Aims. Motivated by the recent detection of single and binary He-core white dwarfs in metal-rich clusters, we present a full set of evolutionary calculations and colors appropriate to the study of these white dwarfs. The paper is also aimed at investigatingwhether stable hydrogen burning may constitute a major source of energy for massive He-core white dwarfs resulting from high-metallicity progenitors. Methods. White dwarf sequences are derived by considering the evolutionary history of progenitor stars with supersolar metallicities. We also incorporate a self-consistent, time-dependent treatment of gravitational settling and chemical diffusion, as well as of the residual nuclear burning. Results. We find that the influence of residual nuclear burning during the late stages of white dwarf evolution is strongly dependent on the chemical diffusion at the base of the hydrogen-rich envelope. When no diffusion is considered, residual hydrogen burning strongly influences the advanced stages of white dwarf cooling, introducing evolutionary delays of severalGyr. By contrast, when diffusion is taken into account, the role of residual nuclear burning is strongly mitigated, and the evolution is only dictated by the thermal content stored in the ions. In addition, for all of our sequences, we provide accurate color and magnitudes on the basis of new and improved non-gray model atmospheres that explicitly include Lyquasi-molecular opacity. Key words: stars: evolution - stars: white dwarfs - diffusion - galaxies: clusters: general
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