Issue |
A&A
Volume 519, September 2010
|
|
---|---|---|
Article Number | A101 | |
Number of page(s) | 9 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/200811026 | |
Published online | 17 September 2010 |
Rotation and lithium abundance of solar-analog stars
Theoretical analysis of observations
J. D. do Nascimento Jr - J. S. da Costa - J. R. De Medeiros
Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil
Received 24 September 2008 / Accepted 27 May 2010
Abstract
Context. Rotational velocity, lithium abundance, and the
mass depth of the outer convective zone are key parameters in the study
of the processes at work in the stellar interior, in particular when
examining the poorly understood processes operating in the interior of
solar-analog stars.
Aims. We investigate whether the large dispersion in the
observed lithium abundances of solar-analog stars can be explained by
the depth behavior of the outer convective zone masses, within the
framework of the standard convection model based on the local
mixing-length theory. We also analyze the link between rotation and
lithium abundance in solar-analog stars.
Methods. We computed a new extensive grid of stellar
evolutionary models, applicable to solar-analog stars, for a finely
discretized set of mass and metallicity. From these models, the stellar
mass, age, and mass depth of the outer convective zone were estimated
for 117 solar-analog stars, using Teff and [Fe/H] available in the
literature, and the new HIPPARCOS trigonometric parallax measurements.
Results. We determine the age and mass of the outer convective
zone for a bona fide sample of 117 solar-analog stars. No significant
one-to-one correlation is found between the computed convection zone
mass and published lithium abundance, indicating that the large
dispersion
in solar analogs cannot be explained by the classical framework of
envelope convective mixing coupled with lithium depletion at the bottom
of the convection zone.
Conclusions. These results illustrate the need for an
extra-mixing process to explain lithium behavior in solar-analog stars,
such as, shear mixing caused by differential rotation. To derive a more
realistic definition of solar-analog stars, as well as solar-twin
stars, it seems important to consider the inner physical properties of
stars, such as convection, hence rotation and magnetic properties.
Key words: Hertzsprung-Russell and C-M diagrams - stars: rotation - stars: abundances - stars: fundamental parameters
1 Introduction
The evolutionary behavior of lithium abundance and rotation, and the
convective properties of stars depend strongly on stellar mass. The
genesis of this dependence is of obvious interest in stellar
astrophysics, in particular for the study of solar-analog stars, but
very little is known about this subject. For the convective properties,
perhaps the foremost difficulty lies in the criteria used to the define
solar-analog or solar twin, stars that are spectroscopically and
photometrically identical to the Sun (Cayrel de Strobel 1996). Different studies have suggested that the Sun could be: (i) an abnormally slow rotator; and (ii) lithium-poor
by a factor of 10 (Lambert & Reddy 2004) relative to similar solar-type disk stars, which raises the question of whether
there is anything unusual about the solar rotation rate and Li abundance? King (2005), Takeda et al. (2007), Meléndez and Ramirez (2007) demostrated that, at least in terms of its lithium content, the Sun is a normal star at its present evolutionary stage.
In spite of dozens of stars having been classified as solar-analogs (e.g: Takeda et al. 2007), only three solar twins are known:
18 Sco (Porto de Mello & da Silva 1997), HD 98618 (Meléndez et al. 2006), and HIP 100963 (Takeda et al. 2007),
all of witch have a Li abundance higher than the solar value by a
factor of beetwen 3 and 6. For instance, spectroscopic analysis of
the solar twin 18 Sco by Porto de Mello and Da Silva (1997) demostrated that the atmospheric parameters, chromospheric activity, and UBV
colors of this object are indistinguishable from solar values, but that
the system has an excess of Sc, V, and heavier elements. In addition,
Meléndez and Ramirez (2007)
presented data for two solar twins of low Li abundance
(HIP 56948 and HIP 73815), pointing to a factor of about 200
in Li depletion relative to that found in meteorites. This finding
clearly contradicts some standard model predictions (models without
rotation at any depth with the hypothesis that stellar convective
regions are instantly mixed and that no chemical transport occurs in
the radiative regions) and represents a long-standing puzzle in stellar
astrophysics. Pasquini et al. (2008)
showed that five bona-fide main-sequence stars of the open cluster
M 67 are potential solar-twins. These stars have low Li content,
comparable to the photospheric solar value, probably indicating similar
mixing evolution. In addition, these authors confirmed the presence of
a large Li spread among the solar-type stars of M 67, showing for
the first time that extra Li depletion appears only in stars cooler
than 6000 K. This behavior indicates that these stars very likely
experience a depletion in their Li during the main sequence (MS)
stage, although their convective zones do not reach sufficiently deep
into the stellar interior to meet the zone of Li destruction. The
scatter in Li abundance in the solar cluster M 67 by a factor of 10 around the solar-age (Spite et al. 1987;
García López et al. 1988)
is a solid example of the disagreement between observations and the
theoretical predictions of standard models, implying that depletion
must be affected by an additional parameter besides mass, age, and
chemical composition (Pasquini et al. 1997; Jones et al. 1999; Randich et al. 2006).
