Broad-band photometric colors and effective temperature calibrations for late-type giants. II. Z<0.02
Astronomy (2006)
- DOI: 10.1051/0004-6361:20053028
- arXiv: astro-ph/0510434
Available from arxiv.org
or
Abstract
We present new synthetic broad-band photometric colors for late-type giants based on synthetic spectra calculated with the PHOENIX model atmosphere code. The grid covers effective temperatures Teff=3000...5000K, gravities log g=-0.5...+3.5, and metallicities M/H=+0.5...-4.0. We show that individual broad-band photometric colors are strongly affected by model parameters such as molecular opacities, gravity, microturbulent velocity, and stellar mass. Our exploratory 3D modeling of a prototypical late-type giant shows that convection has a noticeable effect on the photometric colors too, as it alters significantly both the vertical and horizontal thermal structures in the outer atmosphere. The differences between colors calculated with full 3D hydrodynamical and 1D model atmospheres are significant (e.g., Delta(V-K)~0.2 mag), translating into offsets in effective temperature of up to ~70K. For a sample of 74 late-type giants in the Solar neighborhood, with interferometric effective temperatures and broad-band photometry available in the literature, we compare observed colors with a new PHOENIX grid of synthetic photometric colors, as well as with photometric colors calculated with the MARCS and ATLAS model atmosphere codes. (abridged)
Available from arxiv.org
Page 1
Broad-band photometric colors and effective temperature calibrations for late-type giants. II. Z<0.02
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Astronomy & Astrophysics manuscript no. 4431 February 5, 2008
(DOI: will be inserted by hand later)
Broad-band photometric colors and effective temperature
calibrations for late-type giants. II. Z<0.02
A. Kucˇinskas1,2,3, P.H. Hauschildt4, I. Brott4,5, V. Vansevicˇius6
L. Lindegren1, T. Tanabe´7, F. Allard8
1 Lund Observatory, Lund University, Box 43, SE-221 00, Lund, Sweden
2 National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan
3 Institute of Theoretical Physics and Astronomy, Gosˇtauto 12, Vilnius 01108, Lithuania
4 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
5 INTEGRAL Science Data Centre, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
6 Institute of Physics, Savanoriu 231, Vilnius 02300, Lithuania
7 Institute of Astronomy, The University of Tokyo, Mitaka, Tokyo, 181-0015, Japan
8 Centre de Recherche Astronomique de Lyon, E´cole Normale Supe´rieure, Lyon, Cedex 07, 69364 France
Received 28 October 2005 / Accepted 7 March 2006
Abstract. We investigate the effects of metallicity on the broad-band photometric colors of late-type giants, and
make a comparison of synthetic colors with observed photometric properties of late-type giants over a wide range
of effective temperatures (Teff = 3500− 4800K) and gravities (log g = 0.0− 2.5), at [M/H] = −1.0 and −2.0. The
influence of metallicity on the synthetic photometric colors is small at effective temperatures above ∼ 3800K, but
the effects grow larger at lower Teff , due to the changing efficiency of molecule formation which reduces molecular
opacities at lower [M/H]. To make a detailed comparison of the synthetic and observed photometric colors of late
type giants in the Teff–color and color–color planes (which is done at two metallicities, [M/H] = −1.0 and −2.0), we
derive a set of new Teff–log g–color relations based on synthetic photometric colors, at [M/H] = −0.5, −1.0, −1.5,
and −2.0. These relations are based on the Teff–log g scales that we derive employing literature data for 152 late-
type giants in 10 Galactic globular clusters (with metallicities of the individual stars between [M/H] = −0.7 and
−2.5), and synthetic colors produced with the PHOENIX, MARCS and ATLAS stellar atmosphere codes. Combined with
the Teff–log g–color relations at [M/H] = 0.0 (Kucˇinskas et al. 2005), the set of new relations covers metallicities
[M/H] = 0.0 . . .−2.0 (∆ [M/H] = 0.5), effective temperatures Teff = 3500 . . . 4800K (∆Teff = 100K), and gravities
log g = −0.5 . . . 3.0. The new Teff–log g–color relations are in good agreement with published Teff–color relations
based on observed properties of late-type giants, both at [M/H] = −1.0 and −2.0. The differences in all Teff–color
planes are typically well within ∼ 100K. We find, however, that effective temperatures predicted by the scales
based on synthetic colors tend to be slightly higher than those resulting from the Teff–color relations based on
observations, with the offsets up to ∼ 100K. This is clearly seen both at [M/H] = −1.0 and −2.0, especially in
the Teff–(B − V ) and Teff–(V − K) planes. The consistency between Teff–log g–color scales based on synthetic
colors calculated with different stellar atmosphere codes is very good, with typical differences being well within
∆Teff ∼ 70K at [M/H] = −1.0 and ∆Teff ∼ 40K at [M/H] = −2.0.
Key words. Stars: atmospheres – Stars: late-type – Stars: fundamental parameters – Techniques: photometric
1. Introduction
Stars on the red giant branch and asymptotic giant branch
(RGB and AGB, respectively) are important constituents
of intermediate age and old stellar populations. In this age
range they contribute significantly to the total radiative
energy output of a given population, especially at near-
infrared wavelengths (e.g., Mouhcine & Lanc¸on 2002). A
realistic representation of the atmospheres and observed
spectral properties of late-type giants with current stel-
Send offprint requests to: A. Kucˇinskas, e-mail: ak@itpa.lt
lar atmosphere models is, therefore, of crucial importance,
both for understanding evolution of single stars and stellar
systems. This is especially vital for the studies of distant
stellar populations which have to rely on the most lumi-
nous stars, and frequently on RGB and AGB stars alone.
While theoretical modeling of late-type giant atmo-
spheres has undergone significant development during the
last decade, with major improvements in the modeling
procedure, current stellar atmosphere models still use a
number of simplifications in the model physics and other
assumptions (see, e.g., Gustafsson 2003). Indeed, the
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Astronomy & Astrophysics manuscript no. 4431 February 5, 2008
(DOI: will be inserted by hand later)
Broad-band photometric colors and effective temperature
calibrations for late-type giants. II. Z<0.02
A. Kucˇinskas1,2,3, P.H. Hauschildt4, I. Brott4,5, V. Vansevicˇius6
L. Lindegren1, T. Tanabe´7, F. Allard8
1 Lund Observatory, Lund University, Box 43, SE-221 00, Lund, Sweden
2 National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan
3 Institute of Theoretical Physics and Astronomy, Gosˇtauto 12, Vilnius 01108, Lithuania
4 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
5 INTEGRAL Science Data Centre, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
6 Institute of Physics, Savanoriu 231, Vilnius 02300, Lithuania
7 Institute of Astronomy, The University of Tokyo, Mitaka, Tokyo, 181-0015, Japan
8 Centre de Recherche Astronomique de Lyon, E´cole Normale Supe´rieure, Lyon, Cedex 07, 69364 France
Received 28 October 2005 / Accepted 7 March 2006
Abstract. We investigate the effects of metallicity on the broad-band photometric colors of late-type giants, and
make a comparison of synthetic colors with observed photometric properties of late-type giants over a wide range
of effective temperatures (Teff = 3500− 4800K) and gravities (log g = 0.0− 2.5), at [M/H] = −1.0 and −2.0. The
influence of metallicity on the synthetic photometric colors is small at effective temperatures above ∼ 3800K, but
the effects grow larger at lower Teff , due to the changing efficiency of molecule formation which reduces molecular
opacities at lower [M/H]. To make a detailed comparison of the synthetic and observed photometric colors of late
type giants in the Teff–color and color–color planes (which is done at two metallicities, [M/H] = −1.0 and −2.0), we
derive a set of new Teff–log g–color relations based on synthetic photometric colors, at [M/H] = −0.5, −1.0, −1.5,
and −2.0. These relations are based on the Teff–log g scales that we derive employing literature data for 152 late-
type giants in 10 Galactic globular clusters (with metallicities of the individual stars between [M/H] = −0.7 and
−2.5), and synthetic colors produced with the PHOENIX, MARCS and ATLAS stellar atmosphere codes. Combined with
the Teff–log g–color relations at [M/H] = 0.0 (Kucˇinskas et al. 2005), the set of new relations covers metallicities
[M/H] = 0.0 . . .−2.0 (∆ [M/H] = 0.5), effective temperatures Teff = 3500 . . . 4800K (∆Teff = 100K), and gravities
log g = −0.5 . . . 3.0. The new Teff–log g–color relations are in good agreement with published Teff–color relations
based on observed properties of late-type giants, both at [M/H] = −1.0 and −2.0. The differences in all Teff–color
planes are typically well within ∼ 100K. We find, however, that effective temperatures predicted by the scales
based on synthetic colors tend to be slightly higher than those resulting from the Teff–color relations based on
observations, with the offsets up to ∼ 100K. This is clearly seen both at [M/H] = −1.0 and −2.0, especially in
the Teff–(B − V ) and Teff–(V − K) planes. The consistency between Teff–log g–color scales based on synthetic
colors calculated with different stellar atmosphere codes is very good, with typical differences being well within
∆Teff ∼ 70K at [M/H] = −1.0 and ∆Teff ∼ 40K at [M/H] = −2.0.
Key words. Stars: atmospheres – Stars: late-type – Stars: fundamental parameters – Techniques: photometric
1. Introduction
Stars on the red giant branch and asymptotic giant branch
(RGB and AGB, respectively) are important constituents
of intermediate age and old stellar populations. In this age
range they contribute significantly to the total radiative
energy output of a given population, especially at near-
infrared wavelengths (e.g., Mouhcine & Lanc¸on 2002). A
realistic representation of the atmospheres and observed
spectral properties of late-type giants with current stel-
Send offprint requests to: A. Kucˇinskas, e-mail: ak@itpa.lt
lar atmosphere models is, therefore, of crucial importance,
both for understanding evolution of single stars and stellar
systems. This is especially vital for the studies of distant
stellar populations which have to rely on the most lumi-
nous stars, and frequently on RGB and AGB stars alone.
While theoretical modeling of late-type giant atmo-
spheres has undergone significant development during the
last decade, with major improvements in the modeling
procedure, current stellar atmosphere models still use a
number of simplifications in the model physics and other
assumptions (see, e.g., Gustafsson 2003). Indeed, the
Page 2
2 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
atmospheres of late-type giants are complex, thus de-
tailed modeling of certain physical phenomena (convec-
tion, pulsations, shock waves, grain formation, mass loss)
should ideally be done using 3-D radiation hydrodynam-
ics. Obviously, while the classical 1-D model atmospheres
may still be very valuable in providing the time-averaged
properties of late-type giants (for instance, their broad-
band photometric colors), it is important to know how
well these theoretically predicted quantities reproduce the
observations of real stars.
In the first paper of this series (Kucˇinskas et al. 2005,
Paper I) we made a detailed comparison of synthetic pho-
tometric colors produced using current stellar model at-
mosphere codes (PHOENIX, MARCS, and ATLAS) with obser-
vations of late-type giants in the Solar neighborhood, at
Solar metallicity. Generally, we found that observed and
theoretical colors agree at the level of ±100K, over a wide
range of effective temperatures (Teff = 3000 . . .4800K)
and gravities (log g = 0.0 . . .+3.0; see Paper I for a de-
tailed discussion). Here we extend this analysis to sub-
Solar metallicities, assuming Solar-scaled abundances of
individual chemical species at [M/H] < 0.
There are 3 parts of this paper. First, we investigate
the influence of metallicity, [M/H], on the synthetic broad-
band photometric colors calculated with the PHOENIX stel-
lar model atmosphere code. Second, we derive a set of new
Teff–log g relations at different metallicities, based on the
published spectroscopic effective temperatures and gravi-
ties of 152 giants in Galactic globular clusters. We further
employ these relations to derive three new Teff–log g–color
scales based on the synthetic colors of PHOENIX, MARCS and
ATLAS, for [M/H] = −0.5, −1.0, −1.5, and −2.0. Finally,
we provide a detailed comparison of the new Teff–log g–
color scales based on the synthetic photometric colors
with a number of Teff–color relations available from the
literature. This comparison is done for two metallicities,
[M/H] = −1.0 and −2.0.
The paper is structured as follows. In Sect. 2 we briefly
describe synthetic spectra calculated with the PHOENIX,
MARCS and ATLASmodel atmospheres, and outline the pro-
cedure used to calculate synthetic photometric colors. The
effects of metallicity on the photometric colors are dis-
cussed in Sect. 3. The new Teff–log g scales for different
metallicities are derived in Sect. 4. Here we also discuss
a sample of Galactic globular cluster giants which is em-
ployed in the derivation of the Teff–log g relations. Finally,
the new Teff–log g–color relations based on the synthetic
colors of PHOENIX, MARCS, and ATLAS are derived in Sect. 5.
