The present work is designed to explore the evolution of helium-core white dwarf ( He WD ) stars for the case of metallicities much lower than the solar metallicity ( Z = 0.001 and Z = 0.0002 ) .
Evolution is followed in a self-consistent way with the predictions of detailed and new non-grey model atmospheres , time-dependent element diffusion and the history of the white dwarf progenitor .
Reliable initial models for low mass He WDs are obtained by applying mass loss rates to a 1 M _ { \odot } stellar model in such a way that the stellar radius remains close to the Roche lobe radius .
The loss of angular momentun caused by gravitational wave emission and magnetic stellar wind braking are considered .
Model atmospheres , based on a detailed treatment of the microphysics entering the WD atmosphere ( such as the formalism of Hummer-Mihalas to deal with non-ideal effects ) as well as hydrogen line and pseudo-continuum opacities , enable us to provide accurate colours and magnitudes at both early and advanced evolutionary stages .

We find that most of our evolutionary sequences experience several episodes of hydrogen thermonuclear flashes .
In particular , the lower the metallicity , the larger the minimum stellar mass for the occurrence of flashes induced by CNO cycle reactions .
The existence of a mass threshold for the occurrence of diffusion-induced CNO flashes leads to a marked dichotomy in the age of our models .
Another finding of this study is that our He WD models experience unstable hydrogen burning via PP nuclear reactions at late cooling stages as a result of hydrogen chemically diffusing inwards .
Such PP flashes take place in models with very low metal content .

We also find that models experiencing CNO flashes exhibit a pronounced turn-off in most of their colours at M _ { V } \approx 16.Finally , colour-magnitude diagrams for our models are presented and compared with recent observational data of He WD candidates in the globular clusters NGC 6397 and 47 Tucanae .