Effective temperatures, rotational velocities, microturbulent velocities and abundances in the atmospheres of the Sun,. HD1835 and HD10700

Abstract

We describe our procedure to determine effective temperatures, rotational
velocities, microturbulent velocities, and chemical abundances in the
atmospheres of Sun-like stars. We use independent determinations of iron
abundances using the fits to the observed Fe I and Fe II atomic absorption
lines. We choose the best solution from the fits to these spectral features for
the model atmosphere that provides the best confidence in the determined log
N(Fe), Vt, and vsini. First, we compute the abundance of iron for a set of
adopted microturbulent velocities. To determine the most self-consistent
effective temperature and microturbulent velocity in any star's atmosphere, we
used an additional constraint where we minimise the dependence of the derived
abundances of Fe I and Fe II on the excitation potential of the corresponding
lines. We analyse the spectra of the Sun and two well known solar type stars,
HD1835 and HD10700 to determine their abundances, microturbulent velocity and
rotational velocity. For the Sun abundances of elements obtained from the fits
of their absorption features agree well enough (+/- 0.1 dex) with the known
values for the Sun. We determined a rotational velocity of vsini = 1.6 +/- 0.3
km/s for the spectrum of the Sun as a star. For HD1835 the self-consistent
solution for Fe I and Fe II lines log N(Fe)=+0.2 was obtained with a model
atmosphere of 5807/4.47/+0.2 andmicroturbulent velocity Vt = 0.75 km/s, and
leads to vsini = 7.2 $\pm$ 0.5 km/s. For HD10700 the self-consistent solution
log N(Fe) = -4.93 was obtained using a model atmosphere of 5383/4.59/-0.6and
microturbulent velocity Vt = 0.5 km/s. The Fe I and Fe II lines give rise to a
vsini = 2.4 +/- 0.4 km/s. Using the Teff found from the ionisation equilibrium
parameters for all three stars, we found abundances of a number of other
elements: Ti, Ni, Ca, Si, Cr. ... Abriged.

Full text

Page 1

arXiv:1201.5099v2 [astro-ph.SR] 7 Feb 2012
Mon. Not. R. Astron. Soc. 000, 1–11 (2002)Printed 8 February 2012(MN LATEX style file v2.2)
Effective temperatures, rotational velocities,
microturbulent velocities and abundances in the
atmospheres of the Sun, HD1835 and HD10700
Ya. V. Pavlenko1,2∗, J.S. Jenkins2,3, H.R.A.Jones2, O.M. Ivanyuk1, D.J. Pinfield2
1Main Astronomical Observatory, Academy of Sciences of Ukraine, Golosiiv Woods, Kyiv-127, 03680 Ukraine
2Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK
3Departamento de Astronom´ ıa, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile
ABSTRACT
We describe our procedure to determine effective temperatures, rotational veloci-
ties, microturbulent velocities, and chemical abundances in the atmospheres of Sun-like
stars. We use independent determinations of iron abundances using the fits to the ob-
served Fe I and Fe II atomic absorption lines. We choose the best solution from the
fits to these spectral features for the model atmosphere that provides the best confi-
dence in the determined log N(Fe), Vt, and v sin i .Computations were done in the
framework of LTE. Blending effects were accounted for explicitly. First, we compute
the abundance of iron for a set of adopted microturbulent velocities. In some cases,
a few points of log N(Fe I) = log N(Fe II) can be found. To determine the most self-
consistent effective temperature and microturbulent velocity in any star’s atmosphere,
we used an additional constraint where we minimise the dependence of the derived
abundances of Fe I and Fe II on the excitation potential of the corresponding lines.
