Astron. Nachr. / AN , No. , 1 – 7 () / DOI please set DOI!
Effective temperature vs line-depth ratio for ELODIE spectra.
Gravity and rotational velocity effects ⋆
K. Biazzo1,2,⋆⋆, A. Frasca1, S. Catalano1, and E. Marilli1
1 INAF - Catania Astrophysical Observatory, via S. Sofia 78, I-95123 Catania, Italy
2 Department of Physics and Astronomy, University of Catania, via S. Sofia 78, I-95123 Catania, Italy
The dates of receipt and acceptance should be inserted later
Key words stars: fundamental parameters – stars: late-type – techniques: spectroscopy
The dependence on the temperature of photospheric line-depth ratios (LDRs) in the spectral range 6190–6280 Å is in-
vestigated by using a sample of 174 ELODIE Archive stellar spectra of luminosity class from V to III. The rotational
broadening effect on LDRs is also studied. We provide useful calibrations of effective temperature versus LDRs for giant
and main sequence stars with 3800 <∼ Teff
∼ 6000 K and v sin i in the range 0–30 km s
−1. We found that, with the ex-
ception of very few line pairs, LDRs, measured at a spectral resolution as high as 42 000, depend on v sin i and that, by
neglecting the rotational broadening effect, one can mistake the Teff determination of ∼100 K in the worst cases.
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
The stellar effective temperature is one of the most impor-
tant astrophysical parameters. It is not easy to measure it
with high accuracy and this situation worsens for stars that
have already left the main sequence and that are expanding
their envelopes and redistributing their angular momentum.
In addition, surface inhomogeneities, such as spots and fac-
ulae can significantly affect the average temperature of ac-
tive stars.
Several diagnostics, based on color indices and spectral-
type classification, are available for temperature measure-
ments, but errors greater than 100 Kelvin degrees are often
encountered. On the other hand, the analysis of line profiles
and their dependence upon the stellar effective temperature
is a very powerful tool for the study of the photospheric
temperature, as well as for the investigation of stellar sur-
face structures.
As a matter of fact, it has been demonstrated that the ra-
tio of the depths of two lines having different sensitivity to
temperature is an excellent diagnostics for measuring small
temperature differences between stars or small temperature
variations of a given star. Although the effective temperature
scale can be set to within a few tens of degrees, temperature
differences can be measured with a precision down to a few
Kelvin degrees in the most favorable cases (e.g., Gray & Jo-
hanson 1991, Strassmeier & Schordan 2000, Gray & Brown
2001, Catalano et al. 2002a, 2002b). This allows putting a
star sample in a “relative” temperature scale or to detect tiny
temperature variations in individual stars. Starspot tempera-
⋆ Based on spectral data retrieved from the ELODIE Archive at Obser-
vatoire de Haute-Provence (OHP).
⋆⋆ Corresponding author: e-mail: katia.biazzo@oact.inaf.it.
tures from line-depth ratios (LDRs) variations, indeed, have
been determined in the slowly rotating dwarf star σ Draco-
nis (Gray et al. 1992), in the very young and rapidly rotating
star LQ Hydrae (Strassmeier et al. 1993), in some young
solar-type stars (Biazzo et al. 2007), and in three single-
lined RS CVn binaries (Frasca et al. 2005). However, all
these works do not explicitly take into account the effects of
stellar rotation on spectral line depths and consequently on
LDRs.
In the present work, we primarily explore the influence
of the rotational velocity on LDRs and provide calibration
relations between individual LDRs and effective tempera-
ture at different rotation velocities for high-resolution spec-
tra (R = 42 000) taken from the ELODIE Archive (Moul-
taka et al. 2004), taking also into account the effect of grav-
The effect of slightly different metallicity for the stars in
our sample is also examined. Its influence on LDRs is found
to be negligible for stars around solar metallicity (within
±0.3).
2 The star sample
2.1 Sample selection
We selected 174 stellar spectra of giant and main sequence
stars (MS) from the on-line ELODIE Archive (Moultaka et
al. 2004). Their spectral types range from F5 to M0 (Hoffleit
& Warren 1991). The criteria for the choice of the stellar
sample are the following:
– low rotation rate, v sin i <∼ 5 km s
−1 (values mainly
taken from Bernacca & Perinotto 1970, de Medeiros &
Mayor 1999, Glebocki et al. 2000);
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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2 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
– good Hipparcos parallaxes (π) with errors less than 15%
(ESA 1997);
– accurate B−V color indices (Mermilliod & Mermilliod
1998) ranging from 0.49 to 1.37 for the 102 MS stars
and from 0.64 to 1.54 for the 72 giant stars;
– nearly solar metallicity, [Fe/H]=0.0±0.3 (Soubiran et al.
1998).
