arXiv:0704.1462v1  [astro-ph]  11 Apr 2007
Physical parameters of evolved stars in
clusters and in the field from line-depth ratios
K. Biazzo1,2, L. Pasquini2, A. Frasca1, L. da Silva3, L. Girardi4, A. P.
Hatzes5, J. Setiawan6, S. Catalano1, and E. Marilli1
1 Osservatorio Astrofisico di Catania-INAF, Catania, Italy
kbiazzo@oact.inaf.it
2 European Southern Observatory, Garching bei München, Germany
3 Observatório Nacional-MCT, Rio de Janeiro, Brazil
4 Osservatorio Astronomico di Padova-INAF, Padova, Italy
5 Thüringer Landessternwarte, Tauterburg, Germany
6 Max-Planck-Institute für Astronomie, Heidelberg, Germany
Summary. We present a high-resolution spectroscopic analysis of two samples of
evolved stars selected in the field and in the intermediate-age open cluster IC 4651,
for which detailed measurements of chemical composition were made in the last few
years. Applying the Gray’s method based on ratios of line depths, we determine
the effective temperature and compare our results with previous ones obtained by
means of the curves of growth of iron lines. The knowledge of the temperature
enables us to estimate other fundamental stellar parameters, such as color excess,
age, and mass.
1 Introduction
The study of stellar populations in our Galaxy and in its neighborhoods
has received in the last years a big impulse, especially thanks to the use
of large telescopes and to the detailed spectroscopic analysis performed on
high-resolution spectra. In this context, open clusters, that are homogeneous
samples of stars having the same age and chemical composition, are very
suitable to investigate the stellar and Galactic formation and evolution. In
spite of this, the data on stars belonging to open clusters are often insuffi-
cient to adequately constrain age, distance, metallicity, mass, color excess,
and temperature. This is due to the fact that the main classical tool to study
cluster properties is the color-magnitude diagram, which suffers of several un-
certainties and intrinsic biases due to, for example, the uncertain knowledge
of the chemical composition and the reddening of the stars. As a consequence,
spectroscopic methods, being independent of the reddening, are very efficient
to evaluate temperatures of stars in clusters.
Spectroscopic effective temperatures are usually determined imposing
that the abundance of one chemical element with many lines in the spectrum
(typically iron) does not depend on the excitation potential of the lines. An-
other method for determining effective temperature is based on line-depth
ratios (LDRs). It has been widely demonstrated that the ratio of the depths
http://arxiv.org/abs/0704.1462v1
2 K. Biazzo et al.
of two lines having different sensitivity to temperature is an excellent measure
of stellar temperatures with a sensitivity as small as a few Kelvin degrees in
the most favorable cases ([14, 13, 12]).
In the present paper, we apply the LDR method to high-resolution UVES
and FEROS spectra for deriving effective temperatures in nearby evolved field
stars with very good Hipparcos distances and in giants of the intermediate-age
open cluster IC 4651. For both the star samples, the temperature was already
derived spectroscopically, together with the element abundances, with the
curves of growth of absorption lines spread throughout the optical spectrum
([17, 18]). In addition, for the stars belonging to the open cluster IC 4651,
we make the first robust determination of the average color excess, based on
spectroscopic measurements.
2 Star samples
We have analysed seventy-one evolved field stars and six giant stars belonging
to the open cluster IC 4651. The sample of field stars was already analysed
by [18] for the determination of radii, temperatures, masses and chemical
composition. The stars in the intermediate-age cluster IC 4651 have been
selected from the sample studied by [17] for abundance estimates.
The field stars data were acquired with the FEROS spectrograph (R =
48 000) at the ESO 1.5m-telescope in La Silla (Chile), while the IC 4651
spectra were acquired with UVES (R = 100 000) at the ESO VLT Kueyen
8.2m-telescope in Cerro Paranal (Chile). In both cases, the signal-to-noise
ratio (S/N) was greater than 150 for all the spectra, which make them very
suitable for the temperature determination described in Sec. 3.
3 Effective temperature determination
The wavelength range covered by FEROS and UVES spectrographs contain
a series of weak metal lines which can be used for temperature determination
with the LDR method. Lines from similar elements such as iron, vanadium,
titanium, but with different excitation potentials (χ) have indeed different
sensitivity to temperature. This is due to the fact that the line strength, de-
pending on excitation and ionization processes, is a function of temperature
and, to a lesser extent, of the electron pressure. For this reason, the better line
couples are those with the largest χ-difference. In the range 6150 Å <∼ λ
6300Å there are several lines of this type whose ratios of their depths have
been exploited for temperature calibrations ([14, 13, 7, 5]), and for studies
of the rotational modulation of the average effective temperature of mag-
netically active stars ([10, 4]) or for investigating the pulsational variations
during the phases of a Cepheid star ([15, 3]). In particular, we choose 15 line
pairs for which [5] already made suitable calibrations.
