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The Physics of Crystallization from Globular Cluster White Dwarf Stars in NGC 6397
Abstract
We explore the physics of crystallization in the deep interiors of white dwarf (WD) stars using the color-magnitude diagram and luminosity function constructed from proper-motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397. We demonstrate that the data are consistent with the theory of crystallization of the ions in the interior of WD stars and provide the first empirical evidence that the phase transition is first order: latent heat is released in the process of crystallization as predicted by van Horn. We outline how these data can be used to observationally constrain the value of Γ ≡ E
Coulomb/E
thermal near the onset of crystallization, the central carbon/oxygen abundance, and the importance of phase separation.
... Are there other stellar candidates, apart from SNe events, by which carbonado may form? White dwarfs (WD) are an attractive possibility because they are the end-products in the stellar evolution of~97% of all stars (Hansen and Liebert, 2003;Winget et al., 2009). With atmospheres dominated by hydrogen, and cores by carbon (Hansen and Liebert, 2003), we have the two most important constituents of carbonado in a single stellar object. ...
... Kanaan et al., 2005), or more accurately oxygen-contaminated diamonds referred to as ion-Coulomb crystals (Metcalfe et al., 2004). The oxygen contents of WDs, however, are judged to be "very small or zero" (Winget et al., 2009), so that the use of the mineral term diamond is perfectly appropriate. In white dwarf BPM 37093, the solid core is estimated to be~90% of the stellar mass (Metcalfe et al., 2004), and given that the star is~4000 km in diameter, a substantial diamond content would be available on disruption (Fig. 17a). ...
... In white dwarf BPM 37093, the solid core is estimated to be~90% of the stellar mass (Metcalfe et al., 2004), and given that the star is~4000 km in diameter, a substantial diamond content would be available on disruption (Fig. 17a). Although low in oxygen and because WDs crystallize from the center outwards, latent heat of crystallization and gravitational energy are released (Winget et al., 2009), as the heavier and sinking oxygen differentiates from the carbon-bearing component. Separation would lead to decreases in f O2 in the C-unit and to an environment conducive to the nucleation and growth of carbonado and to the incorporation of small concentrations of exotic metals, metal alloys, carbides and nitrides sequestered from the surroundings. ...
... Just like any phase transition from a liquid to a solid, core crystallization leads to the release of latent heat. This additional energy source causes a delay in the WD cooling time, as evidenced by pile-ups in the WD luminosity function and in the CMD (Winget et al. 2009;Tremblay et al. 2019). For WDs ≳ 1 M ⊙ , the crystallization temperature coincides with the temperature range of the ZZ Ceti instability strip which allows us to probe their crystalline interiors with asteroseismology (Metcalfe et al. 2004). ...
White dwarfs (WDs) polluted by exoplanetary material provide the unprecedented opportunity to directly observe the interiors of exoplanets. However, spectroscopic surveys are often limited by brightness constraints, and WDs tend to be very faint, making detections of large populations of polluted WDs difficult. In this paper, we aim to increase considerably the number of WDs with multiple metals in their atmospheres. Using 96,134 WDs with Gaia DR3 BP/RP (XP) spectra, we constructed a 2D map using an unsupervised machine learning technique called Uniform Manifold Approximation and Projection (UMAP) to organize the WDs into identifiable spectral regions. The polluted WDs are among the distinct spectral groups identified in our map. We have shown that this selection method could potentially increase the number of known WDs with 5 or more metal species in their atmospheres by an order of magnitude. Such systems are essential for characterizing exoplanet diversity and geology.
... One important physical process that can modify WD cooling timescales is the first-order phase transition of the carbonoxygen (C/O) mixtures in WD cores from liquid to solid when they cool to the point of crystallization (van Horn 1968;Winget et al. 2009). The latent heat associated with this phase transition can temporarily slow WD cooling, and phase separation into O-enriched solid material and C-enriched liquid mantle material can induce mixing that also impacts WD interior thermodynamics and further delays WD cooling (Stevenson 1977;Mochkovitch 1983;Segretain & Chabrier 1993;Horowitz et al. 2010;Blouin et al. 2020a). ...
We enhance the treatment of crystallization for models of white dwarfs (WDs) in the stellar evolution software Modules for Experiments in Stellar Astrophysics (MESA) by implementing carbon–oxygen (C/O) phase separation. The phase separation process during crystallization leads to transport of oxygen toward the centers of WDs, resulting in a more compact structure that liberates gravitational energy as additional heating that modestly slows WD cooling timescales. We quantify this cooling delay in MESA C/O WD models over the mass range 0.5–1.0 M ⊙ , finding delays of 0.5–0.8 Gyr for typical C/O interior profiles. MESA WD cooling timescales including this effect are generally comparable to other WD evolution models that make similar assumptions about input physics. When considering phase separation alongside ²² Ne sedimentation, however, we find that both MESA and BaSTI WD cooling models predict a more modest sedimentation delay than the latest LPCODE models, and this may therefore require a reevaluation of previously proposed solutions to some WD cooling anomalies that were based on LPCODE models of ²² Ne sedimentation. Our implementation of C/O phase separation in the open-source stellar evolution software MESA provides an important tool for building realistic grids of WD cooling models, as well as a framework for expanding on our implementation to explore additional physical processes related to phase transitions and associated fluid motions in WD interiors.
... One important physical process that can modify WD cooling timescales is the first-order phase transition of the carbonoxygen (C/O) mixtures in WD cores from liquid to solid Corresponding author: Evan B. Bauer evan.bauer@cfa.harvard.edu when they cool to the point of crystallization (van Horn 1968;Winget et al. 2009). The latent heat associated with this phase transition can temporarily slow WD cooling, and phase separation into O-enriched solid material and C-enriched liquid mantle material can induce mixing that also impacts WD interior thermodynamics and further delays WD cooling (Stevenson 1977;Mochkovitch 1983;Segretain & Chabrier 1993;Horowitz et al. 2010;Blouin et al. 2020a). ...
We enhance the treatment of crystallization for models of white dwarfs (WDs) in the stellar evolution software MESA by implementing carbon-oxygen (C/O) phase separation. The phase separation process during crystallization leads to transport of oxygen toward the center of WDs, resulting in a more compact structure that liberates gravitational energy as additional heating that modestly slows WD cooling timescales. We quantify this cooling delay in MESA C/O WD models over the mass range 0.5-1.0 $M_\odot$, finding delays of 0.5-0.8 Gyr for typical C/O interior profiles. MESA WD cooling timescales including this effect are generally comparable to other WD evolution models that make similar assumptions about input physics. When considering phase separation alongside $^{22}$Ne sedimentation, however, we find that some other sets of WD evolution models may overestimate the cooling delay associated with sedimentation, and this may therefore require a re-evaluation of previously proposed solutions to some WD cooling anomalies. Our implementation of C/O phase separation in the open-source stellar evolution software MESA provides an important tool for building realistic grids of WD cooling models, as well as a framework for expanding on our implementation to explore additional physical processes related to phase transitions and associated fluid motions in WD interiors.
... during WD cooling, suggesting that it may slow down the cooling process by the release of latent heat. Indirect evidence for the slowdown due to crystallization was observed for WDs in globular clusters (Winget et al. 2009;García-Berro et al. 2010;Campos et al. 2016). However, it is only recently that strong observational evidence for the existence of an isolated crystallization sequence of WDs in the Hertzsprung-Russell diagram has been obtained by the Gaia space telescope (Tremblay et al. 2019). ...
Long predicted more than fifty years ago, strong evidence for the existence of crystalline cores inside white dwarfs has recently been obtained by the Gaia space telescope. It is thus important to investigate how a crystalline core may affect the properties and dynamics of white dwarfs. In this paper, we first study the dependence of the frequencies of the fundamental (f), interfacial (i), and shear (s) oscillation modes on the size of the crystalline core. We find that the frequencies of the i- and s-modes depend sensitively on the size of the core, while the frequency of the f-mode is affected only slightly by at most a few percent for our chosen white dwarf models. We next consider the tidal deformability of crystallized white dwarfs and find that the effect of crystallization becomes significant only when the radius of the core is larger than about 70% of the stellar radius. The tidal deformability can change by a few to about 10 percent when a white dwarf becomes fully crystallized. We also show that there exist approximate equation-of-state insensitive relations connecting the mass, moment of inertia, tidal deformability, and f-mode frequency for pure fluid white dwarfs. Depending on the stellar mass and composition, however, these relations can be affected by a few percent when the white dwarf is crystallized. These changes could leave an imprint on the gravitational waves emitted from the late inspiral or merger of white dwarf binaries, which may be detectable by future space-borne gravitational wave detectors.
... This temperature is dependent on the internal composition of the star. Through observations of the globular cluster NGC 6397, Winget et al. ( 2009 ) report that the crystallization of the WD core is similar to that of a pure carbon core. According to the phase diagram produced in Horowitz et al. ( 2010 ) and their limits for the maximum crystallization temperature, this would require a limit to the oxygen mass fraction of X O ≤ 0.64. ...
One of the largest uncertainties in stellar evolutionary computations is the accuracy of the considered reaction rates. The 12C(α, γ)16O reaction is particularly important for the study of low- and intermediate-mass stars as it determines the final C/O ratio in the core which influences the white dwarf cooling evolution. Thus, there is a need for a study of how the computations of white dwarfs and their progenitors that are made to date may be affected by the uncertainties of the 12C(α, γ)16O reaction rates. In this work we compute fully evolutionary sequences using the mesa code with initial masses in the range of 0.90 ≤ Mi/M⊙ ≤ 3.05. We consider different adopted reaction rates, obtained from the literature, as well as the extreme limits within their uncertainties. As expected, we find that previous to the core helium burning stage, there are no changes to the evolution of the stars. However, the subsequent stages are all affected by the uncertainties of the considered reaction rate. In particular, we find differences to the convective core mass during the core helium burning stage which may affect pulsation properties of subdwarfs, the number of thermal pulses during the asymptotic giant branch and trends between final oxygen abundance in the core and the progenitor masses of the remnant white dwarfs.
... This temperature is dependent on the internal composition of the star. Through observations of the globular cluster NGC 6397, Winget et al. (2009) report that the crystallisation of the WD core is similar to that of a pure carbon core. According to the phase diagram produced in Horowitz et al. (2010) and their limits for the maximum crystallisation temperature, this would require a limit to the oxygen mass fraction of O ≤ 0.64. ...
One of the largest uncertainties in stellar evolutionary computations is the accuracy of the considered reaction rates. The 12C(alpha,gamma)16O reaction is particularly important for the study of low- and intermediate-mass stars as it determines the final C/O ratio in the core which influences the white dwarf cooling evolution. Thus, there is a need for a study of how the computations of white dwarfs and their progenitors that are made to date may be affected by the uncertainties of the 12C(alpha,gamma)16O reaction rates. In this work we compute fully evolutionary sequences using the MESA code with initial masses in the range of 0.90 <= Mi/Msun <= 3.05. We consider different adopted reaction rates, obtained from the literature, as well as the extreme limits within their uncertainties. As expected, we find that previous to the core helium burning stage there are no changes to the evolution of the stars. However, the subsequent stages are all affected by the uncertainties of the considered reaction rate. In particular, we find differences to the convective core mass during the core helium burning stage which may affect pulsation properties of subdwarfs, the number of thermal pulses during the asymptotic giant branch and trends between final oxygen abundance in the core and the progenitor masses of the remnant white dwarfs.
... In recent years, observers have resolved core crystallization in white dwarfs (WDs) at the population level, as the latent heat of crystallization delays cooling (Van Horn 1968;Winget et al. 2009;Gaia Collaboration et al. 2018;Tremblay et al. 2019). Data Release 2 from the Gaia mission has likewise identified a population of massive WDs with an anomalous heat source (the 'Q branch') which is now thought to be caused by the settling of neutron-rich nuclides toward the core (Cheng et al. 2019;Bauer et al. 2020;Camisassa et al. 2021;Blouin et al. 2021). ...
Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate at weak coupling ($\Gamma \ll 1$), but they have errors as large as a factor of two in the strongly coupled liquid regime ($1 \lesssim \Gamma \lesssim 200$). With modern molecular dynamics codes it is possible to accurately determine diffusion coefficients in select systems with percent-level precision. In this work, we develop a theoretically motivated law for diffusion coefficients which works across the wide range of parameters typical for white dwarf interiors. We perform molecular dynamics simulations of pure systems and two mixtures that respectively model a typical-mass C/O white dwarf and a higher-mass O/Ne white dwarf, and resolve diffusion coefficients for several trace neutron-rich nuclides. We fit the model to the pure systems and propose a physically motivated generalization for mixtures. We show that this model is accurate to roughly 15% when compared to molecular dynamics for many individual elements under conditions typical of white dwarfs, and is straightforward to implement in stellar evolution codes.