Using this procedure we analyse the spectra of the Sun and two well known solar type
stars, HD1835 and HD10700 to determine their abundances, microturbulent velocity
and rotational velocity. Our approach allows us to determine self-consistent values for
the effective temperatures, abundances, Vt and v sin i . For the Sun we obtain the
best agreement for a model atmosphere of Teff /log g/[Fe/H] = 5777/4.44/0.0, iron
abundances and microturbulent velocities of log N(Fe) =4.44, Vt= 0.75 km/s, for the
Fe I lines, and log N(Fe) = -4.47, Vt= 1.5 km/s for the Fe II lines. Furthermore, abun-
dances of other elements obtained from the fits of their absorption features agree well
enough (± 0.1 dex) with the known values for the Sun. We determined a rotational
velocity of v sin i = 1.6 ± 0.3 km/s for the spectrum of the Sun as a star. For HD1835
the self-consistent solution for Fe I and Fe II lines log N(Fe)=+0.2 was obtained with
a model atmosphere of 5807/4.47/+0.2 and microturbulent velocity Vt= 0.75 km/s,
and leads to v sin i = 7.2 ± 0.5 km/s. For HD10700 the self-consistent solution log
N(Fe) = -4.93 was obtained using a model atmosphere of 5383/4.59/-0.6 and micro-
turbulent velocity Vt = 0.5 km/s. The Fe I and Fe II lines give rise to a v sin i =
2.4 ± 0.4 km/s. Using the Teff found from the ionisation equilibrium parameters for
all three stars, we found abundances of a number of other elements: Ti, Ni, Ca, Si,
Cr. We show that uncertainties in the adopted values of Teff of 100 K and Vtof 0.5
km/s change the abundances of elements up to 0.1 and 0.2 dex respectively. Galactic
abundances variations can generally be larger than this measurement precision and
therefore we can study abundance variations throughout the Galaxy.
Key words: stars: molecular spectra stars: fundamental parameters – stars: late-type
– stars: evolution –
∗ E-mail: yp@mao.kiev.ua Based on observations made with the
ESO telescopes at the La Silla Paranal observatory under pro-
gramme ID’s 076.C-0578(B) and 077.C-0192(A).

Page 2

2
Ya. V. Pavlenko et al.
Table 1. Temperatures, gravities and abundances used in studies
of HD1835.
Teff
log g[Fe/H]Comp.
Star
Reference
5857
5764
5767
5857
5673
5793
5793
5793
5860
5793
5860
4.47
4.40
4.45
4.47
4.22
4.50
4.60
–
4.40
4.50
4.40
+0.23
+0.21
+0.16
+0.22
-0.01
+0.20
+0.24
+0.16
+0.28
+0.19
-0.09
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
This Paper
Jenkins et al. (2008)
Soubiran et al. (2008)
Valenti & Fisher (2005)
Pasquini et al. (1994)
Boesgaard & Friel (1990)
Abia et al. (1988)
Boesgaard & Budge (1988)
Rebolo et al. (1986)
Cayrel de Strobel et al. (1985)
Cayrel de Strobel et al. (1981)
1 INTRODUCTION
In the past the majority of research conducted on solar-type
stars was focused on accurately constraining their physical
parameters, such as effective temperature, bolometric mag-
nitude, radius, metallicity and color indices using a variety
of different photometric and spectroscopic techniques (e.g.
Glushneva et al. 2002). However, with the advance of tech-
nology, high resolution echelle spectrographs and more ob-
serving time, the field is pushing to even higher precision
measurements for a larger database of atomic and molecular
species in stellar atmospheres (e.g. Valenti & Fischer 2005;
Neves et al. 2009; Mashonkina et al. 2011) and more pre-
cise physical parameters from the latest evolutionary models
(Lopez-Santiago et al. 2010; Ghezzi et al. 2010; Takeda et
al. 2010; Tabernero et al. 2011). One of the main reasons for
the growing interest into solar-type stars is that the metal
content of planet-hosting stars is an important ingredient
that seems to affect the formation and evolution of plane-
tary systems (see Israelian 2010; Santos et al. 2011; Sousa
et al. 2012, and reference therein).
Valenti & Fischer have published an extended uniform
catalog of stellar properties for 1040 nearby F, G, and K
stars that were observed by the Keck, Lick, and AAT planet
search programs. Accurate stellar abundances from spec-
tral synthesis fitting requires the determination of reliable
physical parameters, namely the effective temperature, sur-
face gravity, microturbulent velocity, rotational velocity and
atomic abundances (see Jenkins et al. 2008; Jenkins et al.
