New evolutionary sequences for extremely low-mass white dwarfs Homogeneous mass and age determinations and asteroseismic prospects

Context. The number of detected extremely low-mass (ELM) white dwarf stars has increased drastically in recent years, thanks to the results of many surveys. In addition, some of these stars have been found to exhibit pulsations, making them potential targets for asteroseismology. Aims. We provide a fine and homogeneous grid of evolutionary sequences for helium (He) core white dwarfs for the whole range of their expected masses (0.15 less than or similar to M-*/M-circle dot less than or similar to 0.45), including the mass range for ELM white dwarfs (M-*/M-circle dot less than or similar to 0.20). The grid is appropriate for mass and age determination of these stars, as well as for studying their adiatabic pulsational properties. Methods. White dwarf sequences have been computed by performing full evolutionary calculations that consider the main energy sources and processes of chemical abundance changes during white dwarf evolution. Realistic initial models for the evolving white dwarfs have been obtained by computing the nonconservative evolution of a binary system consisting of an initially 1 M-circle dot ZAMS star and a 1.4 M-circle dot neutron star for various initial orbital periods. To derive cooling ages and masses for He-core white dwarfs, we perform a least square fitting of the M(T-eff, g) and Age(T-eff, g) relations provided by our sequences by using a scheme that takes into account the time spent by models in different regions of the T-eff - g plane. This is particularly useful when multiple solutions for cooling age and mass determinations are possible in the case of CNO-flashing sequences. We also explore in a preliminary way the adiabatic pulsational properties of models near the critical mass for the development of CNO flashes (similar to 0.2 M-circle dot). This is motivated by the discovery of pulsating white dwarfs with stellar masses near this threshold value. Results. We obtain reliable and homogeneous mass and cooling age determinations for 58 very low-mass white dwarfs, including three pulsating stars. Also, we find substantial differences in the period spacing distributions of g-modes for models with stellar masses near similar to 0.2 M-circle dot, which could be used as a seismic tool to distinguish stars that have undergone CNO flashes in their early cooling phase from those that have not. Finally, for an easy application of our results, we provide a reduced grid of values useful to obtain the masses and ages of He-core white dwarfs.