Pulsating white dwarf stars and asteroseismology

At present, a large number of pulsating white dwarf (WD) stars is being discovered either from Earth-based surveys such as the Sloan Digital Sky Survey, or through observations from space (e.g., the Kepler mission). The asteroseismological techniques allow us to infer details of internal chemical stratification, the total mass, and even the stellar rotation profile. In this paper, we first describe the basic properties of WD stars and their pulsations, as well as the different sub-types of these variables known so far. Subsequently, we describe some recent findings about pulsating low-mass WDs.Comment: 10 pages, 4 figures. To be published in the proceedings of the "THIRD CONFERENCE ON STELLAR ASTROPHYSICS" to honor Prof. Dr. Juan J. Clari\'a, June 21 st to 24rd, 2016, C\'ordoba, Argentina, AAA Workshop Series, Vol. 9, 201

White-dwarf asteroseismology: an update

The vast majority of stars that populate the Universe will end their evolution as white-dwarf stars. Applications of white dwarfs include cosmochronology, evolution of planetary systems, and also as laboratories to study non-standard physics and crystallization. In addition to the knowledge of their surface properties from spectroscopy combined with model atmospheres, the global pulsations that they exhibit during several phases of their evolution allow spying on the deep interior of these stars. Indeed, by means of asteroseismology, an approach based on the comparison between the observed pulsation periods of variable white dwarfs and the periods predicted by representative theoretical models, we can infer details of the internal chemical stratification, the total mass, and even the stellar rotation profile and strength of magnetic fields. In this article, we review the current state of the area, emphasizing the latest findings provided by space-mission data.Comment: 14 pages, 4 figures, 2 tables; contributed to the Proceedings of IAU Symposium No. 357, "White Dwarfs as Probes of Fundamental Physics and Tracers of Planetary, Stellar, and Galactic Evolution," held in Hilo, Hawaii, 21-25 October 201

Asteroseismology of the GW Virginis stars SDSS J0349-0059 and VV 47

We present an asteroseismological study of SDSS J0349-0059 and VV 47 aimed mainly at deriving their total mass on the basis of state-of-the-art PG 1159 evolutionary models. We compute adiabatic nonradial $g$-mode pulsation periods for PG 1159 evolutionary models with stellar masses ranging from $0.515$ to 0.741\ M_{\sun}, that take into account the complete evolution of the progenitor stars. We first estimate a mean period spacing for both SDSS J0349-0059 and VV 47. By comparing the observed period spacing with the asymptotic period spacing we obtain M_{\star}\sim 0.569\ M_{\sun} for SDSS J0349-0059 and M_{\star}\sim 0.523\ M_{\sun} for VV 47. If we compare the observed period spacing with the average of the computed period spacings we found M_{\star}\sim 0.535\ M_{\sun} for SDSS J0349-0059 and M_{\star}\sim 0.528 M_{\sun} for VV 47. Searching for the best period fit we found, in the case of SDSS J0349-0059, an asteroseismological model with $M_{\star}= 0.542\ M_{\sun}$and$T_{\rm eff}= 91\, 255\ $K. For VV 47, we could not find a unique and unambiguous asteroseismological model. Finally, for SDSS J0349-0059, we determined the rotation period as being$P_{\rm rot}= 1/\Omega \sim 0.407$ days. The results presented in this work constitute a further step in the study of GW Vir stars through asteroseismology in the frame of fully evolutionary models of PG 1159 stars. In particular, once again it is shown the potential of asteroseismology to derive stellar masses of PG 1159 stars with an unprecedented precision.Comment: 13 pages, 16 figures, 6 tables. To be published in Astronomy and Astrophysic

New evolutionary sequences for extremely low mass white dwarfs: Homogeneous mass and age determinations, and asteroseismic prospects

We provide a fine and homogeneous grid of evolutionary sequences for He-core white dwarfs with masses 0.15-0.45 Msun, including the mass range for ELM white dwarfs (<0.20Msun). The grid is appropriate for mass and age determination, and to study their pulsational properties. White dwarf sequences have been computed by performing full evolutionary calculations that consider the main energy sources and processes of chemical abundance changes during white dwarf evolution. Initial models for the evolving white dwarfs have been obtained by computing the non-conservative evolution of a binary system consisting of a Msun ZAMS star and a 1.4 Msun neutron star for various initial orbital periods. To derive cooling ages and masses for He-core white dwarf we perform a least square fitting of the M(Teff, g) and Age(Teff, g) relations provided by our sequences by using a scheme that takes into account the time spent by models in different regions of the Teff-g plane. This is useful when multiple solutions for cooling age and mass determinations are possible in the case of CNO-flashing sequences. We also explore the adiabatic pulsational properties of models near the critical mass for the development of CNO flashes (~0.2 Msun). This is motivated by the discovery of pulsating white dwarfs with stellar masses near this threshold value. We obtain reliable and homogeneous mass and cooling age determinations for 58 very low-mass white dwarfs, including 3 pulsating stars. Also, we find substantial differences in the period spacing distributions of g-modes for models with stellar masses ~ 0.2 Msun, which could be used as a seismic tool to distinguish stars that have undergone CNO flashes in their early cooling phase from those that have not. Finally, for an easy application of our results, we provide a reduced grid of values useful to obtain masses and ages of He-core white dwarf.Comment: 12 pages, 9 figures, to be published in Astronomy and Astrophysic