In the present work, we investigate the influence of mass,
,
age, and
mass depth of the outer convective zone on the behavior of Li abundance
and rotational velocity in solar-analog stars and twins. A close examination of some stellar parameters
(stellar mass and convection-zone mass deepening) may shed new
light on the lithium behavior in this family of stars.
We redetermine the evolutionary status and individual masses for a sample of 117 solar-analogs, using HIPPARCOS parallaxes and by comparing the observational Hertzsprung-Russell diagram with evolutionary tracks, following the procedure described in Sect. 2. As in do Nascimento et al. (2009), we show that it is possible to precisely determine the mass and age of solar analogs and twins using evolutionary models calibrated to reproduce solar luminosity, radius, and Li depletion. The characteristics of the working sample are also described in Sect. 2. In Sect. 3, the main lithium and rotation features are presented, with an analysis of the influence of mass and convection zone depth on these parameters. Finally, the main conclusions are outlined in Sect. 4.
2 Stellar evolutionary models and working sample
In the next sections, we discuss about the stellar evolutionary models ingredients and the characteristics of the observational data used in this study.
2.1 Stellar evolutionary models
For the purposes of the present study, evolutionary tracks were
computed with the Toulouse-Geneva stellar evolution code TGEC
(Hui-Bon-Hoa 2007). Details about the underlying physics of these models can be found in Richard et al. (1996), do Nascimento et al. (2000),
Hui-Bon-Hoa (2007), and do Nascimento et al. (2009). Here, we provide a short description of the main physical stellar model ingredients.
Input physics
We used the OPAL2001 equation of state by Rogers and Nayfonov (2002) and the radiative opacities by Iglesias & Rogers
(1996), in addition to the low temperature atomic and molecular opacities by Alexander & Ferguson (1994). The nuclear
reactions are from the analytical formulae of the NACRE (Angulo et al. 1999) compilation, taking into account the three pp
chains and the CNO tricycle, with the Bahcall & Pinsonneault (1992) screening routine. Convection is treated according to the Böhm-Vitense (1958) formalism of the mixing-length theory with
.
For the atmosphere, we used a grey atmosphere following the Eddington
relation. The abundance variations of the following chemical species
were individually computed in the stellar evolution code: H, He, C, N,
O, Ne, and Mg. The heavier elements were gathered in Z.
The initial composition followed the Grevesse and Noels (1993) mixture, with initial helium abundance
.
All models
included gravitational settling with diffusion coefficients computed as in Paquette et al. (1986). Radiative accelerations were not computed here, as we only focus on solar-type stars whose effects are negligible.
Our model grid includes 17 mass tracks spanning the mass range from 0.70 to 1.1
for four different metallicities,
([Fe/H] = 0.15, 0.0, -0.20 and -0.40). The evolution was
followed from the zero-age main sequence (ZAMS) to the end of hydrogen
exhaustion in the core. Evolution calculations were computed with a
short step to match the effective solar temperature observed and
luminosity at the solar age. The model calibration method was based on
Richard et al. (1996), as follows: for a 1.00
star, we calibrated the mixing-length parameter (
)
and initial helium abundance (
)
to match the observed solar luminosity and radius at solar age. The
observed values that we used were those obtained by Richard et al.