A comparison of the new Teff–log g–color scales with Teff–
color relations available in the literature is also provided.
2. Stellar atmosphere models, spectra and
synthetic colors of late-type giants
The comparison of synthetic photometric colors with
observations of late-type giants made in Sect. 5 uti-
lizes colors calculated with the PHOENIX, MARCS, and
ATLAS model atmospheres. A detailed description of the
model atmosphere codes can be found in relevant papers
(PHOENIX: Hauschildt et al. (2003) and references therein;
ATLAS: Castelli & Kurucz (2003); MARCS: Plez (2003) and
Gustafsson et al. (2003)). In the following subsections we
briefly summarize only the most crucial issues related to
the calculation of synthetic spectra and broad-band pho-
tometric colors.
2.1. PHOENIX spectra and broad-band colors
PHOENIX photometric colors used in this work were calcu-
lated in Paper I employing a new grid of PHOENIX spec-
tra. This grid is an update and extension of the previous
NextGen library of synthetic spectra of late-type giants
(Hauschildt et al. 1999b) to lower effective temperatures
and metallicities (Hauschildt et al. 2006, in preparation1).
The atmospheres and spectra in this grid were calculated
under the assumption of spherical symmetry and LTE,
for a single stellar mass M⋆ = 1M⊙. Microturbulent ve-
locity was set to ξ = 2 km s−1. Typical spectral resolution
is 0.2 nm in the optical wavelength range and gradually
decreases towards the infrared wavelengths.
The broad-band photometric colors were calculated
in the Johnson-Cousins-Glass system, using filter defini-
tions from Bessell (1990) for the Johnson-Cousins BVRI
bands and Bessell & Brett (1988) for Johnson-Glass JHKL
bands. Conversion of instrumental magnitudes to the stan-
dard Johnson-Cousins-Glass system was done using zero
points derived from the synthetic colors of Vega (equating
all color indices of Vega to zero). The Vega spectrum used
for this purpose was calculated with the PHOENIX code
employing full NLTE treatment (see Paper I for details).
A detailed description of the PHOENIX models, spectra,
and colors is given in Paper I. The influence of various
model parameters (such as gravity, microturbulent veloc-
ity, stellar mass) on the the broad-band photometric colors
is discussed there as well.
2.2. MARCS and ATLAS spectra and colors
Complementary to the new PHOENIX colors, we also use
synthetic colors calculated with MARCS and ATLAS model
atmospheres. MARCS spectra were kindly provided to us
by B. Plez (private communication, 2003), ATLAS colors
were taken from Castelli & Kurucz (2003). In both cases
synthetic spectra were calculated in the approximation of
plane-parallel geometry, but employing up-to-date lists of
line and molecular opacities (see e.g. Plez 2003; Castelli
& Kurucz 2003, for more details).
MARCS broad-band photometric colors were calculated
in the Johnson-Cousins-Glass photometric system employ-
ing the same procedure as with PHOENIX spectra and using
zero points obtained from the PHOENIX spectrum of Vega
(Paper I).
1 The spectra are available at the following URL: ftp://
ftp.hs.uni-hamburg.de/pub/outgoing/phoenix/GAIA/v2.6.1/.
atmospheres of late-type giants are complex, thus de-
tailed modeling of certain physical phenomena (convec-
tion, pulsations, shock waves, grain formation, mass loss)
should ideally be done using 3-D radiation hydrodynam-
ics. Obviously, while the classical 1-D model atmospheres
may still be very valuable in providing the time-averaged
properties of late-type giants (for instance, their broad-
band photometric colors), it is important to know how
well these theoretically predicted quantities reproduce the
observations of real stars.
In the first paper of this series (Kucˇinskas et al. 2005,
Paper I) we made a detailed comparison of synthetic pho-
tometric colors produced using current stellar model at-
mosphere codes (PHOENIX, MARCS, and ATLAS) with obser-
vations of late-type giants in the Solar neighborhood, at
Solar metallicity. Generally, we found that observed and
theoretical colors agree at the level of ±100K, over a wide
range of effective temperatures (Teff = 3000 . . .4800K)
and gravities (log g = 0.0 . . .+3.0; see Paper I for a de-
tailed discussion). Here we extend this analysis to sub-
Solar metallicities, assuming Solar-scaled abundances of
individual chemical species at [M/H] < 0.
There are 3 parts of this paper. First, we investigate
the influence of metallicity, [M/H], on the synthetic broad-
band photometric colors calculated with the PHOENIX stel-
lar model atmosphere code. Second, we derive a set of new
Teff–log g relations at different metallicities, based on the
published spectroscopic effective temperatures and gravi-
ties of 152 giants in Galactic globular clusters. We further
employ these relations to derive three new Teff–log g–color
scales based on the synthetic colors of PHOENIX, MARCS and
ATLAS, for [M/H] = −0.5, −1.0, −1.5, and −2.0. Finally,
we provide a detailed comparison of the new Teff–log g–
color scales based on the synthetic photometric colors
with a number of Teff–color relations available from the
literature. This comparison is done for two metallicities,
[M/H] = −1.0 and −2.0.
The paper is structured as follows. In Sect. 2 we briefly
describe synthetic spectra calculated with the PHOENIX,
MARCS and ATLASmodel atmospheres, and outline the pro-
cedure used to calculate synthetic photometric colors. The
effects of metallicity on the photometric colors are dis-
cussed in Sect. 3. The new Teff–log g scales for different
metallicities are derived in Sect. 4. Here we also discuss
a sample of Galactic globular cluster giants which is em-
ployed in the derivation of the Teff–log g relations. Finally,
the new Teff–log g–color relations based on the synthetic
colors of PHOENIX, MARCS, and ATLAS are derived in Sect. 5.
A comparison of the new Teff–log g–color scales with Teff–
color relations available in the literature is also provided.
2. Stellar atmosphere models, spectra and
synthetic colors of late-type giants
The comparison of synthetic photometric colors with
observations of late-type giants made in Sect. 5 uti-
lizes colors calculated with the PHOENIX, MARCS, and
ATLAS model atmospheres. A detailed description of the
model atmosphere codes can be found in relevant papers
(PHOENIX: Hauschildt et al. (2003) and references therein;
ATLAS: Castelli & Kurucz (2003); MARCS: Plez (2003) and
Gustafsson et al. (2003)). In the following subsections we
briefly summarize only the most crucial issues related to
the calculation of synthetic spectra and broad-band pho-
tometric colors.
2.1. PHOENIX spectra and broad-band colors
PHOENIX photometric colors used in this work were calcu-
lated in Paper I employing a new grid of PHOENIX spec-
tra. This grid is an update and extension of the previous
NextGen library of synthetic spectra of late-type giants
(Hauschildt et al. 1999b) to lower effective temperatures
and metallicities (Hauschildt et al. 2006, in preparation1).
The atmospheres and spectra in this grid were calculated
under the assumption of spherical symmetry and LTE,
for a single stellar mass M⋆ = 1M⊙. Microturbulent ve-
locity was set to ξ = 2 km s−1. Typical spectral resolution
is 0.2 nm in the optical wavelength range and gradually
decreases towards the infrared wavelengths.
The broad-band photometric colors were calculated
in the Johnson-Cousins-Glass system, using filter defini-
tions from Bessell (1990) for the Johnson-Cousins BVRI
bands and Bessell & Brett (1988) for Johnson-Glass JHKL
bands. Conversion of instrumental magnitudes to the stan-
dard Johnson-Cousins-Glass system was done using zero
points derived from the synthetic colors of Vega (equating
all color indices of Vega to zero). The Vega spectrum used
for this purpose was calculated with the PHOENIX code
employing full NLTE treatment (see Paper I for details).
A detailed description of the PHOENIX models, spectra,
and colors is given in Paper I. The influence of various
model parameters (such as gravity, microturbulent veloc-
ity, stellar mass) on the the broad-band photometric colors
is discussed there as well.
2.2. MARCS and ATLAS spectra and colors
Complementary to the new PHOENIX colors, we also use
synthetic colors calculated with MARCS and ATLAS model
atmospheres. MARCS spectra were kindly provided to us
by B. Plez (private communication, 2003), ATLAS colors
were taken from Castelli & Kurucz (2003). In both cases
synthetic spectra were calculated in the approximation of
plane-parallel geometry, but employing up-to-date lists of
line and molecular opacities (see e.g. Plez 2003; Castelli
& Kurucz 2003, for more details).
MARCS broad-band photometric colors were calculated
in the Johnson-Cousins-Glass photometric system employ-
ing the same procedure as with PHOENIX spectra and using
zero points obtained from the PHOENIX spectrum of Vega
(Paper I).
1 The spectra are available at the following URL: ftp://
ftp.hs.uni-hamburg.de/pub/outgoing/phoenix/GAIA/v2.6.1/.
Page 3
Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II. 3
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
2500
3000
3500
4000
4500
5000
5500
2 4 6 8 10
2500
3000
3500
4000
4500
5000
5500
0.4 0.6 0.8 1.0 1.2 1.4 1.6
2500
3000
3500
4000
4500
5000
5500
0.8 1.0 1.2 1.4 1.6 1.8 2.0
2500
3000
3500
4000
4500
5000
5500
V-I
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
T
e
f
f
V-K
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
J-K
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
T
e
f
f
B-V
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
Fig. 1. Influence of metallicity on synthetic photometric colors in different Teff–color planes. Late-type giants from Paper I are
shown as filled and open circles, indicating non-variable and variable stars, respectively (see Paper I for more details; stars are
only plotted to indicate the spread in the observed Teff–color sequences at Solar metallicity, not for a detailed comparison).
Thin lines with symbols are PHOENIX colors at log g = 1.5 and different metallicities. Symbols are spaced at every 100K.
3. The influence of metallicity on synthetic
photometric colors
It can be anticipated that metallicity has a significant ef-
fect on the synthetic photometric colors of late-type gi-
ants, as both atomic and molecular opacities of various
chemical species have a large influence on the emitted
spectrum at the low effective temperatures typical for late-
type giants (Paper I). In the following we will focus on the
effects due to the variations in overall metallicity, [M/H]
(assuming Solar-scaled abundances at [M/H] < 0); the in-
fluence of α-element abundances, [α/Fe], will be discussed
in a separate paper (Kucˇinskas et al. 2006, in preparation).
The influence of metallicity on the broad-band pho-
tometric colors is shown in Fig. 1 (Teff–color planes) and
Fig. 2 (color–color planes). Together with synthetic colors
of PHOENIX at several metallicities ([M/H] = 0,−1.0,−2.0;
log g = 1.5), the figures also display observations of indi-
vidual late-type giants at Solar metallicity from Paper I
(with Teff available from interferometry), to illustrate the
typical scatter in the observed sequences in Teff–color and
color–color planes.
Generally, the effects of metallicity are small in all col-
ors of the Teff–color planes for Teff >∼ 4000K. Most insen-
sitive to the changes in [M/H] is V − K, which remains
essentially unaffected at Teff >∼ 3700K. This behavior sim-
ply reflects the fact that photometric colors are little af-
fected by molecular opacities at higher effective temper-
atures (Paper I), thus the trends in the Teff–color planes
are governed by changes in atomic opacities which have
relatively little influence on the broad-band photometric
colors (note that these effects become non-negligible at
shorter wavelengths, λ <∼ 450 nm).
However, the importance of molecular opacities, and
thus the sensitivity to metallicity effects, increases rapidly
at lower effective temperatures. This is especially pro-
nounced in the Teff–(B − V ) plane, where photometric
colors develop a strong dependence on metallicity below
Teff ∼ 3800K (with redder B − V colors at lower [M/H]
values in this Teff range; note that the trend is opposite
at higher temperatures). The ‘turn-off’ towards the bluer
colors (which sets in at Teff ∼ 3800K at [M/H] = 0.0)
also tends to occur at lower Teff and redder colors at lower
metallicities. As the ‘turn-off’ in the Teff–(B − V ) plane
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
2500
3000
3500
4000
4500
5000
5500
2 4 6 8 10
2500
3000
3500
4000
4500
5000
5500
0.4 0.6 0.8 1.0 1.2 1.4 1.6
2500
3000
3500
4000
4500
5000
5500
0.8 1.0 1.2 1.4 1.6 1.8 2.0
2500
3000
3500
4000
4500
5000
5500
V-I
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
T
e
f
f
V-K
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
J-K
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
T
e
f
f
B-V
[M/H]=0.0
[M/H]=-1.0
[M/H]=-2.0
Fig. 1. Influence of metallicity on synthetic photometric colors in different Teff–color planes. Late-type giants from Paper I are
shown as filled and open circles, indicating non-variable and variable stars, respectively (see Paper I for more details; stars are
only plotted to indicate the spread in the observed Teff–color sequences at Solar metallicity, not for a detailed comparison).
