The pulsating low-mass He-core white dwarfs

Recent years have witnessed the discovery of many low-mass ($\lesssim 0.45 M_{\odot}$) white dwarf (WD) stars --- expected to harbor He cores--- in the field of the Milky Way and in several galactic globular and open clusters. Recently, three pulsating objects of this kind have been discovered: SDSS J1840+6423, SDSS J1112+1117, and SDSS J1518+0658. Motivated by these very exciting findings, and in view of the valuable asteroseismological potential of these objects, we present here the main outcomes of a detailed theoretical study on the seismic properties of low-mass He-core WDs based on fully evolutionary models representative of these objects. This study is aimed to provide a theoretical basis from which to interpret present and future observations of variable low-mass WDs.