2.2 Effective temperature and luminosity
In order to determine the Teff and luminosity of the stars in
our sample and to put them onto the HR diagram, it is neces-
sary to evaluate the interstellar extinction (AV ) and redden-
ing (EB−V ). We have evaluated AV from the star distance,
assuming a mean extinction of 1.7 mag/kpc for stars on the
galactic plane (|b| < 5◦) and of 0.7 mag/kpc for stars out of
the plane (|b| > 5◦). The reddening was estimated accord-
ing to the standard law AV = 3.1EB−V (Savage & Mathis
1979), with EB−V color excess. However, the color excess
of these nearby stars is always less than 0.m03 for MS stars
and less than 0.m09 for giant stars. The only two exceptions
are HD 176737 and HD 54489 where EB−V ∼ 0.20 since
they have |b| < 5◦ and π < 3 mas. Fig. 1 shows the distri-
butions of the de-reddened color (B − V )0 for the MS and
giant stars. The de-reddened V magnitude was converted
into absolute magnitude MV through the parallax and sub-
sequently into bolometric magnitude by means of the bolo-
metric corrections tabulated by Flower (1996) as a function
of the effective temperature. A solar bolometric magnitude
of Mbol = 4.64 (Cox 2000) was used to express the stellar
luminosity in solar units. From (B − V )0 values we have
deduced the effective temperature by means of the follow-
ing empirical relation given by Gray (2005) and valid for
0.00≤ (B − V )0 <∼ 1.5:
logTeff = 3.981− 0.4728(B − V )0
+ 0.2434(B − V )2
− 0.062(B − V )3
We have verified the consistency of Teff values derived
in this way with those listed by Prugniel & Soubiran (2001)
and compiled from the literature (Fig. 2). The latter temper-
atures appear to be systematically lower than Gray’s temper-
atures by about 120 K, on average. The root mean square
(rms) of data compared to the linear fits is around 130 K
both for giant and MS stars. This comparison allows us to
estimate an average temperature uncertainty of about 100–
150 K for the FGK stars of our sample, as already found
in previous studies (see, e.g., Gray 2005, and references
therein). We find analogous results by plotting the Teff de-
rived from Gray’s relation with those obtained by means of
the Teff–(V − I) calibration by Alonso et al. (1996, 1999).
After several tests made on the LDR–Teff calibrations, we
have chosen to use Gray’s effective temperatures for the
following analysis, because they give the smallest scatter
in the calibrations (rms≃0.13, 0.14, and 0.06 for Prugniel
& Soubiran, Alonso et al., and Gray temperature sets, re-
spectively). Anyway, the use of Alonso et al.’s temperature
Fig. 1 B − V distribution of the giant (III) and MS (V)
calibration stars.
Fig. 2 Comparison between the effective temperatures of
the giant (triangles) and MS (squares) stars obtained using
the Gray’s calibration (Gray 2005) and those listed by Prug-
niel & Soubiran (2001). The two continuous lines represent
the linear fits to the two star groups, while the dashed line is
the bisector.
scale, instead of Gray’s scale, does not affect significantly
the LDR–Teff calibrations.
The position onto the Hertzsprung-Russel (HR) diagram
of the ELODIE stars used in this work is shown in Fig. 3
together with the evolutionary tracks and isochrones calcu-
lated by Girardi et al. (2000).
3 LDR analysis and results
3.1 Line identification
Within the visible region of cool star spectra, there are sev-
eral pairs of lines suitable for temperature determination.
Most works are based on line pairs in the spectral domain
around 6200 Å (Gray & Johanson 1991, Gray & Brown
2001, Catalano et al. 2002a, 2002b, Biazzo 2006) and 6400
Å (Strassmeier & Fekel 1990, Strassmeier & Schordan
2000).
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Astron. Nachr. / AN () 3
Fig. 3 HR diagram of the stars in our sample. The evolu-
tionary tracks for different masses are taken from Girardi et
al. (2000) and are shown by continuous and dotted lines.
The isochrones at an age of 6.31×107 yrs (ZAMS) with
Z = 0.019 ([Fe/H]=0) and Z = 0.01 ([Fe/H]∼ −0.3) are
also displayed with dashed and dash-dotted lines, respec-
tively.
For this work, several spectral lines have been chosen
in the 6190–6280 Å range. A sample of ELODIE spectra
of different spectral types is shown in Fig. 4. The lines were
identified through the solar (Moore et al. 1966) and Arcturus
(Griffin 1968) atlases, choosing those appearing unblended
at the very high resolution of the aforementioned atlases.
The chosen lines, their excitation potential χ (Moore et al.
1966) and ionization energy I (Allen 1973) in electron volts
are listed in Table 1 together with a code number in the
fifth column. The lines for each ratio are chosen to be close
together in order to minimize the errors in the continuum
setting. Fifteen line ratios are used altogether in this work.
Each spectral line has an intensity depending specifically
on temperature and gravity (or electronic pressure) through
the line and continuum absorption coefficients (lν and κν).
These parameters are related to the excitation and ionization
potentials, χ and I , by means of Boltzmann and Saha equa-
tions. For these reasons, for example, the lines λ6243.11
V I and λ6247.56 Fe II change in opposite directions with
temperature, as displayed in Fig. 4, where the effect of tem-
perature and gravity on line intensities is apparent.
The measure of line depths (d), LDRs (r), and the eval-
uation of errors has been carried out according to the guide-
lines of Catalano et al. (2002a).
3.2 Metallicity effect
Before proceeding with the calibration, it is important to
evaluate the dependence of line-depth ratios on metallicity.
Gray (1994) has investigated the influence of metallicity on
color indices, finding an empirical relation between B − V
and the logarithm of the iron abundance normalized to the
Sun ([Fe/H]). A calibration relation between B−V and Teff
depending on [Fe/H] has been also proposed by Alonso et
Table 1 Spectral lines. Each line printed in italics is fully
blended with the preceding one.