2009a). Studying stars with spectral types similar to the
Sun but with other physical differences can help to test new
analysis techniques.
HD1835 is a variable and magnetically active G3V star
(see Jenkins et al. 2006, Mart´ ınez-Arn´ aiz, 2010) In Table 1
we show the iron abundances studied by different authors for
HD1835. When we look at past studies there is a fairly large
spread in metallicities for this star, however, in recent times
there is more convergence towards the star having super-
solar metallicity. Only two studies found this star to have
sub-solar metallicity, the last back in 1994.
HD10700 is a high proper-motion dwarf star, studied
by many authors. Simbad lists 756 references as of February
2012, ranging from chromospheric activity studies (Jenkins
et al. 2006, Mart´ ınez-Arn´ aiz et al. 2010) through to stel-
Table 2. Temperatures, gravities and abundances used in studies
of HD10700.
Teff
log g[Fe/H] Comp.
Star
Reference
5383
5377
5522
5344
5310
5264
5283
5320
5330
5500
5250
5143
5305
5250
4990
5305
5362
5538
5196
5305
4.59
4.53
4.50
4.45
4.44
4.36
4.59
4.30
4.30
4.32
4.65
3.60
4.32
4.50
4.50
4.33
4.59
-
-
-
-0.55
-0.49
-0.37
-0.52
-0.52
-0.50
-0.52
-0.50
-0.59
-0.38
-0.46
-0.60
-0.66
-0.58
-0.56
-0.49
-0.34
-0.13
-0.39
-0.39
Sun
Sun
Sun
Sun
-
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
Sun
This Paper
Mashonkina et al. (2011)
Jenkins et al. (2008)
Soubiran et al. (2008)
Sousa et al. (2008)
Cenarro et al. (2007)
Valenti & Fischer (2005)
Castro et al. (1999)
Tomkin et al. (1999)
Mallik et al. (1998)
Arribas et al. (1989)
Barbuy et al. (1989)
Gratton (1989)
Abia et al. (1988)
Francois (1986)
Steenbock (1983)
Hearnshaw (1974)
Herbig (1965)
Pagel et al. (1964)
Pagel (1963)
lar oscillation studies (Teixeira et al. 2009). In Table 2 we
show the iron abundances studied by different authors for
HD10700.
The overall goal of this paper is to outline our new pro-
cedure to measure precise and accurate iron abundances,
microturbulent velocities and rotational velocities for solar-
type stars through analysis of high resolution stellar spectra
of the Sun, HD1835 and HD10700.
2 PROCEDURE
2.1Observed data
The adopted parameters for our stars are listed in Table 3.
The spectra and all calibration data were observed using the
Fibre-fed Extended Range Optical Spectrograph (FEROS)
mounted on the MPG/ESO - 2.2m telescope on the La Silla
site in Chile. The exposure times were long enough to en-
sure that the spectra were observed with S/N ratios of well
over 150 in the continuum around the iron lines at 6100˚ A
at the operating resolution of FEROS (R ∼48′000). All cal-
ibration files needed for the reduction of the stellar spectra
(flat-fields, bias and arc frames) were obtained at the begin-
ning and end of each nights observing, following the stan-
dard ESO calibration plan. The reduction of all the spec-
tra followed the standard reduction techniques described by
Jenkins et al. (2008).
The observed spectrum of the Sun (Kurucz et al. 1984)
is used as the reference star. The resolution of the solar
spectrum is much higher, (R = 100′000), however profiles
of observed lines in the solar spectrum are broadened by
macroturbulence. We adopt a gaussian for the macroturbu-
lence profile with a FWHM = 0.1˚ A at 6000˚ A. This corre-
sponds to Vmacro = 2.2 km s−1which agrees well with the
reference value (Gurtovenko & Sheminova 1986).