(2004):
erg s-1,
cm and
Gyr. For our best solar model, we obtained
erg s-1 and
cm at age = 4.57 Gyr. The input parameters for the other masses were the same as those of the 1.00
model. To verify model deviations
in the mass determination, we compared the evolutionary tracks
computed of this study with those used by Takeda et al. (2007)
(evolutionary tracks from Girardi et al. 2000). Both evolutionary tracks are of solar metallicity, with stellar masses by Takeda et al. (2007) covering only three values, namely 0.9, 1.0, and 1.1
.
2.2 Working sample
Our analysis is based on the observational data obtained by Takeda et al. (2007) for a sample of 117 field solar-analog stars selected
from the HIPPARCOS catalog (ESA 1997), according to the criteria V < 8.5,
and
.
These authors determined lithium abundance from the resonance Li I
6707.8 Å doublet, with associated errors around 0.1 dex,
(caused by uncertainties in atmospheric parameters). Rotational
velocities were obtained from Nordström et al. (2004) and Holmberg et al. (2007), with
typical errors of about 1 km s-1.
The reader is referred to these papers for observational procedures,
data reduction, and error analysis. We also re-examined the kinematic
properties of each star based on the proper motion data taken from the
HIPPARCOS catalog and radial velocity measurements, confirming the
result found by Takeda et al. (2007) that all 117 field solar-analog stars selected belong to the normal
thin-disk population.
Following the procedure of do Nascimento et al. (2000), we used the new HIPPARCOS trigonometric parallax measurements to
precisely locate the objects in the HR diagram. Intrinsic absolute magnitudes
were derived from the parallaxes, the V magnitudes also being taken from HIPPARCOS. Stellar luminosity and the associated error were computed from the
error in the parallax.
The uncertainties in luminosity,
0.1, have an effect of
0.03 in the determination of the masses. Figure 1
shows the HR diagram with the evolutionary tracks computed for
four different metallicity values ([Fe/H] = 0.15, 0.0, -0.20, and
-0.40), which encompasses most of the stars contained in the present
working sample.
![]() |
Figure 1:
The distribution of the analog sample stars in the
Hertzsprung-Russell diagram. Luminosities and related errors have
been derived from the Hipparcos parallaxes. The typical error in
|
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Table 1 shows a comparison between the theoretical luminosities, effective temperatures, and ages of the Toulouse-Geneve evolution code (TGEC) and Girardi et al. (2000) to examine the difference around the observed effective solar temperature and luminosity. Our values for age, luminosity, and effective temperature are in close agreement with both those of Richard et al. (1996) and helioseismological predictions. Some discrepancies were found between our values and those of Girardi et al. (2000).
Table 1: Comparison between effective temperature and luminosity at the solar age from the Toulouse-Geneve evolution code TGEC and Girardi et al. (2000).
2.3 Mass, age, and convective mass determination
We computed a careful star-by-star model for each star in our sample, with metallicity that matching that observed for
each solar analog. The errors in
,
luminosity, and [Fe/H] correspond to a mean error of 0.05
in
the mass. As a consistency check, a comparison between our mass
determination and those obtained by Takeda et al. (2007) is shown in Fig. 2. Except for some minor discrepancies for stars with masses lower than 0.8
bacause of a lack of models used by Takeda et al. (2007),
there is generally close agreement between the two sets of masses.
Stellar ages were inferred simultaneously with the masses, from the
evolutionary tracks. The error in these ages, due to the uncertainties
in
,
luminosity, and [Fe/H], is about 15% and depends strongly on parallax
uncertainties. Stars located close to the ZAMS have much larger errors.
A comparison with age values computed by Holmberg et al. (2007) and
Takeda et al. (2007), again finds no significant differences. Figure 3
shows the convective zone mass deepening as a function of the
decreasing effective temperature for 0.875, 0.900, 0.925, 0.950, 0.975,
1.00, 1.025, 1.050, 1.075, and 1.100
,
where only the solar metallicity models are considered. In this figure, solid circles represent the convection
mass zone,
,
for the stars of the present sample of solar-analogs, determined in the
scope of this study, where we have taken into
consideration the metallicity of each star. Solar-analog stars
typically, exhibit outer convective zone masses of around 0.02
(see
values in Table 2). A close look at Fig. 3
also indicates that the onset of convection zone deepening (in mass) is
a strong function of stellar mass at the end of the pre-main-sequence
phase. The depth of the outer convective zone in main-sequence stars
depends primarily on mass. Deepening of the outer convective zone is
also sensitive to metallicity. Quantitatively, a reduction in the
initial metallicity
from 0.0 to -0.4 should lead to a decrease in the outer convective zone
from 0.022 to 0.004 at the Sun's age. Lithium data can be used to
constrain the mass and metallicity-dependent process of the outer
convective zone.
