Astron. Astrophys. 347, 272-276 (1999)

1. Introduction

The contemporary standard solar model (SSM) appears to be a highly accurate representation of the true solar structure, as is infered from the inversion of solar p -mode frequencies. This is demonstrated, for example, in Bahcall et al. (1998), whose model has a rms deviation from the seismic model of Basu et al. (1996) of only 0.001. This gain in accuracy, as compared to models calculated only a few years ago (e.g. Turck-Chieze et al. 1993) is due to the inclusion of new opacities and equations of state and the consideration of microscopic particle diffusion (see Bahcall et al. 1995 for details of the SSM).

Notwithstanding the success of the SSM - which in particular has helped to identify the reason for the solar neutrino problem to be found in particle physics - there are still significant discrepancies (significant because of the high precision of the p-mode frequency measurements) and the Li-problem. With regard to the first point, all SSM have the largest deviation from the seismic model just below the convective envelope's boundary, which itself is very well reproduced by the models (at ; Basu 1998). The relative deviation in sound speed is as large as 0.003 and therefore at least comparable to the error in the seismic model. This situation is illustrated in Fig. 1, which shows the comparison between our own SSM ("GARSOM4"; Schlattl et al. 1999) and the seismic model of Basu et al. (1996), along with the error range of the seismic model as given by Degl'Innocenti et al. (1997). We note that the model by Christensen-Dalsgaard et al. (1996), which better reproduces the seismic model in the critical region below the convective zone, was calculated using the OPAL92 opacities (Rogers & Iglesias 1992), while ours and that by Bahcall et al. (1998) employ the OPAL96 opacities (Iglesias & Rogers 1996). The latter two SSM use the most recent compilation of nuclear reaction rates (Adelberger et al. 1998), too. The effect that these improvements in the physical input lead to a slight deterioration in the comparison has been discussed already by Brun et al. (1998a) and Turck-Chieze et al. (1998). Nevertheless, this also demonstrates that the good agreeement with the seismic model is not just a fortunate coincidence.

Fig. 1. Comparison of modern solar models with the seismic model by Basu et al. (1996): shown is the relative (seismic-solar model) difference of sound speed for the model of Bahcall et al. (1998) (dashed line), Christensen-Dalsgaard et al. (1996) (dot-dash) and our best model GARSOM4 (solid). The grey area indicates a conservative error range of seismic models according to Degl'Innocenti et al. (1997)

The solar lithium problem manifests itself in the fact that the ⁷Li abundance in the solar atmosphere (and therefore the solar convective envelope) is only about 1/140 of the meteoritic value of  ¹ (Anders & Grevesse 1989), while the SSM predicts a depletion of only a factor 2-3, if the evolution is started on the zero-age main sequence (ZAMS; for a discussion of this subject, see Chaboyer 1998). The situation changes, if pre-main sequence (PMS) evolution is taken into account. Here, a significant depletion can be obtained, depending on the treatment of convection and the particular set of opacities used, because these factors determine to which temperature the convective envelope extends. D'Antona & Mazzitelli (1994) find a PMS depletion of a factor of 10, but with an updated version of their models also complete destruction of ⁷Li during the PMS. They discuss these new results, their sensitivity on physical and stellar parameters (notably metallicity) and possible solutions to this inverse lithium problem of complete destruction in great detail (Ventura et al. 1998). Our own standard solar model, calculated with the PMS included leads to a lithium abundance of 0.107 of the initial one when arriving on the ZAMS, and a further reduction to 0.092 thereafter. Since the lithium abundance in open clusters appears to decline with age (Charbonnel et al. 1994; Chaboyer 1998), with young clusters such as the Hyades at  Gyr showing a depletion of only a factor of two, this amount of PMS-depletion might potentially be in contradiction with observed lithium abundances in young open clusters, if one ignores all differences between the cluster compositions and assumes that the derived cluster age-lithium relation is the same as that for the Sun (but see Jones et al. 1999). In any case, our SSM including PMS-evolution and diffusion does not reproduce the present solar lithium abundance.

Since the solution to the Li-problem lies in an additional mixing from the bottom of the convective layer to those hot enough to burn ⁷Li at K and this is exactly the region of highest deviation of the SSM from the seismic model, it is reasonable to try to solve both problems at the same time. Richard et al. (1996) have, rather successfully, done so by introducing additional diffusive mixing due to differential rotation in their solar model. This solution, of course, contains free parameters, and an approximative treatment of the poorly known effects of rotation on mixing inside a star.

Recently, a different attempt to solve the Li-problem has been reconsidered with a new approach. Motivated by the results of 2d-hydrodynamical simulations of the (thin) convective envelopes of A-stars, Blöcker et al. (1998) introduced a parametrized treatment of overshooting from the convective envelope to reach ⁷Li-burning temperatures. However, their model did not comply with the definition of the SSM. In particular, it did not contain particle diffusion. In addition, the influence of the additional mixing process on the solar structure was not discussed and a comparison with a seismic model or with measured p-mode frequencies was lacking. Stimulated by a preliminary result by Richard and Charbonnel (Richard 1999 and Charbonnel, private communication) that the agreement with the seismic model worsens for the overshooting case, we decided to perform a study about the effect of the new overshooting approach, which complies with the standard ways of comparisons for any model of the Sun. In the next section, we will briefly introduce the diffusion approach and its implementation in our solar model code, and summarize the results of Blöcker et al. (1998). In Sect. 3 we will present our own results including the comparison with the seismic model (Basu et al. 1996). A short summary will close the paper.

© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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