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Teff, v sin i , Vtand abundances in the Sun, HD1835 and HD10700
3
Table 3. Parameters of stars of our interest
Star
Teff(VF05)log g (VF05) [Fe/H] (VF05)
Vr (km/s)
v sin i (km/s)
the Sun
HD1835
HD10700
57774.44
4.47
4.59
0 1.7
5857.0±22
5283±22
+0.22
-0.52
-2.7±1.8 (Jenkins et al. 2011)
-16.9±1.6 (Jenkins et al. 2011)
6 (VF05), 8 (Jenkins et al. 2008)
2 (VF05)
2.2Model atmospheres
HD1835 and HD10700 are stars which are similar to the
Sun, validating the Sun as our reference star. For each star
we computed plane-parallel model atmospheres in LTE, with
no energy divergence, using the SAM12 program (Pavlenko
2003), which is a modification of ATLAS12 (Kurucz 1999).
In this study as “the zeroth approach” we adopt values
given by Valenti & Fischer (2005) for both stars HD1835
and HD10700, i.e.. Teff /log g/[Fe/H] = 5857/4.47/+0.22
and 5383/4.75/-0.36, respectively, for faster convergence of
the code. For the Sun we used a model atmosphere of
5777/4.44/0.00. All models were recomputed with the new
abundances found by ourselves. Chemical equilibrium is
computed for molecular species assuming LTE and we use
the opacity sampling approach from Sneden (1976) to ac-
count for absorption of atoms, ions and molecules (see more
details in Pavlenko 2003). The 1-D convective mixing length
theory, modified by Kurucz (1999) in ATLAS12, was used to
account for convection. The computed model atmospheres
are available on the web1.
2.3 Synthetic spectra
Synthetic spectra are calculated with the WITA6 program
(Pavlenko 1997), using the same approximations and opaci-
ties as SAM12. To compute the synthetic spectra we use line
lists taken from VALD2 (Kupka et al. 1999). The shape of
each atomic line is determined using a Voigt function and all
damping constants are taken from line databases, or com-
puted using Unsold’s approach (Unsold 1954). A wavelength
step of ∆λ = 0.025˚ A is employed in the synthetic spectra
computations to match our observed FEROS spectrum. It is
worth noting that different atomic species provide different
contributions to the formation of the spectrum of solar-like
stars. In particular, iron lines dominate the solar spectrum.
2.4 Best fit parameters selection
In our work we used two spectroscopic datasets to carry out
the abundance analysis. The first one consists of the spec-
troscopic data taken from the VALD (Kupka et al. 1999).
For any absorption line we identify the atom, molecule or
ion, its central wavelength, λo, the oscillator strength of
the transition gf, the excitation potential of the lower level
E
stants C2,C4,C6. The second one contains the list of pre-
selected spectral regions (NL) governed by absorption of the
atom and/or ion of interest.
′′of the corresponding transition and the damping con-
1
ftp://ftp.mao.kiev.ua/pub/users/yp/MA2010
2.4.1 Pre-selection of spectral features in the solar
spectrum
We used the Sun as a template star to verify our procedure.
Indeed, the solar abundances were determined by many au-
thors using different procedures and the results do not differ
very little.
The first step of our selection procedure was to com-
pute a spectrum of the Sun taking into account only lines of
elements of interest. A comparison with the observed spec-
trum provides a list of spectral features in which absorption
of our element dominates. Blending by other lines was ac-
counted for directly where the contribution of other lines
can be estimated in a simple way from the analysis of the
ratio r(Fe)/r(Sun), where r(Fe) and r(Sun) are residual
fluxes from the continuum normalisation in our theoretical
spectrum of iron lines and the observed spectrum of the Sun.
Then, from the analysis of the shape of the r(Fe)/r(Sun)
ratio we determine the central wavelengths of every feature
and spectral region in which we compare the theoretical and
observed spectra to determine the iron abundance. The spec-
tral range of comparison was chosen to be approximately
between -0.1˚ A and +0.1˚ A from the blue and red edge of the
corresponding spectral feature, a method shown to be effec-
tive in Jenkins et al. (2008). We do note that the synthetic
spectra were computed across a broader spectral region of
approximately ±5˚ A.
From a comparison of the observed and computed spec-
tra we obtained a list of strong features governed by the ab-
sorption of a given element. Strong features were selected to
reduce the possible effects of noise. As a limit for our strong
lines we choose the value r(Fe) = 0.8.
