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Lower Main Sequence Stars of Pop I

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Atomic Diffusion in Stars

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

Abstract

In main sequence Pop I stars with effective temperatures smaller than 10,000K, atomic diffusion occurs below a surface convection zone where a simple evaluation first shows that the settling time scale varies by 4 or 5 orders of magnitude over the effective temperature range from 4000 to 10,000K. The mixing length was determined using the Sun and the evolutionary calculations then calculated without adjustable parameters. In stars of around 1.4 solar mass, the iron peak opacity increases at the bottom of the surface convection zone causing its extension. If one neglected radiative accelerations, the reverse occurs so that including the settling of metals and helium without including the effect of radiative accelerations should not be done in such stars. Around 1.5 solar mass, an iron convection zone appears. The expected surface abundance anomalies are compared to observed ones showing the importance of a competing process. The effects of both mass loss and turbulence have been calculated in detail and are described. It is found that both processes have similar effects on surface abundances. The abundance anomalies on AmFm stars can be reasonably well represented by including either process in the calculations. However when it leads to the same surface abundances as turbulence, mass loss leads to different internal concentrations of metals so that asteroseismology may distinguish the two. The Li gap stars are also discussed.

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Notes

  1. 1.

    Except for stars with surface magnetic fields strong enough to stabilize their atmosphere, which were discussed in the preceding chapter (§ 8.3).

  2. 2.

    Using Eqs. (37), (8) and (10) of Michaud et al. (1976).

  3. 3.

    See Fig. 2 of Smith (1996b).

  4. 4.

    The value of α determined by solar properties is different for diffusive and non-diffusive solar models. In their review of age determinations using globular clusters, VandenBerg et al. (1996) emphasized that the giant branch T eff is sensitive to α. This turns out to be important in fitting M 67 color magnitude isochrones (Michaud et al. 2004b).

  5. 5.

    Note that in Bahcall et al. (1995), all metals including CNO diffuse as fully ionized iron and have the same surface abundance variation.

  6. 6.

    See Fig. 12 of Turcotte et al. (1998b).

  7. 7.

    Note that in Fig. 11 of Turcotte et al. (1998b) the curve for carbon is erroneous and does not correspond to the correct g rad(C) which was used in the calculations. It is g rad(12C) + g rad(13C) which was plotted instead of \(g_{\mathrm{rad}}(^{12}\mbox{ C})\). This plotting error is responsible for the largest discrepancy found by Delahaye and Pinsonneault (2005) and Seaton (2007).

  8. 8.

    In the case of Si for instance, shown on Fig. 11 of Seaton (2007), factors of 2 appear in the solar model. This difference can be traced to the effect of redistribution (see § 3.5.2.1) which was included in Turcotte et al. (1998b). The effect of redistribution was not included for the calculations on the grid of Richer et al. (1998) with which Delahaye and Pinsonneault (2005) and Seaton (2007) get better agreement. See also § 2.2 of Michaud and Richer (2008).

  9. 9.

    See Figs. 10 and 11 and § 3.3 of Turcotte et al. (1998a).

  10. 10.

    See the right panel of Fig. 11 of Richard et al. (2001).

  11. 11.

    The turbulent diffusion coefficient used is shown by the solid line in Fig. 2 of Richard et al. (2001). It is smaller than the Fe atomic diffusion coefficient both above and below the Fe convection zone so that it does not influence its evolution.

  12. 12.

    See Fig. 9.3 or the lower right panel of Fig. 3 of Richard et al. (2001).

  13. 13.

    See the solid line on the lower right panel of Fig. 3 of Richard et al. (2001).

  14. 14.

    Compare, at \(\log \Delta M/M_{{\ast}} = -6.2\), the solid line on Fig. 2 of Richard et al. (2001) to the dashed line on Fig. 7 of Théado et al. (2012).

  15. 15.

    See Fig. 8 of Théado et al. (2009).

  16. 16.

    See Figs. 8 and 9 of Richer et al. (2000).

  17. 17.

    See Fig. 8 of Vick et al. (2010).

  18. 18.

    For instance, it does not occur during the part of the 1. 5 M \(_{\odot }\) evolution shown on Fig. 9.3.

  19. 19.

    See the discussion in § 5.3 of Michaud et al. (2011a).

  20. 20.

    From § 5.1.1 of Vick et al. (2010).

  21. 21.

    This equation is not used for the calculations. For more details see Turcotte et al. (1998b).

  22. 22.

    An example is the solution for Fe in the 1. 5 M \(_{\odot }\) model with a mass loss rate of 10−14 M \(_{\odot }\,\mathrm{yr}^{-1}\), as shown in Fig. 5 of Vick et al. (2010).

  23. 23.

    See Fig. 3 of Talon et al. (2006).

  24. 24.

    The need to increase settling time scales below the surface convection zone of Am stars led Schatzman (1969) to develop a diffusion equation to model turbulent transport (see § 7.3.1). In his introduction, he describes the work of Praderie though incorrectly referring to Praderie (1968). He should have referred to the fifth chapter of her thesis (Praderie 1967), which chapter was never published as a paper.

  25. 25.

    See § 3.3 of Praderie (2005).

  26. 26.

    See Fig. 1 of Watson (1970). Details on the calculations, including those of g rad, are found in Watson (1971). Smith (1971) made the same suggestion independently.

  27. 27.

    See Table 1 of Preston (1974).

  28. 28.

    For a more detailed discussion, see § 5.1.1 and 5.3.4 of Vick et al. (2010).

  29. 29.

    See Figs. 2a and 3a of Alecian (1996). An appropriate extension of the bottom of the convection zone is required since to accommodate underabundances of both Ca and Sc it must occur at a well defined temperature.

  30. 30.

    See Fig. 12 of Vick et al. (2010).

  31. 31.

    See Fig. 15 of Richer et al. (2000).

  32. 32.

    See for instance Fig. 2 of Michaud et al. (1976).

  33. 33.

    See Bertin et al. (1995) and the discussion in § 1 of Michaud et al. (2011b).

  34. 34.

    See Turcotte et al. (2000) for an evaluation of the effect of diffusion in evolutionary models for Am stars with a mixed zone. The equivalent for the mass loss case is not currently available.

  35. 35.

    With ω = 300, n = 2 and \(\rho _{0} = 8 \times 10^{-8}\,\mathrm{g\,cm}^{-3}\). This gives a mixed mass \(\sim 10^{-5}\,M_{{\ast}}\) according to Table 1 of Richer et al. (2000).

  36. 36.

    See § 7.1 of Vick et al. (2010).

  37. 37.

    See for instance Lambert (1991).

  38. 38.

    For a brief review, see Smith (1996b).

  39. 39.

    For a review, see Michaud and Charbonneau (1991).

  40. 40.

    See for instance Vauclair (1988), Pinsonneault (1997), Talon and Charbonnel (2010), and Garaud and Bodenheimer (2010).

  41. 41.

    See the end of § 3.2 of Richer and Michaud (1993).

  42. 42.

    For g rad(Li) see § 3.1 of Vick et al. (2010) and Richer et al. (1997).

  43. 43.

    See the discussion around Fig. 3 of Vick et al. (2010).

  44. 44.

    Like, for instance, that of Dziembowski et al. (1994) used here.

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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

Authors
  1. Georges Michaud
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  2. Georges Alecian
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  3. Jacques Richer
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Michaud, G., Alecian, G., Richer, J. (2015). Lower Main Sequence Stars of Pop I. In: Atomic Diffusion in Stars. Astronomy and Astrophysics Library. Springer, Cham. https://doi.org/10.1007/978-3-319-19854-5_9

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