Thin lines with symbols are PHOENIX colors at log g = 1.5 and different metallicities. Symbols are spaced at every 100K.
3. The influence of metallicity on synthetic
photometric colors
It can be anticipated that metallicity has a significant ef-
fect on the synthetic photometric colors of late-type gi-
ants, as both atomic and molecular opacities of various
chemical species have a large influence on the emitted
spectrum at the low effective temperatures typical for late-
type giants (Paper I). In the following we will focus on the
effects due to the variations in overall metallicity, [M/H]
(assuming Solar-scaled abundances at [M/H] < 0); the in-
fluence of α-element abundances, [α/Fe], will be discussed
in a separate paper (Kucˇinskas et al. 2006, in preparation).
The influence of metallicity on the broad-band pho-
tometric colors is shown in Fig. 1 (Teff–color planes) and
Fig. 2 (color–color planes). Together with synthetic colors
of PHOENIX at several metallicities ([M/H] = 0,−1.0,−2.0;
log g = 1.5), the figures also display observations of indi-
vidual late-type giants at Solar metallicity from Paper I
(with Teff available from interferometry), to illustrate the
typical scatter in the observed sequences in Teff–color and
color–color planes.
Generally, the effects of metallicity are small in all col-
ors of the Teff–color planes for Teff >∼ 4000K. Most insen-
sitive to the changes in [M/H] is V − K, which remains
essentially unaffected at Teff >∼ 3700K. This behavior sim-
ply reflects the fact that photometric colors are little af-
fected by molecular opacities at higher effective temper-
atures (Paper I), thus the trends in the Teff–color planes
are governed by changes in atomic opacities which have
relatively little influence on the broad-band photometric
colors (note that these effects become non-negligible at
shorter wavelengths, λ <∼ 450 nm).
However, the importance of molecular opacities, and
thus the sensitivity to metallicity effects, increases rapidly
at lower effective temperatures. This is especially pro-
nounced in the Teff–(B − V ) plane, where photometric
colors develop a strong dependence on metallicity below
Teff ∼ 3800K (with redder B − V colors at lower [M/H]
values in this Teff range; note that the trend is opposite
at higher temperatures). The ‘turn-off’ towards the bluer
colors (which sets in at Teff ∼ 3800K at [M/H] = 0.0)
also tends to occur at lower Teff and redder colors at lower
metallicities. As the ‘turn-off’ in the Teff–(B − V ) plane
Page 5
Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II. 5
Table 1. Properties of the Galactic globular cluster sample used in the derivation of Teff–log g relations (see text for details).
Group Cluster nstar nspec N 〈[Fe/H]CG97〉 〈[Fe/H]other〉 Reference Age, Gyr
1 M71, NGC 104 21 10 36 −0.74± 0.12 −0.81 ± 0.08 M71: CG97, KI03, R01 M71: 10.2 ± 1.4
NGC 104: CG97 NGC 104: 10.7 ± 1.0
2 M4, M5 31 17 31 −1.11± 0.12 −1.17 ± 0.03 M4: I99 M4: 11.7 ± 0.8
M5: CG97 M5: 11.3 ± 1.1
3 M10, M13, 46 35 70 −1.40± 0.09 −1.58 ± 0.09 M10: KI03 M10: 12.0 ± 1.1
NGC 7006 M13: CG97, KI03 M13: 12.5 ± 1.2
NGC 7006: KI03 NGC 7006: 13.1± 1.0
4 NGC 6397 10 5 18 −1.81± 0.13 −1.98 ± 0.02 CG97, MPG96 NGC 6397: 12.3± 1.1
5 M15, M92 54 15 66 −2.16± 0.06 −2.36 ± 0.05 M15: KI03, S00 M15: 11.8 ± 0.8
M92: CG97, KI03, S00 M92: 12.6 ± 0.9
generally well observed, with precise atmospheric param-
eters of individual stars available over a wide range of ef-
fective temperatures and gravities. Second, GGCs span a
wide metallicity range, which is crucial for the derivation
of Teff–log g relations at different [M/H]. Finally, they are
of similar age which implies a similarity in the atmospheric
parameters of individual stars in clusters of similar metal-
licity. This allows binning of stars from different clusters
into groups according to their metallicities, to increase the
number of individual stars available in a given metallicity
group.
4.1. Stellar sample
Ideally, the new Teff–log g relations should be derived us-
ing a sample of late-type giants with their effective tem-
peratures and gravities measured using direct methods,
e.g., effective temperatures obtained via the interferomet-
ric measurements of stellar radii, and gravities from par-
allaxes (i.e., ‘evolutionary’ gravities, see Sect. 4.1.2 be-
low). Unfortunately, direct measurements of atmospheric
parameters are currently available only for the nearby
giants, the majority of which have metallicities close to
Solar. Needless to say, late-type giants in the GGCs are
not accessible, due to the large distances involved. For this
reason, our new relations derived in this Section are based
on spectroscopic effective temperatures and gravities of
GGC giants (in combination with Teff and log g from pho-
tometry, see below), with temperatures obtained under
the assumption of excitation equilibrium of Fe I lines, and
gravities derived assuming the ionization equilibrium of
Fe II lines.
The core of our sample is based on the GGCs analyzed
by the Lick-Texas group, in particular, their recent spec-
troscopic study of late-type giants in 16 GGCs (Kraft &
Ivans 2003, KI03, and references therein). Whenever avail-
able, data from other sources were also used, providing a
consistency check between the results of different groups.
We made every attempt to assure that the Teff used in
our study are derived from the analysis of recently ob-
tained high quality spectroscopic data, or literature data
re-analyzed in a self-consistent and homogeneous way, em-
ploying the advantages of improved stellar model atmo-
spheres, analysis techniques, and so forth.
The final sample consists of 82 GGC late-type giants
with precise estimates of effective temperatures, gravi-
ties and metallicities from high-resolution spectroscopy.
Additionally, we use 70 stars with Teff and log g avail-
able from photometry, which nearly doubles the number
of stars and individual measurements of stellar parame-
ters available for the analysis. We justify the latter choice
by making a careful verification of the effective tempera-
tures and gravities derived with photometry, spectroscopy
and the infrared flux method (IRFM; Blackwell et al.
1990), finding a generally good agreement in Teff and log g
obtained with these different methods (Sect. 4.1.1 and
Sect. 4.1.2). Metallicities of the individual sample stars
are in the range of [Fe/H] = −0.7 . . .− 2.5.
Individual clusters with similar [Fe/H] values were
binned into five metallicity groups, to increase the number
of stars in each group. In fact, this procedure may smear
intrinsic morphological differences in the giant branches
of different clusters in the Teff–log g plane. However, as
will be shown in Sect. 5, differences between the RGB se-
quences of individual clusters in the Teff–log g plane are
always considerably smaller than the typical errors in the
derivations of Teff and log g.
Properties of the five cluster groups are summarized in
Table 1. The contents of columns 3–5 are: nstar is a total
number of stars in a given group for which a total of N
(spectroscopic plus photometric) independent derivations
of Teff and log g is available; nspec gives the number of stars
with both effective temperatures and gravities available
from high-resolution spectroscopy.
Below we focus on the atmospheric parameters of the
sample stars in more detail.
4.1.1. Effective temperatures
Approximately half of the individual cluster giants used
in this study (77 stars) have effective temperatures avail-
able from spectroscopic analysis (i.e., derived under the as-
sumption of excitation equilibrium of Fe I lines). However,
spectroscopic estimates are rather sensitive to different
model assumptions, details of the analysis procedure, etc.
Table 1. Properties of the Galactic globular cluster sample used in the derivation of Teff–log g relations (see text for details).
Group Cluster nstar nspec N 〈[Fe/H]CG97〉 〈[Fe/H]other〉 Reference Age, Gyr
1 M71, NGC 104 21 10 36 −0.74± 0.12 −0.81 ± 0.08 M71: CG97, KI03, R01 M71: 10.2 ± 1.4
NGC 104: CG97 NGC 104: 10.7 ± 1.0
2 M4, M5 31 17 31 −1.11± 0.12 −1.17 ± 0.03 M4: I99 M4: 11.7 ± 0.8
M5: CG97 M5: 11.3 ± 1.1
3 M10, M13, 46 35 70 −1.40± 0.09 −1.58 ± 0.09 M10: KI03 M10: 12.0 ± 1.1
NGC 7006 M13: CG97, KI03 M13: 12.5 ± 1.2
NGC 7006: KI03 NGC 7006: 13.1± 1.0
4 NGC 6397 10 5 18 −1.81± 0.13 −1.98 ± 0.02 CG97, MPG96 NGC 6397: 12.3± 1.1
5 M15, M92 54 15 66 −2.16± 0.06 −2.36 ± 0.05 M15: KI03, S00 M15: 11.8 ± 0.8
M92: CG97, KI03, S00 M92: 12.6 ± 0.9
generally well observed, with precise atmospheric param-
eters of individual stars available over a wide range of ef-
fective temperatures and gravities. Second, GGCs span a
wide metallicity range, which is crucial for the derivation
of Teff–log g relations at different [M/H]. Finally, they are
of similar age which implies a similarity in the atmospheric
parameters of individual stars in clusters of similar metal-
licity. This allows binning of stars from different clusters
into groups according to their metallicities, to increase the
number of individual stars available in a given metallicity
group.
4.1. Stellar sample
Ideally, the new Teff–log g relations should be derived us-
ing a sample of late-type giants with their effective tem-
peratures and gravities measured using direct methods,
e.g., effective temperatures obtained via the interferomet-
ric measurements of stellar radii, and gravities from par-
allaxes (i.e., ‘evolutionary’ gravities, see Sect. 4.1.2 be-
low). Unfortunately, direct measurements of atmospheric
parameters are currently available only for the nearby
giants, the majority of which have metallicities close to
Solar. Needless to say, late-type giants in the GGCs are
not accessible, due to the large distances involved. For this
reason, our new relations derived in this Section are based
on spectroscopic effective temperatures and gravities of
GGC giants (in combination with Teff and log g from pho-
tometry, see below), with temperatures obtained under
the assumption of excitation equilibrium of Fe I lines, and
gravities derived assuming the ionization equilibrium of
Fe II lines.
The core of our sample is based on the GGCs analyzed
by the Lick-Texas group, in particular, their recent spec-
troscopic study of late-type giants in 16 GGCs (Kraft &
Ivans 2003, KI03, and references therein). Whenever avail-
able, data from other sources were also used, providing a
consistency check between the results of different groups.
We made every attempt to assure that the Teff used in
our study are derived from the analysis of recently ob-
tained high quality spectroscopic data, or literature data
re-analyzed in a self-consistent and homogeneous way, em-
ploying the advantages of improved stellar model atmo-
spheres, analysis techniques, and so forth.
The final sample consists of 82 GGC late-type giants
with precise estimates of effective temperatures, gravi-
ties and metallicities from high-resolution spectroscopy.
Additionally, we use 70 stars with Teff and log g avail-
able from photometry, which nearly doubles the number
of stars and individual measurements of stellar parame-
ters available for the analysis. We justify the latter choice
by making a careful verification of the effective tempera-
tures and gravities derived with photometry, spectroscopy
and the infrared flux method (IRFM; Blackwell et al.
1990), finding a generally good agreement in Teff and log g
obtained with these different methods (Sect. 4.1.1 and
Sect. 4.1.2). Metallicities of the individual sample stars
are in the range of [Fe/H] = −0.7 . . .− 2.5.
Individual clusters with similar [Fe/H] values were
binned into five metallicity groups, to increase the number
of stars in each group. In fact, this procedure may smear
intrinsic morphological differences in the giant branches
of different clusters in the Teff–log g plane. However, as
will be shown in Sect. 5, differences between the RGB se-
quences of individual clusters in the Teff–log g plane are
always considerably smaller than the typical errors in the
derivations of Teff and log g.
Properties of the five cluster groups are summarized in
Table 1. The contents of columns 3–5 are: nstar is a total
number of stars in a given group for which a total of N
(spectroscopic plus photometric) independent derivations
of Teff and log g is available; nspec gives the number of stars
with both effective temperatures and gravities available
from high-resolution spectroscopy.