Physical parameters in evolved stars 3
Field giant stars
The comparison between the temperatures obtained by us (T LDR
) and those
obtained by [18] (T SPEC
) is plotted in Fig. 1. We find a very good agreement
between T SPEC
and T LDR
in all the temperature range 4000–6000 K.
Fig. 1. Comparison between the temperatures obtained from LDR and curve-of-
growth analyses for the field stars (left) and the giants belonging to IC 4651 (right).
Giant stars in IC 4651
T LDR
is systematically lower than T SPEC
by an amount typically between
70 and 90 K. The only exception is the star E95 for which the difference
amounts to about 320 K. [17] already found for this star the largest difference
between photometric and spectroscopic temperature among their giant star
sample. However, the position on the HR diagram of this star corresponds to
a subgiant and this could be the reason for the disagreement.
4 Color excess of IC 4651
We can evaluate for each star the intrinsic color index (B−V )0 by inverting
for example the (B − V ) − Teff calibrations of [12] and [1, 2] with the aim
to compute the color excess E(B − V ) of the cluster IC 4651. Thus, for
the two temperature sets, T LDR
and T SPEC
, we obtain E(B − V ) ≈ 0.12
and 0.16 for the Gray’s calibration, and E(B − V ) = 0.13 and 0.17 for the
Alonso’s calibration. It is worth noticing that there is not a large difference
between color excesses obtained with the two calibrations. From a preliminary
analysis, we find an improving of the agreement if we properly take into
account the metallicity effects ([6]). Moreover, our color excess values are in
good agreement with the results of E(B − V ) = 0.13 and E(b − y) = 0.091
obtained by [9] and [17], respectively (E(b − y) = 0.72E(B − V ), [8]). The
4 K. Biazzo et al.
present determination of E(B − V ) is a strong argument in favor of such a
low reddening notwithstanding the distance of ≈ 900pc estimated by [16]
and the low galactic latitude of IC 4651 (≃ 9◦).
5 Conclusion
In this paper we have derived accurate atmospheric parameters for field
evolved stars and giant stars in the open cluster IC 4651 by means of high-
resolution spectra acquired with the ESO spectrographs FEROS and UVES.
For the field giant stars, we find a good agreement between temperatures
computed by [18] with the curves-of-growthmethod and by ourselves with the
LDR technique. For the giants in the intermediate-age open cluster IC 4651,
we have determined the effective temperatures by means of the LDR method,
that allowed us to compute the reddening. We find a rather low reddening
towards the cluster, E(B − V ) ≃ 0.13, that needs to be explained, given the
high distance (≃ 900pc) and the low galactic latitude of IC 4651.
We conclude that our technique is well suited to derive accurate effective
temperatures and reddening of clusters with a nearly-solar metallicity. The
determination of very precise temperatures is of great importance to derive
stellar age and mass distributions ([11]), representing a powerful tool for
stellar population studies in addition to those based on photometric data.
References
1. A. Alonso, S. Arribas & C. Mart́ınez-Roger: A&A, 313, 873 (1996)
2. A. Alonso, S. Arribas & C. Mart́ınez-Roger: A&A, 140, 261 (1999)
3. K. Biazzo, S. Catalano, A. Frasca & E. Marilli: MSAIS, 5, 109 (2004)
4. K. Biazzo, A. Frasca, G.W. Henry et al.: ApJ, in press (2006)
5. K. Biazzo, A. Frasca, S. Catalano & E. Marilli: AN, submitted (2006)
6. K. Biazzo, L. Pasquini, L. Girardi et al.: A&A, in preparation (2006)
7. S. Catalano, K. Biazzo, A. Frasca, E. Marilli: A&A, 394, 1009 (2002)
8. J.A. Cardelli, G.C. Clayton & J.S. Mathis: ApJ, 345, 245 (1989)
9. O.J. Eggen: ApJ, 166, 87 (1971)
10. A. Frasca, K. Biazzo, S. Catalano et al.: A&A, 432, 647 (2005)
11. L. Girardi, L. da Silva, L. Pasquini et al.: in Resolved Stellar Populations, ed
by D. Valls-Gaband, M. Chavez (ASP Conf. Ser.: San Francisco) in press
12. D.F. Gray: The Observation and Analysis of Stellar Photospheres, 3rd edn
(Cambridge University Press 2005)
13. G.F. Gray & K. Brown: PASP, 113, 723 (2001)
14. D.F. Gray & H.L. Johanson: 1991, ApJ, 103, 439 (1991)
15. V.V. Kovtyukh & N.I. Gorlova: A&A, 358, 587 (2000)
16. S. Meibom, J. Andersen, & B. Nordström: A&A 386, 187 (2002)
17. L. Pasquini, S. Randich, M. Zoccali et al.: A&A 951, 963 (2004)
18. L. da Silva, L. Girardi, L. Pasquini et al.: A&A, 458, 609 (2006)

  We present a high-resolution spectroscopic analysis of two samples of evolved
stars selected in the field and in the intermediate-age open cluster IC 4651,
for which detailed measurements of chemical composition were made in the last
few years. Applying the Gray's method based on ratios of line depths, we
determine the effective temperature and compare our results with previous ones
obtained by means of the curves of growth of iron lines. The knowledge of the
temperature enables us to estimate other fundamental stellar parameters, such
as color excess, age, and mass.

