . The number and shape of the chemical interfaces present in the interior of DA white dwarf models strongly affect the propagation properties of nonradial pulsation modes, in particular through mode trapping and confinement ( Brassard et al. 1992 ; Bradley 1996 ; Córsico et al. 2002 ). Mode trapping or confinement results in a strong departure from uniformity of the forward period separation, (), when plotted in terms of the pulsation period , where is the radial order of the mode. Thus, the period difference between an observed mode and adjacent modes can be considered as an observational diagnostic of mode trapping. For a helium-core white dwarf, which is characterized by a single chemical interface such as that of the model of mass considered here, local minima in usually correspond to modes trapped in the hydrogen envelope; this is in contrast to local maxima in , which are associated with modes trapped in the inner core. The forward period spacing for modes in terms of the periods corresponding to the helium-core model of mass is depicted in panel a of Fig. 10 . We also show the asymptotic period spacing, computed as in Tassoul et al. (1990) , with a dotted blue line. Mode-trapping signatures are clearly noticeable, particularly for periods shorter than 1500 s. Longer periods seem to fit the asymptotic predictions, although small departures from constant period spacing are still clearly seen. In the case of white dwarfs with carbon-oxygen cores, the presence of multiple chemical transition regions causes much more complex patterns of mode-trapping/confinement, as can be seen in panels b, c, and d of Fig. 10 . In particular, strong departures from uniform period separation are evident for the models with , , and . These features persist for the entire range of periods analyzed here. Also, we note some “beating” modulating the amplitudes of the departures of . This beating is due to the combined mode-trapping and confinement effects caused by the various steps in the C/O profile in the core; see Córsico Althaus (2006) for the case of PG1159 star models. Clearly, the mode trapping and confinement features of models with C/O