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*Astron. Astrophys. 317, 90-98 (1997)*
## 3. Theoretical VLM stellar structures
Selected sequences of metal poor stellar models have been computed
to cover the range of
*H* burning stars below
, assuming Y=0.23 everywhere. In this section we
will discuss some structural evolutionary features of the computed
models which represent a common feature for all VLM structures
independently of the assumed amount of metal and/or the treatment of
stellar atmospheres. According to the calibration of solar models, all
computations assume a mixing length parameter as given by
=2.2. However, numerical experiments confirmed
that below, about, M=0.5 M
varying the assumption on the mixing length
within reasonable limit (1.5
2.5) or varying Y within
Y
0.02 have quite a negligible influence on the
results. All models have been followed from an early pre-main sequence
phase till, at least, an age of 20 Gyr. Selected models have been
followed till the last phases of exhaustion of central
*H*, often for a time much larger than the Hubble time. Of
course, in this way stellar structures that will populate the Universe
only in an extremely far future, have been computed. However, similar
unrealistic models have been used to learn some interesting features
of the VLM evolutionary scenario that we will discuss here in the
following.
**Table 1.** Selected evolutionary quantities (see text) for VLM stellar structures.
As well known, when reaching the range of VLM structures, the
common notion of Zero Age Main Sequence, as given by structures where
secondary elements in
*H* burning already attained their equilibrium values, becomes
more and more meaningless since
behaves as a pseudo primary element, with a
lifetime becoming comparable to the lifetime for central
*H* burning, so that models start depleting
*H* with
still well below its equilibrium value. This is
shown in Table 1 where for selected values of stellar masses the
typical time spent by the structures burning
*H* (
), the age at which the contribution of
gravitational energy vanishes (
), the age of the models attaining
equilibrium (
), the ratio between the amount of
*H* at the center of this model and the initial
*H* abundance, and the abundance by mass of
at the equilibrium, are reported. However, the
same table shows that after 1 Gyr the structures are in all cases
already supported by nuclear burning only, placed on what we can
regard as the initial Main Sequence location. Last column in Table 1
reports the convective structure of these models. As already known,
below about
only fully convective stellar structures, with
a progressive amount of electronic degeneracy which, eventually,
succeeds in inhibiting the release of gravitational heating and the
ignition of central
*H* nuclear burning, are found. Top and bottom panels of Fig. 1
disclose the time behavior of selected structural parameters for two
models with 0.4 and
, respectively. The
model behaves like the well known models with
moderately larger masses populating the upper portion of the cluster
main sequence. The increase of
toward its equilibrium value increases the
efficiency of the burning and the structure reacts decreasing both
central temperature and density, which start increasing again only
when the equilibrium value for
has been attained. However, fully convective
structures behave quite differently, and central density keeps
decreasing all along the major phase of
*H* burning. A similar steady decrease of central density is a
well known feature but not yet discussed of the
*He* burning ignition in the center of more massive stars.
| **Fig. 1.** The variation with time of stellar luminosity (L) in solar unit, contribution of gravitation to the total luminosity (
), central density (
), central temperature (
), size of the convective core (
) as fraction of the total mass, mass location of the bottom of the convective envelope (
), and central abundances by mass of
*H* and
for models with
(top panel) and
(lower panel) with
. |
According to plain mathematical elaborations, one finds that the
curious behavior of VLM fully convective structures is just the one
expected in homological models with increasing molecular weight. As a
matter of the fact, as shown in the same Fig. 1, one finds that the
central density of the
model starts suddenly increasing again in the
very last phases of central
*H* burning, when the increased abundance of
*He* and the corresponding decrease of radiative opacities
induces a radiative shell which rapidly grows to eventually form a
radiative core. Further details on the argument, as well as a detailed
description of VLM evolutionary features, can be found in Ciacio
(1994).
| **Fig. 2.** The evolution with time of the HR diagram location of models with Z=0.0003 for the labeled assumptions on the cluster age. |
Fig. 2 shows the effect of age on the HR diagram distribution of a
typical set of models. Data in this figure are presented as an example
of evolutionary effects, showing that in "not-too-young" VLM stellar
systems, the age plays a negligible role on the HR diagram location of
stars below, about
. Interesting enough, the
model appears the less affected by age, less
massive models shoving a progressively increasing sensitivity to the
adopted ages. The reason for such a behavior is disclosed by Fig. 3,
where the variation with time of the amount of central
for selected choices about the stellar mass,
has been reported. It appears that in the
case, at t=10 Gyr central
has already approached its equilibrium value,
so that the following evolution is governed by the depletion of
central
*H* only. On the contrary, less massive models keep increasing
central
, thus increasing the efficiency of
proton-proton burning and readjusting the structure according to such
an occurrence. A readjustment that in the less massive models is
amplified by the decreasing electronic degeneracy induced by the
decrease of central density.
| **Fig. 3.** The behavior with time of the abundance by mass of central
for the labeled assumptions about the stellar masses and for Z=0.0003 - Y=0.23. |
© European Southern Observatory (ESO) 1997
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