![]() |
Figure 2: Comparison between the mass determinations of this study, determined with the Toulouse-Geneva tracks and those computed by Takeda et al. (2007). |
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Table 2: Parameters of the working sample.
![]() |
Figure 3: Convective zone mass
deepening as a function of decreasing effective temperature. Models for
[Fe/H] = 0 and 0.875, 0.900, 0.925, 0.950, 0.975, 1.00,
1.025, 1.050, 1.075, and 1.100
|
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Lithium depletion in solar-twins caused by non-standard mixing is strongly mass-dependent (do Nascimento et al. 2009). A detailed comparison of the mass determinations of Takeda et al. (2007) and Nordström et al. (2004) reveals some discrepancies, such as HIP 45325. The masses obtained by Takeda et al. (2007) are systematically higher than the values obtained by Nordström et al. (2004). These discrepancies may be related to the completeness of the set of evolutionary models used by both authors. We recalculated as precisely as possible the mass of all sample stars. In this study, we used a set of homogeneous evolutionary tracks for main-sequence stars, computed for several masses and metal abundances, as discussed in Sect. 2.2. Mass determination was evaluated taking into account the metallicity effects, using the [Fe/H] values published by Takeda et al. (2007).
3 Results and discussion
We now discuss the relashionsip between the lithium abundance of solar-analog stars and their position in the HR diagram, verifying in particular the influence of the mass and outer convective zone depth on the letter. We consider in addition the rotational behavior of these stars. In addition, we show the important role of inner stellar properties in defining solar-analog stars and twins.
3.1 Main lithium features
Figure 4 shows the distribution of Li abundance for
solar-analog stars in the HR diagram, with stars grouped into four different metallicity intervals, namely [Fe/H] 0.075, -0.075
[Fe/H] < 0.075, -0.3
[Fe/H] < -0.075, and [Fe/H] < -0.3. The evolutionary tracks shown
are those computed in the scope of the present work. A number of features can be observed in this figure:
(i) Stars with masses <0.82
tend to have the lowest lithium content, most likely indicating that the
same depletion level occurred in both the pre-main sequence and the early main sequence;
(ii) stars with masses between 0.82 and 1.1
have
a large
scatter in their lithium content, possibly reflecting the different
levels of lithium depletion. This star-to-star scatter in Li abundance
was also observed in some solar-like field stars (Soderblom et al.
1993; Jones et al. 1999) and in members of the solar-age cluster M 67 (Pasquini et al. 2008).
![]() |
Figure 4: Distribution of Li abundances in the HR diagram. The different symbols represent Li abundances. Filled inverse triangles represent the upper limits Li to the abundances. Evolutionary tracks, as in Fig. 1. |
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The lithium scatter observed for solar-analogs indicates, in part, that
these stars have also had different convection histories, which depend
strongly on stellar mass,
,
metallicity, and age. The classical interpretation is that Li has been
destroyed in the stellar interior by proton-proton reactions at the
bottom of the outer convection, i.e., at
K.
Since the depth of the convection zone
depends primarily on stellar mass, a correlation between Li abundance
and mass is then expected for a given metallicity. This is observed in
Figs. 5 and 6, which show the distribution of lithium abundance as a function of stellar mass and
convection zone mass deepening
,
respectively. In these figures, stars are grouped into the following metallicity
ranges: open circles
,
squares -
,
triangles
,
solid circles
.
The Sun, with
= 1.1 (Grevesse & Sauval 1998) and
(see Table 2), is also displayed in both figures for comparative purposes.
