Crystallization of Carbon Oxygen Mixtures in White Dwarf Stars

We determine the phase diagram for dense carbon/ oxygen mixtures in White Dwarf (WD) star interiors using molecular dynamics simulations involving liquid and solid phases. Our phase diagram agrees well with predictions from Ogata et al. and Medin and Cumming and gives lower melting temperatures than Segretain et al. Observations of WD crystallization in the globular cluster NGC 6397 by Winget et al. suggest that the melting temperature of WD cores is close to that for pure carbon. If this is true, our phase diagram implies that the central oxygen abundance in these stars is less than about 60%. This constraint, along with assumptions about convection in stellar evolution models, limits the effective S factor for the $^{12}$C($\alpha,\gamma$)$^{16}$O reaction to S_{300} <= 170 keV barns.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres

Contribution of brown dwarfs and white dwarfs to recent microlensing observations and to the halo mass budget

We examine the recent results of the MACHO collaboration towards the Large Magellanic Cloud (Alcock et al. 1996) in terms of a halo brown dwarf or white dwarf population. The possibility for most of the microlensing events to be due to brown dwarfs is totally excluded by large-scale kinematic properties. The white dwarf scenario is examined in details in the context of the most recent white dwarf cooling theory (Segretain et al. 1994) which includes explicitely the extra source of energy due to carbon-oxygen differentiation at crystallization, and the subsequent Debye cooling. We show that the observational constraints arising from the luminosity function of high-velocity white dwarfs in the solar neighborhood and from the recent HST deep field counts are consistent with a white dwarf contribution to the halo missing mass as large as 50 %, provided i) an IMF strongly peaked around 1.7 Msol and ii) a halo age older than 18 Gyr.Comment: 14 pages, 2 Postscript figures, to be published in Astrophysical Journal Letters, minor revision in tex

Diffusion of Neon in White Dwarf Stars

Sedimentation of the neutron rich isotope $^{22}$Ne may be an important source of gravitational energy during the cooling of white dwarf stars. This depends on the diffusion constant for $^{22}$Ne in strongly coupled plasma mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a mixture does not differ greatly from earlier one component plasma results. For strong coupling (coulomb parameter $\Gamma>$ few), $D_i$ has a modest dependence on the charge $Z_i$ of the ion species, $D_i \propto Z_i^{-2/3}$. However $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller $\Gamma$). We conclude that the self-diffusion constant $D_{\rm Ne}$ for $^{22}$Ne in carbon, oxygen, and neon plasma mixtures is accurately known so that uncertainties in $D_{\rm Ne}$ should be unimportant for simulations of white dwarf cooling.Comment: 6 pages, 5 figures, minor changes, Phys. Rev. E in pres

Reaching the End of the White Dwarf Cooling Sequence in NGC 6791

We present new observations of the white dwarf sequence of the old open cluster NGC 6791. The brighter peak previously observed in the white dwarf luminosity function (WDLF) is now better delineated, and the second, fainter peak that we suggested earlier is now confirmed. A careful study suggests that we have reached the end of the white dwarf sequence. The WDs that create the two peaks in the WDLF show a significant turn to the blue in the color-magnitude diagram. The discrepancy between the age from the WDs and that from the main sequence turnoff remains, and we have an additional puzzle in the second peak in the WDLF. Canonical WD models seem to fail --at least at ~25%-level-- in reproducing the age of clusters of this metallicity. We discuss briefly possible ways of arriving at a theoretical understanding of the WDLF.Comment: 29 pages, 10 figures (4 in low resolution), 1 table. Accepted (2007 December 19) on Ap

Gravitational Settling of ^{22}Ne in Liquid White Dwarf Interiors--Cooling and Seismological Effects

