Comparing the asteroseismic properties of pulsating pre-extremely low mass white dwarf and

Context. Pulsating extremely low-mass pre-white dwarf stars (pre-ELMV), with masses between ~0.15 M⊙ and ~0.30 M⊙, constitute a new class of variable stars showing g- and possibly p-mode pulsations with periods between 320 and 6000 s (frequencies between 14.4 and 270 c/d), driven by the κ mechanism operating in the second He ionization zone. On the other hand, main sequence δ Scuti stars, with masses between 1.2 and 2.5 M⊙, pulsate in low-order g and p modes with periods in the range [700–28 800] s (frequencies in the range [3–123] c/d), driven by the κ mechanism operating in the He II ionization zone and the turbulent pressure acting in the HI ionization layer. Interestingly enough, the instability strips of pre-ELM white dwarf and δ Scuti stars nearly overlap in the Teff vs. log g diagram, leading to a degeneracy when spectroscopy is the only tool to classify the stars and pulsation periods only are considered. Aims. Pre-ELM white dwarf and δ Scuti stars are in very different stages of evolution and therefore their internal structure is very distinct. This is mirrored in their pulsational behavior, thus employing asteroseismology should allow us to distinguish between these groups of stars despite their similar atmospheric parameters. Methods. We have employed adiabatic and non-adiabatic pulsation spectra for models of pre-ELM white dwarfs and δ Scuti stars, and compare their pulsation periods, period spacings, and rates of period change. Results. Unsurprisingly, we found substantial differences in the period spacing of δ Scuti and pre-ELM white dwarf models. Even when the same period range is observed in both classes of pulsating stars, the modes have distinctive signature in the period spacing and period difference values. For instance, the mean period difference of p-modes of consecutive radial orders for δ Scuti model are at least four times longer than the mean period spacing for the pre-ELM white dwarf model in the period range [2000–4600] s (frequency range [18.78–43.6] c/d). In addition, the rate of period change is two orders of magnitudes larger for the pre-ELM white dwarfs compared to δ Scuti stars. In addition, we also report the discovery of a new variable star, SDSSJ075738.94+144827.50, located in the region of the Teff versus log g diagram where these two kind of stars coexist. Conclusions.The characteristic spacing between modes of consecutive radial orders (p as well as g modes) and the large differences found in the rates of period change for δ Scuti and pre-ELM white dwarf stars suggest that asteroseismology can be employed to discriminate between these two groups of variable stars. Furthermore, we found that SDSSJ075738.94+144827.50 exhibits a period difference between p modes characteristic of a δ Sct star, assuming consecutive radial order for the observed periods