We explore the physics of crystallization in the dense Coulomb plasma of the deep interiors of white dwarf stars using the color-magnitude diagram and luminosity function constructed from Hubble Space Telescope photometry of the globular cluster M 4 and compare it with our results for proper motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397. We demonstrate that the data are consistent with a binary mixture of carbon and oxygen crystallizing at a value of Gamma higher than the theoretical value for a One Component Plasma (OCP). We show that this result is in line with the latest Molecular Dynamics simulations for binary mixtures of C/O. We discuss implications for future work.Astronom

Bergeron, P.

Campos, F.

Kepler, S. O.

Montgomery, M. H.

Winget, D. E.

English

Winget, Donald Earl

Montgomery, Michael Houston

Kepler, Souza Oliveira

Campos, Fabíola

Bergeron, Pierre

Universidade Federal do Rio Grande do Sul

White dwarfs in NGC6397 and M4 : constraints on the physics of crystallization

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White Dwarfs in NGC6397 and M4: Constraints on the Physics ofCrystallizationD. E. Winget, M. H. Montgomery, S. O. Kepler, F. Campos, and P. Bergeron  Citation: AIP Conference Proceedings 1273, 146 (2010); doi: 10.1063/1.3527792 View online: http://dx.doi.org/10.1063/1.3527792 View Table of Contents:http://scitation.aip.org/content/aip/proceeding/aipcp/1273?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Photometric Variability and Rotation in Magnetic White Dwarfs AIP Conf. Proc. 1273, 91 (2010); 10.1063/1.3527897  White Dwarf Pulsations in the Cataclysmic Variables SDSS J0919+08 and VSX J0747+0650 AIP Conf. Proc. 1273, 526 (2010); 10.1063/1.3527880  A Census of White Dwarfs Within 40 Parsecs of the Sun AIP Conf. Proc. 1273, 193 (2010); 10.1063/1.3527801  The White Dwarf Age of NGC 2477 AIP Conf. Proc. 1273, 135 (2010); 10.1063/1.3527789  The atmospheric parameters of nearby white dwarfs revisited AIP Conf. Proc. 1273, 101 (2010); 10.1063/1.3527781   This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34White Dwarfs in NGC6397 and M4: Constraintson the Physics of CrystallizationD.E. Winget∗, M.H. Montgomery∗, S.O. Kepler†, F. Campos†andP. Bergeron∗∗∗Department of Astronomy, McDonald Observatory and the Texas Cosmology Center, University ofTexas at Austin, Austin, TX, USA†Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS - Brasil∗∗Département de Physique, Université de Montréal, C. P. 6128, Succ. Centre-Ville, Montréal,Québec H3C 3J7, CanadaAbstract. We explore the physics of crystallization in the dense Coulomb plasma of the deep inte-riors of white dwarf stars using the color-magnitude diagram and luminosity function constructedfrom Hubble Space Telescope photometry of the globular cluster M 4 and compare it with our resultsfor proper motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397.We demonstrate that the data are consistent with a binary mixture of carbon and oxygen crystalliz-ing at a value of Γ higher than the theoretical value for a One Component Plasma (OCP). We showthat this result is in line with the latest Molecular Dynamics simulations for binary mixtures of C/O.We discuss implications for future work.Keywords: white dwarfs, astrophysical plasma, stellar evolutionPACS: 97.20.Rp, 95.30.Qd, 97.10.CvASTROPHYSICAL CONTEXTIn [9] we showed that the HST observations of the globular cluster NGC 6397 could beused to constrain the physics of crystallization in a dense Coulomb plasma. In particular,we suggested that either there was very little oxygen in the interiors of globular clusterwhite dwarf stars, or the binary mixture of carbon and oxygen must crystallize at amuch higher value of Γ than that for a one component plasma (OCP). This work createdrenewed interest in the crystallization of a binary mixture of carbon and oxygen; severalgroups have since investigated this question and published their ﬁndings, these includeMedin & Cumming (2010) [4], Horowitz, Schneider & Berry (2010) [3], and H. DeWittand collaborators (2010) [2].The melting curve from Figure 2 in Horowitz, Schneider & Berry (2010) [3] is shown,with permission, in our Figure 1. The key result