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*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.
The solar lithium problem manifests itself in the fact that the
^{7}Li 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 ^{7}Li 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
^{7}Li 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
^{7}Li-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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