Below we focus on the atmospheric parameters of the
sample stars in more detail.
4.1.1. Effective temperatures
Approximately half of the individual cluster giants used
in this study (77 stars) have effective temperatures avail-
able from spectroscopic analysis (i.e., derived under the as-
sumption of excitation equilibrium of Fe I lines). However,
spectroscopic estimates are rather sensitive to different
model assumptions, details of the analysis procedure, etc.
Page 6
6 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
For example, The´venin & Idiart (1999) have shown that
at low metallicities Fe I lines may suffer considerably from
overionization, due to the leakage of UV photons into the
outer stellar atmosphere because of the lower opacities as-
sociated with lower [Fe/H] values. This may indeed have
an effect if the effective temperatures are derived under
the assumption of excitation equilibrium of Fe I.
For seventeen late-type giants in three clusters from
Table 1 (M92, M13, M71), effective temperatures are avail-
able both from spectroscopy (KI03) and the infrared flux
method, IRFM (Alonso et al. 1999b, A99). Effective tem-
peratures and angular diameters obtained with the IRFM
usually agree fairly well with direct estimates available
from interferometry and/or lunar occultations, for stars
of different luminosity classes and effective temperatures
(see, e.g., Nordgren et al. 2001; Blackwell & Lynas-Gray
1998; Alonso et al. 1999a, 2000). A comparison with the
IRFM temperatures may thus offer an independent sanity
check for the spectroscopically and photometrically de-
rived effective temperatures. This is done in Fig. 3.
Clearly, the differences between Teff from spectroscopy
and TIRFM (filled circles in Fig. 3) are small in the cases
of M92 and M13; the average offsets are ∆Teff ≃ 30K
and ∆Teff ≃ 40K, respectively, (i.e., spectroscopic Teff are
higher), with RMS residuals of ≃ 60K and ≃ 70K. There
is no evidence for any statistically significant systematic
trends either. Note, however, that in the case of M13 the
average offset is mostly determined by the large offset of
a single star at TIRFM = 3790K (∆Teff ≃ 180K), and
amounts to only ∆Teff ≃ 10K if this star is removed from
the averaging procedure. A larger offset is seen in case
of M71, with spectroscopic temperatures derived by KI03
being higher by ∆Teff ≃ 140K (RMS residual ≃ 30K).
A comparison of photometrically derived effective tem-
peratures of stars in our sample (available for 33 objects)
with those obtained with the IRFM shows that photo-
metric Teff generally tend to be slightly higher, with the
average offsets of about 85K, 90K and 55K for clusters
in groups 5, 3, and 1, respectively (triangles and asterisks
in Fig. 3). While the average offset in group 1 is relatively
small, the RMS residual is large (≃ 150K), due to the
large offset of the photometric temperatures of individual
stars in M71 (≃ 150K) derived by Carretta & Gratton
(1997, CG97).
Interestingly, while KI03 and CG97 stars in M71 are
obvious outliers in Fig. 3, they all lie very close to the av-
erage Teff–log g sequence in the Teff–log g plane (Sect. 4.2,
Fig. 6). At the same time, there are no signs for the
discrepancies between the spectroscopic and evolutionary
gravities of these stars (Sect. 4.1.2). Also, their gravities
agree well with those of stars from other clusters in this
metallicity group. Altogether this may indicate that dis-
crepancies seen in Fig. 3 may in fact be due to somewhat
lower IRFM temperatures of A99 rather than the system-
atically higher temperatures of KI03 and CG97.
One should note, however, that the number of stars
used in this comparison is small, thus the trends hinted
at in Fig. 3 may clearly be influenced (or even governed)
5000 4500 4000 3500
-400
-200
0
200
400
-400
-200
0
200
400
-400
-200
0
200
400
Group 1
NGC104: CG97
T
IRFM
, K
M71: KI03
M71: CG97
M71: R01
Group 3
T
S
P
E
C
/
P
H
O
T
-
T
I
R
F
M
M13: KI03
M13: CG97
M92: KI03
M92: CG97
M92: S00
Group 5
Fig. 3. Comparison of the IRFM temperatures of late-type gi-
ants in Galactic globular clusters used in this work, as derived
by Alonso et al. (1999b, A99), with Teff obtained from spec-
troscopy and photometry (cluster groups 5, 3, 1, top-down;
the contents and properties of individual cluster groups are
given in Table 1). Different symbols indicate original sources
from which spectroscopic (filled circles) and photometric (other
symbols) effective temperatures were taken. Note that in case
of groups 5 and 3 IRFM temperatures are only available for
stars in one cluster.
by selection effects. KI03, for instance, find a good agree-
ment between spectroscopically obtained effective temper-
atures and those resulting from photometry for the major-
ity of late-type giants in their study (containing 149 stars).
Nevertheless, the differences in Teff of individual stars de-
rived by different authors may provide an idea about the
limits of the precision of photometrically derived effec-
tive temperatures, reflecting the influence of various sys-
tematical effects, discrepancies in Teff predicted by differ-
ent Teff–color relations, and so forth. It is obvious that in
many cases these differences are considerably larger than
∼ 100K, a value frequently quoted as a typical uncer-
tainty for the photometrically derived effective tempera-
tures, which suggests that errors in the photometrically
derived Teff are frequently seriously underestimated (see
also discussion in Paper I).
4.1.2. Gravities
Two kinds of gravities are used in spectroscopic abun-
dance analyses. One is ‘evolutionary’ gravity, which is de-
rived through the Teff–L⋆–M⋆–log g relation (L⋆ and M⋆
are stellar luminosity and mass, respectively), where effec-
tive temperature is typically obtained from photometric
colors, luminosity from absolute magnitude and bolomet-
ric correction, and the mass is implied from evolutionary
For example, The´venin & Idiart (1999) have shown that
at low metallicities Fe I lines may suffer considerably from
overionization, due to the leakage of UV photons into the
outer stellar atmosphere because of the lower opacities as-
sociated with lower [Fe/H] values. This may indeed have
an effect if the effective temperatures are derived under
the assumption of excitation equilibrium of Fe I.
For seventeen late-type giants in three clusters from
Table 1 (M92, M13, M71), effective temperatures are avail-
able both from spectroscopy (KI03) and the infrared flux
method, IRFM (Alonso et al. 1999b, A99). Effective tem-
peratures and angular diameters obtained with the IRFM
usually agree fairly well with direct estimates available
from interferometry and/or lunar occultations, for stars
of different luminosity classes and effective temperatures
(see, e.g., Nordgren et al. 2001; Blackwell & Lynas-Gray
1998; Alonso et al. 1999a, 2000). A comparison with the
IRFM temperatures may thus offer an independent sanity
check for the spectroscopically and photometrically de-
rived effective temperatures. This is done in Fig. 3.
Clearly, the differences between Teff from spectroscopy
and TIRFM (filled circles in Fig. 3) are small in the cases
of M92 and M13; the average offsets are ∆Teff ≃ 30K
and ∆Teff ≃ 40K, respectively, (i.e., spectroscopic Teff are
higher), with RMS residuals of ≃ 60K and ≃ 70K. There
is no evidence for any statistically significant systematic
trends either. Note, however, that in the case of M13 the
average offset is mostly determined by the large offset of
a single star at TIRFM = 3790K (∆Teff ≃ 180K), and
amounts to only ∆Teff ≃ 10K if this star is removed from
the averaging procedure. A larger offset is seen in case
of M71, with spectroscopic temperatures derived by KI03
being higher by ∆Teff ≃ 140K (RMS residual ≃ 30K).
A comparison of photometrically derived effective tem-
peratures of stars in our sample (available for 33 objects)
with those obtained with the IRFM shows that photo-
metric Teff generally tend to be slightly higher, with the
average offsets of about 85K, 90K and 55K for clusters
in groups 5, 3, and 1, respectively (triangles and asterisks
in Fig. 3). While the average offset in group 1 is relatively
small, the RMS residual is large (≃ 150K), due to the
large offset of the photometric temperatures of individual
stars in M71 (≃ 150K) derived by Carretta & Gratton
(1997, CG97).
Interestingly, while KI03 and CG97 stars in M71 are
obvious outliers in Fig. 3, they all lie very close to the av-
erage Teff–log g sequence in the Teff–log g plane (Sect. 4.2,
Fig. 6). At the same time, there are no signs for the
discrepancies between the spectroscopic and evolutionary
gravities of these stars (Sect. 4.1.2). Also, their gravities
agree well with those of stars from other clusters in this
metallicity group. Altogether this may indicate that dis-
crepancies seen in Fig. 3 may in fact be due to somewhat
lower IRFM temperatures of A99 rather than the system-
atically higher temperatures of KI03 and CG97.
One should note, however, that the number of stars
used in this comparison is small, thus the trends hinted
at in Fig. 3 may clearly be influenced (or even governed)
5000 4500 4000 3500
-400
-200
0
200
400
-400
-200
0
200
400
-400
-200
0
200
400
Group 1
NGC104: CG97
T
IRFM
, K
M71: KI03
M71: CG97
M71: R01
Group 3
T
S
P
E
C
/
P
H
O
T
-
T
I
R
F
M
M13: KI03
M13: CG97
M92: KI03
M92: CG97
M92: S00
Group 5
Fig. 3. Comparison of the IRFM temperatures of late-type gi-
ants in Galactic globular clusters used in this work, as derived
by Alonso et al. (1999b, A99), with Teff obtained from spec-
troscopy and photometry (cluster groups 5, 3, 1, top-down;
the contents and properties of individual cluster groups are
given in Table 1). Different symbols indicate original sources
from which spectroscopic (filled circles) and photometric (other
symbols) effective temperatures were taken. Note that in case
of groups 5 and 3 IRFM temperatures are only available for
stars in one cluster.
by selection effects. KI03, for instance, find a good agree-
ment between spectroscopically obtained effective temper-
atures and those resulting from photometry for the major-
ity of late-type giants in their study (containing 149 stars).
Nevertheless, the differences in Teff of individual stars de-
rived by different authors may provide an idea about the
limits of the precision of photometrically derived effec-
tive temperatures, reflecting the influence of various sys-
tematical effects, discrepancies in Teff predicted by differ-
ent Teff–color relations, and so forth. It is obvious that in
many cases these differences are considerably larger than
∼ 100K, a value frequently quoted as a typical uncer-
tainty for the photometrically derived effective tempera-
tures, which suggests that errors in the photometrically
derived Teff are frequently seriously underestimated (see
also discussion in Paper I).
4.1.2. Gravities
Two kinds of gravities are used in spectroscopic abun-
dance analyses. One is ‘evolutionary’ gravity, which is de-
rived through the Teff–L⋆–M⋆–log g relation (L⋆ and M⋆
are stellar luminosity and mass, respectively), where effec-
tive temperature is typically obtained from photometric
colors, luminosity from absolute magnitude and bolomet-
ric correction, and the mass is implied from evolutionary
Page 10
10 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
Table 3. Analytical expressions corresponding to the empirical Teff–log g relations given in Table 2, in the form log g =
a0 + a1Teff + a2T 2eff + a3T
3
eff + a4T
4
eff .
Group a0 a1 a2 a3 a4 Teff range, K
[Fe/H] = 0.0 8.07 –1.045e-2 3.997e-6 –5.814e-10 3.240e-14 3300 ≤ Teff ≤ 4800
1 –1.41 –6.761e-4 3.086e-7 – – 3700 ≤ Teff ≤ 4800
2 –1.51 –6.394e-4 2.948e-7 – – 3600 ≤ Teff ≤ 4600
3 –0.95 –1.100e-3 3.597e-7 – – 3600 ≤ Teff ≤ 4900
4 2.60 –2.820e-3 5.596e-7 – – 4000 ≤ Teff ≤ 4900
5 –2.87 –3.360e-4 2.714e-7 – – 4000 ≤ Teff ≤ 4900
Table 4. New Teff–log g relations at several metallicities, obtained by interpolating empirical Teff–log g relations from Table 2.
The new relations are given for the metallicity scales of KI03 and CG97 (see text for details).