2.4.2Fits to pre-selected spectral features
For each preselected spectral region that contains an absorp-
tion line we are interested in, we carry out the fit to the ob-
served spectrum. The synthetic spectra that are computed
across the selected spectral region are convolved with pro-
files that match the instrumental broadening and that take
into account rotational broadening. For instrumental broad-
ening we adopt a Gaussian profile and the rotational broad-
ening was treated following the scheme by Gray (1976). The
instrumental broadening takes care of the spectrograph res-
olution, and v sin i is a parameter used to get the best fit
to the observed profiles of any feature in our spectrum.
For every feature we find the minimisation parameter:
Sl=
?
(1 − rs
ν/ro
ν)2/No
here No is the number of points in the observed spectrum
across the pre-selected spectral region, ro
ual fluxes in the observed and computed spectra, respec-
νand rs
νare resid-

Page 4

4
Ya. V. Pavlenko et al.
tively. Formally a minimum Sl determines our solution,
i.e.. the abundance of an element governed by the associ-
ated absorbing feature on the adopted set of abundances
Xi = log(N(Xi)),i = 1,...,Na, where Na is the dimension-
ality of the abundance grid.
Our measurements are affected by some errors of a dif-
fering nature: uncertainties in gf, blending, presence of noise
in the observed spectrum, etc. Every fitted spectral feature
provides one abundance Xlon min Sl, l = 1, NLwe compute
mean abundance
Xo = (
?
Xl)/L)
and a formal standard error σo
σo =
??
(Xl− Xo)2/(Nl∗ (Nl− 1))
where Nl is the total number of the fitted spectral lines.
It is worth noting that sometimes not all pre-selected
features provide a minimum S on our grid of abundances,
therefore Nl ? NL. In other words, if the minimum of S
cannot be found in the adopted abundance range, or any
absorption feature is too weak in the observed spectrum,
the line was excluded from the following consideration.
Additionally, we compute the abundance of elements
averaged over 1σ, i.e. we averaged all abundances across
Xo+ 1σo:
Xs =
?
(Xl/σl)/
?
(1/σl)
In this paper we adopt Na = 30 with a step of 0.05, Nv
= 6 with a step of 0.5 km/s and Nr = 11 with a step of 0.4
- 0.5 km/s.
In some details our procedure is similar to that used
by Jones et al. (2002) and Pavlenko & Jones (2002), but
in this case we individually fit the synthetic spectra to the
pre-selected features in the observed spectrum.
Our procedure allows us to obtain the iron abundances
from the fits to Fe I and Fe II independently. The Fe I/Fe II
= log N(Fe I)-log N(Fe II), where N(Fe I) and N(Fe II) are
respectively the iron abundance determined from the fits to
Fe I and Fe II lines, is used to verify the log g of the model
atmospheres used in the fits.
It is worth noting a few important points:
– since we deal with blending by absorption lines of
other elements, which allows us to include strong blended
features in the observed spectrum.
– rotational velocity (v sin i ) is determined for every
point (log N(Fe), Vt ) of our synthetic spectral grid for every
spectral line.
2.5General algorithm of solution
2.5.1 Dependence of abundance of iron vs. excitation
potential of absorption lines
In our analysis we use a set of lines of different excitation
potentials of the lower level of the corresponding radiative
transition E
perature in the line-forming region of the stellar atmosphere
can be described by exp(−E′′/kT), where the labels have
′′. In the first approach their response on tem-
-5.2
-5
-4.8
-4.6
-4.4
-4.2
-4
-3.8
-3.6
0 1 2 3
Excitation potential (eV)
4 5 6 7 8 9
log N(Fe)
5777/4.44/0
Vt = 0 km/s: Fe I lines
Fe I, averaged
Fe II lines
Fe 2 averaged
Vt = 2 km/s: Fe I lines
Fe I averaged
Fe II lines
Fe II averaged
Figure 1. Dependence of the iron abundance determined from
the fits to the observed Fe I and Fe II features in the observed
spectrum of the Sun vs. excitation potential computed for a model
atmosphere with parameters 5777/4.44/0.
the conventional meaning. Lines of different E
ent response to T (and respectively, on Teff ). In our case we
work with blends in the stellar spectra too. They are treated
explicitly. If a few lines of the given element form the feature
then we use the “effective” excitation potential
′′show differ-
E
′′= −ln(Σ(gi∗ exp(−Ei/kT))/Σ(gi)) ∗ kT
here values and labels have the conventional meaning, i =
1,...,N. Here N is the total number of lines of the given
element that formed the feature.