λ Element χ I Code
(Å) (eV) (eV)
6199.19 V I 0.29 6.74 1
6200.32 Fe I 2.61 7.87 2
6210.67 Sc I 0.00 6.54 3
6213.44 Fe I 2.22 7.87 4
6213.83 V I 0.30 6.74 5
6215.15 Fe I 4.19 7.87 6
6215.22 Ti I 2.69 6.82
6216.36 V I 0.28 6.74 7
6223.99 Ni I 4.10 7.63 8
6224.51 V I 0.29 6.74 9
6232.65 Fe I 3.65 7.87 10
6233.20 V I 0.28 6.74 11
6242.84 V I 0.26 6.74 12
6243.11 V I 0.30 6.74 13
6243.82 Si I 5.61 8.15 14
6246.33 Fe I 3.60 7.87 15
6247.56 Fe II 3.89 16.18 16
6251.83 V I 0.29 6.74 17
6252.57 Fe I 2.40 7.87 18
6255.95 Fe I ? 7.87 19
6256.35 Ni I 1.68 7.63 20
6256.36 Fe I 2.45 7.87
6256.89 V I 0.28 6.74 21
6265.14 Fe I 2.18 7.87 22
6266.33 V I 0.28 6.74 23
6268.87 V I 0.30 6.74 24
6270.23 Fe I 2.86 7.87 25
6274.66 V I 0.27 6.74 26
al. (1999). However, the B − V color index is only very
slightly dependent on [Fe/H] for stars of nearly solar metal-
licity. Furthermore, Gray (1994) did not find any depen-
dence on [Fe/H] for LDRs of weak lines and only a very
weak dependence for the line pair λ6251.83 V I–λ6252.57
Fe I, amounting to about ±20 K for [Fe/H] in the range
± 0.3. Since all the stars analysed in this work have metal-
licities close to the solar value (within ± 0.3) and taking also
into account the large uncertainty on many [Fe/H] litera-
ture data, no correction for this parameter has been applied.
Anyway, given the high number of stars in our sample, pos-
sible residual effects due to small metallicity differences not
properly accounted for are not expected to significantly af-
fect our calibration.
3.3 Gravity effect
Line depth ratios are sensitive to gravity due to the depen-
dence on the electron pressure of the H− bound-free contin-
uum absorption coefficient. As a consequence, to determine
the temperature of stars with different gravity, such as giants
and MS, it is necessary to evaluate this dependence and/or
to set appropriate temperature scales (Biazzo 2001).
For this reason, in the present work different r − Teff
calibrations have been performed for MS and giant stars. We
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4 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Fig. 4 Three representative normalized spectra for giant (upper panel) and MS (bottom panel) stars. Temperature de-
creases from top to bottom. The spectral lines used for the LDR computation are labeled with their wavelength (in Å),
chemical element and ionization level. The lines, with low excitation potential, such as λ6210.67 Sc I or λ6266.33 V I,
increase their depth with decreasing temperature, while the λ6247.56 Fe II line, with high excitation potential, shows an
opposite behaviour. The lines with intermediate χ, such as λ6256.35 Ni I, don’t display any relevant variation in this
temperature range.
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Astron. Nachr. / AN () 5
have taken into account the gravity spread in each sample in
the following way:
i. for MS stars we have considered the difference ∆L be-
tween their luminosity and that of ZAMS stars of the
same color (Fig. 3) as a gravity index;
ii. for giant stars we have computed their gravity, log g,
according to the evolutionary tracks of Girardi et al.
(2000).
Then, the residuals ∆rMS,GIA of LDRs compared to the fits
in the (B − V )0 − r plane have been plotted against ∆L
and log g for MS and giant stars, respectively. A linear fit
to the data provides very small positive slopes, indicating
slightly increasing LDRs with gravity (Fig. 5). The linear
fit was obtained by means of POLY FIT, an IDL routine
using matrix inversion, which performs a weighted least-
square polynomial fit with error estimates. If a and b are the
intercept and the slope of these linear fits, respectively, the
gravity-corrected line-depth ratio, rc, is
rc = r − (a+ b∆L), (2)
for MS stars and
rc = r − (a+ b log g), (3)
for giant stars. In Eq. 2 and 3, r is the observed LDR. The
final polynomial fits to the corrected LDRs are of the type
Teff = c0 + c1rc + ...+ cnr
both for MS and giant stars, with c0, ..., cn coefficients of the
polynomial fits. An example of calibration is illustrated in
Fig. 6 and the polynomial fit coefficients are listed in Table
2 for the 15 different line pairs.
With the aim of verifying the internal consistency of
our method, we have computed the effective temperature
of each star coming from each rc − Teff calibration and we
have carried out the weighted average on all the 15 LDR.
The resulting < Teff > are plotted as a function of (B−V )0
in Fig. 7, together with the following polynomial fit on the
points (continuous line):
log < Teff > = 3.85478− 0.0582469(B− V )0
− 0.1883(B − V )2
+ 0.0823(B − V )3
In the range 0.5 <∼ (B−V )0
∼ 1.5, our< Teff > −(B−V )0
calibration is perfectly consistent with the one expressed in
Eq. 1 and obtained by Gray (2005). The data scatter is ob-
viously larger than the individual errors in < Teff > (origi-
nating from the LDR errors), due to the errors in the B − V
measurements and to the residual dependence of B − V on
the stellar parameters other than the effective temperature,
like metallicity and microturbulence.
The values of < Teff >, L and rc for all the standard
stars are listed in Table 51.
1 Table 5 is only available in electronic form at the Web site
http://cdsads.u-strasbg.fr/.
Fig. 5 Examples of the residuals of the LDR λ6252 V I-
λ6253 Fe I compared to the polynomial fit as a function of
the gravity index (dots). The continuous lines represent lin-
ear fits to the data of giants and MS stars, respectively.
3.4 Rotational broadening effect
In a moderately rotating star, the depth at the line center
decreases with increasing v sin i at a rate depending on the
line characteristics. Following Stift & Strassmeier (1995), in
a weak line for which the saturation effects are very small,
the residual intensity directly reflects the run of the opacity
profile with frequency. A strong line, in contrast, behaves
differently, because saturation leads to a contribution to the
intensity at the line center that remains fairly high over a
considerable part of the stellar disk, resulting in a slow de-
crease in the central line intensity with v sin i. This implies
that if two lines are of comparable strength and do not dif-
fer radically in the broadening parameters, the LDR will
not depend on rotation. Stift & Strassmeier (1995) investi-
gated the dependence of the LDR on rotation by synthesiz-
ing the spectral region containing the λ6252 V I and λ6253
Fe I lines in a grid of atmospheric models (Kurucz 1993)
for main-sequence stars with v sin i values ranging from 0.0
to 6.0 km s−1. They estimated that, for a fixed microturbu-
lence, the rotation dependence is always present at all tem-
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6 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Fig. 6 rc − Teff calibration for the line pair λ6211 Sc I-λ6215 Fe I+Ti I at different v sin i’s (open circles: v sin i=0 km
s−1; triangles: v sin i=15 km s−1; crosses: v sin i=30 km s−1) for giant stars (left panel) and MS stars (right panel).
