Evolutionary calculations of phase separation in crystallizing white dwarfstars

We present an exploration of the significance of carbon/oxygen phase separa tion in white dwarf stars in the context of self-consistent evolutionary ca lculations; Because phase separation can potentially increase the calculate d ages of the oldest white dwarfs, it can affect the age of the Galactic di sk as derived from the downturn in the white dwarf luminosity function. We find that the largest possible increase in ages due to phase separation is similar to 1.5 Gyr, with a most likely value of approximately 0.6 Gyr, depe nding on the parameters of our white dwarf models. The most important facto rs influencing the size of this delay are the total stellar mass, the initi al, composition profile, and the phase diagram assumed for crystallization. We find a maximum age delay in models with masses of similar to 0.6 M., wh ich is near the peak in the observed white dwarf mass distribution. In addi tion, we note that the prescription that we have adopted for the: mixing du ring crystallization provides an upper bound for the efficiency of this pro cess, and hence a maximum for the age delays. More realistic treatments of the mixing process may reduce the size of this effect. We find that varying the opacities (via the metallicity) has little effect on the calculated ag e delays. In the context of Galactic evolution, age estimates for the oldes t Galactic globular clusters range from 11.5 to 16 Gyr and depend on a vari ety of parameters. In addition, a 4-6 Gyr delay is expected between the for mation of the globular clusters and the formation of the Galactic thin disk , while the observed white dwarf luminosity function gives an age estimate for the thin disk of 9.5(-0.8)(+1.1) Gyr, without including the effect of p hase separation. Using the above numbers, we see that phase separation coul d add between 0 and 3 Gyr to the white dwarf ages and still be consistent w ith the overall picture of Galaxy formation. Our calculated maximum value o f less than or similar to 1.5 Gyr fits within these bounds, as does our bes t-guess value of similar to 0.6 Gyr.