Introduction
The study of stellar populations in our Galaxy and in its neighborhoods
has received in the last years a big impulse, especially thanks to the use
of large telescopes and to the detailed spectroscopic analysis performed on
high-resolution spectra. In this context, open clusters, that are homogeneous
samples of stars having the same age and chemical composition, are very
suitable to investigate the stellar and Galactic formation and evolution. In
spite of this, the data on stars belonging to open clusters are often insuffi-
cient to adequately constrain age, distance, metallicity, mass, color excess,
and temperature. This is due to the fact that the main classical tool to study
cluster properties is the color-magnitude diagram, which suffers of several un-
certainties and intrinsic biases due to, for example, the uncertain knowledge
of the chemical composition and the reddening of the stars. As a consequence,
spectroscopic methods, being independent of the reddening, are very efficient
to evaluate temperatures of stars in clusters.
Spectroscopic effective temperatures are usually determined imposing
that the abundance of one chemical element with many lines in the spectrum
(typically iron) does not depend on the excitation potential of the lines. An-
other method for determining effective temperature is based on line-depth
ratios (LDRs). It has been widely demonstrated that the ratio of the depths
http://arxiv.org/abs/0704.1462v1
2 K. Biazzo et al.
of two lines having different sensitivity to temperature is an excellent measure
of stellar temperatures with a sensitivity as small as a few Kelvin degrees in
the most favorable cases ([14, 13, 12]).
In the present paper, we apply the LDR method to high-resolution UVES
and FEROS spectra for deriving effective temperatures in nearby evolved field
stars with very good Hipparcos distances and in giants of the intermediate-age
open cluster IC 4651. For both the star samples, the temperature was already
derived spectroscopically, together with the element abundances, with the
curves of growth of absorption lines spread throughout the optical spectrum
([17, 18]). In addition, for the stars belonging to the open cluster IC 4651,
we make the first robust determination of the average color excess, based on
spectroscopic measurements.
2 Star samples
We have analysed seventy-one evolved field stars and six giant stars belonging
to the open cluster IC 4651. The sample of field stars was already analysed
by [18] for the determination of radii, temperatures, masses and chemical
composition. The stars in the intermediate-age cluster IC 4651 have been
selected from the sample studied by [17] for abundance estimates.
The field stars data were acquired with the FEROS spectrograph (R =
48 000) at the ESO 1.5m-telescope in La Silla (Chile), while the IC 4651
spectra were acquired with UVES (R = 100 000) at the ESO VLT Kueyen
8.2m-telescope in Cerro Paranal (Chile). In both cases, the signal-to-noise
ratio (S/N) was greater than 150 for all the spectra, which make them very
suitable for the temperature determination described in Sec. 3.
3 Effective temperature determination
The wavelength range covered by FEROS and UVES spectrographs contain
a series of weak metal lines which can be used for temperature determination
with the LDR method. Lines from similar elements such as iron, vanadium,
titanium, but with different excitation potentials (χ) have indeed different
sensitivity to temperature. This is due to the fact that the line strength, de-
pending on excitation and ionization processes, is a function of temperature
and, to a lesser extent, of the electron pressure. For this reason, the better line
couples are those with the largest χ-difference. In the range 6150 Å <∼ λ
6300Å there are several lines of this type whose ratios of their depths have
been exploited for temperature calibrations ([14, 13, 7, 5]), and for studies
of the rotational modulation of the average effective temperature of mag-
netically active stars ([10, 4]) or for investigating the pulsational variations
during the phases of a Cepheid star ([15, 3]). In particular, we choose 15 line
pairs for which [5] already made suitable calibrations.
Physical parameters in evolved stars 3
Field giant stars
The comparison between the temperatures obtained by us (T LDR
) and those
obtained by [18] (T SPEC
) is plotted in Fig. 1. We find a very good agreement
between T SPEC
and T LDR
in all the temperature range 4000–6000 K.