... In the last 25 years, thanks to steady advances in both observations and theory, models of CO-core WDs have been used extensively in conjuction with photometric, spectroscopic and asteroseismic data, to determine the ages of field WDs (e.g., Winget et al. 1987;Oswalt et al. 1996;Torres & García-Berro 2016;Kilic et al. 2017;Tononi et al. 2019) for constraining the star formation history of the Milky Way, the ages of WDs in open clusters (e.g., Richer et al. 1998;von Hippel 2005;Bedin et al. 2008;Bellini et al. 2010;García-Berro et al. 2010;Bedin et al. 2010Bedin et al. , 2015 and glob-⋆ E-mail: M.Salaris@ljmu.ac.uk ular clusters (e.g., Hansen et al. 2004Hansen et al. , 2007Winget et al. 2009;Bedin et al. 2009;Goldsbury et al. 2012;Bedin et al. 2019), and even as probes to investigate open questions in theoretical physics (e.g., Freese 1984;Isern et al. 1992;Garcia-Berro et al. 1995;Córsico et al. 2001;Benvenuto et al. 2004;Bertone & Fairbairn 2008;García-Berro et al. 2011;Isern et al. 2018;Winget et al. 2004). ...
We present new cooling models for carbon-oxygen white dwarfs with both H- and He-atmospheres, covering the whole relevant mass range, to extend our updated BaSTI (a Bag of Stellar Tracks and Isochrones) stellar evolution archive. They have been computed using core chemical stratifications obtained from new progenitor calculations, adopting a semiempirical initial-final mass relation. The physics inputs have been updated compared to our previous BaSTI calculations: ^{22}Ne diffusion in the core is now included, together with an updated CO phase diagram, and updated electron conduction opacities. We have calculated models with various different neon abundances in the core, suitable to study white dwarfs in populations with metallicities ranging from super-solar to metal poor, and have performed various tests/comparisons of the chemical stratification and cooling times of our models. Two complete sets of calculations are provided, for two different choices of the electron conduction opacities, to reflect the current uncertainty in the evaluation of the electron thermal conductivity in the transition regime between moderate and strong degeneracy, crucial for the H and He envelopes. We have also made a first, preliminary estimate of the effect -- that turns out to be generally small -- of Fe sedimentation on the cooling times of white dwarf models, following recent calculations of the phase diagrams of carbon-oxygen-iron mixtures. We make publicly available the evolutionary tracks from both sets of calculations, including cooling times and magnitudes in the Johnson-Cousins, Sloan, Pan-STARSS, Galex, Gaia-DR2, Gaia-eDR3, HST-ACS, HST-WFC3, and JWST photometric systems.
... It has long been understood that as these white dwarf stars cool the degenerate matter within can undergo interior crystallization (Abrikosov, 1960 andSalpeter, 1961). The crystallization phase also influences cooling timescales as well as the overall vibrational behavior of the star (Montgomery and Winget, 1999;Winget et al., 2009;and Tremblay et al., 2019). Asteroseismic methods, associating periodicity in light output and vibrational behavior to stellar composition, in combination with cooling timescales, have been utilized to characterize the internal composition of white dwarf stars and indicate that some pulsating white dwarf stars may be stratified with substantial crystallization (Hansen and Van Horn, 1979;Metcalfe et al., 2004;Giammichele et al., 2016;and 2018). ...
In this work, we present the cubic crystal elastic constants of a fully crystallized white dwarf stellar core. Elastic constants were calculated utilizing modal analysis of three-dimensional single-layer and stratified multi-layer crystalline core models. The models were generated using a Fortran based forward calculation algorithm in combination with a finite element modeling software program and were based on the parameters associated with the pulsating crystallized white dwarf BPM 37093. The calculated cubic crystal elastic constants, in comparison with elastic parameters of theoretical Coulomb crystal models of white dwarf matter, differed by, at most, a few orders of magnitude. In addition, the crystallized stellar core elastic parameters produced associated vibrational modes and frequencies that are consistent with the periodicity observed in BPM 37093.
... The Gaia DR2 has allowed modelers to resolve a number of phenomena in white dwarf (WD) astrophysics with unprecedented precision. The latent heat release from core crystallization, first theorized by Van Horn (1968), has now been confirmed (Winget et al. 2009;Tremblay et al. 2019). Furthermore, the sedimentary heating of neutron rich nuclei, especially 22 Ne (Isern et al. 1991;Bildsten & Hall 2001), has also been resolved and may explain the anomalous heat source in the so-called 'Q branch' WDs . ...
Observations of galactic white dwarfs with Gaia have allowed for unprecedented modeling of white dwarf cooling, resolving core crystallization and sedimentary heating from neutron rich nuclei. These cooling sequences are sensitive to the diffusion coefficients of nuclei in Coulomb plasmas which have order 10\% uncertainty and are often not valid across coupling regimes. Using large scale molecular dynamics simulations we calculate diffusion coefficients at high resolution in the regime relevant for white dwarf modeling. We present a physically motivated law for diffusion with a semi-empirical correction which is accurate at the percent level. Implemented along with linear mixing in stellar evolution codes, this law should reduce the error from diffusion coefficients by an order of magnitude.
... The Gaia DR2 has allowed modellers to resolve a number of phenomena in white dwarf (WD) astrophysics with unprecedented precision (Gaia Collaboration 2018). The latent heat release from core crystallization, first theorized by Van Horn (1968), has now been confirmed (Winget et al. 2009;Tremblay et al. 2019). Furthermore, the sedimentary heating of neutron-rich nuclei, especially 22 Ne (Isern et al. 1991;Bildsten & Hall 2001), has also been resolved and may explain the anomalous heat source in the so-called 'Q branch' WDs (Cheng, Cummings & Ménard 2019). ...
Observations of galactic white dwarfs with Gaia have allowed for unprecedented modeling of white dwarf cooling, resolving core crystallization and sedimentary heating from neutron rich nuclei. These cooling sequences are sensitive to the diffusion coefficients of nuclei in Coulomb plasmas which have order 10 per cent uncertainty and are often not valid across coupling regimes. Using large scale molecular dynamics simulations we calculate diffusion coefficients at high resolution in the regime relevant for white dwarf modeling. We present a physically motivated law for diffusion with a semi-empirical correction which is accurate at the percent level. Implemented along with linear mixing in stellar evolution codes, this law should reduce the error from diffusion coefficients by an order of magnitude.
... Recently, Cheng et al. (2019) found that the population of massive WD known as the "Q branch" appear to have an additional heat source that maintains a luminosity of order 10 −3 L e for gigayears. Latent heat from crystallization (Tremblay et al. 2019;Winget et al. 2009;Horowitz et al. 2010) and gravitational energy released from conventional 22 Ne sedimentation (Bildsten & Hall 2001;Deloye & Bildsten 2002;García-Berro et al. 2008;Hughto et al. 2010) do not appear to be large enough to explain this luminosity (Camisassa et al. 2020;Cheng et al. 2019). Heating from conventional electron capture and pycnonuclear (or density-driven) fusion (Salpeter & van Horn 1969;Yakovlev et al. 2006;Horowitz et al. 2008) reactions appear to need even higher densities and may depend too strongly on the density and or temperature (Horowitz 2020). ...
Recent observations of Galactic white dwarfs (WDs) with Gaia suggest there is a population of massive crystallizing WDs exhibiting anomalous cooling—the Q branch. While single-particle ²² Ne sedimentation has long been considered a possible heat source, recent work suggests that ²² Ne must separate into clusters, enhancing diffusion, in order for sedimentation to provide heating on the observed timescale. We show definitively that ²² Ne cannot separate to form clusters in C/O WDs using molecular dynamics simulations, and we further present a general C/O/Ne phase diagram showing that strong ²² Ne enrichment is not achievable for ²² Ne abundance ≲30%. We conclude that the anomalous heating cannot be due to ²² Ne cluster sedimentation and that Q branch WDs may have an unusual composition, possibly rich with heavier elements.
... Recently, Cheng et al. (2019) found that the population of massive WD known as the 'Q branch' appear to have an additional heat source that maintains a luminosity of order 10 −3 L for Gyrs. Latent heat from crystallization (Tremblay et al. 2019;Winget et al. 2009;Horowitz et al. 2010) and gravitational energy released from conventional 22 Ne sedimentation (Bildsten & Hall 2001a;Deloye & Bildsten 2002;García-Berro et al. 2008;Hughto et al. 2010b) do not appear to be large enough to explain this luminosity (Camisassa et al. 2020;Cheng mecapl1@ilstu.edu horowit@indiana.edu ...
Recent observations of Galactic white dwarfs (WDs) with Gaia suggest there is a population of massive crystallizing WDs exhibiting anomalous cooling -- the Q branch. While single-particle $^{22}$Ne sedimentation has long been considered a possible heat source, recent work suggests that $^{22}$Ne must separate into clusters, enhancing diffusion, in order for sedimentation to provide heating on the observed timescale. We show definitively that $^{22}$Ne cannot separate to form clusters in C/O WDs using molecular dynamics simulations, and we further present a general C/O/Ne phase diagram showing that strong $^{22}$Ne enrichment is not achievable for $^{22}$Ne abundance $\lesssim 30\%$. We conclude that the anomalous heating cannot be due to $^{22}$Ne cluster sedimentation and that Q branch WDs may have an unusual composition, possibly rich with heavier elements.
... Finally, another very important aspect of white dwarfs is that, due to the high density prevailing in their interiors, they are extremely useful as cosmic laboratories to study dense plasma physics and solid state physics (crystallization; Winget et al., 2009;Tremblay et al., 2019), and "exotic physics" (axions, neutrino magnetic dipole moment, variation of fundamental constants, etc; Isern et al., 1992Isern et al., , 2008Isern et al., , 2018Córsico et al., 2001Córsico et al., , 2012bCórsico et al., , 2013Miller Bertolami, 2014;Miller Bertolami et al., 2014). ...
In the course of their evolution, white-dwarf stars go through at least one phase of variability in which the global pulsations they undergo allow astronomers to peer into their interiors, making it possible to shed light on their deep inner structure and evolutionary stage by means of asteroseismology. The study of pulsating white dwarfs has undergone substantial progress in the last decade, and this is largely thanks to the arrival of continuous observations of unprecedented quality from space, like those of the CoRoT, Kepler, and TESS missions. This, along with the advent of new detailed theoretical models and the development of improved asteroseismological techniques, has helped to unravel the internal chemical structure of many pulsating white dwarfs, and, at the same time, has posed new questions that challenge theoreticians. In particular, uninterrupted monitoring of white-dwarf stars for months has allowed discovering phenomena impossible to detect with ground-based observations, despite previous admirable efforts like the Whole Earth Telescope (WET). Here, we start by reviewing the essential properties of white-dwarf and pre-white dwarf stars and their pulsations, and then, we go through the different families of pulsating objects known to date. Finally, we review the most outstanding findings about pulsating white dwarfs and pre-white dwarfs made possible with the unprecedented-quality observations of the Kepler space telescope, although we envisage that future analyses of space data from this mission that still await examination, may reveal new secrets of these extremely interesting variable stars.
... Finally, another very important aspect of white dwarfs is that, due to the high density prevailing in their interiors, they are extremely useful as cosmic laboratories to study dense plasma physics and solid state physics (crystallization; Winget et al., 2009;Tremblay et al., 2019), and "exotic physics" (axions, neutrino magnetic dipole moment, variation of fundamental constants, etc; Isern et al., 1992Isern et al., , 2008Isern et al., , 2018Córsico et al., 2001Córsico et al., , 2012bCórsico et al., , 2013Miller Bertolami, 2014;Miller Bertolami et al., 2014). ...