Ideally, for the properly determined Teff we should not
obtain any dependence of log N(Fe) on E
lines of both Fe I and Fe II. In other words the absence of
dependence of log N(Fe) = f(E
condition for the determination of microturbulent velocity
and abundance. It it worth noting that a similar approach
was used by other authors in the past (see fig.8 in Mashon-
kina et al 2011).
In Fig. 1 we plot the dependence of Fe I and Fe II abun-
dances in the spectrum of the Sun versus their excitation po-
tentials. These computations were carried out for a model
atmosphere of 5777/4.44 and microturbulent velocities of
Vt = 0 km/s and 2 km/s. The results of the approximation
of the dependence of log N(Fe) = f (E
the straight line fits to the data in the figure.
Even visual inspection of Fig. 1 provides a good estima-
tion of microturbulence velocity in the solar atmosphere 0
< Vt < 2 km/s. A more complete set of the approximations
obtained for Vt =0, 0.5, 1, 1.5, 2, 2.5 km/s will be shown in
section 3 for our star of interest.
′′for absorption
′′) we consider as a sufficient
′′) is highlighted by
2.5.2The self-consistent solution
We pay special attention to the ionisation equilibrium Fe
I/Fe II. Lines of these ions are abundant in the spectra of
solar-like stars. Furthermore, the spectroscopic data for Fe
I and Fe II lines are more accurate and complete in compar-
ison with other ions.

Page 5

Teff, v sin i , Vtand abundances in the Sun, HD1835 and HD10700
5
To determine the realistic parameters of our stars we
developed and used the following custom algorithm:
1) Using the fits to the profiles of Fe I and Fe II lines
separately, we compute dependences of log N(Fe) = f(Vt )
for the model atmosphere with adopted Teff on a fixed grid
of microturbulence velocities. In general log N(Fe I) = log
N(Fe II) is a pre-requisite to find the proper Teff .
2) In some cases we obtain a few solutions log N(Fe I)
= log N(Fe II) for different Teff and Vt , and v sin i . To
select the best solution we test if there is any dependence of
derived abundances on excitation potential of lower level of
the corresponding spectral features, as described in section
2.4.2.
3) After the determination of log N(Fe), Teff , Vt we
determined the abundances of other elements.
4) If we obtain large differences in abundances in com-
parison with the results of the previous iteration then we
recompute the model atmosphere and repeat all these pro-
cedures.
It is worth noting that in comparison with the former
papers we reduced the number of free parameters. Namely,
we determined log N(Fe), Vt and v sin i from the best fit to
the observed spectrum. Then, we used an averaging proce-
dure across the 1σ error parameter space to obtain a statis-
tically significant result. Finally, the best solution was found
from the best agreement of all three parameters on the grid
of parameters. Furthermore, the metallicity of the model at-
mosphere agrees with the fitting results, i.e.. we found our
final solution in a few successive approximations taking into
account the variability of the abundances and other param-
eters in only a few iterations.
3 RESULTS
3.1 Formal test of the procedure: abundances, Vt ,
and v sin i for the Sun
To test our procedure we employed a few model atmo-
spheres with parameters 5777/4.44, 5777/4.50, 5527/4.50
and 6027/4.50. We then determined log (Fe) for the adopted
grid of microturbulent velocities Vt = 0, 0.5, 1, 1.5, 2, 2.5
km/s using the fits to Fe I and Fe II lines in the observed so-
lar spectrum. Error bars were computed following the stan-
dard procedure described in section 2.4.2.
