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Aims. We aim to determine the theoretical instability strips of white dwarfs with diverse H and He content in their atmospheres, from a solar composition to a H-depleted atmosphere. Pulsators with mixed H-He atmospheres are indeed known to exist, and these are the white dwarfs in cataclysmic accreting systems of the GW Lib type. We thus also aim to determine the range of periods of excited pulsation modes, and to qualitatively compare these to the observed periods in GW Lib white dwarf pulsators. Methods. In the first full nonadiabatic stability analysis of pulsators of this kind, we applied a time-dependent convection treatment and an energy leakage argument to compute, for cooling models of white dwarfs with various masses and envelope compositions, the location of the blue and the red edges, as well as the properties of pulsation modes. Results. We find that our derived instability strips form a true continuum in the log g-Teff plane and that their individual location depends uniquely on the assumed atmospheric composition, from the solar composition models at low effective temperatures to the H-depleted models at much higher temperatures. Taking into account our previous results from the ZZ Ceti (pure H atmosphere) and V777 Her (pure He atmosphere) white dwarf pulsators, this implies that all of these instability domains are connected via the same fundamental driving mechanism. Applying our results to the case of white dwarf pulsators of the GW Lib type, we find that our theoretical instability strips can qualitatively account for all of the known cases. The computed range of periods of excited modes also compares qualitatively very well to the observed ones. Conclusions. The GW Lib pulsators are very similar in nature to ZZ Ceti and V777 Her white dwarfs. It is the diverse chemical compositions in their atmosphere and envelope that defines their specific pulsation properties. Beyond GW Lib pulsators, white dwarfs can sometimes exhibit mixed H-He atmospheres, such as in the recently found proto-He white dwarf pulsators. Our results open the way towards quantitative asteroseismology of these various kinds of white dwarfs.

A connection between the instability strips of ZZ Ceti and V777 Herculis white dwarfs