In the course of their evolution, white-dwarf stars go through at least one phase of variability in which the global pulsations they undergo allow astronomers to peer into their interiors, this way making possible to shed light on their deep inner structure and evolutionary stage by means of asteroseismology. The study of pulsating white dwarfs has witnessed substantial progress in the last decade, and this has been so largely thanks to the arrival of continuous observations of unprecedented quality from space, like those of the CoRoT, Kepler, and TESS missions. This, along with the advent of new detailed thoretical models and the development of improved asteroseismological techniques, has helped to unravel the internal chemical structure of many pulsating white dwarfs, and, at the same time, has opened new questions that challenge theoreticians. In particular, uninterrupted monitoring of white-dwarf stars for months has allowed discovering phenomena impossible to detect with ground-based observations, despite admirable previous efforts like the Whole Earth Telescope (WET). Here, we start by reviewing the essential properties of white-dwarf and pre-white dwarf stars and their pulsations, and then, we go through the different families of pulsating objects known to date. Finally, we review the most outstanding findings about pulsating white dwarfs and pre-white dwarfs made possible with the unprecedented-quality observations of the Kepler space telescope, although we envisage that future analyzes of space data from this mission that still await to be examined may reveal new secrets of these extremely interesting variable stars.
... Also, WDs are found in binary systems, thus offering a test bed to explore complex stellar interactions amongst stars, including WDs exploding as type Ia supernovae (Maoz et al. 2014). In addition, WDs can be used as cosmic laboratories of extreme physics, ranging from atomic and molecular physics in strong magnetic fields, and high-density plasmas and even solid-state physics (through crystallization; Winget et al. 2009;Tremblay et al. 2019), to exotic physics, like constraining the axion mass and the possible variation of the gravitational constant (Isern et al. 1992;Córsico et al. 2012bCórsico et al. , 2013, and also variations of the fine-structure constant (Hu et al. 2019). Last but not least, fundamental properties of WDs, either individually or collectively, like the mass distribution, core chemical composition, and cooling times are key to place constraints on the stellar evolution theory, including third dredge up and mass loss on the Asymptotic Giant Branch (AGB), the efficiency of extra-mixing during core helium burning, and nuclear reaction rates (Kunz et al. 2002;Salaris et al. 2009;Fields et al. 2016). ...
Stars are extremely important astronomical objects that constitute the pillars on which the Universe is built, and as such, their study has gained increasing interest over the years. White dwarf stars are not the exception. Indeed, these stars constitute the final evolutionary stage for more than 95% 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. Several important studies have emphasized the advantage of using white dwarfs as reliable clocks to date a variety of stellar populations in the solar neighborhood and in the nearest stellar clusters, including the thin and thick disks, the Galactic spheroid and the system of globular and open clusters. In addition, white dwarfs are tracers of the evolution of planetary systems along several phases of stellar evolution. Not less relevant than these applications, the study of matter at high densities has benefited from our detailed knowledge about evolutionary and observational properties of white dwarfs. In this sense, white dwarfs are used as laboratories for astro-particle physics, being their interest focused on physics beyond the standard model, that is, neutrino physics, axion physics and also radiation from “extra dimensions”, and even crystallization. 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.
... Also, WDs are found in binary systems, thus offering a test bed to explore complex stellar interactions amongst stars, including WDs exploding as type Ia supernovae (Maoz et al., 2014). In addition, WDs can be used as cosmic laboratories of extreme physics, ranging from atomic and molecular physics in strong magnetic fields, and high-density plasmas and even solid-state physics (through crystallization; Winget et al., 2009;Tremblay et al., 2019), to exotic physics, like constraining the axion mass and the possible variation of the gravitational constant (Isern et al., 1992;Córsico et al., 2012bCórsico et al., , 2013, and also variations of the fine-structure constant (Hu et al., 2019). Last but not least, fundamental properties of WDs, either individually or collectively, like the mass distribution, core chemical composition, and cooling times are key to place constraints on the stellar evolution theory, including third dredge up and mass loss on the Asymptotic Giant Branch (AGB), the efficiency of extra-mixing during core helium burning, and nuclear reaction rates (Kunz et al., 2002;Salaris et al., 2009;Fields et al., 2016). ...
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.
... interiors, thus representing an independent avenue to confirm the results derived from studies of the WD luminosity function of stellar clusters (Winget et al., 2009;García-Berro et al., 2010) about the occurrence of crystallization in WDs. ...
Ultra-massive hydrogen-rich white dwarfs stars are expected to harbour oxygen/neon cores result- ing from semidegenerate carbon burning when the progenitor star evolves through the super asymp- totic giant branch (S-AGB) phase. These stars are expected to be crystallized by the time they reach the ZZ Ceti domain. We show that crystallization leads to a phase separation of oxygen and neon in the core of ultra-massive white dwarfs, which im- pacts markedly the pulsational properties, thus of- fering a unique opportunity to infer and test the process of crystallization and phase separation in white dwarf stars.
... Theoretical and observational works have suggested that crystallization in C/O mixtures may occur at higher Γ than the classical one-component plasma value of 175 G = (Horowitz et al. 2007;Winget et al. 2009;Medin & Cumming 2010;Althaus et al. 2012). Our updated crystallization controls allow for the effect on stellar evolution of the crystallization at 240 G » to be investigated. ...
We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective core mass during both hydrogen and helium burning phases. Stars with $M<8\,{\rm M_\odot}$ become white dwarfs and cool to the point where the electrons are degenerate and the ions are strongly coupled, a realm now available to study with MESA due to improved treatments of element diffusion, latent heat release, and blending of equations of state. Studies of the final fates of massive stars are extended in MESA by our addition of an approximate Riemann solver that captures shocks and conserves energy to high accuracy during dynamic epochs. We also introduce a 1D capability for modeling the effects of Rayleigh-Taylor instabilities that, in combination with the coupling to a public version of the STELLA radiation transfer instrument, creates new avenues for exploring Type II supernovae properties. These capabilities are exhibited with exploratory models of pair-instability supernova, pulsational pair-instability supernova, and the formation of stellar mass black holes. The applicability of MESA is now widened by the capability of importing multi-dimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, and four new software tools -- MESAWeb, MESA-Docker, pyMESA, and mesastar.org -- to enhance MESA's education and research impact.
Recent Monte Carlo plasma simulations carried out to study the phase separation of $^ Ne $ in crystallizing carbon-oxygen (CO) white dwarfs (WDs; the most abundant metal after carbon and oxygen) have shown that, under the right conditions, a distillation process that transports $^ Ne $ towards the WD centre is efficient and releases a considerable amount of gravitational energy. This can lead to cooling delays of up to several Gyr. Here we present the first CO WD stellar evolution models that self-consistently include the effect of neon distillation and cover the full range of CO WD masses for a twice-solar progenitor metallicity, which is appropriate for the old open cluster NGC 6791. The old age (about 8.5 Gyr) and high metallicity of this cluster -- and hence the high neon content (about 3 by mass) in the cores of its WDs -- maximize the effect of neon distillation in the models. We discuss the effect of distillation on the internal chemical stratification and cooling time of the models, confirming that distillation causes cooling delays of up to several Gyr that depend in a non-monotonic way on the mass. We also show how our models produce luminosity functions (LFs) that can match the faint end of the observed WD LF in NGC 6791, for ages consistent with the range determined from a sample of cluster eclipsing binary stars and the main sequence turn-off. Without the inclusion of distillation, the theoretical WD cooling sequences reach magnitudes that are too faint compared to observations. We also propose James Webb Space Telescope observations that would independently demonstrate the efficiency of neon distillation in the interiors of NGC 6791 WDs and help resolve the current uncertainty on the treatment of the electron conduction opacities for the hydrogen-helium envelope of WD models.
Long predicted more than fifty years ago, strong evidence for the existence of crystalline cores inside white dwarfs has recently been obtained by the Gaia space telescope. It is thus important to investigate how a crystalline core may affect the properties and dynamics of white dwarfs. In this paper, we first study the dependence of the frequencies of the fundamental (f), interfacial (i), and shear (s) oscillation modes on the size of the crystalline core. We find that the frequencies of the i- and s-modes depend sensitively on the size of the core, while the frequency of the f-mode is affected only slightly by at most a few percent for our chosen white dwarf models. We next consider the tidal deformability of crystallized white dwarfs and find that the effect of crystallization becomes significant only when the radius of the core is larger than about 70% of the stellar radius. The tidal deformability can change by a few to about 10 per cent when a white dwarf becomes fully crystallized. We also show that there exist approximate equation-of-state insensitive relations connecting the mass, moment of inertia, tidal deformability, and f-mode frequency for pure fluid white dwarfs. Depending on the stellar mass and composition, however, these relations can be affected by a few percent when the white dwarf is crystallized. These changes could leave an imprint on the gravitational waves emitted from the late inspiral or merger of white dwarf binaries, which may be detectable by future space-borne gravitational wave detectors.
White dwarfs are a class of stars with unique physical properties. They present many challenging problems whose solution requires advanced theories of dense matter, state-of-the-art experimental techniques, and extensive computing efforts. New ground- and space-based observatories will soon provide an increasingly detailed view of white dwarf stars and reveal new phenomena that will challenge our models. This review is an introduction to the nature of white dwarfs, the physical processes that determine their structure and evolution, and the physical conditions they span. We discuss a wide variety of currently unsolved or partially resolved problems in their constitutive physics that are broadly related to equations of state, transport processes and opacities.
Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate at weak coupling (Γ ≪ 1), but they have errors as large as a factor of two in the strongly coupled liquid regime (1 ≲ Γ ≲ 200). With modern molecular dynamics codes it is possible to accurately determine diffusion coefficients in select systems with percent-level precision. In this work, we develop a theoretically motivated law for diffusion coefficients which works across the wide range of parameters typical for white dwarf interiors. We perform molecular dynamics simulations of pure systems and two mixtures that respectively model a typical-mass C/O white dwarf and a higher-mass O/Ne white dwarf, and resolve diffusion coefficients for several trace neutron-rich nuclides. We fit the model to the pure systems and propose a physically motivated generalization for mixtures. We show that this model is accurate to roughly 15% when compared to molecular dynamics for many individual elements under conditions typical of white dwarfs, and is straightforward to implement in stellar evolution codes.
Context. Recent computations of the interior composition of ultra-massive white dwarfs (WDs) have suggested that some WDs could be composed of neon (Ne)-dominated cores. This result is at variance with our previous understanding of the chemical structure of massive WDs, where oxygen is the predominant element. In addition, it is not clear whether some hybrid carbon (C) oxygen (O)-Ne WDs might form when convective boundary mixing is accounted for during the propagation of the C-flame in the C-burning stage. Both the Ne-dominated and hybrid CO-Ne core would have measurable consequences for asteroseismological studies based on evolutionary models.
Aims. In this work, we explore in detail to which extent differences in the adopted micro- and macro-physics can explain the different final WD compositions that have been found by different authors. Additionally, we explore the impact of such differences on the cooling times, crystallization, and pulsational properties of pulsating WDs.
Methods. We performed numerical simulations of the evolution of intermediate massive stars from the zero age main sequence to the WD stage varying the adopted physics in the modeling. In particular, we explored the impact of the intensity of convective boundary mixing during the C-flash, extreme mass-loss rates, and the size of the adopted nuclear networks on the final composition, age, as well crystallization and pulsational properties of WDs.
Results. In agreement with previous authors, we find that the inclusion of convective boundary mixing quenches the carbon flame leading to the formation of hybrid CO-Ne cores. Based on the insight coming from 3D hydro-dynamical simulations, we expect that the very slow propagation of the carbon flame will be altered by turbulent entrainment affecting the inward propagation of the flame. Also, we find that Ne-dominated chemical profiles of massive WDs recently reported appear in their modeling due to a key nuclear reaction being overlooked. We find that the inaccuracies in the chemical composition of the ultra-massive WDs recently reported lead to differences of 10% in the cooling times and degree of crystallization and about 8% in the period spacing of the models once they reach the ZZ Ceti instability strip.
We present new cooling models for carbon–oxygen white dwarfs (WDs) with both H- and He-atmospheres, covering the whole relevant mass range, to extend our updated basti (a Bag of Stellar Tracks and Isochrones) stellar evolution archive. They have been computed using core chemical stratifications obtained from new progenitor calculations, adopting a semi-empirical initial–final mass relation. The physics inputs have been updated compared to our previous basti calculations: 22Ne diffusion in the core is now included, together with an updated CO phase diagram, and updated electron conduction opacities. We have calculated models with various different neon abundances in the core, suitable to study WDs in populations with metallicities ranging from supersolar to metal poor, and have performed various tests/comparisons of the chemical stratification and cooling times of our models. Two complete sets of calculations are provided, for two different choices of the electron conduction opacities, to reflect the current uncertainty in the evaluation of the electron thermal conductivity in the transition regime between moderate and strong degeneracy, crucial for the H- and He-envelopes. We have also made a first, preliminary estimate of the effect – that turns out to be generally small – of Fe sedimentation on the cooling times of WD models, following recent calculations of the phase diagrams of carbon–oxygen-iron mixtures. We make publicly available the evolutionary tracks from both sets of calculations, including cooling times and magnitudes in the Johnson-Cousins, Sloan, Pan-STARSS, GALEX, Gaia-DR2, Gaia-eDR3, HST-ACS, HST-WFC3, and JWST photometric systems.