We assess the impact of the trace element ^{22}Ne on the cooling and seismology of a liquid C/O white dwarf (WD). Due to this elements' neutron excess, it sinks towards the interior as the liquid WD cools. The subsequent gravitational energy released slows the cooling of the WD by 0.25--1.6 Gyrs by the time it has completely crystallized, depending on the WD mass and the adopted sedimentation rate. The effects will make massive WDs or those in metal rich clusters (such as NGC 6791) appear younger than their true age. Our diffusion calculations show that the ^{22}Ne mass fraction in the crystallized core actually increases outwards. The stability of this configuration has not yet been determined. In the liquid state, the settled ^{22}Ne enhances the internal buoyancy of the interior and changes the periods of the high radial order g-modes by approximately 1%. Though a small adjustment, this level of change far exceeds the accuracy of the period measurements. A full assessment and comparison of mode frequencies for specific WDs should help constrain the still uncertain ^{22}Ne diffusion coefficient for the liquid interior.Comment: 26 pages (11 text pages with 15 figures); to appear in The Astrophysical Journa

Phase separation in the crust of accreting neutron stars

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.Comment: 8 pages, 6 figures, minor changes, Physical Review E in pres

A white dwarf cooling age of 8 Gyr for NGC 6791 from physical separation processes

NGC 6791 is a well studied open cluster1 that it is so close to us that can be imaged down to very faint luminosities. The main sequence turn-off age (~8 Gyr) and the age derived from the termination of the white dwarf cooling sequence (~6 Gyr) are significantly different. One possible explanation is that as white dwarfs cool, one of the ashes of helium burning, 22Ne, sinks in the deep interior of these stars. At lower temperatures, white dwarfs are expected to crystallise and phase separation of the main constituents of the core of a typical white dwarf, 12C and 16O, is expected to occur. This sequence of events is expected to introduce significant delays in the cooling times, but has not hitherto been proven. Here we report that, as theoretically anticipated, physical separation processes occur in the cores of white dwarfs, solving the age discrepancy for NGC 6791.Comment: 3 pages, 2 figures, published in Natur

Evolution of white dwarf stars with high-metallicity progenitors: the role of 22Ne diffusion

Motivated by the strong discrepancy between the main sequence turn-off age and the white dwarf cooling age in the metal-rich open cluster NGC 6791, we compute a grid of white dwarf evolutionary sequences that incorporates for the first time the energy released by the processes of 22Ne sedimentation and of carbon/oxygen phase separation upon crystallization. The grid covers the mass range from 0.52 to 1.0 Msun, and it is appropriate for the study of white dwarfs in metal-rich clusters. The evolutionary calculations are based on a detailed and self-consistent treatment of the energy released from these two processes, as well as on the employment of realistic carbon/oxygen profiles, of relevance for an accurate evaluation of the energy released by carbon/oxygen phase separation. We find that 22Ne sedimentation strongly delays the cooling rate of white dwarfs stemming from progenitors with high metallicities at moderate luminosities, whilst carbon/oxygen phase separation adds considerable delays at low luminosities. Cooling times are sensitive to possible uncertainties in the actual value of the diffusion coefficient of 22Ne. Changing the diffusion coefficient by a factor of 2, leads to maximum age differences of approx. 8-20% depending on the stellar mass. We find that the magnitude of the delays resulting from chemical changes in the core is consistent with the slow down in the white dwarf cooling rate that is required to solve the age discrepancy in NGC 6791.Comment: 10 pages, 6 figures, to be published in The Astrophysical Journa

Evolutionary calculations of phase separation in crystallizing white dwarf stars

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, 199

The Physics of Crystallization from Globular Cluster White Dwarf Stars in NGC 6397

We explore the physics of crystallization in the deep interiors of white dwarf 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 white dwarf 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 (1968). We outline how this data can be used to observationally constrain the value of Gamma = E_{Coulomb}/E_{thermal} near the onset of crystallization, the central carbon/oxygen abundance, and the importance of phase separation.Comment: 5 pages, 5 figures, accepted for publication in the Astrophysical Journal Letter