Fig. 1. Comparison between the temperatures obtained from LDR and curve-of-
growth analyses for the field stars (left) and the giants belonging to IC 4651 (right).
Giant stars in IC 4651
T LDR
is systematically lower than T SPEC
by an amount typically between
70 and 90 K. The only exception is the star E95 for which the difference
amounts to about 320 K. [17] already found for this star the largest difference
between photometric and spectroscopic temperature among their giant star
sample. However, the position on the HR diagram of this star corresponds to
a subgiant and this could be the reason for the disagreement.
4 Color excess of IC 4651
We can evaluate for each star the intrinsic color index (B−V )0 by inverting
for example the (B − V ) − Teff calibrations of [12] and [1, 2] with the aim
to compute the color excess E(B − V ) of the cluster IC 4651. Thus, for
the two temperature sets, T LDR
and T SPEC
, we obtain E(B − V ) ≈ 0.12
and 0.16 for the Gray’s calibration, and E(B − V ) = 0.13 and 0.17 for the
Alonso’s calibration. It is worth noticing that there is not a large difference
between color excesses obtained with the two calibrations. From a preliminary
analysis, we find an improving of the agreement if we properly take into
account the metallicity effects ([6]). Moreover, our color excess values are in
good agreement with the results of E(B − V ) = 0.13 and E(b − y) = 0.091
obtained by [9] and [17], respectively (E(b − y) = 0.72E(B − V ), [8]). The
4 K. Biazzo et al.
present determination of E(B − V ) is a strong argument in favor of such a
low reddening notwithstanding the distance of ≈ 900pc estimated by [16]
and the low galactic latitude of IC 4651 (≃ 9◦).
5 Conclusion
In this paper we have derived accurate atmospheric parameters for field
evolved stars and giant stars in the open cluster IC 4651 by means of high-
resolution spectra acquired with the ESO spectrographs FEROS and UVES.
For the field giant stars, we find a good agreement between temperatures
computed by [18] with the curves-of-growthmethod and by ourselves with the
LDR technique. For the giants in the intermediate-age open cluster IC 4651,
we have determined the effective temperatures by means of the LDR method,
that allowed us to compute the reddening. We find a rather low reddening
towards the cluster, E(B − V ) ≃ 0.13, that needs to be explained, given the
high distance (≃ 900pc) and the low galactic latitude of IC 4651.
We conclude that our technique is well suited to derive accurate effective
temperatures and reddening of clusters with a nearly-solar metallicity. The
determination of very precise temperatures is of great importance to derive
stellar age and mass distributions ([11]), representing a powerful tool for
stellar population studies in addition to those based on photometric data.
References
1. A. Alonso, S. Arribas & C. Mart́ınez-Roger: A&A, 313, 873 (1996)
2. A. Alonso, S. Arribas & C. Mart́ınez-Roger: A&A, 140, 261 (1999)
3. K. Biazzo, S. Catalano, A. Frasca & E. Marilli: MSAIS, 5, 109 (2004)
4. K. Biazzo, A. Frasca, G.W. Henry et al.: ApJ, in press (2006)
5. K. Biazzo, A. Frasca, S. Catalano & E. Marilli: AN, submitted (2006)
6. K. Biazzo, L. Pasquini, L. Girardi et al.: A&A, in preparation (2006)
7. S. Catalano, K. Biazzo, A. Frasca, E. Marilli: A&A, 394, 1009 (2002)
8. J.A. Cardelli, G.C. Clayton & J.S. Mathis: ApJ, 345, 245 (1989)
9. O.J. Eggen: ApJ, 166, 87 (1971)
10. A. Frasca, K. Biazzo, S. Catalano et al.: A&A, 432, 647 (2005)
11. L. Girardi, L. da Silva, L. Pasquini et al.: in Resolved Stellar Populations, ed
by D. Valls-Gaband, M. Chavez (ASP Conf. Ser.: San Francisco) in press
12. D.F. Gray: The Observation and Analysis of Stellar Photospheres, 3rd edn
(Cambridge University Press 2005)
13. G.F. Gray & K. Brown: PASP, 113, 723 (2001)
14. D.F. Gray & H.L. Johanson: 1991, ApJ, 103, 439 (1991)
15. V.V. Kovtyukh & N.I. Gorlova: A&A, 358, 587 (2000)
16. S. Meibom, J. Andersen, & B. Nordström: A&A 386, 187 (2002)
17. L. Pasquini, S. Randich, M. Zoccali et al.: A&A 951, 963 (2004)
18. L. da Silva, L. Girardi, L. Pasquini et al.: A&A, 458, 609 (2006)