Teff log g
[Fe/H] according to [Fe/H] according to
CG97 metallicity scale KI03 metallicity scale
–0.5 –1.0 –1.5 –2.0 –0.5 –1.0 –1.5 –2.0
4900 2.80 2.52 2.28 2.09 2.83 2.59 2.37 2.15
4800 2.58 2.29 2.04 1.85 2.61 2.35 2.13 1.90
4700 2.36 2.06 1.81 1.61 2.39 2.12 1.89 1.67
4600 2.14 1.84 1.59 1.38 2.17 1.90 1.67 1.44
4500 1.93 1.63 1.37 1.17 1.96 1.68 1.45 1.22
4400 1.73 1.42 1.16 0.95 1.76 1.48 1.24 1.01
4300 1.53 1.22 0.96 0.75 1.56 1.28 1.04 0.81
4200 1.34 1.03 0.76 0.56 1.37 1.08 0.84 0.61
4100 1.15 0.84 0.57 0.37 1.18 0.90 0.65 0.43
4000 0.97 0.66 0.39 0.19 1.00 0.72 0.47 0.25
3900 0.80 0.49 0.21 0.02 0.82 0.55 0.30 0.08
3800 0.63 0.33 0.04 –0.15 0.65 0.38 0.13 –0.08
3700 0.46 0.17 –0.12 –0.30 0.48 0.23 –0.03 –0.23
3600 0.30 0.02 –0.28 –0.45 0.32 0.08 –0.18 –0.37
3500 0.15 –0.13 –0.42 –0.59 0.17 –0.07 –0.32 –0.51
5000 4500 4000 3500
0.0
0.1
0.2
l
o
g
g
K
I
0
3
-
l
o
g
g
C
G
9
7
T
eff
, K
[Fe/H]=-2.0
[Fe/H]=-1.5
[Fe/H]=-1.0
[Fe/H]=-0.5
Fig. 7. The difference in gravities predicted by the new Teff–
log g relations (Table 4) based on the metallicity scales of KI03
and CG97, at several [Fe/H].
ingly, ∼ 50K in Teff , see Fig. 7). The RMS residuals of the
interpolation procedure do not exceed 0.03 dex in log g.
It is worth remarking that the clusters in our sample
are old; thus the masses of their RGB stars should be low,
typically∼ 0.8−0.9M⊙ (Yi et al. 2001). Though the direct
effect of stellar mass on the broad-band photometric colors
is small (see Paper I), Teff–log g relations will indeed be
different in case of younger stellar populations, because
Table 5. Analytical expressions corresponding to the new Teff–
log g relations given in Table 4, in the form log g = a0+a1Teff+
a2T 2eff .
[Fe/H] a0 a1 a2
CG97 scale
-0.5 –1.85 –3.761e-4 2.703e-7
-1.0 –0.82 –1.010e-3 3.453e-7
-1.5 –1.41 –8.991e-4 3.371e-7
-2.0 –0.48 –1.420e-3 3.969e-7
KI03 scale
-0.5 –1.81 –3.885e-4 2.726e-7
-1.0 –0.52 –1.130e-3 3.600e-7
-1.5 –0.78 –1.150e-3 3.657e-7
-2.0 0.09 –1.650e-3 4.225e-7
of the higher masses of their RGB stars. For example,
at [M/H] = −1.0 and Teff = 4400K, the gravity on the
2Gyr isochrone will be about 0.15 dex lower than log g
corresponding to the same effective temperature on the
15Gyr isochrone (this difference is smaller at lower Teff
and [M/H], Yi et al. 2001). Fortunately, the effect of this
Table 3. Analytical expressions corresponding to the empirical Teff–log g relations given in Table 2, in the form log g =
a0 + a1Teff + a2T 2eff + a3T
3
eff + a4T
4
eff .
Group a0 a1 a2 a3 a4 Teff range, K
[Fe/H] = 0.0 8.07 –1.045e-2 3.997e-6 –5.814e-10 3.240e-14 3300 ≤ Teff ≤ 4800
1 –1.41 –6.761e-4 3.086e-7 – – 3700 ≤ Teff ≤ 4800
2 –1.51 –6.394e-4 2.948e-7 – – 3600 ≤ Teff ≤ 4600
3 –0.95 –1.100e-3 3.597e-7 – – 3600 ≤ Teff ≤ 4900
4 2.60 –2.820e-3 5.596e-7 – – 4000 ≤ Teff ≤ 4900
5 –2.87 –3.360e-4 2.714e-7 – – 4000 ≤ Teff ≤ 4900
Table 4. New Teff–log g relations at several metallicities, obtained by interpolating empirical Teff–log g relations from Table 2.
The new relations are given for the metallicity scales of KI03 and CG97 (see text for details).
Teff log g
[Fe/H] according to [Fe/H] according to
CG97 metallicity scale KI03 metallicity scale
–0.5 –1.0 –1.5 –2.0 –0.5 –1.0 –1.5 –2.0
4900 2.80 2.52 2.28 2.09 2.83 2.59 2.37 2.15
4800 2.58 2.29 2.04 1.85 2.61 2.35 2.13 1.90
4700 2.36 2.06 1.81 1.61 2.39 2.12 1.89 1.67
4600 2.14 1.84 1.59 1.38 2.17 1.90 1.67 1.44
4500 1.93 1.63 1.37 1.17 1.96 1.68 1.45 1.22
4400 1.73 1.42 1.16 0.95 1.76 1.48 1.24 1.01
4300 1.53 1.22 0.96 0.75 1.56 1.28 1.04 0.81
4200 1.34 1.03 0.76 0.56 1.37 1.08 0.84 0.61
4100 1.15 0.84 0.57 0.37 1.18 0.90 0.65 0.43
4000 0.97 0.66 0.39 0.19 1.00 0.72 0.47 0.25
3900 0.80 0.49 0.21 0.02 0.82 0.55 0.30 0.08
3800 0.63 0.33 0.04 –0.15 0.65 0.38 0.13 –0.08
3700 0.46 0.17 –0.12 –0.30 0.48 0.23 –0.03 –0.23
3600 0.30 0.02 –0.28 –0.45 0.32 0.08 –0.18 –0.37
3500 0.15 –0.13 –0.42 –0.59 0.17 –0.07 –0.32 –0.51
5000 4500 4000 3500
0.0
0.1
0.2
l
o
g
g
K
I
0
3
-
l
o
g
g
C
G
9
7
T
eff
, K
[Fe/H]=-2.0
[Fe/H]=-1.5
[Fe/H]=-1.0
[Fe/H]=-0.5
Fig. 7. The difference in gravities predicted by the new Teff–
log g relations (Table 4) based on the metallicity scales of KI03
and CG97, at several [Fe/H].
ingly, ∼ 50K in Teff , see Fig. 7). The RMS residuals of the
interpolation procedure do not exceed 0.03 dex in log g.
It is worth remarking that the clusters in our sample
are old; thus the masses of their RGB stars should be low,
typically∼ 0.8−0.9M⊙ (Yi et al. 2001). Though the direct
effect of stellar mass on the broad-band photometric colors
is small (see Paper I), Teff–log g relations will indeed be
different in case of younger stellar populations, because
Table 5. Analytical expressions corresponding to the new Teff–
log g relations given in Table 4, in the form log g = a0+a1Teff+
a2T 2eff .
[Fe/H] a0 a1 a2
CG97 scale
-0.5 –1.85 –3.761e-4 2.703e-7
-1.0 –0.82 –1.010e-3 3.453e-7
-1.5 –1.41 –8.991e-4 3.371e-7
-2.0 –0.48 –1.420e-3 3.969e-7
KI03 scale
-0.5 –1.81 –3.885e-4 2.726e-7
-1.0 –0.52 –1.130e-3 3.600e-7
-1.5 –0.78 –1.150e-3 3.657e-7
-2.0 0.09 –1.650e-3 4.225e-7
of the higher masses of their RGB stars. For example,
at [M/H] = −1.0 and Teff = 4400K, the gravity on the
2Gyr isochrone will be about 0.15 dex lower than log g
corresponding to the same effective temperature on the
15Gyr isochrone (this difference is smaller at lower Teff
and [M/H], Yi et al. 2001). Fortunately, the effect of this
Page 11
Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II. 11
Table 6. Teff–log g–color relations for the late-type giants based on the synthetic colors calculated with PHOENIX and MARCS
model atmospheres. Photometric colors are given in the Johnson-Cousins-Glass system (see Sect. 2 for details).
PHOENIX MARCS
Teff log g B−V V −I V −K J−K B−V V −I V −K J−K
[Fe/H]=–0.5
4900 2.83 0.931 0.994 2.226 0.596 – – – –
4800 2.61 0.977 1.033 2.328 0.626 – – – –
4700 2.39 1.023 1.075 2.437 0.658 – – – –
4600 2.17 1.076 1.121 2.553 0.693 – – – –
4500 1.96 1.130 1.170 2.677 0.729 1.157 1.138 2.662 0.735
4400 1.76 1.190 1.227 2.813 0.768 1.218 1.190 2.792 0.774
4300 1.56 1.250 1.288 2.958 0.810 1.279 1.245 2.932 0.816
4200 1.37 1.317 1.357 3.118 0.855 1.347 1.312 3.086 0.860
4100 1.17 1.385 1.435 3.291 0.903 1.420 1.387 3.255 0.907
4000 1.00 1.452 1.523 3.479 0.953 1.492 1.472 3.439 0.957
3900 0.82 1.525 1.630 3.692 1.004 1.562 1.570 3.644 1.009
3800 0.65 1.592 1.757 3.932 1.058 1.624 1.690 3.876 1.065
3700 0.48 1.650 1.915 4.212 1.114 1.672 1.841 4.148 1.121
3600 0.32 1.687 2.136 4.566 1.164 1.691 2.046 4.484 1.179
3500 0.17 1.681 2.436 5.021 1.212 – – – –
[Fe/H]=–1.0
4900 2.59 0.880 0.986 2.230 0.605 – – – –
4800 2.35 0.926 1.025 2.329 0.635 – – – –
4700 2.12 0.975 1.067 2.438 0.667 – – – –
4600 1.90 1.031 1.113 2.554 0.702 – – – –
4500 1.68 1.094 1.165 2.681 0.738 1.114 1.135 2.661 0.739
4400 1.48 1.157 1.220 2.816 0.778 1.183 1.185 2.783 0.774
4300 1.28 1.229 1.284 2.966 0.820 1.249 1.247 2.933 0.819
4200 1.08 1.304 1.355 3.128 0.866 1.330 1.312 3.080 0.858
4100 0.90 1.384 1.433 3.302 0.914 1.402 1.387 3.255 0.910
4000 0.72 1.471 1.523 3.498 0.966 1.484 1.466 3.429 0.956
3900 0.55 1.560 1.622 3.707 1.021 1.561 1.559 3.638 1.018
3800 0.38 1.659 1.744 3.945 1.078 1.641 1.663 3.851 1.071
3700 0.23 1.753 1.886 4.211 1.137 – – – –
3600 0.08 1.832 2.068 4.520 1.191 – – – –
3500 –0.07 1.883 2.320 4.910 1.239 – – – –
[Fe/H]=–1.5
4900 2.37 0.846 0.992 2.234 0.606 – – – –
4800 2.13 0.896 1.031 2.335 0.635 – – – –
4700 1.89 0.952 1.074 2.443 0.667 – – – –
4600 1.67 1.014 1.123 2.561 0.701 – – – –
4500 1.45 1.084 1.177 2.691 0.737 1.091 1.147 2.674 0.741
4400 1.24 1.164 1.241 2.832 0.775 1.170 1.207 2.810 0.778
4300 1.04 1.248 1.310 2.987 0.817 1.252 1.273 2.957 0.819
4200 0.84 1.342 1.390 3.159 0.860 1.338 1.343 3.117 0.863
4100 0.65 1.440 1.479 3.351 0.910 1.425 1.418 3.289 0.911
4000 0.47 1.543 1.579 3.557 0.963 1.514 1.501 3.475 0.964
3900 0.30 1.656 1.695 3.789 1.018 1.606 1.592 3.680 1.022
3800 0.13 1.774 1.824 4.043 1.078 – – – –
3700 –0.03 1.896 1.968 4.316 1.139 – – – –
3600 –0.18 2.017 2.150 4.631 1.196 – – – –
3500 –0.32 1.998 2.243 4.941 1.319 – – – –
[Fe/H]=–2.0
4900 2.15 0.820 1.002 2.240 0.604 – – – –
4800 1.90 0.878 1.046 2.341 0.632 – – – –
4700 1.67 0.944 1.094 2.453 0.662 – – – –
4600 1.44 1.018 1.148 2.574 0.692 – – – –
4500 1.22 1.107 1.214 2.711 0.725 1.094 1.183 2.706 0.738
4400 1.01 1.200 1.285 2.858 0.759 1.186 1.253 2.849 0.773
4300 0.81 1.304 1.370 3.029 0.798 1.282 1.327 3.006 0.813
4200 0.61 1.417 1.465 3.218 0.842 1.382 1.406 3.175 0.857
4100 0.43 1.534 1.571 3.426 0.889 1.484 1.490 3.358 0.906
4000 0.25 1.660 1.696 3.664 0.939 1.588 1.580 3.555 0.961
3900 0.08 1.787 1.828 3.918 0.994 – – – –
3800 –0.08 1.917 1.981 4.212 1.059 – – – –
3700 –0.23 2.050 2.150 4.524 1.121 – – – –
3600 –0.37 2.178 2.328 4.843 1.181 – – – –
3500 –0.51 2.207 2.568 5.140 1.175 – – – –
difference is small: a shift in gravity by∼ 0.15dex at Teff =
4400K will translate to ∆(B − V ) ∼ 0.02 for [Fe/H] =
−1.0 and to ∼ 0.03 for [Fe/H] = −2.0, with colors at
lower log g becoming redder (differences in other colors
are smaller).
