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Two of the possibilities for the formation of low-mass ($M_{star}lesssim 0.5,M_{odot}$) hydrogen-deficient white dwarfs are the occurrence of a very-late thermal pulse after the asymptotic giant-branch phase or a late helium-flash onset in an almost stripped core of a red giant star. We aim to asses the potential of asteroseismology to distinguish between the hot flasher and the very-late thermal pulse scenarios for the formation of low-mass hydrogen-deficient white dwarfs. We compute the evolution of low-mass hydrogen-deficient white dwarfs from the zero-age main sequence in the context of the two evolutionary scenarios. We explore the pulsation properties of the resulting models for effective temperatures characterizing the instability strip of pulsating helium-rich white dwarfs. We find that there are significant differences in the periods and in the period spacings associated with low radial-order ($klesssim 10$) gravity modes for white-dwarf models evolving within the instability strip of the hydrogen-deficient white dwarfs. The measurement of the period spacings for pulsation modes with periods shorter than $sim500,$s may be used to distinguish between the two scenarios. Moreover, period-to-period asteroseismic fits of low-mass pulsating hydrogen-deficient white dwarfs can help to determine their evolutionary history.
The initial-final mass relation (IFMR) represents the total mass lost by a star during the entirety of its evolution from the zero age main sequence to the white dwarf cooling track. The semi-empirical IFMR is largely based on observations of DA whit
We present the results of the asteroseismic analysis of the hydrogen-deficient white dwarf PG 0112+104 from the $Kepler$-2 field. Our seismic procedure using the forward method based on physically sound, static models, includes the new core parameter
We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in
Extremely low-mass white dwarfs (ELM WDs) are helium WDs with a mass less than $sim$$0.3rm;M_odot$. Most ELM WDs are found in double degenerates (DDs) in the ELM Survey led by Brown and Kilic. These systems are supposed to be significant gravitationa
In this paper, we present the observations of two new GW Vir stars from the extended textit{TESS} mission in both 120,s short-cadence and 20,s ultra-short-cadence mode of two pre-white dwarf stars showing hydrogen deficiency. We performed an asterose