White Dwarf (WD) stars are the most common stellar remnant in the universe. WDs usually have a hydrogen or helium atmosphere, and helium WD (called DB) spectra can be used to solve outstanding problems in stellar and galactic evolution. DB origins, which are still a mystery, must be known to solve these problems. DB masses are crucial for discriminating between different proposed DB evolutionary hypotheses. Current DB mass determination methods deliver conflicting results. The spectroscopic mass determination method relies on line broadening models that have not been validated at DB atmosphere conditions. We performed helium benchmark experiments using the White Dwarf Photosphere Experiment (WDPE) platform at Sandia National Laboratories' Z-machine that aims to study He line broadening at DB conditions. Using hydrogen/helium mixture plasmas allows investigating the importance of He Stark and van der Waals broadening simultaneously. Accurate experimental data reduction methods are essential to test these line-broadening theories. In this paper, we present data calibration methods for these benchmark He line shape experiments. We give a detailed account of data processing, spectral power calibrations, and instrument broadening measurements. Uncertainties for each data calibration step are also derived. We demonstrate that our experiments meet all benchmark experiment accuracy requirements: WDPE wavelength uncertainties are <1 Å, spectral powers can be determined to within 15%, densities are accurate at the 20% level, and instrumental broadening can be measured with 20% accuracy. Fulfilling these stringent requirements enables WDPE experimental data to provide physically meaningful conclusions about line broadening at DB conditions.
Recently, Cheng et al. identified a number of massive white dwarfs (WD) that appear to have an additional heat source providing a luminosity near ≈10−3 L⊙ for multiple Gyr [S. Cheng, J. D. Cummings, and B. Ménard, Astrophys. J. 886, 100 (2019)]. In this paper we explore heating from electron capture and pycnonuclear reactions. We also explore heating from dark matter annihilation. WD stars appear to be too small to capture enough dark matter for this to be important. Finally, if dark matter condenses to very high densities inside a WD this could ignite nuclear reactions. We calculate the enhanced central density of a WD in the gravitational potential of a very dense dark matter core. While this might start a supernova, it seems unlikely to provide modest heating for a long time. We conclude that electron capture, pycnonuclear, and dark matter reactions are unlikely to provide significant heating in the massive WD that Cheng considers.
Context. Ultra-massive (≳1 M⊙ ) hydrogen-rich (DA) white dwarfs are expected to have a substantial portion of their cores in a crystalline state at the effective temperatures characterising the ZZ Ceti instability strip ( Teff ∼ 12 500 K) as a result of Coulomb interactions in very dense plasmas. Asteroseismological analyses of these white dwarfs can provide valuable information related to the crystallisation process, the core chemical composition, and the evolutionary origin of these stars.
Aims. We present a thorough asteroseismological analysis of the ultra-massive ZZ Ceti star BPM 37093, which exhibits a rich period spectrum, on the basis of a complete set of fully evolutionary models that represent ultra-massive oxygen/neon (ONe) core DA white dwarf stars harbouring a range of hydrogen (H) envelope thicknesses. We also carry out preliminary asteroseismological inferences on two other ultra-massive ZZ Ceti stars that exhibit fewer periods, GD 518, and SDSS J0840+5222.
Methods. We considered g -mode adiabatic pulsation periods for ultra-massive ONe-core DA white dwarf models with stellar masses in the range 1.10 ≲ M⋆ / M⊙ ≲ 1.29, effective temperatures in the range 10 000 ≲ Teff ≲ 15 000 K, and H-envelope thicknesses in the interval −10 ≲ log( MH / M⋆ )≲ − 6. We explored the effects of employing different H-envelope thicknesses on the mode-trapping properties of our ultra-massive ONe-core DA white dwarf models and performed period-to-period fits to ultra-massive ZZ Ceti stars with the aim of finding an asteroseismological model for each target star.
Results. We find that the trapping cycle and trapping amplitude are larger for thinner H envelopes, and that the asymptotic period spacing is longer for thinner H envelopes. We find a mean period spacing of ΔΠ ∼ 17 s in the data of BPM 37093, which is likely to be associated with ℓ = 2 modes. However, we are not able to put constraints on the stellar mass of BPM 37093 using this mean period spacing due to the simultaneous sensitivity of ΔΠ with M⋆ , Teff , and MH , which is an intrinsic property of DAV stars. We find asteroseismological models for the three objects under analysis, two of them (BPM 37093 and GD 518) characterised by canonical (thick) H envelopes, and the third one (SDSS J0840+5222) with a thinner H envelope. The effective temperature and stellar mass of these models are in agreement with the spectroscopic determinations. The percentage of crystallised mass for these asteroseismological models is 92%, 97%, and 81% for BPM 37093, GD 518, and SDSS J0840+5222, respectively. We also derive asteroseismological distances which differ somewhat from the astrometric measurements of Gaia for these stars.
Conclusions. Asteroseismological analyses like the one presented in this paper could lead to a more complete understanding of the processes occurring during crystallisation inside white dwarfs. Also, such analyses could make it possible to deduce the core chemical composition of ultra-massive white dwarfs and, in this way, to infer their evolutionary origin, such as the correlation between a star’s ONe core and its having originated through single-star evolution or a carbon/oxygen (CO) core indicating the star is the product of a merger of the two components of a binary system. However, in order to achieve these objectives, it is necessary to find a greater number of pulsating ultra-massive WDs and to carry out additional observations of known pulsating stars to detect more pulsation periods. Space missions such as TESS can provide a great boost towards achieving these aims.
Ultra-massive white dwarfs are powerful tools used to study various physical processes in the asymptotic giant branch (AGB), type Ia supernova explosions, and the theory of crystallization through white dwarf asteroseismology. Despite the interest in these white dwarfs, there are few evolutionary studies in the literature devoted to them. Here we present new ultra-massive white dwarf evolutionary sequences that constitute an improvement over previous ones. In these new sequences we take into account for the first time the process of phase separation expected during the crystallization stage of these white dwarfs by relying on the most up-to-date phase diagram of dense oxygen/neon mixtures. Realistic chemical profiles resulting from the full computation of progenitor evolution during the semidegenerate carbon burning along the super-AGB phase are also considered in our sequences. Outer boundary conditions for our evolving models are provided by detailed non-gray white dwarf model atmospheres for hydrogen and helium composition. We assessed the impact of all these improvements on the evolutionary properties of ultra-massive white dwarfs, providing updated evolutionary sequences for these stars. We conclude that crystallization is expected to affect the majority of the massive white dwarfs observed with effective temperatures below 40 000 K. Moreover, the calculation of the phase separation process induced by crystallization is necessary to accurately determine the cooling age and the mass-radius relation of massive white dwarfs. We also provide colors in the Gaia photometric bands for our H-rich white dwarf evolutionary sequences on the basis of new model atmospheres. Finally, these new white dwarf sequences provide a new theoretical frame to perform asteroseismological studies on the recently detected ultra-massive pulsating white dwarfs.
We study electrostatic and phonon properties of Yukawa crystals. It is shown that in the harmonic approximation these systems which are used in the theory of dusty plasma can be described analytically by the model from the theory of neutron stars and white dwarfs. Using this approximation, we consider properties of body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and MgB2 lattices. Studies of MgB2 and hcp lattices in the context of Yukawa systems are lacking. It is shown that they never possess the smallest potential energy and the phase diagram of stable Yukawa crystals contains bcc and fcc lattices only. However, corrections to the charge density proportional to (κa)4 can noticeably change the structural diagram of Yukawa systems. The analytical model developed also allows us to describe low-temperature effects where numerical simulations are difficult.
Context. Ultra-massive hydrogen-rich white dwarf stars are expected to harbor oxygen/neon cores resulting from the progenitor evolution through the super-asymptotic giant branch phase. As evolution proceeds during the white dwarf cooling phase, a crystallization process resulting from Coulomb interactions in very dense plasmas is expected to occur, leading to the formation of a highly crystallized core. In particular, pulsating ultra-massive white dwarfs offer a unique opportunity to infer and test the occurrence of crystallization in white dwarf interiors as well as physical processes related with dense plasmas.
Aims. We aim to assess the adiabatic pulsation properties of ultra-massive hydrogen-rich white dwarfs with oxygen/neon cores.
Methods. We studied the pulsation properties of ultra-massive hydrogen-rich white dwarf stars with oxygen/neon cores. We employed a new set of ultra-massive white dwarf evolutionary sequences of models with stellar masses in the range 1.10 ≤ M⋆ / M⊙ ≤ 1.29 computed by taking into account the complete evolution of the progenitor stars and the white dwarf stage. During the white dwarf cooling phase, we considered element diffusion. When crystallization set on in our models, we took into account latent heat release and also the expected changes in the core chemical composition that are due to phase separation according to a phase diagram suitable for oxygen and neon plasmas. We computed nonradial pulsation g -modes of our sequences of models at the ZZ Ceti phase by taking into account a solid core. We explored the impact of crystallization on their pulsation properties, in particular, the structure of the period spectrum and the distribution of the period spacings.
Results. We find that it would be possible, in principle, to discern whether a white dwarf has a nucleus made of carbon and oxygen or a nucleus of oxygen and neon by studying the spacing between periods.
Conclusions. The features found in the period-spacing diagrams could be used as a seismological tool to discern the core composition of ultra-massive ZZ Ceti stars, this should be complemented with detailed asteroseismic analysis using the individual observed periods.
Using images from the Hubble Space Telescope Advanced Camera for Surveys, we measure the rate of cooling of white dwarfs in the globular cluster 47 Tucanae and compare it to modelled cooling curves. We examine the effects of the outer convective envelope reaching the nearly isothermal degenerate core and the release of latent heat during core crystallization on the white dwarf cooling rates. For white dwarfs typical of 47 Tuc, the onset of these effects occur at similar times. The latent heat released during crystallization is a small heat source. In contrast, the heat reservoir of the degenerate core is substantially larger. When the convective envelope reaches the nearly isothermal interior of the white dwarf, the star becomes brighter than it would be in the absence of this effect. Our modelled cooling curves that include this convective coupling closely match the observed luminosity function of the white dwarfs in 47 Tuc.
Context. Extremely low-mass white dwarf (ELM WD; M ⋆ ≲ 0.18–0.20 M ⊙ ) stars are thought to be formed in binary systems via stable or unstable mass transfer. Although stable mass transfer predicts the formation of ELM WDs with thick hydrogen (H) envelopes that are characterized by dominant residual nuclear burning along the cooling branch, the formation of ELM WDs with thinner H envelopes from unstable mass loss cannot be discarded.
Aims. We compute new evolutionary sequences for helium (He) core WD stars with thin H envelopes with the main aim of assessing the lowest T eff that could be reached by this type of stars.
Methods. We generate a new grid of evolutionary sequences of He-core WD stars with thin H envelopes in the mass range from 0.1554 to 0.2025 M ⊙ , and assess the changes in both the cooling times and surface gravity induced by a reduction of the H envelope. We also determine, taking into account the predictions of progenitor evolution, the lowest T eff reached by the resulting ELM WDs.
Results. We find that a slight reduction in the H envelope yields a significant increase in the cooling rate of ELM WDs. Because of this, ELM WDs with thin H envelopes could cool down to ~2500 K, in contrast to their canonical counterparts that cool down to ~7000 K. In addition, we find that a reduction of the thickness of the H envelope markedly increases the surface gravity ( g ) of these stars.
Conclusions. If ELM WDs are formed with thin H envelopes, they could be detected at very low T eff . The detection of such cool ELM WDs would be indicative that they were formed with thin H envelopes, thus opening the possibility of placing constraints on the possible mechanisms of formation of this type of star. Last but not least, the increase in g due to the reduction of the H envelope leads to consequences in the spectroscopic determinations of these stars.
