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Some low-mass white-dwarf (LMWD) stars with H atmospheres show long-periodg-mode pulsations, comprising the class of pulsating WDs called extremelylow-mass variable (ELMV) stars. It is generally believed that these stars havethick H envelopes. However, from stellar evolution considerations, theexistence of LMWDs with thin H envelopes is also possible. We present athorough asteroseismological analysis of ELMV stars based on a complete set offully evolutionary models that represents low-mass He-core WD stars harboring arange of H envelope thicknesses. Although there are currently nine ELMVs, herewe only focus on those that exhibit more than three periods and whose periodsdo not show significant uncertainties. We considered g-mode adiabatic pulsationperiods for low-mass He-core WD models with $M_*$ in the range[0.1554-0.4352]$M_{\odot}$, $T_{\rm eff}$ in the range [6000-10000]K, and Henvelope thicknesses in the range -5.8<log($M_{\rm H}/M_*$)<-1.7. We explorethe effects of employing different H-envelope thicknesses on the adiabaticpulsation properties of low-mass He-core WD models, and performperiod-to-period fits to ELMVs to search for a representative model. We foundthat the mode-trapping effects of g modes depend sensitively on $M_{\rm H}$,with the trapping cycle and trapping amplitude larger for thinner H envelopes.Also, the asymptotic period spacing is longer for thinner H envelopes. Finally,we found asteroseismological models (when possible) characterized by canonical(thick) and by thin H envelope, with $T_{\rm eff}$ and $M_*$ in agreement withthe spectroscopic determinations. The fact that we have foundasteroseismological solutions with H envelopes thinner than canonical gives aclue of the possible scenario of formation of these stars. Indeed, in the lightof our results, some of these stars could have been formed by binary evolutionthrough unstable mass loss.

astronomy and astrophysics

Pulsating low-mass white dwarfs in the frame of new evolutionary  sequences VI. Thin H-envelope sequences and asteroseismology of ELMV stars  revisited