The purpose of this work is to explore the evolution of helium-core white dwarf stars in a self-consistent way with the predictions of detailed non-gray model atmospheres and element diffusion .
To this end , we consider helium-core white dwarf models with stellar masses of 0.406 , 0.360 , 0.327 , 0.292 , 0.242 , 0.196 and 0.169 M _ { \odot } and follow their evolution from the end of mass loss episodes during their pre-white dwarf evolution down to very low surface luminosities .

We find that when the effective temperature decreases below 4000K , the emergent spectrum of these stars becomes bluer within time-scales of astrophysical interest .
In particular , we analyse the evolution of our models in the colour-colour and colour-magnitude diagrams and we find that helium-core white dwarfs with masses ranging from \sim 0.18 to 0.3 M _ { \odot } can reach the turn-off in their colours and become blue again within cooling times much less than 15 Gyr and then remain brighter than M _ { V } \approx 16.5 .
In view of these results , many low-mass helium white dwarfs could have had time enough to evolve to the domain of collision-induced absorption from molecular hydrogen , showing blue colours .