Fig. 7 < Teff > of the standards as a function of the de-
reddened B − V . The continuous and dashed lines are re-
ferred to our and Gray’s calibrations, respectively.
peratures (from 3500 to 6000 K) for a v sin i ≥ 4 − 5 km
We find similar results computing the LDRs obtained
from high-resolution synthetic spectra. In particular, we
have considered the Synthetic Stellar Library described and
made available by Coelho et al. (2005), which contains
spectra synthesized by adopting the model atmospheres of
Castelli & Kurucz (2003). These spectra are sampled at 0.02
Å, range from the near-ultraviolet (300 nm) to the near-
infrared (1.8 µm), and cover the following grid of param-
eters: 3500 ≤ Teff ≤7000 K, 0.0 ≤ log g ≤ 5.0,
−2.5≤[Fe/H]≤+0.5, α-enhanced [α/Fe]=0.0, 0.4 and mi-
croturbulent velocity vt=1.0, 1.8, 2.5 km s
−1. In Fig. 8 we
show, as an example, the behaviour of synthetic LDRs with
v sin i at three different Teff for the line pair λ6211 Sc I-
λ6215 Fe I+Ti I. The synthetic-LDR for this couple de-
creases with the increase in v sin i from 0 to about 20 km
s−1 and then remains nearly constant. This behaviour is ap-
parent in all the three temperatures displayed in Fig. 8, and
is more evident in the lowest one. Neglecting this effect, a
systematic error in the effective temperature can arise. For
instance, if we use the rc − Teff calibration obtained by us
at v sin i=0 km s−1 for a giant star with Teff=4750 K and
v sin i= 20 km s−1, we overestimate its effective tempera-
ture by about 80 K. As a consequence, this LDR appears to
be quite sensitive to the rotation velocity in the range 0–20
km s−1. Thus, the rotational broadening must be taken into
account to perform a reliable calibration for this as well as
for several other LDRs.
To study in detail the influence of rotational broadening
on LDRs, we have computed the LDRs of our star sample
broadening the corresponding spectra at different rotation
velocities from 0 to 30 km s−1 in steps of 5 km s−1. The
LDR calculation has been carried out with a simple code
written in IDL2. The code first convolves the spectrum with
the required rotational profile and then, automatically, com-
putes the 15 LDRs in the selected wavelength range.
An example of an rc − Teff calibration (λ6211 Sc I-
λ6215 Fe I+Ti I) both for giant and MS stars is displayed in
Fig. 6, where only the calibrations for three v sin i values (0,
15, and 30 km s−1) are shown. We find that for some LDRs
the effects of the broadening are already visible at 5 km s−1,
while some other LDRs are practically not affected by the
rotational broadening. The main characteristics of these cal-
ibrations can be summarized as follows.
– Because of blending problems, for some pairs it is not
possible to broaden the lines at any rotational veloc-
ity (e.g., λ6214 V I-λ6213 Fe I, λ6233 V I-λ6232 Fe I,
λ6242V I-λ6244 Si I, λ6252V I-λ6253 Fe I, λ6257 V I-
λ6255 Fe I, λ6257 V I-λ6256 Fe I+Ni I).
– Some LDRs seem not to suffer from rotational broaden-
ing effects in almost all the effective temperature ranges
2 IDL (Interactive Data Language) is a trademark of Research Systems
Incorporated (RSI).
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Astron. Nachr. / AN () 7
Fig. 8 Synthetic LDRs at 3 differentTeff as a function of v sin i for the line pair λ6211 Sc I-λ6215 Fe I+Ti I. The synthetic
spectra are referred to a star with log g=2.5, [Fe/H]=0.0, [α/Fe]=0.0, vt=1.8, and have been degraded to the same resolution
of ELODIE.
(for example λ6199 V I-λ6200 Fe I, λ6214 V I-λ6213
Fe I, λ6275 V I-λ6270 Fe I), as expected for weak lines.
– Some line pairs show variation due to rotational broad-
ening for a temperature lower than about 4500 K and
5000 K for giant and MS stars, respectively (e.g., λ6243
V I-λ6247 Fe II, λ6269 V I-λ6270 Fe I).
– Other couples display changes at any temperature (e.g.,
λ6211 Sc I-λ6215 Fe I+Ti I, λ6216 V I-λ6215 Fe I+Ti I,
λ6252 V I-λ6253 Fe I, λ6266 V I-λ6265 Fe I).
– The slope of rc − Teff calibration in some ratios de-
creases with the increase in the rotation (e.g., λ6243V I-
λ6246 Fe I), while in some other ratios increases with
the rotation (e.g., λ6216 V I-λ6215 Fe I+Ti I).
– In any case, the variation of the slope with v sin i seems
to be more evident for giant stars compared to MS stars
(e.g., λ6243 V I-λ6246 Fe I and λ6269 V I-λ6270 Fe I).
This behaviour can be due to the fact that the giants
have narrower lines compared to MS stars, due to their
lower atmospheric density. As a consequence, they ap-
pear to be sensitive to the rotational broadening, while
the gravity broadening in MS stars is comparable to the
rotational broadening at low rotational velocity and the
effect on LDR comes out to be less prominent.
