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The pulsating DA white dwarfs (ZZ Ceti stars) are g-mode non-radial pulsators. Asteroseismology provides strong constraints on their global parameters and internal structure. Since all the DA white dwarfs falling in the ZZ Ceti instability strip do pulsate, the internal structure derived from asteroseismology brings knowledge for the DA white dwarfs as a whole group. HS 0507+0434B is one of the ZZ Ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study. We carried out multisite observation campaigns in 2007 and from 2009 December to 2010 January. In total, 206 h of photometric time series have been collected. They have been analysed by means of Fourier analysis and simultaneous multifrequency sine wave fitting. In total, 39 frequency values are resolved including six triplets and a number of linear combinations. We identify the triplets as ℓ = 1 g modes split by rotation. We derived the period spacing, the rotational splitting and the rotation rate. From the comparison of the observed periods with the theoretical periods of a series of models, we estimate the fundamental parameters of the star: its total mass M*/M⊙ = 0.675, its luminosity L/L⊙ = 3.5 × 10−3, and its hydrogen mass fraction MH/M* = 10−8.5. [ABSTRACT FROM AUTHOR]

We have acquired new time series photometry of the two pulsating DB white dwarf stars KUV 05134+2605 and PG 1654+160 with the Whole Earth Telescope. Additional single-site photometry is also presented. We use all these data plus all available archival measurements to study the temporal behaviour of the pulsational amplitudes and frequencies of these stars for the first time. We demonstrate that both KUV 05134+2605 and PG 1654+160 pulsate in many modes, the amplitudes of which are variable in time; some frequency variability of PG 1654+160 is also indicated. Beating of multiple pulsation modes cannot explain our observations; the amplitude variability must therefore be intrinsic. We cannot find stable modes to be used for determinations of the evolutionary period changes of the stars. Some of the modes of PG 1654+160 appear at the same periods whenever detected. The mean spacing of these periods (≈40 s) suggests that they are probably caused by non-radial gravity-mode pulsations of spherical degree l = 1. If so, PG 1654+160 has a mass around 0.6 M[sub ⊙]. The time-scales of the amplitude variability of both stars (down to two weeks) are consistent with theoretical predictions of resonant mode coupling, a conclusion which might however be affected by the temporal distribution of our data. [ABSTRACT FROM AUTHOR]