While the new Teff–log g relations provided in Tables 4
and 5 cover the effective temperature range of Teff =
3500 − 4900K, it should be taken into account that un-
certainties in these relations will likely be larger below
Teff ∼ 3900K and above Teff ∼ 4600K, where an extrap-
olation was used to compensate for a lack of stars in cer-
Table 6. Teff–log g–color relations for the late-type giants based on the synthetic colors calculated with PHOENIX and MARCS
model atmospheres. Photometric colors are given in the Johnson-Cousins-Glass system (see Sect. 2 for details).
PHOENIX MARCS
Teff log g B−V V −I V −K J−K B−V V −I V −K J−K
[Fe/H]=–0.5
4900 2.83 0.931 0.994 2.226 0.596 – – – –
4800 2.61 0.977 1.033 2.328 0.626 – – – –
4700 2.39 1.023 1.075 2.437 0.658 – – – –
4600 2.17 1.076 1.121 2.553 0.693 – – – –
4500 1.96 1.130 1.170 2.677 0.729 1.157 1.138 2.662 0.735
4400 1.76 1.190 1.227 2.813 0.768 1.218 1.190 2.792 0.774
4300 1.56 1.250 1.288 2.958 0.810 1.279 1.245 2.932 0.816
4200 1.37 1.317 1.357 3.118 0.855 1.347 1.312 3.086 0.860
4100 1.17 1.385 1.435 3.291 0.903 1.420 1.387 3.255 0.907
4000 1.00 1.452 1.523 3.479 0.953 1.492 1.472 3.439 0.957
3900 0.82 1.525 1.630 3.692 1.004 1.562 1.570 3.644 1.009
3800 0.65 1.592 1.757 3.932 1.058 1.624 1.690 3.876 1.065
3700 0.48 1.650 1.915 4.212 1.114 1.672 1.841 4.148 1.121
3600 0.32 1.687 2.136 4.566 1.164 1.691 2.046 4.484 1.179
3500 0.17 1.681 2.436 5.021 1.212 – – – –
[Fe/H]=–1.0
4900 2.59 0.880 0.986 2.230 0.605 – – – –
4800 2.35 0.926 1.025 2.329 0.635 – – – –
4700 2.12 0.975 1.067 2.438 0.667 – – – –
4600 1.90 1.031 1.113 2.554 0.702 – – – –
4500 1.68 1.094 1.165 2.681 0.738 1.114 1.135 2.661 0.739
4400 1.48 1.157 1.220 2.816 0.778 1.183 1.185 2.783 0.774
4300 1.28 1.229 1.284 2.966 0.820 1.249 1.247 2.933 0.819
4200 1.08 1.304 1.355 3.128 0.866 1.330 1.312 3.080 0.858
4100 0.90 1.384 1.433 3.302 0.914 1.402 1.387 3.255 0.910
4000 0.72 1.471 1.523 3.498 0.966 1.484 1.466 3.429 0.956
3900 0.55 1.560 1.622 3.707 1.021 1.561 1.559 3.638 1.018
3800 0.38 1.659 1.744 3.945 1.078 1.641 1.663 3.851 1.071
3700 0.23 1.753 1.886 4.211 1.137 – – – –
3600 0.08 1.832 2.068 4.520 1.191 – – – –
3500 –0.07 1.883 2.320 4.910 1.239 – – – –
[Fe/H]=–1.5
4900 2.37 0.846 0.992 2.234 0.606 – – – –
4800 2.13 0.896 1.031 2.335 0.635 – – – –
4700 1.89 0.952 1.074 2.443 0.667 – – – –
4600 1.67 1.014 1.123 2.561 0.701 – – – –
4500 1.45 1.084 1.177 2.691 0.737 1.091 1.147 2.674 0.741
4400 1.24 1.164 1.241 2.832 0.775 1.170 1.207 2.810 0.778
4300 1.04 1.248 1.310 2.987 0.817 1.252 1.273 2.957 0.819
4200 0.84 1.342 1.390 3.159 0.860 1.338 1.343 3.117 0.863
4100 0.65 1.440 1.479 3.351 0.910 1.425 1.418 3.289 0.911
4000 0.47 1.543 1.579 3.557 0.963 1.514 1.501 3.475 0.964
3900 0.30 1.656 1.695 3.789 1.018 1.606 1.592 3.680 1.022
3800 0.13 1.774 1.824 4.043 1.078 – – – –
3700 –0.03 1.896 1.968 4.316 1.139 – – – –
3600 –0.18 2.017 2.150 4.631 1.196 – – – –
3500 –0.32 1.998 2.243 4.941 1.319 – – – –
[Fe/H]=–2.0
4900 2.15 0.820 1.002 2.240 0.604 – – – –
4800 1.90 0.878 1.046 2.341 0.632 – – – –
4700 1.67 0.944 1.094 2.453 0.662 – – – –
4600 1.44 1.018 1.148 2.574 0.692 – – – –
4500 1.22 1.107 1.214 2.711 0.725 1.094 1.183 2.706 0.738
4400 1.01 1.200 1.285 2.858 0.759 1.186 1.253 2.849 0.773
4300 0.81 1.304 1.370 3.029 0.798 1.282 1.327 3.006 0.813
4200 0.61 1.417 1.465 3.218 0.842 1.382 1.406 3.175 0.857
4100 0.43 1.534 1.571 3.426 0.889 1.484 1.490 3.358 0.906
4000 0.25 1.660 1.696 3.664 0.939 1.588 1.580 3.555 0.961
3900 0.08 1.787 1.828 3.918 0.994 – – – –
3800 –0.08 1.917 1.981 4.212 1.059 – – – –
3700 –0.23 2.050 2.150 4.524 1.121 – – – –
3600 –0.37 2.178 2.328 4.843 1.181 – – – –
3500 –0.51 2.207 2.568 5.140 1.175 – – – –
difference is small: a shift in gravity by∼ 0.15dex at Teff =
4400K will translate to ∆(B − V ) ∼ 0.02 for [Fe/H] =
−1.0 and to ∼ 0.03 for [Fe/H] = −2.0, with colors at
lower log g becoming redder (differences in other colors
are smaller).
While the new Teff–log g relations provided in Tables 4
and 5 cover the effective temperature range of Teff =
3500 − 4900K, it should be taken into account that un-
certainties in these relations will likely be larger below
Teff ∼ 3900K and above Teff ∼ 4600K, where an extrap-
olation was used to compensate for a lack of stars in cer-
Page 12
12 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
tain cluster groups. It should also be noted that the new
Teff–log g relations provided in Tables 2 and 4 are repre-
sentative for RGB stars. Appropriate care should thus be
taken if these relations are used at higher (or lower) tem-
peratures, where RGB stars may be mixed up with stars
on the horizontal branch (or AGB stars).
5. Synthetic photometric colors versus
observations: results and discussion
The new Teff–log g relations that were discussed in the
previous Section allow us to derive a set of new Teff–log g–
color relations based on the synthetic photometric colors,
and to compare them with various Teff–color and color–
color relations available from the literature. This compar-
ison is done separately for [M/H] = −1.0 and −2.0. Below
we focus on the details of these steps.
5.1. New Teff–log g–color scales
The new Teff–log g–color relations were constructed using
the Teff–log g relations derived in Sect. 4.2 and broad-
band photometric colors calculated with the PHOENIX,
MARCS, and ATLAS stellar model atmospheres (Sect. 2).
These relations are provided in Table 6 (scales employing
PHOENIX and MARCS colors) and Table 7 (relation based
on ATLAS colors). They are based on the new empirical
Teff–log g scales corresponding to the metallicity scale of
KI03 (Sect. 4.2), and are delivered at four metallicities,
[M/H] = −0.5, −1.0, −1.5, and −2.0. Note that the limit-
ing gravities in MARCS and ATLAS grids of synthetic colors
are log g = 0.5 and log g = 0.0, respectively; to extend the
coverage in log g, MARCS and ATLAS colors were linearly
extrapolated to ∼ 0.2dex below these values.
Uncertainties in the new Teff–log g–color relations are
governed by the uncertainties in the empirical Teff–log g
scales that were obtained as best fits to the observed Teff–
log g sequences of late-type giants in Galactic globular
clusters (Sect. 4.2). The typical RMS residual of the fit-
ting procedure is ≃ 0.15 dex in log g, or ≃ 100K in Teff .
At Teff = 4400K, log g = 1.5, and [M/H] = −1.0, the
uncertainty ∆Teff = 100K will be equivalent to changes
in photometric colors ∆(B − V ) ≃ ∆(V − I) ≃ 0.05,
∆(V − K) ≃ 0.13, and ∆(J − K) ≃ 0.04 (correspond-
ingly, to 0.07, 0.05, 0.14, and 0.04mag, at log g = 1.0
and [M/H] = −2.0). The effect on photometric colors will
increase slightly with decreasing gravity. Note, however,
that photometric colors are less sensitive to uncertainties
in log g: at Teff = 4400K, log g = 1.5, and [M/H] = −1.0,
∆ log g = 0.15 will correspond to ∆(B − V ) ≃ 0.02, with
differences in other colors at the level of 0.01mag or lower.
While we will further quote ±100K as a representative un-
certainty of the new Teff–log g–color relations, it is rather
obvious that this may only represent a lower limit on the
true uncertainties, which include various systematical ef-
fects inherent in the spectroscopic derivations of Teff , log g,
and [Fe/H], limitations of the current stellar atmosphere
models, and so forth.
Table 7. Teff–log g–color relations for the late-type giants
based on the synthetic colors calculated with ATLAS model
atmospheres. Photometric colors are given in the Johnson-
Cousins-Glass system (see Sect. 2 for details).
ATLAS
Teff log g B−V V −I V −K J−K
[Fe/H]=–0.5
4750 2.50 1.010 1.033 2.383 0.660
4500 1.96 1.133 1.141 2.671 0.751
4250 1.47 1.273 1.275 3.013 0.857
4000 1.00 1.453 1.465 3.438 0.974
3750 0.56 1.657 1.739 3.975 1.098
3500 0.17 1.811 2.176 4.695 1.196
[Fe/H]=–1.0
4750 2.24 0.959 1.030 2.386 0.666
4500 1.68 1.098 1.142 2.673 0.755
4250 1.18 1.259 1.283 3.019 0.859
4000 0.72 1.465 1.478 3.453 0.978
3750 0.31 1.708 1.747 3.989 1.107
3500 –0.07 1.946 2.109 4.606 1.206
[Fe/H]=–1.5
4750 2.01 0.926 1.037 2.395 0.668
4500 1.45 1.089 1.161 2.688 0.753
4250 0.94 1.285 1.322 3.051 0.853
4000 0.47 1.532 1.542 3.512 0.971
3750 0.05 1.813 1.839 4.090 1.104
3500 –0.32 – – – –
[Fe/H]=–2.0
4750 1.79 0.900 1.052 2.408 0.667
4500 1.22 1.099 1.198 2.715 0.745
4250 0.71 1.344 1.397 3.111 0.838
4000 0.25 1.636 1.666 3.625 0.952
3750 –0.16 – – – –
3500 –0.51 – – – –
5.2. Comparison of Teff–color and color–color relations
In principle, the new Teff–log g–color relations can be read-
ily used to compare synthetic photometric colors with ob-
served effective temperatures and colors of late-type giants
in the Teff–color planes. Such an approach was taken in
Paper I, where for this purpose we used a sample of late-
type giants with effective temperatures derived from inter-
ferometric measurements of stellar radii. Unfortunately, as
was already mentioned in Sect. 4.1, effective temperatures
of late-type giants obtained from interferometry or lunar
occultations are very scarce at sub-Solar metallicities. The
sample of late-type giants in Galactic globular clusters
which was employed in the previous Section to obtain the
new Teff–log g relations can not be used for this purpose
either, since the number of stars in each metallicity group
is too small for a reliable comparison of observed and syn-
thetic photometric colors in different Teff–color planes at
different metallicities.