3.4.1 Temperature sensitivity on LDR
In order to measure the temperature sensitivity of each LDR,
the slopes dT
of the polynomial fits have been calculated.
The dT
absolute values at a temperature of 5000 K are
listed in Table 2 for the calibrations of the giant and MS
stars not rotationally broadened. Values of about 10–30 K
and, in some case, even smaller, have been found for a 0.01
variation of rc, which represents the typical uncertainty for
the LDR determination in well-exposed spectra. Stars below
4000 K and above 6200 K have the most uncertain temper-
atures because of the influence of molecular bands in the
coolest stars and the very small depths of the low-excitation
lines in the hottest stars of our sample, respectively.
Thus, the temperature sensitivity changes from an LDR
to another one, but it is also a function of the rotational ve-
locity. Fig. 9 displays an example of the variation of the tem-
perature sensitivity with the rotational velocity of the cou-
ple λ6211 Sc I-λ6215 Fe I+Ti I obtained for the giant cali-
bration. For this ratio, the temperature sensitivity decreases
with the increasing rotational broadening. As we mentioned
before, other LDRs display different behaviours of the tem-
perature sensitivity as a function of v sin i.
The coefficients (c0, ..., cn) of the fits and the values of
and rms obtained at v sin i=0, 15, and 30 km s−1 are
listed in Tables 2, 3 4, respectively.
4 Conclusion
In this work we have performed LDR–Teff calibrations from
high-resolution spectra taking into account the corrections
for the gravity effect and the rotational broadening. To our
knowledge, this is the first work in which the dependence
of LDRs on rotational velocity has been considered on real
spectra. In previous studies, this dependence had not been
taken into account, also following Gray & Johanson’s
(1991) early suggestions that considered the effect of v sin i
to be negligible. Here we demonstrate that the rotational
broadening effect is already evident at 5 km s−1 both in
synthetic and real spectra of cool stars. Its effect can be ne-
glected only in particular temperature domains and for a few
line pairs. In other situations, the dependency of LDRs on
v sin i must be properly taken into account, at least at a spec-
tral resolution as high as 42 000. We show that neglecting
this effect can lead to temperature overestimates as high as
≈100 K.
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8 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Table 2 Coefficients of the fits Teff = c0 + c1rc + ...+ cnrnc for the ELODIE spectra not rotationally broadened.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5658.52 5630.37 5357.34 8808.49 4976.68 5328.31 5375.97 5435.02
c1 −1565.89 −2563.00 −846.737 −10484.1 697.119 −749.330 −292.110 −8.57992
c2 1384.63 2766.46 −176.810 10403.9 −849.779 −150.672 −25.7998 −654.941
c3 −807.719 −1384.76 −80.6700 −3804.58 184.978 −3.71716 0.715242
0.01 | dT
|5000 K 10.4 11.0 12.4 14.9 5.2 10.9 4.0 12.8
rms 0.080 0.060 0.070 0.071 0.081 0.078 0.085 0.068
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 5479.94 5630.09 5204.23 5407.48 5324.25 5346.80 5335.75
c1 −325.954 −1935.08 −53.5851 −2091.73 −1625.05 −1054.34 −327.402
c2 4.71410 2496.75 −325.674 2640.38 1431.70 619.856 −313.672
c3 1.43373 −1976.03 74.5653 −1956.14 −1193.13 −343.396 −42.0121
0.01 | dT
|5000 K 4.1 13.2 6.3 12.9 13.9 9.2 10.1
rms 0.070 0.054 0.068 0.062 0.063 0.081 0.081
DWARF STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 6592.19 6298.64 6303.41 8075.38 6181.66 6204.32 6122.76 6583.91
c1 −4053.01 −4813.87 −5018.31 −6053.31 −1077.50 −3855.13 −895.008 −3240.32
c2 4020.50 5670.56 6604.68 4843.37 197.649 3379.47 158.882 2763.93
c3 −1663.63 −2457.28 −3562.99 −1688.39 −7.73603 −1175.00 −8.65057 −1211.49
0.01 | dT
|5000 K 11.0 10.1 13.4 15.7 4.5 12.4 2.8 13.2
rms 0.065 0.060 0.040 0.057 0.085 0.047 0.087 0.049
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 6250.15 6486.68 6178.37 6210.10 6228.96 6120.07 6271.19
c1 −732.154 −5065.09 −1203.98 −5244.93 −6031.24 −2734.59 −1994.09
c2 143.714 7059.62 261.964 6959.06 9450.38 1909.74 716.031
c3 −9.97940 −4105.26 −19.2823 −3796.17 −5981.44 −559.915 −138.664
0.01 | dT
|5000 K 1.4 15.2 5.0 16.5 18.0 8.5 9.8
rms 0.074 0.043 0.067 0.047 0.053 0.067 0.076
This paper provides calibrations that can be used for
temperature determinations of stars with 0≤ v sin i <∼ 30
km s−1 and observed with ELODIE as well as with other
spectrographs at a similar resolution. We have shown that
all the LDRs examined in the present paper display a good
sensitivity to the effective temperature which allows us to
reach an uncertainty lower than 10–15 K at R = 42 000
for stars rotating up to v sin i=30 km s−1. The simultaneous
use of several LDRs allows us to improve the temperature
sensitivity and to fully detect and analyse effective tempera-
ture modulations produced by cool starspots in active stars,
as we have already shown in previous works (Frasca et al.
2005, Biazzo et al. 2007).
Acknowledgements. This work has been supported by the Italian
National Institute for Astrophysics (INAF), by the Italian Minis-
tero dell’Istruzione, Università e Ricerca (MIUR) and by the Re-
gione Sicilia which are gratefully acknowledged. We thank the ref-
eree for useful suggestions. We are also grateful to Mrs. Luigia
Santagati for the English revision of the text. This research has
made use of SIMBAD and VIZIER databases, operated at CDS,
Strasbourg, France.
