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Population II Dwarfs

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Atomic Diffusion in Stars

Part of the book series: Astronomy and Astrophysics Library ((AAL))

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Abstract

Population II stellar evolution models have now been calculated for various metallicities. They are compared to observations of globular clusters and of field Pop II stars. Atomic diffusion affects the surface composition through separation occurring below the surface convection zone. It requires that the surface lithium abundance must have been reduced from the cosmological one. In the lowest metallicity clusters, in the absence of a process competing with diffusion, one would expect overabundances of metals and in particular of iron. Comparison to observed surface abundances suggests that turbulence is involved in modifying the efficiency of atomic diffusion. Models calculated with mass loss are less compatible with observations than those with turbulence. The age of globular clusters is reduced by about 2 Gyr which makes it compatible with recent determinations of the age of the universe.

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Notes

  1. 1.

    See § III d) of Michaud et al. (1984a).

  2. 2.

    Vauclair (1988) or, as parametrized in the Yale models, Pinsonneault et al. (1999).

  3. 3.

    See Fig. 2 of Richard et al. (2002a).

  4. 4.

    See Fig. 2 of Richard et al. (2002a) which shows isochrones of M bcz.

  5. 5.

    See Fig. 1 of Richard et al. (2002a).

  6. 6.

    See Fig. 1 of Richer et al. (1998) and Chap. 9

  7. 7.

    Thermal diffusion adds a downward contribution to the diffusion velocity. It is significant and included in the calculations. It does not change qualitatively the discussion in this case.

  8. 8.

    See Figs. 5 and 11 of Richard et al. (2002a).

  9. 9.

    See Figs. 10 and 13 of Richard et al. (2002b).

  10. 10.

    See Fig. 8 of Korn et al. (2007).

  11. 11.

    See Lind et al. (2008) and Lind et al. (2009). There is however an uncertainty coming from the T eff scale, see González Hernández et al. (2009).

  12. 12.

    ​​ cite]Oapenheimer@Önehag et al. (2014) Önehag et al. (2014); see also Michaud et al. (2004b) for calculations of expected anomalies in this cluster.

  13. 13.

    See Fig. 15 of Sbordone et al. (2010).

  14. 14.

    See Casagrande et al. (2010) and Sbordone et al. (2010). The results of 3D−NLTE simulations confirm the 1D−LTE Li abundance determinations in low metallicity Pop II stars (Asplund et al. 2003) though changes to collision rates used in NLTE calculations might slightly lower the measured Li abundance value (Barklem et al. 2003).

  15. 15.

    By VandenBerg et al. (2010) who note in the last paragraph of their paper that there is a variation in ages of galactic clusters from 11 to 13.5 Gyr as their [Fe/H] varies from − 0. 8(47Tuc) to − 2. 4(M92). This probably implies a similar age difference for field stars of different metallicities. It could impact on the different behavior apparently observed by Sbordone et al. (2010) for very low metallicity field stars.

  16. 16.

    See Fig. 15 of Richard et al. (2002a) for the results of a different draw in which Z was also allowed to vary.

  17. 17.

    It has been argued (Salaris and Weiss 2001) that a larger sample of stars is needed to firmly establish this conclusion.

  18. 18.

    The simulated abundances are perhaps more constant than required by observations, so turbulence could be a little smaller.

  19. 19.

    See the discussion of Fig. 3 in Richard et al. (2005).

  20. 20.

    See the end of §3 of Richard et al. (2005).

  21. 21.

    The Li curve on Fig. 9 of Mucciarelli et al. (2011) is nearly identical to the 6.25 curve of Fig. 7 of Richard et al. (2005).

  22. 22.

    The D T of the T6.25 model at ρ = 0. 5 is nearly the same during evolution of the \(0.77\,M_{\odot }\) model as the value at the same ρ in the Sun that best fits the Sun and this up to the current solar age, as seen in Fig. 2 of Richard et al. (2005).

  23. 23.

    That is \(\left \vert E_{\mu }\right \vert = \left \vert E_{\Omega }\right \vert \) in the notation of Eq. (7.32).

  24. 24.

    This age reduction is more than a factor of 2 smaller than had been obtained by Noerdlinger and Arigo (1980) (see Sect. 10.2) because these authors used diffusion coefficients (Noerdlinger 1978) which are larger than the best current estimate (see Chap. 4).

  25. 25.

    See also Salaris et al. (2000) and Weiss (2002).

  26. 26.

    As may be seen from Fig. 3 of VandenBerg et al. (2002).

  27. 27.

    See VandenBerg et al. (2012); note the comparison of diffusion treatments in their § 3.

  28. 28.

    As noted at the end of § 3 of VandenBerg et al. (2012), the use of opacity tables instead of opacities consistent with local abundances of metals and specially CNO , modifies the opacity profile in stellar interiors. This is partly compensated by modifying the mixing length using a comparison of models calculated with opacity tables to those calculated as in Richard et al. (2002b) and Michaud et al. (2004b).

  29. 29.

    More precisely 13.77 ± 0.06 Gyr using WMAP (Bennett et al. 2013) and 13.82 ± 0.06 Gyr using Planck (Ade et al. 2014).

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Authors and Affiliations

  1. Département de physique, Université de Montréal, Montréal, Québec, Canada

    Georges Michaud

  2. Laboratoire Univers et Théorie, CNRS-Observatoire de Paris, Meudon, France

    Georges Alecian & Jacques Richer

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  1. Georges Michaud
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Michaud, G., Alecian, G., Richer, J. (2015). Population II Dwarfs. In: Atomic Diffusion in Stars. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-319-19854-5_10

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