![]() |
Figure 5:
Lithium abundance as a function of mass (in
|
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![]() |
Figure 6:
Lithium abundance as a function of convection zone mass deepening
|
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Figures 5 and 6 show two interesting properties as solar-analog stars. Although the masses of the present sample of
solar-analogs appears to span a narrow range of values, namely masses between 0.82 and 1.1 ,
one observes a strong dispersion in
the distribution of lithium abundance versus stellar mass, once finely discretized sets of mass are considered. For masses
,
in particular, a wide range of about 2.5 orders of magnitude of
is observed in Fig. 5, a dispersion also observed at any given mass.
Since convection zone deepening depends primarily on both stellar mass and age, the
pattern in Fig. 5 should again parallel that observed in Fig. 6, at least in relation to the
dispersion. A comparison between Figs. 5 and 6
indicates that stars with the smallest masses have the lowest Li
abundances. This feature reinforces the claim that the root-cause of
the low lithium content observed in these stars is primarily related to
their previous evolutionary history and that other parameters in
addition to stellar mass and metallicity affect the degree of
depletion.
3.2 Lithium and rotation relationship in solar-analog stars
The behavior of the rotational velocity is of obvious importance to
our understanding of the lithium-rotation relationships in solar-analog
stars because it is largely accepted that rotation has a major
influence on Li abundances. Different studies, again suggest that the
Sun may be an abnormally slow rotator (Lambert & Reddy 2004),
compared to similar solar-type disk stars. Unfortunately, there are two
major difficulties in this analysis caused by stellar rotational
velocity. First, the true rotation of the vast majority of
solar-analogs is unknown, because the main detection procedure
currently in use gives provides the projected rotational velocity,
namely the minimum stellar rotation ().
The definitive rotation rate can only be derived using a photometry
procedure. To date, the literature lists the rotational period for only
a small percentage of the identified solar-analog stars. For instance,
Messina & Guinan (2004)
provide the photometric rotation period for 6 apparent
solar-analogues, all the stars with periods between 2.6 and
9.21 days rotating more rapidly than the Sun. Unfortunately, only
one of these 6 solar-analog stars is listed in the literature. In
addition, Butler et al. (1998)
measure a period of about 30 d for the solar analog
HD 187123. In spite of these difficulties, the preliminary study
by Takeda et al. (2007) illustrates that solar analogues with lower rotational velocity (
)
also have lower Li abundances. This conclusion is based on measurements
of line widths, from which theses authors estimated the
+macroturbulence of each star. This result is confirmed by Gonzalez (2008), using
measurements, separated from the macroturbulence, for a sample of stars with planets.
We now revisit the rotational behavior analyses of solar-analog stars
by considering the same sample of solar-analogues studied by Takeda
et al. (2007), but now using
from Nordström et al. (2004), which corresponds to the difference in
rotation from the macroturbulence. Figure 7 shows the distribution of the projected rotational velocity (
)
in
the HR diagram, for the aforementioned stellar sample, with evolutionary tracks computed in the scope of the present
work. We can clearly observe, an important scatter in the distribution of
with mass, in particularly among stars of mass
0.95
.
For more massive stars, one also observes
significant scatter in
at a given mass. This latter result implies that parameters others than stellar mass and
may also be controlling the rotation of solar-analog stars.
![]() |
Figure 7:
Distribution of projected rotational velocity measurements ( |
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The strong dispersion in
at a given stellar mass or convection zone depth, for
and
mass >0.9
,
as shown in the previous section, indicates that Li depletion depends
on parameters other than stellar mass,
such as age and early rotational history. To analyze in detail the role
of rotation and age in this context, we illustrate in Fig. 5
the distribution of
versus mass, with the stars segregated by metallicity, age, and
.
First, it is clear that solar-analogs
show the same trends between lithium content and rotation observed for other stellar families, where the largest
is associated with the largest
.
For instance, except for one star, HD 166435 (HIP 88945), all
the stars with enhanced rotation exhibit a large
. In contrast, among
slow rotators one observes a large spread in lithium content, from the smallest
-0.8 to the largest
3 values.
Furthermore, this figure shows an inhabited region for low mass stars,
in the sense that for masses lower than about 0.84
,
stars with larger
than about 1 and enhanced rotation seem unusual, a pattern that is clearly associated with stellar age.