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Astron. Nachr. / AN () 9
Table 3 Coefficients of the fits Teff = c0 + c1rc + ... + cnrnc for the ELODIE spectra rotationally broadened to 15 km
s−1. The empty columns relate to the line pairs completely blended at this rotational velocity.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5249.84 5559.50 8090.67 5453.71 5355.55 5662.56
c1 245.810 −2741.36 −9105.81 −489.599 −879.618 −670.393
c2 −1064.84 3273.61 9705.52 −34.6856 −138.541 −13.6821
c3 306.601 −1888.48 −3948.66 33.7288 35.1345
0.01 | dT
|5000 K 9.8 13.5 15.6 5.1 12.6 8.0
rms 0.090 0.057 0.065 0.087 0.068 0.070
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 5400.03 5051.44 5605.92 5297.24 5237.87 5202.02
c1 −231.533 −1505.89 −3632.92 −1585.45 −526.586 203.540
c2 13.1768 4285.89 5882.55 940.850 −111.045 −1183.49
c3 −0.368023 −1829.64 −4511.96 −817.658 47.8455 391.671
0.01 | dT
|5000 K 2.4 15.5 15.9 15.8 7.9 10.0
rms 0.072 0.055 0.050 0.056 0.087 0.088
DWARF STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 6537.09 6205.81 7824.72 6216.99 6451.17 6522.90
c1 −3721.86 −5454.44 −5415.18 −1442.34 −5424.86 −2833.56
c2 3167.41 7964.98 3678.15 532.435 5770.74 1687.54
c3 −1119.43 −4361.33 −1198.04 −70.4289 −2439.22 −485.220
0.01 | dT
|5000 K 10.7 11.8 17.9 3.2 16.0 11.0
rms 0.061 0.054 0.048 0.089 0.036 0.053
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 6194.16 6312.44 6347.22 5964.93 5988.72 6264.03
c1 −549.734 −4404.66 −7231.99 −4180.21 −2177.96 −2135.85
c2 83.9286 5255.34 12331.5 4047.15 1527.77 1057.32
c3 −4.27056 −3379.88 −8240.08 −1716.93 −483.352 −322.180
0.01 | dT
|5000 K 1.0 18.6 16.4 18.7 6.9 10.1
rms 0.075 0.033 0.053 0.049 0.082 0.087
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http://obswww.unige.ch/gcpd/cgi-bin/photoSys.cgi
10 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Table 4 Coefficients of the fits Teff = c0 + c1rc + ... + cnrnc for the ELODIE spectra rotationally broadened to 30 km
s−1. The empty columns relate to the line pairs completely blended at this rotational velocity.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5481.25 5496.39 7025.27 5695.10
c1 −596.797 −2961.51 −5597.99 −800.163
c2 −43.7139 4228.71 5957.99 75.3450
c3 −48.3037 −3087.51 −2710.79
0.01 | dT
|5000 K 9.3 16.1 16.5 8.4
rms 0.095 0.058 0.061 0.075
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 5337.08 5150.51 5190.59 5357.17
c1 −166.813 −825.095 −500.186 −591.566
c2 8.35369 70.5176 28.5439 −202.882
c3 −0.153085 −989.250 6.34586 92.0652
0.01 | dT
|5000 K 1.7 15.1 7.5 9.5
rms 0.075 0.071 0.089 0.085
DWARF STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 6432.25 5999.97 7479.52 6874.46
c1 −3039.71 −4545.30 −3706.65 −3697.12
c2 2161.86 6247.09 1147.46 2312.46
c3 −692.710 −3573.28 −116.692 −595.265
0.01 | dT
|5000 K 10.3 11.6 18.9 11.1
rms 0.066 0.046 0.051 0.079
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 6082.76 5895.59 5712.75 6039.12
c1 −329.412 −4065.13 −1362.68 −885.351
c2 30.3591 5641.78 931.915 −863.622
c3 −0.945513 −5297.51 −312.388 527.239
0.01 | dT
|5000 K 1.0 20.0 5.0 10.1
rms 0.080 0.033 0.085 0.090
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org
	Introduction
	The star sample
	Sample selection
	Effective temperature and luminosity
	LDR analysis and results
	Line identification
	Metallicity effect
	Gravity effect
	Rotational broadening effect
	Temperature sensitivity on LDR
	Conclusion

  The dependence on the temperature of photospheric line-depth ratios (LDRs) in
the spectral range 6190-6280 A is investigated by using a sample of 174 ELODIE
Archive stellar spectra of luminosity class from V to III. The rotational
broadening effect on LDRs is also studied. We provide useful calibrations of
effective temperature versus LDRs for giant and main sequence stars with
3800<Teff<6000 K and vsini in the range 0-30 km/s. We found that, with the
exception of very few line pairs, LDRs, measured at a spectral resolution as
high as 42000, depend on vsini and that, by neglecting the rotational
broadening effect, one can mistake the Teff determination of 100 K in the worst
cases.

Introduction
The stellar effective temperature is one of the most impor-
tant astrophysical parameters. It is not easy to measure it
with high accuracy and this situation worsens for stars that
have already left the main sequence and that are expanding
their envelopes and redistributing their angular momentum.
In addition, surface inhomogeneities, such as spots and fac-
ulae can significantly affect the average temperature of ac-
tive stars.
Several diagnostics, based on color indices and spectral-
type classification, are available for temperature measure-
ments, but errors greater than 100 Kelvin degrees are often
encountered. On the other hand, the analysis of line profiles
and their dependence upon the stellar effective temperature
is a very powerful tool for the study of the photospheric
temperature, as well as for the investigation of stellar sur-
face structures.