We present an asteroseismological analysis of four ZZ Ceti stars observed with Kepler : GD 1212, SDSS J113655.17+040952.6, KIC 11911480 and KIC 4552982, based on a grid of full evolutionary models of DA white dwarf stars. We employ a grid of carbon-oxygen core white dwarfs models, characterized by a detailed and consistent chemical inner profile for the core and the envelope. In addition to the observed periods, we take into account other information from the observational data, as amplitudes, rotational splittings and period spacing, as well as photom-etry and spectroscopy. For each star, we present an asteroseismological model that closely reproduce their observed properties. The asteroseismological stellar mass and effective temperature of the target stars are (0.632 ± 0.027M ⊙ , 10737 ± 73K) for GD 1212, (0.745 ± 0.007M ⊙ , 11110 ± 69K) for KIC 4552982, (0.5480 ± 0.01M ⊙ , 12721 ± 228K) for KIC1191480 and (0.570 ± 0.01M ⊙ , 12060 ± 300K) for SDSS J113655.17+040952.6. In general, the asteroseismological values are in good agreement with the spectroscopy. For KIC 11911480 and SDSS J113655.17+040952.6 we derive a similar seismological mass, but the hydrogen envelope is an order of magnitude thinner for SDSS J113655.17+040952.6, that is part of a binary system and went through a common envelope phase.
Abstract In this chapter addresses the physics of degenerate carbon burning, a critical issue for understanding Type Ia supernovae (SN Ia). In models of accreting white dwarfs pertinent to the single-degenerate model for SN Ia, carbon burning begins under degenerate conditions when the rate of nuclear burning exceeds that of neutrino losses. A phase of convective burning eventually occurs at a dynamical rate, leading to explosion. The subsequent dynamics depend on whether the point of runaway is near the center or further away and whether there is a single ignition site leading to a buoyant bubble or multiple sites of runaway. The chapter gives a basic introduction to the physics of subsonic and supersonic nuclear burning and associated instabilities as well as their application in the context of SN Ia. Dynamical carbon burning could, in principle, lead to either supersonic detonation or subsonic deflagration, but observations preclude the prompt formation of a detonation in the environment of a carbon-oxygen white dwarf that accretes to near the Chandrasekhar mass limit. The chapter also presents a discussion of the critical issue of deflagration-to-detonation transition. Current work suggests that this transition occurs in the context of a turbulent flame-brush instability rather than in a distributed-flame environment.
Some globular clusters host multiple stellar populations with different chemical abundance patterns. This is particularly true for $\omega$ Centauri, which shows clear evidence of a helium- enriched sub-population characterized by a helium abundance as high as $Y= 0.4$. We present a whole and consistent set of evolutionary tracks from the ZAMS to the white dwarf stage appropriate for the study of the formation and evolution of white dwarfs resulting from the evolution of helium-rich progenitors. Different issues of the white dwarf evolution and their helium-rich progenitors have been explored. In particular, the final mass of the remnants, the role of overshooting during the thermally-pulsing phase, and the cooling of the resulting white dwarfs differ markedly from the evolutionary predictions of progenitor stars with standard initial helium abundance. Finally, the pulsational properties of the resulting white dwarfs are also explored. We find that, for the range of initial masses explored in this paper, the final mass of the helium-rich progenitors is markedly larger than the final mass expected from progenitors with the usual helium abundance. We also find that progenitors with initial mass smaller than $M_\star \simeq 0.65\,M_\odot$ evolve directly into helium-core white dwarfs in less than 14~Gyr, and that for larger progenitor masses the evolution of the resulting low-mass carbon-oxygen white dwarfs is dominated by residual nuclear burning. For helium-core white dwarfs, we find that they evolve markedly faster than their counterparts coming from standard progenitors. Also, in contrast with what occurs for white dwarfs resulting from progenitors with the standard helium abundance, the impact of residual burning on the cooling time of white dwarfs is not affected by the occurrence of overshooting during the thermally-pulsing phase of progenitor stars.
The heavens contain a variety of materials that range from conventional to extraordinary and extreme. For this colloquium, we define Astromaterial Science as the study of materials, in astronomical objects, that are qualitatively denser than materials on earth. Astromaterials can have unique properties, related to their density, such as extraordinary mechanical strength, or alternatively be organized in ways similar to more conventional materials. The study of astromaterials may suggest ways to improve terrestrial materials. Likewise, advances in the science of conventional materials may allow new insights into astromaterials. We discuss Coulomb crystals in the interior of cold white dwarfs and in the crust of neutron stars and review the limited observations of how stars freeze. We apply astromaterial science to the generation of gravitational waves. According to Einstein's Theory of General Relativity accelerating masses radiate gravitational waves. However, very strong materials may be needed to vigorously accelerate large masses in order to produce continuous gravitational waves that are observable in present detectors. We review large-scale molecular dynamics simulations of the breaking stress of neutron star crust that suggest it is the strongest material known, some ten billion times stronger than steel. Nuclear pasta is an example of a soft astromaterial. It is expected near the base of the neutron star crust at densities of ten to the fourteen grams per cubic centimeter. Competition between nuclear attraction and Coulomb repulsion rearrange neutrons and protons into complex non-spherical shapes such as flat plates (lasagna) or thin rods (spaghetti). We review semi-classical molecular dynamics simulations of nuclear pasta. We illustrate some of the shapes that are possible and discuss transport properties including shear viscosity and thermal and electrical conductivities.
Because of the large neutron excess of $^{22}$Ne, this isotope rapidly sediments in the interior of the white dwarfs. This process releases an additional amount of energy, thus delaying the cooling times of the white dwarf. This influences the ages of different stellar populations derived using white dwarf cosmochronology. Furthermore, the overabundance of $^{22}$Ne in the inner regions of the star, modifies the Brunt-V\"ais\"al\"a frequency, thus altering the pulsational properties of these stars. In this work, we discuss the impact of $^{22}$Ne sedimentation in white dwarfs resulting from Solar metallicity progenitors ($Z=0.02$). We performed evolutionary calculations of white dwarfs of masses $0.528$, $0.576$, $0.657$ and $0.833$ M$_{\sun}$, derived from full evolutionary computations of their progenitor stars, starting at the Zero Age Main Sequence all the way through central hydrogen and helium burning, thermally-pulsing AGB and post-AGB phases. Our computations show that at low luminosities ($\log(L/L_{\sun})\la -4.25$), $^{22}$Ne sedimentation delays the cooling of white dwarfs with Solar metallicity progenitors by about 1~Gyr. Additionally, we studied the consequences of $^{22}$Ne sedimentation on the pulsational properties of ZZ~Ceti white dwarfs. We find that $^{22}$Ne sedimentation induces differences in the periods of these stars larger than the present observational uncertainties, particularly in more massive white dwarfs.
We present a robust statistical analysis of the white dwarf cooling sequence in 47 Tucanae. We combine Hubble Space Telescope UV and optical data in the core of the cluster, Modules for Experiments in Stellar Evolution (MESA) white dwarf cooling models, white dwarf atmosphere models, artificial star tests, and a Markov Chain Monte Carlo sampling method to fit white dwarf cooling models to our data directly. We use a technique known as the unbinned maximum likelihood to fit these models to our data without binning. We use these data to constrain neutrino production and the thickness of the hydrogen layer in these white dwarfs. The data prefer thicker hydrogen layers (qH = 3.2 × 10-5) and we can strongly rule out thin layers (qH = 10-6) . The neutrino rates currently in the models are consistent with the data. This analysis does not provide a constraint on the number of neutrino species. © 2016. The American Astronomical Society. All rights reserved.
White Dwarf CosmochronologyCool White Dwarf AtmospheresIdentification of Large Samples of Cool White DwarfsObservational Properties of Cool White DwarfsSpectral Evolution of Cool White DwarfsAges for Individual White DwarfsThe White Dwarf Luminosity FunctionHalo White DwarfsConclusions and Future ProspectsReferences
We calculate electrostatic, spectral, and thermal properties of two-component Coulomb crystals of ions and determine the limits of applicability of the linear mixing theory to such systems.
NGC 6397 is one of the most interesting, well observed and theoretically
studied globular clusters. The existing wealth of observations allows us to
study the reliability of the theoretical white dwarf cooling sequences of low
metallicity progenitors,to determine its age and the percentage of unresolved
binaries, and to assess other important characteristics of the cluster, like
the slope of the initial mass function, or the fraction of white dwarfs with
hydrogen deficient atmospheres. We present a population synthesis study of the
white dwarf population of NGC 6397. In particular, we study the shape of the
color-magnitude diagram, and the corresponding magnitude and color
distributions. We do this using an up-to-date Monte Carlo code that
incorporates the most recent and reliable cooling sequences and an accurate
modeling of the observational biases. We find a good agreement between our
theoretical models and the observed data. In particular, we find that this
agreement is best for those cooling sequences that take into account residual
hydrogen burning. This result has important consequences for the evolution of
progenitor stars during the thermally-pulsing asymptotic giant branch phase,
since it implies that appreciable third dredge-up in low-mass, low-metallicity
progenitors is not expected to occur. Using a standard burst duration of 1.0
Gyr, we obtain that the age of the cluster is 12.8+0.50-0.75 Gyr. Larger ages
are also compatible with the observed data, but then realistic longer durations
of the initial burst of star formation are needed to fit the luminosity
function. We conclude that a correct modeling of the white dwarf opulation of
globular clusters, used in combination with the number counts of main sequence
stars provides an unique tool to model the properties of globular clusters.
We present a theoretical study on the metallicity dependence of the
initial$-$to$-$final mass relation and its influence on white dwarf age
determinations. We compute a grid of evolutionary sequences from the main
sequence to $\sim 3\, 000$ K on the white dwarf cooling curve, passing through
all intermediate stages. During the thermally-pulsing asymptotic giant branch
no third dredge-up episodes are considered and thus the photospheric C/O ratio
is below unity for sequences with metallicities larger than $Z=0.0001$. We
consider initial metallicities from $Z=0.0001$ to $Z=0.04$, accounting for
stellar populations in the galactic disk and halo, with initial masses below
$\sim 3M_{\odot}$. We found a clear dependence of the shape of the
initial$-$to$-$final mass relation with the progenitor metallicity, where metal
rich progenitors result in less massive white dwarf remnants, due to an
enhancement of the mass loss rates associated to high metallicity values. By
comparing our theoretical computations with semi empirical data from globular
and old open clusters, we found that the observed intrinsic mass spread can be
accounted for by a set of initial$-$to$-$final mass relations characterized by
different metallicity values. Also, we confirm that the lifetime spent before
the white dwarf stage increases with metallicity. Finally, we estimate the mean
mass at the top of the white dwarf cooling curve for three globular clusters
NGC 6397, M4 and 47 Tuc, around $0.53 M_{\odot}$, characteristic of old stellar
populations. However, we found different values for the progenitor mass, lower
for the metal poor cluster, NGC 6397, and larger for the younger and metal rich
cluster 47 Tuc, as expected from the metallicity dependence of the
initial$-$to$-$final mass relation.
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.
Vibration modes and thermodynamic properties of a body‐centered cubic (bcc) Coulomb crystal with a small admixture of substitutional isotopic impurities are studied analytically applying the perturbation theory of disordered crystal spectra and the Lifshitz‐Krein trace formula. We calculate the density of phonon states of the perfect bcc Coulomb crystal and use it to compute the heat capacity of the crystal with impurities in a wide range of temperatures. It is shown that the ratio of an impurity contribution to the crystal heat capacity over the perfect crystal specific heat tends to a constant in the low‐temperature quantum regime and decays as T –2 in the classic regime of high temperatures. It is also shown that even a small concentration of heavy impurities amplifies significantly the total crystal heat capacity. The results are compared with those obtained using the more conventional linear mixing theory. It is demonstrated that both methods give similar results at all tempera‐tures when the impurity mass is not too different from that of the base ions but a strong discrepancy is observed at low and intermediate temperatures when impurities are noticeably lighter or heavier. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
At very high densities, electrons react with protons to form neutron-rich matter. This material is central to many fundamental questions in nuclear physics and astrophysics. Moreover, neutron-rich matter is being studied with an extraordinary variety of new tools such as Facility for Rare Isotope Beams (FRIB) and the Laser Interferometer Gravitational Wave Observatory (LIGO). We describe the Lead Radius Experiment (PREX) that uses parity violating electron scattering to measure the neutron radius in 208Pb. This has important implications for neutron stars and their crusts. We discuss X-ray observations of neutron star radii. These also have important implications for neutron-rich matter. Gravitational waves (GW) open a new window on neutron-rich matter. They come from sources such as neutron star mergers, rotating neutron star mountains, and collective r-mode oscillations. Using large scale molecular dynamics simulations, we find neutron star crust to be very strong. It can support mountains on rotating neutron stars large enough to generate detectable gravitational waves. Finally, neutrinos from core collapse supernovae (SN) provide another, qualitatively different probe of neutron-rich matter. Neutrinos escape from the surface of last scattering known as the neutrino-sphere. This is a low density warm gas of neutron-rich matter. Neutrino-sphere conditions can be simulated in the laboratory with heavy ion collisions. Observations of neutrinos can probe nucleosyntheses in SN. Simulations of SN depend on the equation of state (EOS) of neutron-rich matter. We discuss a new EOS based on virial and relativistic mean field calculations. We believe that combing astronomical observations using photons, GW, and neutrinos, with laboratory experiments on nuclei, heavy ion collisions, and radioactive beams will fundamentally advance our knowledge of compact objects in the heavens, the dense phases of QCD, the origin of the elements, and of neutron-rich matter.
