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

On the systematics of asteroseismological mass determinations of PG1159 stars

We analyze systematics in the asteroseismological mass determination methods in pulsating PG 1159 stars. We compare the seismic masses resulting from the comparison of the observed mean period spacings with the usually adopted asymptotic period spacings, and the average of the computed period spacings. Computations are based on full PG1159 evolutionary models with stellar masses ranging from 0.530 to 0.741 Mo that take into account the complete evolution of progenitor stars. We conclude that asteroseismology is a precise and powerful technique that determines the masses to a high internal accuracy, but it depends on the adopted mass determination method. In particular, we find that in the case of pulsating PG 1159 stars characterized by short pulsation periods, like PG 2131+066 and PG 0122+200, the employment of the asymptotic period spacings overestimates the stellar mass by about 0.06 Mo as compared with inferences from the average of the period spacings. In this case, the discrepancy between asteroseismological and spectroscopical masses is markedly reduced when use is made of the mean period spacing instead of the asymptotic period spacing.Comment: 7 pages, 4 figures, 1 table. To be published in Astronomy and Astrophysic

Asteroseismology of the Kepler V777 Her variable white dwarf with fully evolutionary models

DBV stars are pulsating white dwarfs with atmospheres rich in He. Asteroseismology of DBV stars can provide valuable clues about the origin, structure and evolution of hydrogen-deficient white dwarfs, and may allow to study neutrino and axion physics. Recently, a new DBV star, KIC 8626021, has been discovered in the field of the \emph{Kepler} spacecraft. It is expected that further monitoring of this star in the next years will enable astronomers to determine its detailed asteroseismic profile. We perform an asteroseismological analysis of KIC 8626021 on the basis of fully evolutionary DB white-dwarf models. We employ a complete set of evolutionary DB white-dwarf structures covering a wide range of effective temperatures and stellar masses. They have been obtained on the basis of a complete treatment of the evolutionary history of progenitors stars. We compute g-mode adiabatic pulsation periods for this set of models and compare them with the pulsation properties exhibited by KIC 8626021. On the basis of the mean period spacing of the star, we found that the stellar mass should be substantially larger than spectroscopy indicates. From period-to-period fits we found an asteroseismological model characterized by an effective temperature much higher than the spectroscopic estimate. In agreement with a recent asteroseismological analysis of this star by other authors, we conclude that KIC 8626021 is located near the blue edge of the DBV instability strip, contrarily to spectroscopic predictions. We also conclude that the mass of KIC 8626021 should be substantially larger than thought.Comment: 7 pages, 5 figures, 3 tables. To be published in Astronomy and Astrophysic

Probing the internal rotation of pre-white dwarf stars with asteroseismology: the case of PG 122+200

We put asteroseismological constraints on the internal rotation profile of the GW Vir (PG1159-type) star PG 0122+200. To this end we employ a state-of-the-art asteroseismological model for this star and we assess the expected frequency splittings induced by rotation adopting a forward approach in which we compare the theoretical frequency separations with the observed ones assuming different types of plausible internal rotation profiles. We also employ two asteroseismological inversion methods for the inversion of the rotation profile of PG 0122+200. We find evidence for differential rotation in this star. We demonstrate that the frequency splittings of the rotational multiplets exhibited by PG 0122+200 are compatible with a rotation profile in which the central regions are spinning about 2.4 times faster than the stellar surface.Comment: 8 pages, 6 figures, 2 tables. To be published in MNRA

Asteroseismological constraints on the coolest GW Vir variable star (PG 1159-type)PG 0122+200

We present an asteroseismological study on PG 0122+200, the coolest known pulsating PG1159 (GW Vir) star. Our results are based on an augmented set of the full PG1159 evolutionary models recently presented by Miller Bertolami & Althaus (2006). We perform extensive computations of adiabatic g-mode pulsation periods on PG1159 evolutionary models with stellar masses ranging from 0.530 to 0.741 Msun. We derive a stellar mass of 0.626 Msun from a comparison between the observed period spacing and the computed asymptotic period spacing, and a stellar mass of 0.567 Msun by comparing the observed period spacing with the average of the computed period spacing. We also find, on the basis of a period-fit procedure, an asteroseismological model representative of PG 0122+200 which is able to reproduce the observed period pattern with an average of the period differences of 0.88 s. The model has an effective temperature of 81500 K, a stellar mass of 0.556 Msun, a surface gravity log g= 7.65, a stellar luminosity and radius of log(L/Lsun)= 1.14 and log(R/Rsun)= -1.73, respectively, and a He-rich envelope thickness of Menv= 0.019 Msun. We derive a seismic distance of about 614 pc and a parallax of about 1.6 mas. The results of the period-fit analysis carried out in this work suggest that the asteroseismological mass of PG 0122+200 could be 6-20 % lower than thought hitherto and in closer agreement (to within 5 %) with the spectroscopic mass. This result suggests that a reasonable consistency between the stellar mass values obtained from spectroscopy and asteroseismology can be expected when detailed PG1159 evolutionary models are considered.Comment: 10 pages, 6 figures. To be published in Astronomy & Astrophysic

Asteroseismological constraints on the pulsating planetary nebula nucleus (PG1159-type) RX J2117.1+3412

We present asteroseismological inferences on RX J2117.1+3412, the hottest known pulsating PG1159 star. Our results are based on full PG1159 evolutionary models recently presented by Miller Bertolami & Althaus (2006). We performed extensive computations of adiabatic g-mode pulsation periods on PG1159 evolutionary models with stellar masses ranging from 0.530 to 0.741 Mo. PG1159 stellar models are extracted from the complete evolution of progenitor stars started from the ZAMS, through the thermally pulsing AGB and born-again phases to the domain of the PG 1159 stars. We constrained the stellar mass of RX J2117.1+3412 by comparing the observed period spacing with the asymptotic period spacing and with the average of the computed period spacings. We also employed the individual observed periods to find a representative seismological model. We derive a stellar mass of 0.56-0.57 Mo from the period spacing data alone. In addition, we found a best-fit model representative for RX J2117.1+3412 with an effective temperature of 163,400 K, a stellar mass of 0.565 Mo, and a surface gravity log g= 6.61. The derived stellar luminosity and radius are log(L/Lo)= 3.36 and log(R/Ro)= -1.23, respectively, and the He-rich envelope thickness is Menv= 0.02 Mo. We derive a seismic distance of 452 pc and a linear size of the planetary nebula of 1.72 pc. These inferences seem to solve the discrepancy between the RX J2117.1+3412 evolutionary timescale and the size of the nebula. All of the seismological tools we use concur to the conclusion that RX J2117.1+3412 must have a stellar mass of 0.565 Mo much in agreement with recent asteroseismology studies and in clear conflict with the predictions of spectroscopy plus evolutionary tracks.Comment: 10 pages, 6 figures, 2 tables. Accepted for publication in Astronomy and Astrophysics. Erratum available as a separate fil

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