Pulsating low-mass white dwarfs in the frame of new evolutionary   sequences: I. Adiabatic properties
  The discovery of pulsations in some low-mass white dwarfs, including the so-called extremely low-mass white dwarfs, 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 a new set of He-core white-dwarf models with masses ranging from $0.1554$ to $0.4352 M_{\odot}$ derived by computing the non-conservative evolution of a binary system consisting of an initially $1 M_{\odot}$ ZAMS star and a $1.4 M_{\odot}$ neutron star. We computed adiabatic radial ($\ell= 0$) and non-radial ($\ell= 1, 2$) $p$ 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 $\sim 0.18 M_{\odot}$, $g$ 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 $M_* \gtrsim 0.18 M_{\odot}$, 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 $\sim 0.18 M_{\odot}$ as ELM (extremely low-mass) white dwarfs, and white dwarfs with $M_* \gtrsim 0.18 M_{\odot}$ as LM (low-mass) white dwarfs. 
A. H. C\'orsico and L. G. Althaus
astro-ph.SR