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White dwarf stars constitute the final evolutionary stage for more than 95 per cent of all stars. The Galactic population of white dwarfs conveys a wealth of information about several fundamental issues and are of vital importance to study the structure, evolution and chemical enrichment of our Galaxy and its components ---including the star formation history of the Milky Way. In addition, white dwarfs are tracers of the evolution of planetary systems along several phases of stellar evolution. Also, white dwarfs are used as laboratories for astro-particle physics, being their interest focused on physics beyond the standard model. The last decade has witnessed a great progress in the study of white dwarfs. In particular, a wealth of information of these stars from different surveys has allowed us to make meaningful comparison of evolutionary models with observations. While some information like surface chemical composition, temperature and gravity of isolated white dwarfs can be inferred from spectroscopy, and the total mass and radius can be derived as well when they are in binaries, the internal structure of these compact stars can be unveiled only by means of asteroseismology, an approach based on the comparison between the observed pulsation periods of variable stars and the periods predicted by appropriate theoretical models. The asteroseismological techniques allow us to infer details of the internal chemical stratification, the total mass, and even the stellar rotation profile. In this review, we first revise the evolutionary channels currently accepted that lead to the formation of white-dwarf stars, and then, we give a detailed account of the different sub-types of pulsating white dwarfs known so far, emphasizing the recent observational and theoretical advancements in the study of these fascinating variable stars.
The Sloan Digital Sky Survey has allowed us to increase the number of known white dwarfs by a factor of five and consequently the number of known pulsating white dwarfs also by a factor of five. It has also led to the discovery of new types of variab
The unprecedented extent of coverage provided by Kepler observations recently revealed outbursts in two hydrogen-atmosphere pulsating white dwarfs (DAVs) that cause hours-long increases in the overall mean flux of up to 14%. We have identified two ne
We report the discovery of four massive ($M > 0.8,M_odot$) ZZ Ceti white dwarfs, including an ultramassive $1.16,M_odot$ star. We obtained ground based, time-series photometry for thirteen white dwarfs from the Sloan Digital Sky Survey Data Release 7
We present the results of the asteroseismological analysis of two rich DAVs, G38-29 and R808, recent targets of the Whole Earth Telescope. 20 periods between 413 s and 1089 s were found in G38-29s pulsation spectrum, while R808 is an even richer puls
Many low-mass white dwarfs are being discovered in the field of our galaxy and some of them exhibit $g$-mode pulsations, comprising the extremely low-mass variable (ELMV) stars class. Despite it is generally believed that these stars are characterize