from this work and that of Medin &Cumming (2010) [4] is that for oxygen mass fractions less than about 60%, the meltingtemperature is very close to that for pure carbon. This has profound consequences forour understanding of the interiors of globular cluster white dwarfs. In this paper weuse this melting curve to recalculate the theoretical luminosity function for NGC 6397using models with equal mass fractions of carbon and oxygen using the constraints andtechniques described in [9] to compare with the observed luminosity function fromHST data using a proper motion cleaned sample obtained by Richer et al. (2008) [6].We perform a similar calculation of the theoretical luminosity function for the globular146 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34FIGURE 1. Theoretical phase diagram taken from Figure 2 of Horowitz, Schneider & Berry (2010)[3], with permission. The plot shows the excellent agreement between the results of [4], the solid blacklines, and the ﬁlled red circles of the molecular dynamics simulations of [3]. The liquid and solid phaseare shown as two separate lines. The additional calculations shown are density functional calculations ofSegretain (1996) [7], the dot-dashed green lines, and Ogata et al. (1993) [5], the dotted blue line; the dotdashed grey lines represent the value of Γ = 178 connecting the pure carbon point with pure oxygen.cluster M4 and compare with the HST observations of Bedin et al. (2009) [1].NGC 6397 REVISITED WITH THE NEW MELTING CURVEWe used the same theoretical colors from model atmosphere grid computed by one of us(PB) and the same values of distance and reddening as our earlier work [9]. These lastare obtained by ﬁtting the main sequence and the white dwarf cooling sequence sim-ulataneously; this serves to anchor the cooling tracks in the observed color-magnitudediagram, thereby constraining the white dwarf masses. In Figure 2 we plot the observedluminosity function in the F814W ﬁlter against a set of theoretical models. All modelsare computed with 50/50 carbon and oxygen and include phase separation. The modelslabeled PSSC use the old Segretain and Chabrier [8] phase diagram, and the modelslabeled PSHB use the new [3] phase diagram. This veriﬁes the conclusions of [3] andillustrates that evolutionary models computed with the new phase diagram, computed147 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34FIGURE 2. Theoretical Luminosity Functions plotted with the observed Luminosity Function forNGC 6397.for a binary (50/50) mixture of carbon and oxygen using new molecular dynamics cal-culations, provide a comparable ﬁt to that obtained with the old pure carbon models.We stand to gain considerable conﬁdence in these new phase diagram results if we canuse them successfully for another cluster. In the next section we examine this question.A COLOR-MAGNITUDE DIAGRAM FOR M4In ﬁgure 3 we see the color magnitude diagram for the white dwarf stars created fromthe HST observations of M4 by Bedin et al. (2009). We obtained reddening and distanceparameters to place the models in the color-magnitude plane by again simulatneouslyﬁtting both the main sequence and the white dwarf cooling sequence as in [9]. i Notethat presence of a blue hook, presumably the result of low temperature opacity effectsfrom collisionally induced absorption, necessitates the division of the color-magnitudediagram into color regions as shown in the ﬁgure in red and blue boxes. The inclusion ofthe stars in red boxes in the luminosity function results in a piling-up of stars that is onlyan artifact of the blue hook on the left-hand side and possible DB stars on the right-handside. We also note that M4 may be less well characterized by a single mass through theregion of the luminosity function maximum than was the case for NGC 6397.148 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34FIGURE 3. We plot the observed color-magnitude diagram for M4. The results of summing the stars ineach of the quarter-magnitude bins are shown as a number printed inside each shaded rectangle.APPLICATION OF THE NEW MELTING CURVES TO M4We construct the luminosity function for the white dwarfs in M4 by plotting the numbersin each of the