Massive pulsating white dwarf stars are extremely rare, because of their small size and because they are the final product of high-mass stars, which are less common. Because of their intrinsic smaller size, they are fainter than the normal size white dwarf stars. The motivation to look for this type of stars is to be able to study in detail their internal structure and also derive generic properties for the sub-class of variables, the massive ZZ Ceti stars. Our goal is to investigate whether the internal structures of these stars differ from the lower-mass ones, which in turn could have been resultant from the previous evolutionary stages.
In this paper, we present the ensemble seismological analysis of the known massive pulsating white dwarf stars. Some of these pulsating stars might have substantial crystallized cores, which would allow us to probe solid physics in extreme conditions.
White dwarfs are the final stage for more than 95% of all stars. Their population statistics and properties contain a wealth of information about the history of star formation in our galaxy, the ages of stellar systems, and the relation between original mass at birth and that of the final remnant. They are also interesting individually as laboratories for physical conditions not easily reached in terrestrial labs: macroscopic manifestation of the Pauli principle, high densities and pressures, and extremely high magnetic fields. After a brief introduction with some historical milestones the observational status is reviewed: spectroscopic classification, determination of stellar parameters from spectroscopic and photometric observations, effective temperatures, surface gravities, radii, and masses. The next sections deal with the physics of the interior and evolution of white dwarfs, leading to the mass–radius relation and cooling times. Going back closer to the observations again, the physical processes in the outer layers are discussed: gravitational separation, diffusion, radiative levitation, accretion, and convective mixing. This leads to a review of our current understanding of the origin of spectral types and their interrelation. A final section gives brief introductions to topics at the center of current research: white dwarfs in open and globular clusters, debris disks, the origin of accreted metals in the atmospheres, magnetic fields and their origin, variable white dwarfs, and white dwarfs in binaries. This chapter was finished in February 2010 and reflects the status of knowledge at that time.
Keywords: Accretion, Chandrasekhar mass, Convective mixing, Debris disks, Gravitational settling, Initial–final mass relation, Magnetic fields, Mass–radius relation, Stellar remnants, White dwarfs
Using the SOuthern Astrophysical Research telescope (SOAR) Optical Imager at the SOAR 4.1 m telescope, we report on the discovery
of five new massive pulsating white dwarf stars. Our results represent an increase of about 20 per cent in the number of massive
pulsators. We have detected both short and long periods, low and high amplitude pulsation modes, covering the whole range
of the ZZ Ceti instability strip.
In this paper, we present a first seismological study of the new massive pulsators based on the few frequencies detected.
Our analysis indicates that these stars have masses higher than average, in agreement with the spectroscopic determinations.
In addition, we study for the first time the ensemble properties of the pulsating white dwarf stars with masses above 0.8 M⊙. We found a bimodal distribution of the main pulsation period with the effective temperature for the massive DAVs, which
indicates mode selection mechanisms.
Aims. We discuss the importance of pure hydrogen white dwarf atmosphere
models with Ly-alpha far red wing opacity in the analysis of the white
dwarf cooling sequence of the globular cluster NGC 6397.
Methods. Our recently improved atmosphere models account for the
previously missing opacity from the Ly-alpha hydrogen line broadened by
collisions of the absorbing hydrogen atoms with molecular and atomic
hydrogen. These models are the first that well reproduce the UV colors
and spectral energy distributions of cool white dwarfs with T-eff< 6000
K observed in the Galactic Disk.
Results. Fitting the observed F814W magnitude and F606W-F814W color we
obtained a value for the true distance modulus, mu = 12.00 +/- 0.02,
that is in agreement with recent analyses. We show that the stars at the
end of the cooling sequence appear to be similar to 160 K cooler when
models that account for Ly-alpha opacity are used. This indicates that
the age of NGC 6397
derived from the white dwarf cooling sequence using
atmosphere models that do not include the correct Ly-alpha opacity is underestimated by similar to 0.5 Gyr.
Conclusions. Our analysis shows that it is essential to use white dwarf
atmosphere models with Ly-alpha opacity for precise dating of old stellar populations from white dwarf cooling sequences.
A new experiment to determine the thermonuclear cross section of the 12C(α,γ)16O reaction has been performed in regular kinematics using an intense α-particle beam of up to 340 μA from the Stuttgart DYNAMITRON. For the first time, a 4π-germanium-detector setup has been used to measure the angular distribution of the γ rays at all angles simultaneously. It consisted of an array of nine EUROGAM high-purity Ge detectors in close geometry, actively shielded individually with bismuth germanate crystals. The 12C targets were isotopically enriched by magnetic separation during implantation. The depth profiles of the implanted carbon in the 12C targets were determined by Rutherford backscattering for purposes of cross-section normalization and absolute determination of the E1 and E2 S factors. Angular distributions of the γ decay to the 16O ground state were measured in the energy range Ec.m.=1.30–2.78 MeV and in the angular range (lab.) 30°–130°. From these distributions, astrophysical E1 and E2 S-factor functions vs energy were calculated, both of which are indispensable to the modeling of this reaction and the extrapolation toward lower energies. The separation of the E1 and E2 capture channels was done both by taking the phase value ϕ12 as a free parameter and by fixing it using the results of elastic α-particle scattering on 12C in the same energy range.
We present the results of a deep Hubble Space Telescope (HST) exposure of the nearby globular cluster NGC 6397, focussing attention on the cluster's white dwarf cooling sequence. This sequence is shown to extend over 5 mag in depth, with an apparent cutoff at magnitude F814W ~ 27.6. We demonstrate, using both artificial star tests and the detectability of background galaxies at fainter magnitudes, that the cutoff is real and represents the truncation of the white dwarf luminosity function in this cluster. We perform a detailed comparison between cooling models and the observed distribution of white dwarfs in color and magnitude, taking into account uncertainties in distance, extinction, white dwarf mass, progenitor lifetimes, binarity, and cooling model uncertainties. After marginalizing over these variables, we obtain values for the cluster distance modulus and age of μ0 = 12.02 ± 0.06 and Tc = 11.47 ± 0.47 Gyr (95% confidence limits). Our inferred distance and white dwarf initial-final mass relations are in good agreement with other independent determinations, and the cluster age is consistent with, but more precise than, prior determinations made using the main-sequence turnoff method. In particular, within the context of the currently accepted ΛCDM cosmological model, this age places the formation of NGC 6397 at a redshift z ~ 3, at a time when the cosmological star formation rate was approaching its peak.
Using recent photometric calibrations, we develop greatly improved distance estimates for DA white dwarfs using multi-band synthetic photometry based on spectroscopic temperatures and gravities. Very good correlations are shown to exist between our spectroscopically based photometric distance estimates and those derived from trigonometric parallaxes. We investigate the uncertainties involved in our distance estimates, as well as discuss the circumstances where such techniques are most likely to fail. We apply our techniques to the large sample of Sloan Digital Sky Survey DA white dwarfs where automated fitting of H I Balmer profiles yields spectrometric temperatures and gravities. We determine simple empirical corrections to these temperatures and gravities with respect to published slit spectroscopy. After applying these T
eff-log g corrections as well as appropriate interstellar extinction corrections, where necessary, we derive spectroscopically based photometric distances for 7062 DA stars from this sample.
White dwarfs are the remnants of stars of low and intermediate masses on the main sequence. Since they have exhausted all of their nuclear fuel, their evolution is just a gravothermal process. The release of energy only depends on the detailed internal structure and chemical composition and on the properties of the envelope equation of state and opacity; its consequences on the cooling curve (i.e., the luminosity vs. time relationship) depend on the luminosity at which this energy is released. The internal chemical profile depends on the rate of the 12C(α, γ)16O reaction as well as on the treatment of convection. High reaction rates produce white dwarfs with oxygen-rich cores surrounded by carbon-rich mantles. This reduces the available gravothermal energy and decreases the lifetime of white dwarfs. In this paper we compute detailed evolutionary models providing chemical profiles for white dwarfs having progenitors in the mass range from 1.0 to 7 M☉, and we examine the influence of such profiles in the cooling process. The influence of the process of separation of carbon and oxygen during crystallization is decreased as a consequence of the initial stratification, but it is still important and cannot be neglected. As an example, the best fit to the luminosity functions of Liebert et al. and Oswalt et al. gives an age of the disk of 9.3 and 11.0 Gyr, respectively, when this effect is taken into account, and only 8.3 and 10.0 Gyr when it is neglected.
We present the white dwarf sequence of the globular cluster M4, based on a 123 orbit Hubble Space Telescope exposure, with a limiting magnitude of V ~ 30 and I ~ 28. The white dwarf luminosity function rises sharply for I > 25.5, consistent with the behavior expected for a burst population. The white dwarfs of M4 extend to approximately 2.5 mag fainter than the peak of the local Galactic disk white dwarf luminosity function. This demonstrates a clear and significant age difference between the Galactic disk and the halo globular cluster M4. Using the same standard white dwarf models to fit each luminosity function yields ages of 7.3 ± 1.5 Gyr for the disk and 12.7 ± 0.7 Gyr for M4 (2 σ statistical errors).
We present a homogeneous photometric and spectroscopic analysis of 18 stars along the evolutionary sequence of the metal-poor globular cluster NGC 6397 (½Fe/ H % À2), from the main-sequence turnoff point to red giants below the bump. The spectroscopic stellar parameters, in particular stellar parameter differences between groups of stars, are in good agreement with broadband and Strömgren photometry calibrated on the infrared flux method. The spectro-scopic abundance analysis reveals, for the first time, systematic trends of iron abundance with evolutionary stage. Iron is found to be 30% less abundant in the turnoff point stars than in the red giants. An abundance difference in lithium is seen between the turnoff point and warm subgiant stars. The impact of potential systematic errors on these abundance trends (stellar parameters, the hydrostatic and LTE approximations) is quantitatively evaluated and found not to alter our conclusions significantly. Trends for various elements (Li, Mg, Ca, Ti, and Fe) are compared with stellar structure models including the effects of atomic diffusion and radiative acceleration. Such models are found to describe the observed element-specific trends well, if extra (turbulent) mixing just below the convection zone is introduced. It is concluded that atomic diffusion and turbulent mixing are largely responsible for the subprimordial stellar lithium abundances of warm halo stars. Other consequences of atomic diffusion in old metal-poor stars are also discussed.
We present the color-magnitude diagram (CMD) from deep Hubble Space Telescope imaging in the globular cluster NGC 6397. The Advanced Camera for Surveys (ACS) was used for 126 orbits to image a single field in two colors (F814W, F606W) 5' SE of the cluster center. The field observed overlaps that of archival WFPC2 data from 1994 and 1997 which were used to proper motion (PM) clean the data. Applying the PM corrections produces a remarkably clean CMD which reveals a number of features never seen before in a globular cluster CMD. In our field, the main-sequence stars appeared to terminate close to the location in the CMD of the hydrogen-burning limit predicted by two independent sets of stellar evolution models. The faintest observed main-sequence stars are about a magnitude fainter than the least luminous metal-poor field halo stars known, suggesting that the lowest-luminosity halo stars still await discovery. At the bright end the data extend beyond the main-sequence turnoff to well up the giant branch. A populous white dwarf cooling sequence is also seen in the cluster CMD. The most dramatic features of the cooling sequence are its turn to the blue at faint magnitudes as well as an apparent truncation near F814W = 28. The cluster luminosity and mass functions were derived, stretching from the turnoff down to the hydrogen-burning limit. It was well modeled with either a very flat power-law or a lognormal function. In order to interpret these fits more fully we compared them with similar functions in the cluster core and with a full N-body model of NGC 6397 finding satisfactory agreement between the model predictions and the data. This exercise demonstrates the important role and the effect that dynamics has played in altering the cluster initial mass function.