Instead of using effective temperatures and photomet-
ric colors of individual stars we thus will make a compari-
son of synthetic photometric colors with the Teff–color and
color–color relations available from the literature. For this
purpose we use relations based both on the observed and
theoretical colors of late-type giants, at [M/H] = −1.0 and
−2.0.
The baseline set of Teff–color and color–color rela-
tions used in our comparisons is that of Alonso et al.
(1999b, A99). These relations are built on the observed
tain cluster groups. It should also be noted that the new
Teff–log g relations provided in Tables 2 and 4 are repre-
sentative for RGB stars. Appropriate care should thus be
taken if these relations are used at higher (or lower) tem-
peratures, where RGB stars may be mixed up with stars
on the horizontal branch (or AGB stars).
5. Synthetic photometric colors versus
observations: results and discussion
The new Teff–log g relations that were discussed in the
previous Section allow us to derive a set of new Teff–log g–
color relations based on the synthetic photometric colors,
and to compare them with various Teff–color and color–
color relations available from the literature. This compar-
ison is done separately for [M/H] = −1.0 and −2.0. Below
we focus on the details of these steps.
5.1. New Teff–log g–color scales
The new Teff–log g–color relations were constructed using
the Teff–log g relations derived in Sect. 4.2 and broad-
band photometric colors calculated with the PHOENIX,
MARCS, and ATLAS stellar model atmospheres (Sect. 2).
These relations are provided in Table 6 (scales employing
PHOENIX and MARCS colors) and Table 7 (relation based
on ATLAS colors). They are based on the new empirical
Teff–log g scales corresponding to the metallicity scale of
KI03 (Sect. 4.2), and are delivered at four metallicities,
[M/H] = −0.5, −1.0, −1.5, and −2.0. Note that the limit-
ing gravities in MARCS and ATLAS grids of synthetic colors
are log g = 0.5 and log g = 0.0, respectively; to extend the
coverage in log g, MARCS and ATLAS colors were linearly
extrapolated to ∼ 0.2dex below these values.
Uncertainties in the new Teff–log g–color relations are
governed by the uncertainties in the empirical Teff–log g
scales that were obtained as best fits to the observed Teff–
log g sequences of late-type giants in Galactic globular
clusters (Sect. 4.2). The typical RMS residual of the fit-
ting procedure is ≃ 0.15 dex in log g, or ≃ 100K in Teff .
At Teff = 4400K, log g = 1.5, and [M/H] = −1.0, the
uncertainty ∆Teff = 100K will be equivalent to changes
in photometric colors ∆(B − V ) ≃ ∆(V − I) ≃ 0.05,
∆(V − K) ≃ 0.13, and ∆(J − K) ≃ 0.04 (correspond-
ingly, to 0.07, 0.05, 0.14, and 0.04mag, at log g = 1.0
and [M/H] = −2.0). The effect on photometric colors will
increase slightly with decreasing gravity. Note, however,
that photometric colors are less sensitive to uncertainties
in log g: at Teff = 4400K, log g = 1.5, and [M/H] = −1.0,
∆ log g = 0.15 will correspond to ∆(B − V ) ≃ 0.02, with
differences in other colors at the level of 0.01mag or lower.
While we will further quote ±100K as a representative un-
certainty of the new Teff–log g–color relations, it is rather
obvious that this may only represent a lower limit on the
true uncertainties, which include various systematical ef-
fects inherent in the spectroscopic derivations of Teff , log g,
and [Fe/H], limitations of the current stellar atmosphere
models, and so forth.
Table 7. Teff–log g–color relations for the late-type giants
based on the synthetic colors calculated with ATLAS model
atmospheres. Photometric colors are given in the Johnson-
Cousins-Glass system (see Sect. 2 for details).
ATLAS
Teff log g B−V V −I V −K J−K
[Fe/H]=–0.5
4750 2.50 1.010 1.033 2.383 0.660
4500 1.96 1.133 1.141 2.671 0.751
4250 1.47 1.273 1.275 3.013 0.857
4000 1.00 1.453 1.465 3.438 0.974
3750 0.56 1.657 1.739 3.975 1.098
3500 0.17 1.811 2.176 4.695 1.196
[Fe/H]=–1.0
4750 2.24 0.959 1.030 2.386 0.666
4500 1.68 1.098 1.142 2.673 0.755
4250 1.18 1.259 1.283 3.019 0.859
4000 0.72 1.465 1.478 3.453 0.978
3750 0.31 1.708 1.747 3.989 1.107
3500 –0.07 1.946 2.109 4.606 1.206
[Fe/H]=–1.5
4750 2.01 0.926 1.037 2.395 0.668
4500 1.45 1.089 1.161 2.688 0.753
4250 0.94 1.285 1.322 3.051 0.853
4000 0.47 1.532 1.542 3.512 0.971
3750 0.05 1.813 1.839 4.090 1.104
3500 –0.32 – – – –
[Fe/H]=–2.0
4750 1.79 0.900 1.052 2.408 0.667
4500 1.22 1.099 1.198 2.715 0.745
4250 0.71 1.344 1.397 3.111 0.838
4000 0.25 1.636 1.666 3.625 0.952
3750 –0.16 – – – –
3500 –0.51 – – – –
5.2. Comparison of Teff–color and color–color relations
In principle, the new Teff–log g–color relations can be read-
ily used to compare synthetic photometric colors with ob-
served effective temperatures and colors of late-type giants
in the Teff–color planes. Such an approach was taken in
Paper I, where for this purpose we used a sample of late-
type giants with effective temperatures derived from inter-
ferometric measurements of stellar radii. Unfortunately, as
was already mentioned in Sect. 4.1, effective temperatures
of late-type giants obtained from interferometry or lunar
occultations are very scarce at sub-Solar metallicities. The
sample of late-type giants in Galactic globular clusters
which was employed in the previous Section to obtain the
new Teff–log g relations can not be used for this purpose
either, since the number of stars in each metallicity group
is too small for a reliable comparison of observed and syn-
thetic photometric colors in different Teff–color planes at
different metallicities.
Instead of using effective temperatures and photomet-
ric colors of individual stars we thus will make a compari-
son of synthetic photometric colors with the Teff–color and
color–color relations available from the literature. For this
purpose we use relations based both on the observed and
theoretical colors of late-type giants, at [M/H] = −1.0 and
−2.0.
The baseline set of Teff–color and color–color rela-
tions used in our comparisons is that of Alonso et al.
(1999b, A99). These relations are built on the observed
Page 13
Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II. 13
properties of a homogenous sample of 250 late-type gi-
ants in Galactic globular clusters, with precise optical
and near-infrared photometry of individual stars and Teff
from IRFM. The sample covers the metallicity range
[Fe/H] = 0 . . . − 3.0, with [Fe/H] estimates obtained ei-
ther from spectroscopy or Stro¨mgren photometry (with
typical accuracies of ±0.15dex and 0.2 to 0.3 dex, re-
spectively). The IRFM temperatures of individual stars
are typically in good agreement with those obtained by
direct methods within a large range of effective tem-
peratures (Teff ∼ 3700 . . .5200K). The mean difference
between the interferometric and IRFM temperatures is
Tdirect − TIRFM = 3 ± 51K, based on 20 stars (Alonso et
al. 1999a). The internal accuracy of the individual Teff–
color relations varies between 40 and 125K, which com-
pares well with the accuracies of the Teff–color scales de-
rived by us in Paper I employing a sample of stars with
interferometric temperatures (which are of the order of
±150K). Before making the comparisons, the Teff–color
relations of A99 (Table 6 of A99, Johnson system) were
transformed to the standard Johnson-Cousins-Glass sys-
tem (Sect. 2), using transformation equations from Fernie
(1983) for (V − I), and from Bessell & Brett (1988) for
(V −K) and (J −K).
Recently, the Teff–color and color–color relations of
A99 were updated by Rami´rez & Mele´ndez (2005a,b). We
include these new relations into our analysis, too. The
transformation of Rami´rez & Mele´ndez (2005b, RM05)
colors involving the 2MASS bandpasses (V −K2, J2−K2;
subscript 2 denotes the 2MASS system) to the standard
Johnson-Cousins-Glass system was made using transfor-
mation equations given by Carpenter (2001).
Several additional widely used Teff–color and color–
color relations that were employed in our study are:
– Bell & Gustafsson (1989, BG89): Teff–color and color–
color relations based on theoretical photometric col-
ors. The BG89 scales employed in this study were
constructed using B − V colors taken from Bell &
Gustafsson (1978), V −I, V −K, and J−K colors from
Bell & Gustafsson (1989). According to Vandenberg &
Clem (2003), the scale of BG89 reproduces well the
observed CMDs of Galactic open and globular clus-
ters at different metallicities. In the effective temper-
ature range of interest for this study, the agreement
seems to be very good, both at [M/H] = −1.0 and
−2.0 (Vandenberg & Clem 2003);
– BaSeL 2.2 (Lejeune et al. 1998, BaSeL 2.2): a semiem-
pirical library of photometric colors based on the the-
oretical spectra. While photometric colors of BaSeL
2.2 are calibrated to match empirical Teff–color rela-
tions at [Fe/H] = 0.0, with presumably poorer con-
sistency at lower metallicities, we employ this scale in
the present study too, partially to compare it with the
BaSeL 3.1 colors (see below). BaSeL 2.2 colors used
in this work were calculated using the interactive web-
based BaSeL server2;
2 http://tangerine.astro.mat.uc.pt/BaSeL/
– BaSeL 3.1 (Westera et al. 2002, BaSeL 3.1): extension
of the BaSeL 2.2 library to lower metallicities, cali-
brated using the photometric data of Galactic globular
clusters. This scale is designed to reproduce the Teff–
color and color-color relations at metallicities down to
[M/H] ∼ −2.0. BaSeL 3.1 colors used in this study
were calculated using the web-based BaSeL server;
– Houdashelt et al. (2000, H00): synthetic colors based
on theoretical spectra calculated with the MARCS and
SSG codes, with TiO opacities adjusted to reproduce
the observed spectra of M giants from Fluks et al.
(1994). The H00 scale should be used with care below
Teff ∼ 3800K since no H2O opacities were included in
the calculations (see Paper I for more details on the
influence of different molecular opacities on the photo-
metric colors);
– Sekiguchi & Fukugita (2000, SF00): an empirical Teff–
(B−V ) scale based on the observed colors and effective
temperatures of 537 Infrared Space Observatory (ISO)
standard stars from Di Benedetto (1998). Effective
temperatures of individual stars were derived from the
Teff–(V −K) relation, calibrated on a sample of nearby
stars with angular diameters available from interferom-
etry;
– Vandenberg & Clem (2003, VC03): empirical scales
based on synthetic BVRI colors of Bell & Gustafsson
(1978, 1989), adjusted to satisfy observational con-
strains from the observed CMDs of Galactic globular
and open clusters, field stars in the Solar neighbor-
hood, empirical Teff–color relations and color–color re-
lations for field giants.
Note that in all cases photometric colors were se-
lected according to the new Teff–log g relations derived
in Sect. 4.2.
Extensive comparisons of these relations with vari-
ous other Teff–color scales have been published in numer-
ous studies (e.g., Alonso et al. 1999b; Houdashelt et al.
2000; Sekiguchi & Fukugita 2000; Westera et al. 2002;
Vandenberg & Clem 2003; Rami´rez & Mele´ndez 2005b).
Some of these relations (BaSeL 2.2, A99, H00, SF00, and
VC03) were also employed in our comparison of the ob-
served and theoretical colors of late-type giants at Solar
metallicity (Paper I). Altogether, this provides a further
reference list for a comparison of the new Teff–color and
color–color scales with similar relations available in the
literature.