central, blue-shaded, boxes shown in ﬁgure 3 as a function of magnitude.We then apply the same tools and techniques to construct the theoretical luminostityfunctions to compare with M4. Although the same model atmospheres were used, thereis a difference in the ﬁlters used on HST for the observations as noted in the axes. Inﬁgure 4 we present the results of the theoretical luminosity functions with the old andnew phase diagrams to the observed luminosity function constructed as described above.Our results are very consistent with those for NGC 6397 as the ﬁgure clearly shows.Although we have only plotted the lower mass models in the ﬁgure for the M4 cluster,We do note that these models are likely the best-ﬁtting mass for both clusters.CONCLUSIONS AND DISCUSSIONWe ﬁnd that our results from ﬁtting the observed luminsity functions in the globular clus-ters NGC 6397 and M4 with models constructed using the phase diagram of Horowitz,Schneider, and Berry (2010) [3] allow us to draw two important conclusions. First, and149 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34FIGURE 4. Theorecital Luminosity Functions plotted with the observed Luminosity Function for M4.perhaps least surprising, the internal composition of the white dwarf stars in globularclusters are consistent with the conclusions of asteroseismology for the internal abun-cances of disk white dwarfs: roughly equal parts carbon and oxygen in the core. Thisis not surprising as there was no a priori reason to suspect that the metallicity of thestar on the main sequence would affect the results of helium burning in the core. Sec-ond, the ratio of the Coulomb to the thermal energy of the ions at crystallization in adense Coulomb plasma is substantially higher for a binary C/O mixture than for a onecomponent plasma (OCP).What might be less obvious, is that the two conclusions above may be strongly linked.The deep interior is not a pure binary mixture, but contains trace elements in proportionto the parent metallicity, as well as those resulting from by-products of helium burning.Does this alter the Γ of crystallization relative to a pure binary mixture? The effect maybe signiﬁcantly enhanced near the centers by the settling of heavier elements in thecore–this is more fully described by Garcia-Berro et al. in a paper in these proceedings.As they point out, this releases additional graviational energy, slowing cooling. Thisraises an interesting question. Does increasing the fractional abundance in the core ofelements heavier than carbon and oxygen, beyond trace levels associated with the parentmetallicity, have the potential to further affect the value of Γ at crystallization? Thisremains to be investigated.150 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34ACKNOWLEDGMENTSThis work was supported by the National Science Foundation under grant AST-0909107,by the Norman Hackerman Advanced Research Program under grants 003658-0255-2007 and 003658-0252-2009, by the Delaware Asteroseismic Research Center, CNPq-Brazil, and NSERC Canada.REFERENCES1. L. R. Bedin, M. Salaris, G. Piotto, J. Anderson, I. R. King, and S. Cassisi, Astrophys. J. 697, 965(2009).2. H. DeWitt, private communication (2010).3. C. J. Horowitz, A. S. Schneider, and D. K. Berry, Phys. Rev. Letters 104, 231101 (2010).4. Z. Medin and A. Cumming, Phys. Rev. E 81, 036107 (2010).5. S. Ogata, H. Iyetomi, S. Ichimaru, and H. M. Van Horn, Phys. Rev. E 48, 016411 (2009).6. H. B. Richer, et al. A.J. 135, 2141 (2008).7. S. Segretain, Astron. Astrophys. 310, 485 (1996).8. L. Segretain, and G. Chabrier, Astron. Astrophys. 271, L13 (1993).9. D. E. Winget, S. O. Kepler, F. Campos, M. H. Montgomery, L. Girardi, P. Bergeron, and K. Williams,Astrophys. J. 693, L6 (2009).151 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.Downloaded to  IP:  128.83.205.78 On: Mon, 09 Mar 2015 20:54:34

White Dwarfs In Ngc6397 And M4: Constraints On The Physics Of Crystallization

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White Dwarfs In Ngc6397 And M4: Constraints On The Physics Of Crystallization

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Universidade Federal do Rio Grande do Sul

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