Nucleosynthesis, on the surface of accreting neutron stars, produces a range of chemical elements. We perform molecular dynamics simulations of crystallization to see how this complex composition forms new neutron star crust. We find chemical separation, with the liquid ocean phase greatly enriched in low atomic number elements compared to the solid crust. This phase separation should change many crust properties such as the thermal conductivity and shear modulus. The concentration of carbon, if present, is enriched in the ocean. This may allow unstable thermonuclear burning of the carbon and help explain the ignition of the very energetic explosions known as superbursts.
We present an exploration of the significance of Carbon/Oxygen phase separation in white dwarf stars in the context of self-consistent evolutionary calculations. Because phase separation can potentially increase the calculated ages of the oldest white dwarfs, it can affect the age of the Galactic disk as derived from the downturn in the white dwarf luminosity function. We find that the largest possible increase in ages due to phase separation is 1.5 Gyr, with a most likely value of approximately 0.6 Gyr, depending on the parameters of our white dwarf models. The most important factors influencing the size of this delay are the total stellar mass, the initial composition profile, and the phase diagram assumed for crystallization. We find a maximum age delay in models with masses of 0.6 solar masses, which is near the peak in the observed white dwarf mass distribution. We find that varying the opacities (via the metallicity) has little effect on the calculated age delays. In the context of Galactic evolution, age estimates for the oldest Galactic globular clusters range from 11.5 to 16 Gyr, and depend on a variety of parameters. In addition, a 4 to 6 Gyr delay is expected between the formation of the globular clusters and that of the Galactic thin disk, while the observed white dwarf luminosity function gives an age estimate for the thin disk of 9.5 +/-1.0 Gyr, without including the effect of phase separation. Using the above numbers, we see that phase separation could add between 0 to 3 Gyr to the white dwarf ages and still be consistent with the overall picture of Galaxy formation. Our calculated maximum value of 1.5 Gyr fits within these bounds, as does our best guess value of 0.6 Gyr. Comment: 13 total pages, 8 figures, 3 tables, accepted for publication in the Astrophysical Journal on May 25, 1999
The analytic equation of state of nonideal Coulomb plasmas consisting of pointlike ions immersed in a polarizable electron background (physics/9807042) is improved, and its applicability range is considerably extended. First, the fit of the electron screening contribution in the free energy of the Coulomb liquid is refined at high densities where the electrons are relativistic. Second, we calculate the screening contribution for the Coulomb solid (bcc and fcc) and derive an analytic fitting expression. Third, we propose a simple approximation to the internal and free energy of the liquid one-component plasma of ions, accurate within the numerical errors of the most recent Monte Carlo simulations. We obtain an updated value of the coupling parameter at the solid-liquid phase transition for the one-component plasma: Gamma_m = 175.0 (+/- 0.4).
We present a large set of theoretical isochrones, whose distinctive features mostly reside on the greatly improved treatment of the thermally pulsing asymptotic giant branch (TP-AGB) phase. Essentially, we have coupled the TP-AGB tracks described in Paper I, at their stages of pre-flash quiescent H-shell burning, with the evolutionary tracks for the previous evolutionary phases from Girardi et al. (2000). Theoretical isochrones for any intermediate value of age and metallicity are then derived by interpolation in the grids. We take care that the isochrones keep, to a good level of detail, the several peculiarities present in these TP-AGB tracks. Theoretical isochrones are then converted to about 20 different photometric systems -- including traditional ground-based systems, and those of recent major wide-field surveys such as SDSS, OGLE, DENIS, 2MASS, UKIDSS, etc., -- by means of synthetic photometry applied to an updated library of stellar spectra, suitably extended to include C-type stars. Finally, we correct the predicted photometry by the effect of circumstellar dust during the mass-losing stages of the AGB evolution, which allows us to improve the results for the optical-to-infrared systems, and to simulate mid- and far-IR systems such as those of Spitzer and AKARI. Access to the data is provided both via a web repository of static tables (http://stev.oapd.inaf.it/dustyAGB07 and CDS), and via an interactive web interface (http://stev.oapd.inaf.it/cmd) that provides tables for any intermediate value of age and metallicity, for several photometric systems, and for different choices of dust properties. Comment: 25 pages, accepted for publication in A&A, revised according to the latest referee's indications, isochrones are available at http://stev.oapd.inaf.it/cmd
It was predicted more than 40 years ago that the cores of the coolest white dwarf stars should eventually crystallize. This effect is one of the largest sources of uncertainty in white dwarf cooling models, which are now routinely used to estimate the ages of stellar populations in both the Galactic disk and the halo. We are attempting to minimize this source of uncertainty by calibrating the models, using observations of pulsating white dwarfs. In a typical mass white dwarf model, crystallization does not begin until the surface temperature reaches 6000-8000 K. In more massive white dwarf models the effect begins at higher surface temperatures, where pulsations are observed in the ZZ Ceti (DAV) stars. We use the observed pulsation periods of BPM 37093, the most massive DAV white dwarf presently known, to probe the interior and determine the size of the crystallized core empirically. Our initial exploration of the models strongly suggests the presence of a solid core containing about 90% of the stellar mass, which is consistent with our theoretical expectations. Comment: minor changes for length, accepted for ApJ Letters
Following Paczy\'{n}ski & Zi\'{o}lkowski (1968) and Han et al. (1994), we assume that the envelope of an asymptotic giant branch (AGB) or a first giant branch (FGB) star is lost when the binding energy of the envelope is equal to zero ($\Delta W=0$) and the core mass of the AGB star or the FGB star at the point ($\Delta W=0$) is taken as the final mass. Using this assumption, we calculate the IFMRs for stars of different metallicities.We find that the IFMRs depends strongly on the metallicity, i.e. $Z=0.0001, 0.0003, 0.001, 0.004, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08$ and 0.1. From $Z=0.04$, the final mass of the stars with a given initial mass increases with increasing or decreasing metallicity. The difference of the final mass due to the metallicity may be up to 0.4 $M_{\odot}$. A linear fit of the initial-final mass relationship in NGC 2099 (M37) shows a potential evidence of the effect of metallicity on the IFMR. The IFMR for stars of $Z=0.02$ obtained in the paper matches well with those inferred observationally in the Galaxy. For $Z\geq 0.02$, helium WDs are obtained from the stars of $M_{\rm i}\leq 1.0 M_{\odot}$ and this result is upheld by the discovery of numerous low-mass WDs in NGC 6791 which is a metal-rich old open cluster. Using the IFMR for stars of $Z=0.02$ obtained in the paper, we have reproduced the mass distribution of DA WDs in Sloan DR4 except for some ultra-massive white dwarfs. The trend that the mean mass of WDs decreases with effective temperature may originate from the increase of the initial metallicities of stars. We predict that metal-rich low-mass stars may become under-massive white dwarfs.
We present the first phase in our ongoing work to use Sloan Digital Sky Survey (SDSS) data to create separate white dwarf (WD) luminosity functions (LFs) for two or more different mass ranges. In this paper, we determine the completeness of the SDSS spectroscopic WD sample by comparing a proper-motion selected sample of WDs from SDSS imaging data with a large catalog of spectroscopically determined WDs. We derive a selection probability as a function of a single color (g − i) and apparent magnitude (g) that covers the range −1.0 < g − i < 0.2 and 15 < g < 19.5. We address the observed upturn in log g for WDs with T
eff 12,000 K and offer arguments that the problem is limited to the line profiles and is not present in the continuum. We offer an empirical method of removing the upturn, recovering a reasonable mass function for WDs with T
eff< 12,000 K. Finally, we present a WD LF with nearly an order of magnitude (3358) more spectroscopically confirmed WDs than any previous work.
We now have a good measurement of the cooling rate of G117-B15A. In the near future, we will have equally well determined cooling rates for other pulsating white dwarfs, including R548. The ability to measure their cooling rates offers us a unique way to study weakly interacting particles that would contribute to their cooling. Working toward that goal, we perform a careful asteroseismological analysis of G117-B15A and R548. We study them side by side because they have similar observed properties. We carry out a systematic, fine grid search for best fit models to the observed period spectra of those stars. We freely vary 4 parameters: the effective temperature, the stellar mass, the helium layer mass, and the hydrogen layer mass. We identify and quantify a number of uncertainties associated with our models. Based on the results of that analysis and fits to the periods observed in R548 and G117-B15A, we clearly define the regions of the 4 dimensional parameter space ocuppied by the best fit models. Comment: The first author would love to hear from you if you found this paper interesting. email agnes@astro.as.utexas.edu
We present the white dwarf sequence of the globular cluster M4, based on a
123 orbit Hubble Space Telescope exposure, with limiting magnitude V = 30, I =
28. The white dwarf luminosity function rises sharply for I >25.5, consistent
with the behaviour expected for a burst population. The white dwarfs of M4
extend to approximately 2.5 magnitudes fainter than the peak of the local
Galactic disk white dwarf luminosity function. This demonstrates a clear and
significant age difference between the Galactic disk and the halo globular
cluster M4. Using the same standard white dwarf models (Hansen 1999) to fit
each luminosity function yields ages of 7.3 +/- 1.5 Gyr for the disk and 12.7
+/- 0.7 Gyr for M4 (2-sigma statistical errors).
We calculate the internal energy of the classical one-component plasma using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for 1<Γ<300 in order to determine the effect of a differing number of particles on the thermodynamics. By fitting the internal energy to a function of Γ and N (the particle number), we find the free energy for both the liquid and solid for an infinite number of particles.
The deep interiors of cold, degenerate stars consist of a
mixture of elements, either because of primordial
inhomogeneities or because of incomplete nuclear burning.
However, most existing calculations for the cooling of such
bodies (subsequent to any nuclear burning) assume that the
only source of luminosity is the heat content of the star. An
additional (and potentially much larger) energy source is
available if the elements have limited mutual solubility below
some temperature. The resulting differentiation and
gravitational settling can dramatically decrease the rate of
cooling, enhance the number of (potentially) observable low
luminosity bodies, and may deplete the atmosphere of heavy
elements (if substantial mixing between the atmosphere and
deep interior occurs). The observational evidence for these
phenomena is equivocal at present.
The equation of state is considered for matter consisting of electrons
and nuclei of atomic weight A and charge Z, at zero temperature and at densities
much larger than that of the solid at zero pressure. Corrections are evaluated
to the energy and pressure of a degenerate Fermi gas of noninteracting electrons,
due to the following effectsn classical Coulomb energy of an ion lattice with
uniformly distributed electrons (this is the largest correction); Thomas-Fermi
deviations from uniform charge distribution of the electrons; and exehange energy
and spin-spin interactions between the electrons. The corrections increase with
decreasing density, and the approximations break down when the spacing between
nuclei is greater than the mean radius of the free Thomas-Fermi atom, and the
formulas are not applicable to the interior of planets. At very high densities,
where the electrons are extremely relativistic, the correction to the pressure is
a multiplying constant factor which is 0.994, 0.986, and 0.960, respectively, for
Z = 2, 6, and 26. It is shown that the nuclei form a lattice rather than a gas.
At very high densities, restrictions are found on possible values for A and Z due
to inverse beta decays and pycnonuclear reactions. For instance, C/sup 12/
changes to Ne/sup 24/ at densities above 6 x 10/sup 9/ gm/cc. (auth).
New high signal-to-noise optical spectrophotometry is presented for 22
ZZ Ceti stars. The atmospheric parameters (Teff log g) and
the mass are derived for each object using new model atmospheres and
synthetic spectra calculated within the mixing-length theory, as well as
recent published mass-radius relationships. Various parameterizations of
the convective efficiency are explored. The mass distribution obtained
from the optical solutions indicate that the so-called ML2
parameterization of the mixing-length theory yields a mean mass of 0.58
Msun, in excellent agreement with that of hotter DA stars
(0.59 Msun) whose atmospheres are completely radiative. ML1
and ML3 models, on the other hand, yield mean masses which are,
respectively, too high (0.70 Msun) and too low (0.51
Msun). With ML2 models, ZZ Ceti stars are found within a
narrow instability strip located in the range 13,650 ≥
Teff ≥ 11,960 K.