Pulsations powered by hydrogen shell burning in white dwarfs

In the absence of a third dredge-up episode during the asymptotic giant branch phase, white dwarf models evolved from low-metallicity progenitors have a thick hydrogen envelope, which makes hydrogen shell burning be the most important energy source. We investigate the pulsational stability of white dwarf models with thick envelopes to see whether nonradial $g$-mode pulsations are triggered by hydrogen burning, with the aim of placing constraints on hydrogen shell burning in cool white dwarfs and on a third dredge-up during the asymptotic giant branch evolution of their progenitor stars. We construct white-dwarf sequences from low-metallicity progenitors by means of full evolutionary calculations, and analyze their pulsation stability for the models in the range of effective temperatures $T_{\rm eff} \sim 15\,000\,-\, 8\,000$ K. We demonstrate that, for white dwarf models with masses M_{\star} \lesssim 0.71\,\rm M_{\sun} and effective temperatures $8\,500 \lesssim T_{\rm eff} \lesssim 11\,600$ K that evolved from low-metallicity progenitors ($Z= 0.0001$, $0.0005$, and $0.001$) the dipole ($\ell= 1$) and quadrupole ($\ell=2$) $g_1$ modes are excited mostly due to the hydrogen-burning shell through the $\varepsilon$-mechanism, in addition to other $g$ modes driven by either the $\kappa-\gamma$ or the convective driving mechanism. However, the $\varepsilon$ mechanism is insufficient to drive these modes in white dwarfs evolved from solar-metallicity progenitors. We suggest that efforts should be made to observe the dipole $g_1$ mode in white dwarfs associated with low-metallicity environments, such as globular clusters and/or the galactic halo, to place constraints on hydrogen shell burning in cool white dwarfs and the third dredge-up episode during the preceding asymptotic giant branch phase.Comment: 6 pages, 4 figures, 1 table. To be published in Astronomy and Astrophysic

An independent constraint on the secular rate of variation of the gravitational constant from pulsating white dwarfs

A secular variation of the gravitational constant modifies the structure and evolutionary time scales of white dwarfs. Using an state-of-the-art stellar evolutionary code and an up-to-date pulsational code we compute the effects of a secularly varying $G$ on the pulsational properties of variable white dwarfs. Comparing the the theoretical results obtained taking into account the effects of a running $G$ with the observed periods and measured rates of change of the periods of two well studied pulsating white dwarfs, G117--B15A and R548, we place constraints on the rate of variation of Newton's constant. We derive an upper bound $\dot G/G\sim -1.8\times 10^{-10}$ yr$^{-1}$ using the variable white dwarf G117--B15A, and $\dot G/G\sim -1.3\times 10^{-10}$ yr$^{-1}$ using R548. Although these upper limits are currently less restrictive than those obtained using other techniques, they can be improved in a future measuring the rate of change of the period of massive white dwarfs.Comment: 13 pages, 4 tables, 3 figures. To be published in the Journal of Cosmology and Astroparticle Physic

White dwarf evolutionary sequences for low-metallicity progenitors: The impact of third dredge-up

We present new white dwarf evolutionary sequences for low-metallicity progenitors. White dwarf sequences have been derived from full evolutionary calculations that take into account the entire history of progenitor stars, including the thermally-pulsing and the post-asymptotic giant branch phases. We show that for progenitor metallicities in the range 0.00003--0.001, and in the absence of carbon enrichment due to the occurrence of a third dredge-up episode, the resulting H envelope of the low-mass white dwarfs is thick enough to make stable H burning the most important energy source even at low luminosities. This has a significant impact on white dwarf cooling times. This result is independent of the adopted mass-loss rate during the thermally-pulsing and post-AGB phases, and the planetary nebulae stage. We conclude that in the absence of third dredge-up episodes, a significant part of the evolution of low-mass white dwarfs resulting from low-metallicity progenitors is dominated by stable H burning. Our study opens the possibility of using the observed white dwarf luminosity function of low-metallicity globular clusters to constrain the efficiency of third dredge up episodes during the thermally-pulsing AGB phase of low-metallicity progenitors.Comment: To be published in Astronomy and Astrophysics. 12 pages, 11 figure

Constraining the neutrino magnetic dipole moment from white dwarf pulsations

Pulsating white dwarf stars can be used as astrophysical laboratories to constrain the properties of weakly interacting particles. Comparing the cooling rates of these stars with the expected values from theoretical models allows us to search for additional sources of cooling due to the emission of axions, neutralinos, or neutrinos with magnetic dipole moment. In this work, we derive an upper bound to the neutrino magnetic dipole moment using an estimate of the rate of period change of the pulsating DB white dwarf star PG 1351+489. By comparing the theoretical rate of change of period expected for this star with the rate of change of period with time of PG 1351+489, we assess the possible existence of additional cooling by neutrinos with magnetic dipole moment. Our models suggest the existence of some additional cooling in this pulsating DB white dwarf, consistent with a non-zero magnetic dipole moment. Our upper limit for the neutrino magnetic dipole moment is somewhat less restrictive than, but still compatible with, other limits inferred from the white dwarf luminosity function or from the color-magnitude diagram of the Globular cluster M5. Further improvements of the measurement of the rate of period change of the dominant pulsation mode of PG 1351+489 will be necessary to confirm our bound.Comment: 18 pages, 10 figures, 3 tables. Accepted for publication in Journal of Cosmology and Astroparticle Physic