4 Conclusions
In the past decade, different studies of low-mass stars have
provided important information about the physical properties of
solar-analog
stars. Spectroscopic data have offered important border conditions to
choose good candidates, based on the surface composition of
photometrically solar-analog stars. Nevertheless, the important scatter
in the distribution of different physical parameters, such as lithium
abundance and rotation, indicates, in the broad sense, that information
regarding surface convection and angular momentum may be essential to
the classification of solar-analog and solar twins stars. To
investigate the evolutionary status, mass, and any correlation
between Li abundance, convection, and rotation of solar-analog
G dwarf stars, we computed a grid of hundreds of evolutionary
models for stars of different metallicity and mass range, from 0.7 to
1.1
.
These evolutionary tracks were computed using the Toulouse-Geneva
code with updated physical inputs, as described in do Nascimento et al. (2009).
Our analysis of lithium abundance in a sample of solar-analog stars
found different degrees of lithium depletion, a large scatter in the
abundance being observed for stars over a narrow range of mass and
metallicity. Low Li abundance among solar-analog stars strongly
supports the hypothesis that these stars have depleted Li during the MS
phases. These results illustrate the need for an extra-mixing process
to explain lithium behavior in solar-analog stars, such as, shear
mixing caused by differential rotation proposed by Bouvier (1995).
The aforementioned dispersion in the lithium abundance of solar-analog
stars at a given age and mass may also reflect their different
rotational histories.
In spite of the short range of mass in the solar-analog stars, this
study shows how sensitive
scatter is as a function of stellar mass,
metallicity, age and,
.
It cannot however be excluded that the Galactic cosmic Li abundance
dispersion could contributes to the scattering in lithium abundance.
Even if solar-analog stars were chosen according to their spectroscopic
and photometric similarity with the Sun, our conclusion in this study
reinforces the need for information about the stellar interior.
Furthermore, the Li depletion observed in the solar-analog
stars and the large spread in Li abundances among the five known solar
twins cannot be explained only by standard convective mixing.
At a given
or age, a small percentage difference in stellar mass, and consequently in the depth (in mass) of the stellar
convective envelope, can produce a
scatter, which tends to increase with stellar mass and
.
This illustrates that in producing a more realistic definition of
solar-analog and solar-twin stars, it seems important to consider the
inner physical properties of stars, such as the depth of the convective
envelope mass and consequently rotation and magnetic properties.
Finally, we note that asteroseismology offers a unique opportunity to
study the extension of outer convection zones of
solar-analogs. This study and a determination of the chemical abundance
pattern of solar-analog and solar-twins stars could play an important
role in answering the fundamental question about how normal the Sun as
a star really is.
This research made use of the SIMBAD data base, operated at CDS, Strasbourg, France. J.D.N. and J.R.M. are research fellows of the CNPq Brazilian agency. Research activities of the Stellar Board at the Federal University of Rio Grande do Norte are supported by continuous grants from CNPq and FAPERN Brazilian Agencies. We thank the anonymous referee for the useful comments and suggestions.
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All Tables
Table 1: Comparison between effective temperature and luminosity at the solar age from the Toulouse-Geneve evolution code TGEC and Girardi et al. (2000).
Table 2: Parameters of the working sample.
All Figures
![]() |
Figure 1:
The distribution of the analog sample stars in the
Hertzsprung-Russell diagram. Luminosities and related errors have
been derived from the Hipparcos parallaxes. The typical error in
|
Open with DEXTER | |
In the text |
![]() |
Figure 2: Comparison between the mass determinations of this study, determined with the Toulouse-Geneva tracks and those computed by Takeda et al. (2007). |
Open with DEXTER | |
In the text |
![]() |
Figure 3: Convective zone mass
deepening as a function of decreasing effective temperature. Models for
[Fe/H] = 0 and 0.875, 0.900, 0.925, 0.950, 0.975, 1.00,
1.025, 1.050, 1.075, and 1.100
|
Open with DEXTER | |
In the text |
![]() |
Figure 4: Distribution of Li abundances in the HR diagram. The different symbols represent Li abundances. Filled inverse triangles represent the upper limits Li to the abundances. Evolutionary tracks, as in Fig. 1. |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Lithium abundance as a function of mass (in
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Lithium abundance as a function of convection zone mass deepening
|
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Distribution of projected rotational velocity measurements ( |
Open with DEXTER | |
In the text |
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