A similar analysis of IUE and HST spectroscopic observations is
presented as well. It is first shown that a unique solution for
Teff and log g cannot be achieved on the basis of ultraviolet
spectroscopy alone, and that one of these parameters needs to be
constrained independently. When log g values from the optical analysis
are adopted, the analysis of the ultraviolet data requires a
parameterization less efficient than ML2. Models calculated with
ML2/α = 0.6 are shown to provide an excellent internal consistency
between ultraviolet and optical temperatures. The corresponding
instability strip becomes cooler and narrower (12,460 ≥
Teff ≥ 11,160 K) than that inferred from ML2 models.
Furthermore, the atmospheric parameters obtained with these models are
consistent with the observed photometry, the trigonometric parallax
measurements, and the gravitational redshift masses. However, the mean
mass of the sample increases to a value ˜0.06 Msun
larger than that of hotter DA stars. An explanation for this discrepancy
is offered in the light of recent nonadiabatic calculations. The overall
consistency of our analysis for DA stars outside the ZZ Ceti instability
strip is discussed as well.
I will discuss the results of a very deep HST observation of the
globular cluster M4, with special focus on the white dwarf cooling
sequence. I will discuss how one can place constraints on the cluster
age by fitting white dwarf cooling models to the observed cooling
sequence and explore the various systematic uncertainties of this
cluster dating method.
We examine extensively the effect of the different crystallization
related to the presence of major and minor chemical species, on the
binding energy and the cooling time of old white dwarfs. We use improved
equations of state for the solid and the liquid, and crystallization
diagrams calculated within the modern theory of freezing. We show that,
in spite of their small abundance, trace elements severely alter the
cooling process and lengthen the cooling time of the star for a given
luminosity by several gigayears. In particular, Ne-22 is shown to
provide enough gravitational energy at crystallization to sustain the
star at the same luminosity for a time larger than the one due to the
crystallization of C/O itself. These calculations demonstrate the
necessity of including a proper treatment of crystallization in modern
white dwarf cooling theory. We also consider the effect of an initial
composition gradient in the distribution of carbon and oxygen throughout
the star. Finally, we show that a substantial portion of the interior of
massive white dwarfs is already in a quantum state in the fluid phase
and that Debye cooling probably occurs prior to crystallization in these
stars.
We have calibrated four major ground-based photometric systems with respect to the Hubble Space Telescope (HST) absolute flux scale, which is defined by Vega and four fundamental DA white dwarfs. These photometric systems include the Johnson-Kron-Cousins UBVRI, the Strömgren uvby filters, the Two Micron All Sky Survey JHKs, and the Sloan Digital Sky Survey ugriz filters. Synthetic magnitudes are calculated from model white dwarf spectra folded through the published filter response functions; these magnitudes in turn are absolutely calibrated with respect to the HST flux scale. Effective zero-magnitude fluxes and zero-point offsets of each system are determined. In order to verify the external observational consistency, as well as to demonstrate the applicability of these definitions, the synthetic magnitudes are compared with the respective observed magnitudes of larger sets of DA white dwarfs that have well-determined effective temperatures and surface gravities and span a wide range in both of these parameters.
BPM 37093 is a pulsating white dwarf of the ZZ Ceti type massive enough to have undergone partial crystallization. Metcalfe et al. recently claimed to have measured the fraction of crystallized matter in that star on the basis of asteroseismological techniques and determined a value upward of 90%. If true, this is a most significant achievement, well worthy of further scrutiny. In this spirit, we have reexamined the data available—eight periods—with our own independent model-building code and period-matching code in parameter space. In contrast to the above authors, we find that the likely value of the fraction of solidified matter in BPM 37093 is substantially less than 90%, but also that we cannot pin it down with any reasonable accuracy. Our results instead suggest that the value probably lies between 32% and 82%, depending on the unknown chemical composition of the core. We stress that, in principle, asteroseismology can be used to derive the fundamental parameters of BPM 37093, possibly including its core composition, but that, in this specific case, the information contained in the current period data appears insufficient. Indeed, we find full families of different models in parameter space that provide equally valid matches to the available period data. We suggest that the "lack of information" that appears to characterize the set of eight observed periods in BPM 37093 is related to the fact that these periods all correspond to high-order modes reaching into the asymptotic regime (k 1). We also point out that asteroseismology cannot provide a direct test of crystallization theory; the crystallized mass fraction is merely a secondary quantity derived by fixing the interior equation of state of the models and using the inferred fundamental parameters (including the core composition).
During helium burning in the core of a red giant, the relative rates of the 3α and 12C(α, γ)16O reactions largely determine the final ratio of carbon to oxygen in the resulting white dwarf star. The uncertainty in the 3α reaction at stellar energies due to the extrapolation from high-energy laboratory measurements is relatively small, but this is not the case for the 12C(α, γ)16O reaction. Recent advances in the analysis of asteroseismological data on pulsating white dwarf stars now make it possible to obtain precise measurements of the central ratio of carbon to oxygen, providing a more direct way to measure the 12C(α, γ)16O reaction rate at stellar energies. We assess the systematic uncertainties of this approach and quantify small shifts in the measured central oxygen abundance originating from the observations and from model settings that are kept fixed during the optimization. Using new calculations of white dwarf internal chemical profiles, we find a rate for the 12C(α, γ)16O reaction that is significantly higher than most published values. The accuracy of this method might improve as we modify some of the details of our description of white dwarf interiors that were not accessible through previous model-fitting methods.
Key Words evolution of stars, interiors of stars, atmospheres of stars, white dwarfs, stellar content of the Galaxy s Abstract Old, cool white dwarfs convey valuable information about the early history of our Galaxy. They have been used to determine the age of the galactic disk, several open clusters, and a globular cluster. We review the current understanding of the physics of cool white dwarfs, including their mass distribution, chemical evolution, magnetism, and cooling. We also examine the role of white dwarfs as tracers of various stellar populations, both in terms of observational searches and theoretical models.
In the light of recent significant progress on both the observational and theoretical fronts, we review the status of white dwarf stars as cosmochronometers. These objects represent the end products of stellar evolution for the vast majority of stars and, as such, can be used to constrain the ages of various populations of evolved stars in the Galaxy. For example, the oldest white dwarfs in the solar neighborhood (the remnants of the very first generation of intermediate-mass stars in the Galactic disk) are still visible and can be used, in conjunction with cooling theory, to estimate the age of the disk. More recent observations suggest the tantalizing possibility that a population of very old white dwarfs inhabits the Galactic halo. Such a population may contribute significantly to baryonic "dark" matter in the Milky Way and may be used to obtain an independent estimate of the age of the halo. In addition, white dwarf cosmochronology is likely to play a very significant role in the coming era of giant 8–10 m telescopes when faint white dwarf populations should be routinely discovered and studied in open and globular clusters.
The observed number of white dwarfs in a given volume of space increases monotonically with decreasing luminosity, as expected from cooling rate considerations. However, their number drops abruptly at a luminosity of log (L/L_sun;) ≈ -4.5, due to the finite age of our Galaxy. Comparing this sudden drop in the observed luminosity distribution with the best theoretical evolutionary white dwarf models, the authors derive an age for the Galactic disk of 9.3±2.0 Gyr. To obtain the age of the universe, one must add the time between the big bang and the first appearance of stars in the Galactic disk. The authors choose a value (and stated error) that can include all of the currently reasonable models describing this early era. They estimate the age of the universe to be 10.3±2.2 Gyr.
This paper presents the equation of state of the one-component plasma derived from precision Monte Carlo calculations. Using only data for N = 686, linear least-squares fits are generated and compared. The thermal energy is accurately represented by a simple power-series fit with the leading term given by Gamma exp 1/3, but it requires a small correction to the bcc Madelung term that brings that coefficient down to about the value (-0.90) derived for hypernetted-chain theory. The fluid thermal energy data are reproduced to better than 0.2 percent over all Gamma values in the fits. The location of the fluid-solid phase transition utilizing these new fits yields Gamma(bcc) = 178 and Gamma(fcc) = 192.
The white dwarf disk luminosity function is explored using observational results of Liebert et al. (1988, 1989) as a template for comparison, and the cooling curves of Wood (1990, 1991) as the input basis functions for the integration. The star formation rate over the history of the Galaxy is found to be constant to within an order of magnitude, and the disk age lies in the range 6-13.5 Gyr, where roughly 40 percent of the uncertainty is due to the observational uncertainties. Using the best current estimates as inputs to the integration, the disk ages range from 7.5 to 11 Gyr, i.e., they are substantially younger than most estimates for the halo globular clusters but in reasonable agreement with those for the disk globular clusters and open clusters. The ages of these differing populations, taken together, are consistent with the pressure-supported collapse models of early spiral Galactic evolution.
We present the first detailed study of the properties (temperatures, gravities, and masses) of the NGC 6791 white dwarf population. This unique stellar system is both one of the oldest (8 Gyr) and most metal-rich ([Fe/H] ~ 0.4) open clusters in our Galaxy, and has a color-magnitude diagram (CMD) that exhibits both a red giant clump and a much hotter extreme horizontal branch. Fitting the Balmer lines of the white dwarfs in the cluster, using Keck/LRIS spectra, suggests that most of these stars are undermassive, = 0.43 +/- 0.06 Msun, and therefore could not have formed from canonical stellar evolution involving the helium flash at the tip of the red giant branch. We show that at least 40% of NGC 6791's evolved stars must have lost enough mass on the red giant branch to avoid the flash, and therefore did not convert helium into carbon-oxygen in their core. Such increased mass loss in the evolution of the progenitors of these stars is consistent with the presence of the extreme horizontal branch in the CMD. This unique stellar evolutionary channel also naturally explains the recent finding of a very young age (2.4 Gyr) for NGC 6791 from white dwarf cooling theory; helium core white dwarfs in this cluster will cool ~3 times slower than carbon-oxygen core stars and therefore the corrected white dwarf cooling age is in fact ~7 Gyr, consistent with the well measured main-sequence turnoff age. These results provide direct empirical evidence that mass loss is much more efficient in high metallicity environments and therefore may be critical in interpreting the ultraviolet upturn in elliptical galaxies. Comment: 15 pages, 9 figures, 2 tables. Accepted for publication in Astrophys. J. Very minor changes from first version
The evolution of white dwarfs is a cooling process that depends on the energy stored in the core and on the way in which it is transferred through the envelope. In this paper we show that despite some (erroneous) claims, the redistribution of chemical elements ensuing the crystallization of C/O white dwarfs provides between the 10% and the 20% of the total energy released during the crystallization process, depending on the internal chemical composition, which is not negligible at all, given the present state of the art of the white dwarf cooling theory. Comment: 16 pages, 2 figures, accepted for publication in Astrophysical Journal
We present new synthetic models of the TP-AGB evolution. They are computed for 7 values of initial metal content (Z from 0.0001 to 0.03) and for initial masses between 0.5 and 5.0 Msun, thus extending the low- and intermediate-mass tracks of Girardi et al. (2000) until the beginning of the post-AGB phase. The calculations are performed by means of a synthetic code that incorporates many recent improvements, among which we mention: (1) the use of detailed and revised analytical relations to describe the evolution of quiescent luminosity, inter-pulse period, third dredge-up, hot bottom burning, pulse cycle luminosity variations, etc.; (2) the use of variable molecular opacities -- i.e. opacities consistent with the changing photospheric chemical composition -- in the integration of a complete envelope model, instead of the standard choice of scaled-solar opacities; (3) the use of formalisms for the mass-loss rates derived from pulsating dust-driven wind models of C- and O-rich AGB stars; and (4) the switching of pulsation modes between the first overtone and the fundamental one along the evolution, which has consequences in terms of the history of mass loss. It follows that, in addition to the time evolution on the HR diagram, the new models predict in a consistent fashion also variations in surface chemical compositions, pulsation modes and periods, and mass-loss rates. The onset and efficiency of the third dredge-up process are calibrated in order to reproduce basic observables like the carbon star luminosity functions in the Magellanic Clouds, and TP-AGB lifetimes (star counts) in Magellanic Cloud clusters. Forthcoming papers will present the theoretical isochrones and chemical yields derived from these tracks, and additional tests performed with the aid of a complete population synthesis code.
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