Formation and evolution of a 0.242 M⊙ helium white dwarf in the presence of element diffusion

The evolution of a 0.242 M-circle dot object that finally becomes a helium white dwarf is modeled from Roche lobe detachment down to very low luminosities (log L/L-circle dot = -5). In doing so, we employ our stellar code, to which we have added a set of routines that compute the e+ects due to gravitational settling and chemical and thermal diffusion. Initial models are constructed by abstracting mass from a 1 M-circle dot red giant branch model up to the moment at which the model begins to evolve blueward. From then on, two detailed sequences have been computed: one sequence with element diffusion and the other without that phenomenon. Results without diffusion are very similar to those of Driebe and collaborators. We find that element diffusion introduces important changes in the internal structure of the star. In particular, models with diffusion undergo three thermonuclear flashes, whereas models without diffusion experience only one. This fact has a large effect on the fraction of total hydrogen mass left in the star (about 3 times less hydrogen compared to models without diffusion) at the start of the final cooling track. As a result, at late stages of evolution models with diffusion are characterized by a much smaller nuclear energy release. Consequently, the star has to take energy from its relic thermal content, causing its further evolution to be significantly faster compared with the standard treatment. Notably, these new, more detailed structures strongly resemble those we have assumed in previous work on helium white dwarfs with hydrogen envelopes. Conventional wisdom indicates that a millisecond pulsar is recycled during the mass transfer stage in a binary system. Usually, the companion to the pulsar is a low-mass white dwarf. If zero ages are set at the end of mass transfer, the ages of both objects should be the same. Available models characterized by dominant hydrogen burning lead to a strong discrepancy between the ages of PSR B1855+09 and its white dwarf companion. We interpret such a discrepancy as a direct consequence of ignoring element diffusion in the stellar models. We show that in the frame of models in which diffusion is properly accounted for, ages naturally come into a nice agreement. Consequently, we do not have to invoke any ad hoc mass loss or exotic mechanisms to account for the ages of the stars that belong to the binary system PSR B1855+09.