Recent advances in the theoretical modeling of pulsating low-mass   He-core white dwarfs
  Many extremely low-mass (ELM) white-dwarf (WD) stars are currently being found in the field of the Milky Way. Some of these stars exhibit long-period nonradial $g$-mode pulsations, and constitute the class of ELMV pulsating WDs. In addition, several low-mass pre-WDs, which could be precursors of ELM WDs, have been observed to show short-period photometric variations likely due to nonradial $p$ modes and radial modes. They could constitute a new class of pulsating low-mass pre-WD stars, the pre-ELMV stars. Here, we present the recent results of a thorough theoretical study of the nonadiabatic pulsation properties of low-mass He-core WDs and pre-WDs on the basis of fully evolutionary models representative of these stars. 
A. H. C\'orsico, L. G. Althaus, L. M. Calcaferro, A. M. Serenelli, S.   O. Kepler, and C. S. Jeffery
astro-ph.SR