Astron. Astrophys. 331, 1011-1021 (1998)
6. Chemistry, magnetic field, diffusion and overshooting
As anticipated, Z=0.02 is likely to be an upper limit for the solar
metallicity. In Fig. 2 we present our results obtained by varying
the chemical composition of a solar mass star. A relatively large
change in abundance causes small variations in
the final abundance, while a
decrease in the value of Z makes the
abundance to vary by almost two orders of
magnitude. The higher Z track results in a larger depletion, as in
that case we know that opacity is larger and the convective envelope
gets deeper. The assumption might give a value
for the final abundance which is in excellent
agreement with that presently observed. However, we are not claiming
that this solves the problem of the sun, both since Z=0.017 is only a
lower limit for the solar metallicity, and because of the still
unknown effect possibly due to other physical inputs (see later).
![[FIGURE]](img85.gif) |
Fig. 2. Effects of different chemical abundance on solar pre-MS Li depletion. A reduction of Z within values still acceptable leads to a decrease of two orders of magnitude in depletion, and to the observed abundance. Also the results obtained with a diffusive algorithm coupling nuclear burning and turbulent mixing are shown. Li-depletion is decreased by a factor 3; this is to be kept in mind, since diffusion is a more physically sound approximation than instantaneous mixing.
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In this framework, it is interesting to speculate that even small
chemical inhomogeneities in a cloud giving birth to an open cluster
might be responsible of a fraction of the observed
abundances spread detected in young
clusters.
We then discuss the results obtained for the solar model when
including the effect of the magnetic field as discussed in
Sect. 4.4. As already mentioned, the magnetic field forces larger
convective temperature gradients, thus leading to a minor penetration
of the convective envelope and to less
depletion. We therefore expect higher abundances
for higher values of , which is actually what we
observe from Fig. 3. We see that a value of the solar magnetic
field of G might lead to the observed Li
abundance in the Sun with no need of further hypotheses.
![[FIGURE]](img89.gif) |
Fig. 3. Effects of different magnetic fields on solar pre-MS Li depletion. The larger is , the lower is Li depletion. Note that the value of (extra-gradient) for all the tracks shown never reached up .
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This result, although only semi-quantitative as above noted, is to
be taken seriously. At present, the debate about the mechanisms
generating magnetic fields in stellar structures (including fossil
magnetic fields) is still open, and even in the presence of rotating
stellar models it would not be so easy to give sound quantitative
estimates of the internal profiles of B starting from first
principles. Nevertheless, hints about the solar internal constitution
and measurements of surface magnetic fields (and rotation periods) of
pre-MS stars do not exclude at all -not to say suggest- the presence
of internal magnetic fields of magnitude even larger than those
adopted in the present computations. As an example, the track
=20 G would require, at the base of the
convective envelope and at the end of the pre-MS Li-burning phase,
G.
We also tested the diffusive algorithm for coupled Li-burning and
mixing. Although the nuclear lifetimes of lithium at the bottom of
convection turned out relatively long with respect to mixing
times, a profile of was indeed detected inside
the convective region, and this led to a not negligible cumulative
effect at the end of pre-MS burning: Li-depletion turned out to be 3
times less than with instantaneous mixing.
Although this result cannot yet be assumed as definitive, since it
depends on the approximations adopted to model the diffusive
coefficient, it is nevertheless instructive. A "sensible" model for
diffusion, which is already likely to be more physically sound than
instantaneous mixing, does affect pre-MS Li-depletion and has to be
included in all the future computations if absolute, quantitative
results are to be looked for. We recall the reader's attention on the
fact that, like in the case of Li-production in the convective
envelopes of asymptotic giant stars (Sackmann et al. 1974), nuclear
depletion and mixing are to be treated together. Separately
applying nuclear evolution and then diffusive mixing would lead
nowhere.
Overshooting too may influence the amount of lithium which is
burnt: this is because it carries inside deeper
regions, where it is destroyed: models computed with overshooting will
necessarily have smaller residual abundance of Li. D'Antona &
Mazzitelli (1984) found that an overshooting distance
was necessary to fit the Hyades
curve; yet this extra-mixing was not enough to
reproduce the solar observed value. Vandenberg & Poll (1989),
adopting more recent (and larger) opacities (LAOL: Huebner et al.
1977), showed that a lower extra-mixing ( ) was
required to fit the same cluster.
These attempts to increase Li-depletion were justified by the large
values of residual Li-abundances found in low mass stars with solar
metallicity, with the opacities of the epoch and by adopting the MLT
to describe turbulent convection. As we have seen, the problem is now
reversed. And yet overshooting can be present, and we better study
also the effect of this feature on pre-MS Li depletion.
The effect of an overshooting from the base
of the convective envelope in our models can be seen in Table 1
in the model OV01B00. Li-depletion is increased by more than six
orders orders of magnitude; this effect, however, can be more than
completely reset by a magnetic field of G only
(model OV01B30). It seems then reasonable that a balance between
metallicity, magnetic field and overshooting can play a key-role in
determining the real extent of pre-MS depletion
inside the stars.
A possible reasonable metallicity for the solar model might be
(Grevesse & Noels 1993). Together with an
overshooting of , model OV005B15 shows that the
current solar situation may be easily reproduced if we hypothesize
that a magnetic field G was present in the Sun
during the pre-MS phase, and working with diffusive mixing. This is
our present reasonable guess for the pre-MS evolution of the Sun. With
G (model OV005B20), room is left for some MS
depletion associated with slow mixing mechanisms.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998
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