Pulsations of massive ZZ Ceti stars with carbon/oxygen and oxygen/neon cores

We explore the adiabatic pulsational properties of massive white dwarf stars with hydrogen-rich envelopes and oxygen/neon and carbon/oxygen cores. To this end, we compute the cooling of massive white dwarf models for both core compositions taking into account the evolutionary history of the progenitor stars and the chemical evolution caused by time-dependent element diffusion. In particular, for the oxygen/neon models, we adopt the chemical profile resulting from repeated carbon-burning shell flashes expected in very massive white dwarf progenitors. For carbon/oxygen white dwarfs we consider the chemical profiles resulting from phase separation upon crystallization. For both compositions we also take into account the effects of crystallization on the oscillation eigenmodes. We find that the pulsational properties of oxygen/neon white dwarfs are notably different from those made of carbon/oxygen, thus making asteroseismological techniques a promising way to distinguish between both types of stars and, hence, to obtain valuable information about their progenitors.Comment: 11 pages, including 11 postscript figures. Accepted for publication in Astronomy and Astrophysic

New phase diagrams for dense carbon-oxygen mixtures and white dwarf evolution

Cool white dwarfs are reliable and independent stellar chronometers. The most common white dwarfs have carbon-oxygen dense cores. Consequently, the cooling ages of very cool white dwarfs sensitively depend on the adopted phase diagram of the carbon-oxygen binary mixture. A new phase diagram of dense carbon-oxygen mixtures appropriate for white dwarf interiors has been recently obtained using direct molecular dynamics simulations. In this paper, we explore the consequences of this phase diagram in the evolution of cool white dwarfs. To do this we employ a detailed stellar evolutionary code and accurate initial white dwarf configurations, derived from the full evolution of progenitor stars. We use two different phase diagrams, that of Horowitz et al. (2010), which presents an azeotrope, and the phase diagram of Segretain & Chabrier (1993), which is of the spindle form. We computed the evolution of 0.593 and 0.878M_sun white dwarf models during the crystallization phase, and we found that the energy released by carbon-oxygen phase separation is smaller when the new phase diagram of Horowitz et al. (2010) is used. This translates into time delays that are on average a factor about 2 smaller than those obtained when the phase diagram of Segretain & Chabrier (1993) is employed. Our results have important implications for white dwarf cosmochronology, because the cooling ages of very old white dwarfs are different for the two phase diagrams. This may have a noticeable impact on the age determinations of very old globular clusters, for which the white dwarf color-magnitude diagram provides an independent way of estimating their age.Comment: 7 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Evolution of a 3 \msun star from the main sequence to the ZZ Ceti stage: the role played by element diffusion

The purpose of this paper is to present new full evolutionary calculations for DA white dwarf stars with the major aim of providing a physically sound reference frame for exploring the pulsation properties of the resulting models in future communications. Here, white dwarf evolution is followed in a self-consistent way with the predictions of time dependent element diffusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to the white dwarf formation. In particular, we follow the evolution of a 3 \msun model from the zero-age main sequence (the adopted metallicity is Z=0.02) all the way from the stages of hydrogen and helium burning in the core up to the thermally pulsing phase. After experiencing 11 thermal pulses, the model is forced to evolve towards its white dwarf configuration by invoking strong mass loss episodes. Further evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch. Emphasis is placed on the evolution of the chemical abundance distribution due to diffusion processes and the role played by hydrogen burning during the white dwarf evolution. Furthermore, the implications of our evolutionary models for the main quantities relevant for adiabatic pulsation analysis are discussed. Interestingly, the shape of the Ledoux term is markedly smoother as compared with previous detailed studies of white dwarfs. This is translated into a different behaviour of the Brunt-Vaisala frequency.Comment: 11 pages, 11 figures, accepted for publication in MNRA