As a matter of fact, it has been demonstrated that the ra-
tio of the depths of two lines having different sensitivity to
temperature is an excellent diagnostics for measuring small
temperature differences between stars or small temperature
variations of a given star. Although the effective temperature
scale can be set to within a few tens of degrees, temperature
differences can be measured with a precision down to a few
Kelvin degrees in the most favorable cases (e.g., Gray & Jo-
hanson 1991, Strassmeier & Schordan 2000, Gray & Brown
2001, Catalano et al. 2002a, 2002b). This allows putting a
star sample in a “relative” temperature scale or to detect tiny
temperature variations in individual stars. Starspot tempera-
⋆ Based on spectral data retrieved from the ELODIE Archive at Obser-
vatoire de Haute-Provence (OHP).
⋆⋆ Corresponding author: e-mail: katia.biazzo@oact.inaf.it.
tures from line-depth ratios (LDRs) variations, indeed, have
been determined in the slowly rotating dwarf star σ Draco-
nis (Gray et al. 1992), in the very young and rapidly rotating
star LQ Hydrae (Strassmeier et al. 1993), in some young
solar-type stars (Biazzo et al. 2007), and in three single-
lined RS CVn binaries (Frasca et al. 2005). However, all
these works do not explicitly take into account the effects of
stellar rotation on spectral line depths and consequently on
LDRs.
In the present work, we primarily explore the influence
of the rotational velocity on LDRs and provide calibration
relations between individual LDRs and effective tempera-
ture at different rotation velocities for high-resolution spec-
tra (R = 42 000) taken from the ELODIE Archive (Moul-
taka et al. 2004), taking also into account the effect of grav-
The effect of slightly different metallicity for the stars in
our sample is also examined. Its influence on LDRs is found
to be negligible for stars around solar metallicity (within
±0.3).
2 The star sample
2.1 Sample selection
We selected 174 stellar spectra of giant and main sequence
stars (MS) from the on-line ELODIE Archive (Moultaka et
al. 2004). Their spectral types range from F5 to M0 (Hoffleit
& Warren 1991). The criteria for the choice of the stellar
sample are the following:
– low rotation rate, v sin i <∼ 5 km s
−1 (values mainly
taken from Bernacca & Perinotto 1970, de Medeiros &
Mayor 1999, Glebocki et al. 2000);
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
http://arxiv.org/abs/0704.1456v1
2 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
– good Hipparcos parallaxes (π) with errors less than 15%
(ESA 1997);
– accurate B−V color indices (Mermilliod & Mermilliod
1998) ranging from 0.49 to 1.37 for the 102 MS stars
and from 0.64 to 1.54 for the 72 giant stars;
– nearly solar metallicity, [Fe/H]=0.0±0.3 (Soubiran et al.
1998).
2.2 Effective temperature and luminosity
In order to determine the Teff and luminosity of the stars in
our sample and to put them onto the HR diagram, it is neces-
sary to evaluate the interstellar extinction (AV ) and redden-
ing (EB−V ). We have evaluated AV from the star distance,
assuming a mean extinction of 1.7 mag/kpc for stars on the
galactic plane (|b| < 5◦) and of 0.7 mag/kpc for stars out of
the plane (|b| > 5◦). The reddening was estimated accord-
ing to the standard law AV = 3.1EB−V (Savage & Mathis
1979), with EB−V color excess. However, the color excess
of these nearby stars is always less than 0.m03 for MS stars
and less than 0.m09 for giant stars. The only two exceptions
are HD 176737 and HD 54489 where EB−V ∼ 0.20 since
they have |b| < 5◦ and π < 3 mas. Fig. 1 shows the distri-
butions of the de-reddened color (B − V )0 for the MS and
giant stars. The de-reddened V magnitude was converted
into absolute magnitude MV through the parallax and sub-
sequently into bolometric magnitude by means of the bolo-
metric corrections tabulated by Flower (1996) as a function
of the effective temperature. A solar bolometric magnitude
of Mbol = 4.64 (Cox 2000) was used to express the stellar
luminosity in solar units. From (B − V )0 values we have
deduced the effective temperature by means of the follow-
ing empirical relation given by Gray (2005) and valid for
0.00≤ (B − V )0 <∼ 1.5:
logTeff = 3.981− 0.4728(B − V )0
+ 0.2434(B − V )2
− 0.062(B − V )3
We have verified the consistency of Teff values derived
in this way with those listed by Prugniel & Soubiran (2001)
and compiled from the literature (Fig. 2). The latter temper-
atures appear to be systematically lower than Gray’s temper-
atures by about 120 K, on average. The root mean square
(rms) of data compared to the linear fits is around 130 K
both for giant and MS stars. This comparison allows us to
estimate an average temperature uncertainty of about 100–
150 K for the FGK stars of our sample, as already found
in previous studies (see, e.g., Gray 2005, and references
therein). We find analogous results by plotting the Teff de-
rived from Gray’s relation with those obtained by means of
the Teff–(V − I) calibration by Alonso et al. (1996, 1999).
After several tests made on the LDR–Teff calibrations, we
have chosen to use Gray’s effective temperatures for the
following analysis, because they give the smallest scatter
in the calibrations (rms≃0.13, 0.14, and 0.06 for Prugniel
& Soubiran, Alonso et al., and Gray temperature sets, re-
spectively). Anyway, the use of Alonso et al.’s temperature
Fig. 1 B − V distribution of the giant (III) and MS (V)
calibration stars.
Fig. 2 Comparison between the effective temperatures of
the giant (triangles) and MS (squares) stars obtained using
the Gray’s calibration (Gray 2005) and those listed by Prug-
niel & Soubiran (2001). The two continuous lines represent
the linear fits to the two star groups, while the dashed line is
the bisector.
scale, instead of Gray’s scale, does not affect significantly
the LDR–Teff calibrations.
