2014A&A...569A.106C

Many low-mass white dwarfs with masses M_*/M_☉≲0.45, including the so-called extremely low-mass white dwarfs (M_*/M_☉≲0.20-0.25), have recently been discovered in the field of our Galaxy through dedicated photometric surveys. The subsequent discovery of pulsations in some of them has opened the unprecedented opportunity of probing the internal structure of these ancient stars. We present a detailed adiabatic pulsational study of these stars based on full evolutionary sequences derived from binary star evolution computations. The main aim of this study is to provide a detailed theoretical basis of reference for interpreting present and future observations of variable low-mass white dwarfs.Our pulsational analysis is based on a new set of He-core white-dwarf models with masses ranging from 0.1554 to 0.4352M_☉ derived by computing the non-conservative evolution of a binary system consisting of an initially 1M_☉ ZAMS star and a 1.4M_☉ neutron star. We computed adiabatic radial (l= 0) and non-radial (l= 1, 2) p and g modes to assess the dependence of the pulsational properties of these objects on stellar parameters such as the stellar mass and the effective temperature, as well as the effects of element diffusion.We found that for white dwarf models with masses below ∼0.18M_☉, g modes mainly probe the core regions and p modes the envelope, therefore pulsations offer the opportunity of constraining both the core and envelope chemical structure of these stars via asteroseismology. For models with M_*>0.18M_☉, on the other hand, g modes are very sensitive to the He/H compositional gradient and therefore can be used as a diagnostic tool for constraining the H envelope thickness. Because both types of objects have not only very distinct evolutionary histories (according to whether the progenitor stars have experienced CNO-flashes or not), but also have strongly different pulsation properties, we propose to define white dwarfs with masses below ∼0.18M_☉ as ELM (extremely low-mass) white dwarfs, and white dwarfs with M_*>0.18M_☉ as LM (low-mass) white dwarfs.