An efficient graph algorithm for dominance constraints

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known

SCIL - Symbolic Constraints in Integer Linear Programming

We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute significantly to the expressive power, ease of use, and efficiency of constraint programs

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

The Effects of Element Diffusion on the Pulsational Properties of Variable DA White Dwarf Stars

We explore the effects of element diffusion due to gravitational settling and thermal and chemical diffusion on the pulsational properties of DA white dwarfs. To this end, we employ an updated evolutionary code coupled with a pulsational, finite difference code for computing the linear, non-radial g-modes in the adiabatic approximation. We follow the evolution of a 0.55 \msun white dwarf model in a self-consistent way with the evolution of chemical abundance distribution as given by time dependent diffusion processes. Results are compared with the standard treatment of diffusive equilibrium in the trace element approximation. Appreciable differences are found between the two employed treatments. We conclude that time dependent element diffusion plays an important role in determining the whole oscillation pattern and the temporal derivative of the periods in DAV white dwarfs. In addition, we discuss the plausibility of the standard description employed in accounting for diffusion in most of white dwarf asteroseismological studies.Comment: 6 pages, 5 figures, accepted for publication in MNRA

New nonadiabatic pulsation computations on full PG1159 evolutionary models: the theoretical GW Vir instability strip revisited

We reexamine the theoretical instability domain of pulsating PG1159 stars (GW Vir variables). We performed an extensive g-mode stability analysis on PG1159 evolutionary models with stellar masses ranging from 0.530 to 0.741 Mo for which the complete evolutionary stages of their progenitors from the ZAMS, through the thermally pulsing AGB and born-again phases to the domain of the PG1159 stars have been considered. We found that pulsations in PG1159 stars are excited by the kappa-mechanism due to partial ionization of carbon and oxygen, and that no composition gradients are needed between the surface layers and the driving region, much in agreement with previous studies. We show, for the first time, the existence of a red edge of the instability strip at high luminosities. We found that all of the GW Vir stars lay within our theoretical instability strip. Our results suggest a qualitative good agreement between the observed and the predicted ranges of unstable periods of individual stars. Finally, we found that generally the seismic masses (derived from the period spacing) of GW Vir stars are somewhat different from the masses suggested by evolutionary tracks coupled with spectroscopy. Improvements in the evolution during the thermally pulsing AGB phase and/or during the core helium burning stage and early AGB could help to alleviate the persisting discrepancies.Comment: 10 pages, 8 figures. To be published in Astronomy and Astrophysic

Modeling He-rich subdwarfs through the hot-flasher Scenario

We present 1D numerical simulations aimed at studying the hot-flasher scenario for the formation of He-rich subdwarf stars. Sequences were calculated for a wide range of metallicities and physical assumptions, such as the stellar mass at the moment of the helium core flash. This allows us to study the two previously proposed flavors of the hot-flasher scenario ("deep" and "shallow" mixing cases) and to identify a third transition type. Our sequences are calculated by solving simultaneously the mixing and burning equations within a diffusive convection picture, and in the context of standard mixing length theory. We are able to follow chemical evolution during deep-mixing events in which hydrogen is burned violently, and therefore able to present a homogeneous set of abundances for different metallicities and varieties of hot-flashers. We extend the scope of our work by analyzing the effects of non-standard assumptions, such as the effect of chemical gradients, extra-mixing at convective boundaries, possible reduction in convective velocities, or the interplay between difussion and mass loss. Particular emphasis is placed on the predicted surface properties of the models. We find that the hot-flasher scenario is a viable explanation for the formation and surface properties of He-sdO stars. Our results also show that, during the early He-core burning stage, element diffusion may produce the transformation of (post hot-flasher) He-rich atmospheres into He-deficient ones. If this is so, then we find that He-sdO stars should be the progenitors of some of the hottest sdB stars.Comment: 13 pages, including 8 figures and 6 tables. Accepted for publication in A&A. Replaced to match the final version, including a note added in proof regarding PG 1544+48