Results of the iron determinations for three model at-
mospheres are shown in Fig. 2. As was expected, only model
atmospheres with Teff = 5777 K provide similar values of
iron abundances obtained from the fits of Fe I and Fe II
lines. Model atmospheres of lower Teffprovide overestimated
abundances of Fe II ions in the atmosphere of the Sun
and underestimate the abundances of Fe I, respectively, and
vice versa, model atmospheres of higher Teff , underestimate
abundances of Fe II and overestimate Fe I.
It is worth briefly noting two points:
• Visual inspection of the plots similar to that shown in
Fig 2 can be used to determine the proper Teff .
• We see good agreement in iron abundances obtained
from the fits of Fe I and Fe II lines across the wide
range of microturbulent velocities for the model atmospheres
5777/4.44 and 5777/4.5.
To solve the last problem we investigated the obtained
abundances versus excitation potential of the main absorb-
ing lines. We approximate the obtained dependence of com-
puted abundances versus E
squares fitting. The dependence log N(Fe) vs.. E
for a model atmosphere of the Sun of 5777/4.44/0.0 and dif-
ferent microturbulent velocities is shown in the lower panel
of Fig. 2. Results of fits to Fe I lines show the absence of
the log N(Fe) vs. E
-4.40. It is worth noting that Sheminova & Gadun (2010)
analysed the Sun at high resolution (R=200000) and found
Vt =0.8 ± 0.2 km/s. Nevertheless, our value of iron abun-
dance corresponds well enough with Grevesse and Anders
(1979) log N(Fe) = -4.37 and Gurtovenko and Kostik (1989)
log N(Fe)= -4.40. However, our fits to Fe II lines provide a
little lower abundance log N(Fe)= -4.6. The differences of
iron obtained from the fits to Fe I and Fe II lines are dis-
cussed in many papers (see the most recent paper Mashon-
kina et al. 2011 and discussion therein). On the other hand,
our sample of Fe I lines is larger, therefore the results ob-
tained from the fits to the the neutral ion lines in the ob-
served spectrum are more robust.
′′by a linear function using least-
′′computed
′′for Vt = 0.75 km/s and log N(Fe) =
Using the derived estimations of Teff , log g, and Vt we
obtained abundances of other elements using the aforemen-
tioned scheme. The comparison of our results with known
abundances for the Sun is presented in Table 7. For most
abundances where we found satisfactory agreement, the
residuals do not exceed 0.1 dex. However, we found a dif-
ference of 0.16 dex against the Cr I abundance measured
by Grevese and Anders (1989). On the other hand our value
agrees well with the Gurtovenko & Kostik value log N(Cr) =
-8.07. Therefore, we estimate our accuracy of abundance de-
termination as < 0.1 dex. This level of precision provides us
with a good opportunity to investigate absolute differences
in the abundances of stars like the Sun.
To investigate the dependence of abundances on the
adopted microturbulent velocity we repeat our abundance
determination procedure for the case of Vt = 1.25 km/s (see
Table 4). For all elements we obtained similar results, i.e.
difference in the adopted microturbulent velocity of 0.5 km/s
provide changes in the obtained abundances by a factor of
0.2 dex.
In Table 4 we show the rotational velocity of the Sun
determined from the fits of our features to the observed spec-
trum of the Sun as a star (Kurucz et al. 1984). For the solar
spectrum we adopt an effective resolution R = 70′000, the
formal resolution limited by the presence of macroturbulent
velocity Vma= 1 - 2.6 km/s (Gurtovenko & Sheminova 1986,
Sheminova & Gadun 2010). Our determined v sin i = 1.6
± 0.3 agrees well with the known rotational velocity of the
Sun v sin i ∼ 1.85 ± 0.1 km/s (see Bruning 1984), and cor-
responds well with v sin i =1.63 km/s obtained by Valenti
& Fisher (2005).
One may expect that the determined rotational veloc-
ity for the Sun depends on the adopted resolution. Indeed,
even a slightly lower resolution of R = 60′000 will overesti-
mate the contribution from macroturbulence into the total
broadening and underestimate the v sin i = 1.2 ± 0.3 km/s.
However, it does not affect the results of abundance de-
terminations because the observed spectra are broadened by
the combined profile formed by rotation + macroturbulence