Comparisons of the new Teff–log g–color relations
based on PHOENIX, MARCS and ATLAS colors (Tables 6 and
7) with the published Teff–color relations are given in
Fig. 8 (Teff–color planes) and Fig. 9 (color–color planes)
at [M/H] = −1.0, and, correspondingly, in Figs. 10 and 11
at [M/H] = −2.0 (all comparisons are made with respect
to the scale of A99). We discuss the trends at these two
metalicities in the sections below.
properties of a homogenous sample of 250 late-type gi-
ants in Galactic globular clusters, with precise optical
and near-infrared photometry of individual stars and Teff
from IRFM. The sample covers the metallicity range
[Fe/H] = 0 . . . − 3.0, with [Fe/H] estimates obtained ei-
ther from spectroscopy or Stro¨mgren photometry (with
typical accuracies of ±0.15dex and 0.2 to 0.3 dex, re-
spectively). The IRFM temperatures of individual stars
are typically in good agreement with those obtained by
direct methods within a large range of effective tem-
peratures (Teff ∼ 3700 . . .5200K). The mean difference
between the interferometric and IRFM temperatures is
Tdirect − TIRFM = 3 ± 51K, based on 20 stars (Alonso et
al. 1999a). The internal accuracy of the individual Teff–
color relations varies between 40 and 125K, which com-
pares well with the accuracies of the Teff–color scales de-
rived by us in Paper I employing a sample of stars with
interferometric temperatures (which are of the order of
±150K). Before making the comparisons, the Teff–color
relations of A99 (Table 6 of A99, Johnson system) were
transformed to the standard Johnson-Cousins-Glass sys-
tem (Sect. 2), using transformation equations from Fernie
(1983) for (V − I), and from Bessell & Brett (1988) for
(V −K) and (J −K).
Recently, the Teff–color and color–color relations of
A99 were updated by Rami´rez & Mele´ndez (2005a,b). We
include these new relations into our analysis, too. The
transformation of Rami´rez & Mele´ndez (2005b, RM05)
colors involving the 2MASS bandpasses (V −K2, J2−K2;
subscript 2 denotes the 2MASS system) to the standard
Johnson-Cousins-Glass system was made using transfor-
mation equations given by Carpenter (2001).
Several additional widely used Teff–color and color–
color relations that were employed in our study are:
– Bell & Gustafsson (1989, BG89): Teff–color and color–
color relations based on theoretical photometric col-
ors. The BG89 scales employed in this study were
constructed using B − V colors taken from Bell &
Gustafsson (1978), V −I, V −K, and J−K colors from
Bell & Gustafsson (1989). According to Vandenberg &
Clem (2003), the scale of BG89 reproduces well the
observed CMDs of Galactic open and globular clus-
ters at different metallicities. In the effective temper-
ature range of interest for this study, the agreement
seems to be very good, both at [M/H] = −1.0 and
−2.0 (Vandenberg & Clem 2003);
– BaSeL 2.2 (Lejeune et al. 1998, BaSeL 2.2): a semiem-
pirical library of photometric colors based on the the-
oretical spectra. While photometric colors of BaSeL
2.2 are calibrated to match empirical Teff–color rela-
tions at [Fe/H] = 0.0, with presumably poorer con-
sistency at lower metallicities, we employ this scale in
the present study too, partially to compare it with the
BaSeL 3.1 colors (see below). BaSeL 2.2 colors used
in this work were calculated using the interactive web-
based BaSeL server2;
2 http://tangerine.astro.mat.uc.pt/BaSeL/
– BaSeL 3.1 (Westera et al. 2002, BaSeL 3.1): extension
of the BaSeL 2.2 library to lower metallicities, cali-
brated using the photometric data of Galactic globular
clusters. This scale is designed to reproduce the Teff–
color and color-color relations at metallicities down to
[M/H] ∼ −2.0. BaSeL 3.1 colors used in this study
were calculated using the web-based BaSeL server;
– Houdashelt et al. (2000, H00): synthetic colors based
on theoretical spectra calculated with the MARCS and
SSG codes, with TiO opacities adjusted to reproduce
the observed spectra of M giants from Fluks et al.
(1994). The H00 scale should be used with care below
Teff ∼ 3800K since no H2O opacities were included in
the calculations (see Paper I for more details on the
influence of different molecular opacities on the photo-
metric colors);
– Sekiguchi & Fukugita (2000, SF00): an empirical Teff–
(B−V ) scale based on the observed colors and effective
temperatures of 537 Infrared Space Observatory (ISO)
standard stars from Di Benedetto (1998). Effective
temperatures of individual stars were derived from the
Teff–(V −K) relation, calibrated on a sample of nearby
stars with angular diameters available from interferom-
etry;
– Vandenberg & Clem (2003, VC03): empirical scales
based on synthetic BVRI colors of Bell & Gustafsson
(1978, 1989), adjusted to satisfy observational con-
strains from the observed CMDs of Galactic globular
and open clusters, field stars in the Solar neighbor-
hood, empirical Teff–color relations and color–color re-
lations for field giants.
Note that in all cases photometric colors were se-
lected according to the new Teff–log g relations derived
in Sect. 4.2.
Extensive comparisons of these relations with vari-
ous other Teff–color scales have been published in numer-
ous studies (e.g., Alonso et al. 1999b; Houdashelt et al.
2000; Sekiguchi & Fukugita 2000; Westera et al. 2002;
Vandenberg & Clem 2003; Rami´rez & Mele´ndez 2005b).
Some of these relations (BaSeL 2.2, A99, H00, SF00, and
VC03) were also employed in our comparison of the ob-
served and theoretical colors of late-type giants at Solar
metallicity (Paper I). Altogether, this provides a further
reference list for a comparison of the new Teff–color and
color–color scales with similar relations available in the
literature.
Comparisons of the new Teff–log g–color relations
based on PHOENIX, MARCS and ATLAS colors (Tables 6 and
7) with the published Teff–color relations are given in
Fig. 8 (Teff–color planes) and Fig. 9 (color–color planes)
at [M/H] = −1.0, and, correspondingly, in Figs. 10 and 11
at [M/H] = −2.0 (all comparisons are made with respect
to the scale of A99). We discuss the trends at these two
metalicities in the sections below.
Page 14
14 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
3500
4000
4500
5000
5500
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
-200
-100
0
100
200
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
3500
4000
4500
5000
5500
2.0 2.5 3.0 3.5 4.0 4.5 5.0
-200
-100
0
100
200
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(a)
A99
BaSeL2.2
BaSeL3.1
BG89
SF00
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
B-V
(b)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
V-I
(d)(c)
A99
BaSeL2.2
BaSeL3.1
BG89
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
V-K
A99
BaSeL2.2
BaSeL3.1
BG89
H00
ATLAS
MARCS
PHOENIX
J-K
Fig. 8. Empirical and theoretical Teff–color relations for late-type giants at [M/H] = −1.0, in different Teff–color planes (a-d,
top panels). The thick solid line shows Teff–color relation of A99, the thick dashed line is the empirical Teff–color relation at
Solar metallicity (Paper I). Several existing Teff–color relations are shown as well, together with the scales constructed using
synthetic colors of PHOENIX, MARCS and ATLAS (Tables 6 and 7). The bottom panels in each figure show the difference between
various Teff–color relations and the A99 scale in a given Teff–color plane (∆Teff = T othereff − T A99eff .)
3500
4000
4500
5000
5500
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
-200
-100
0
100
200
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
3500
4000
4500
5000
5500
2.0 2.5 3.0 3.5 4.0 4.5 5.0
-200
-100
0
100
200
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(a)
A99
BaSeL2.2
BaSeL3.1
BG89
SF00
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
B-V
(b)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
V-I
(d)(c)
A99
BaSeL2.2
BaSeL3.1
BG89
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
V-K
A99
BaSeL2.2
BaSeL3.1
BG89
H00
ATLAS
MARCS
PHOENIX
J-K
Fig. 8. Empirical and theoretical Teff–color relations for late-type giants at [M/H] = −1.0, in different Teff–color planes (a-d,
top panels). The thick solid line shows Teff–color relation of A99, the thick dashed line is the empirical Teff–color relation at
Solar metallicity (Paper I). Several existing Teff–color relations are shown as well, together with the scales constructed using
synthetic colors of PHOENIX, MARCS and ATLAS (Tables 6 and 7). The bottom panels in each figure show the difference between
various Teff–color relations and the A99 scale in a given Teff–color plane (∆Teff = T othereff − T A99eff .)
Page 17
Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II. 17
3500
4000
4500
5000
5500
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
-200
-100
0
100
200
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
3500
4000
4500
5000
5500
2.0 2.5 3.0 3.5 4.0 4.5 5.0
-200
-100
0
100
200
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(a)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
B-V
(b)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
V-I
(c)
A99
BaSeL2.2
BaSeL3.1
BG89
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
V-K
(d)
A99
BaSeL2.2
BaSeL3.1
BG89
H00
ATLAS
MARCS
PHOENIX
J-K
Fig. 10. Empirical and theoretical Teff–color relations at [Fe/H] = −2.0, in different Teff–color planes (a-d, top panels). The
thick solid line is the Teff–color relation of A99, the thick dashed line is empirical Teff–color relation at Solar metallicity (Paper I).
Several existing Teff–color relations are shown as well, together with the scales constructed using synthetic colors of PHOENIX,
MARCS and ATLAS (Tables 6 and 7). The bottom panels in each figure show the difference between various Teff–color relations
and the A99 scale in a given Teff–color plane (∆Teff = T othereff − T A99eff .)
3500
4000
4500
5000
5500
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
-200
-100
0
100
200
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
3500
4000
4500
5000
5500
2.0 2.5 3.0 3.5 4.0 4.5 5.0
-200
-100
0
100
200
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(a)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
B-V
(b)
A99
BaSeL2.2
BaSeL3.1
BG89
VC03
RM05
H00
ATLAS
MARCS
PHOENIX
V-I
(c)
A99
BaSeL2.2
BaSeL3.1
BG89
RM05
H00
ATLAS
MARCS
PHOENIX
T
e
f
f
T
e
f
f
V-K
(d)
A99
BaSeL2.2
BaSeL3.1
BG89
H00
ATLAS
MARCS
PHOENIX
J-K
Fig. 10. Empirical and theoretical Teff–color relations at [Fe/H] = −2.0, in different Teff–color planes (a-d, top panels). The
thick solid line is the Teff–color relation of A99, the thick dashed line is empirical Teff–color relation at Solar metallicity (Paper I).
Several existing Teff–color relations are shown as well, together with the scales constructed using synthetic colors of PHOENIX,
MARCS and ATLAS (Tables 6 and 7). The bottom panels in each figure show the difference between various Teff–color relations
and the A99 scale in a given Teff–color plane (∆Teff = T othereff − T A99eff .)
Page 20
20 Kucˇinskas et al.: Broad-band colors and effective temperature calibrations for late-type giants. II.
ric colors are considerably larger at Solar metallicity; see
Paper I).
Acknowledgements. We are grateful to Bertrand Plez
(GRAAL, Universite´ Montpellier) for calculating MARCS grid
of synthetic spectra, and numerous comments and discus-
sions. We also thank Glenn Wahlgren (Lund Observatory)
for a careful reading of the manuscript and his valuable
comments and suggestions. AK acknowledges support from
the Wenner-Gren Foundations. This work was supported
in part by grant-in-aids for Scientific Research (C) and for
International Scientific Research (Joint Research) from the
Ministry of Education, Science, Sports and Culture in Japan,
and by a Grant of the Lithuanian State Science and Studies
Foundation. This work was also supported in part by the Poˆle
Scientifique de Mode´lisation Nume´rique at ENS-Lyon. Some
of the calculations presented in this paper were performed
on the IBM pSeries 690 of the Norddeutscher Verbund fu¨r
Hoch- und Ho¨chstleistungsrechnen (HLRN), and on the IBM
SP “seaborg” of the NERSC, with support from the DoE.
We thank all these institutions for a generous allocation
of computer time. This research has also made use of the
SIMBAD and VizieR databases, operated by the CDS,
Strasbourg, France.
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Zinn, R., West, M.J. 1984, ApJS, 55, 45
ric colors are considerably larger at Solar metallicity; see
Paper I).
Acknowledgements. We are grateful to Bertrand Plez
(GRAAL, Universite´ Montpellier) for calculating MARCS grid
of synthetic spectra, and numerous comments and discus-
sions. We also thank Glenn Wahlgren (Lund Observatory)
for a careful reading of the manuscript and his valuable
comments and suggestions. AK acknowledges support from
the Wenner-Gren Foundations. This work was supported
in part by grant-in-aids for Scientific Research (C) and for
International Scientific Research (Joint Research) from the
Ministry of Education, Science, Sports and Culture in Japan,
and by a Grant of the Lithuanian State Science and Studies
Foundation. This work was also supported in part by the Poˆle
Scientifique de Mode´lisation Nume´rique at ENS-Lyon. Some
of the calculations presented in this paper were performed
on the IBM pSeries 690 of the Norddeutscher Verbund fu¨r
Hoch- und Ho¨chstleistungsrechnen (HLRN), and on the IBM
SP “seaborg” of the NERSC, with support from the DoE.
We thank all these institutions for a generous allocation
of computer time. This research has also made use of the
SIMBAD and VizieR databases, operated by the CDS,
Strasbourg, France.
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