2017A&A...607A..33C

Context. Many pulsating low-mass white dwarf stars have been detected in the past years in the field of our Galaxy. Some of them exhibit multiperiodic brightness variation, therefore it is possible to probe their interiors through asteroseismology.
Aims. We present a detailed asteroseismological study of all the known low-mass variable white dwarf stars based on a complete set of fully evolutionary models that are representative of low-mass He-core white dwarf stars.
Methods. We employed adiabatic radial and nonradial pulsation periods for low-mass white dwarf models with stellar masses ranging from 0.1554 to 0.4352M_☉ that were derived by simulating the nonconservative evolution of a binary system consisting of an initially 1M_☉ zero-age main-sequence (ZAMS) star and a 1.4M_☉ neutron star companion. We estimated the mean period spacing for the stars under study (where this was possible), and then we constrained the stellar mass by comparing the observed period spacing with the average of the computed period spacings for our grid of models. We also employed the individual observed periods of every known pulsating low-mass white dwarf star to search for a representative seismological model.
Results. We found that even though the stars under analysis exhibit few periods and the period fits show multiplicity of solutions, it is possible to find seismological models whose mass and effective temperature are in agreement with the values given by spectroscopy for most of the cases. Unfortunately, we were not able to constrain the stellar masses by employing the observed period spacing because, in general, only few periods are exhibited by these stars. In the two cases where we were able to extract the period spacing from the set of observed periods, this method led to stellar mass values that were substantially higher than expected for this type of stars.
Conclusions. The results presented in this work show the need for further photometric searches, on the one hand, and that some improvements of the theoretical models are required on the other hand in order to place the asteroseismological results on a firmer ground.