The position onto the Hertzsprung-Russel (HR) diagram
of the ELODIE stars used in this work is shown in Fig. 3
together with the evolutionary tracks and isochrones calcu-
lated by Girardi et al. (2000).
3 LDR analysis and results
3.1 Line identification
Within the visible region of cool star spectra, there are sev-
eral pairs of lines suitable for temperature determination.
Most works are based on line pairs in the spectral domain
around 6200 Å (Gray & Johanson 1991, Gray & Brown
2001, Catalano et al. 2002a, 2002b, Biazzo 2006) and 6400
Å (Strassmeier & Fekel 1990, Strassmeier & Schordan
2000).
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org
Astron. Nachr. / AN () 3
Fig. 3 HR diagram of the stars in our sample. The evolu-
tionary tracks for different masses are taken from Girardi et
al. (2000) and are shown by continuous and dotted lines.
The isochrones at an age of 6.31×107 yrs (ZAMS) with
Z = 0.019 ([Fe/H]=0) and Z = 0.01 ([Fe/H]∼ −0.3) are
also displayed with dashed and dash-dotted lines, respec-
tively.
For this work, several spectral lines have been chosen
in the 6190–6280 Å range. A sample of ELODIE spectra
of different spectral types is shown in Fig. 4. The lines were
identified through the solar (Moore et al. 1966) and Arcturus
(Griffin 1968) atlases, choosing those appearing unblended
at the very high resolution of the aforementioned atlases.
The chosen lines, their excitation potential χ (Moore et al.
1966) and ionization energy I (Allen 1973) in electron volts
are listed in Table 1 together with a code number in the
fifth column. The lines for each ratio are chosen to be close
together in order to minimize the errors in the continuum
setting. Fifteen line ratios are used altogether in this work.
Each spectral line has an intensity depending specifically
on temperature and gravity (or electronic pressure) through
the line and continuum absorption coefficients (lν and κν).
These parameters are related to the excitation and ionization
potentials, χ and I , by means of Boltzmann and Saha equa-
tions. For these reasons, for example, the lines λ6243.11
V I and λ6247.56 Fe II change in opposite directions with
temperature, as displayed in Fig. 4, where the effect of tem-
perature and gravity on line intensities is apparent.
The measure of line depths (d), LDRs (r), and the eval-
uation of errors has been carried out according to the guide-
lines of Catalano et al. (2002a).
3.2 Metallicity effect
Before proceeding with the calibration, it is important to
evaluate the dependence of line-depth ratios on metallicity.
Gray (1994) has investigated the influence of metallicity on
color indices, finding an empirical relation between B − V
and the logarithm of the iron abundance normalized to the
Sun ([Fe/H]). A calibration relation between B−V and Teff
depending on [Fe/H] has been also proposed by Alonso et
Table 1 Spectral lines. Each line printed in italics is fully
blended with the preceding one.
λ Element χ I Code
(Å) (eV) (eV)
6199.19 V I 0.29 6.74 1
6200.32 Fe I 2.61 7.87 2
6210.67 Sc I 0.00 6.54 3
6213.44 Fe I 2.22 7.87 4
6213.83 V I 0.30 6.74 5
6215.15 Fe I 4.19 7.87 6
6215.22 Ti I 2.69 6.82
6216.36 V I 0.28 6.74 7
6223.99 Ni I 4.10 7.63 8
6224.51 V I 0.29 6.74 9
6232.65 Fe I 3.65 7.87 10
6233.20 V I 0.28 6.74 11
6242.84 V I 0.26 6.74 12
6243.11 V I 0.30 6.74 13
6243.82 Si I 5.61 8.15 14
6246.33 Fe I 3.60 7.87 15
6247.56 Fe II 3.89 16.18 16
6251.83 V I 0.29 6.74 17
6252.57 Fe I 2.40 7.87 18
6255.95 Fe I ? 7.87 19
6256.35 Ni I 1.68 7.63 20
6256.36 Fe I 2.45 7.87
6256.89 V I 0.28 6.74 21
6265.14 Fe I 2.18 7.87 22
6266.33 V I 0.28 6.74 23
6268.87 V I 0.30 6.74 24
6270.23 Fe I 2.86 7.87 25
6274.66 V I 0.27 6.74 26
al. (1999). However, the B − V color index is only very
slightly dependent on [Fe/H] for stars of nearly solar metal-
licity. Furthermore, Gray (1994) did not find any depen-
dence on [Fe/H] for LDRs of weak lines and only a very
weak dependence for the line pair λ6251.83 V I–λ6252.57
Fe I, amounting to about ±20 K for [Fe/H] in the range
± 0.3. Since all the stars analysed in this work have metal-
licities close to the solar value (within ± 0.3) and taking also
into account the large uncertainty on many [Fe/H] litera-
ture data, no correction for this parameter has been applied.
Anyway, given the high number of stars in our sample, pos-
sible residual effects due to small metallicity differences not
properly accounted for are not expected to significantly af-
fect our calibration.
3.3 Gravity effect
Line depth ratios are sensitive to gravity due to the depen-
dence on the electron pressure of the H− bound-free contin-
uum absorption coefficient. As a consequence, to determine
the temperature of stars with different gravity, such as giants
and MS, it is necessary to evaluate this dependence and/or
to set appropriate temperature scales (Biazzo 2001).
For this reason, in the present work different r − Teff
calibrations have been performed for MS and giant stars. We
www.an-journal.org c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
4 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Fig. 4 Three representative normalized spectra for giant (upper panel) and MS (bottom panel) stars. Temperature de-
creases from top to bottom. The spectral lines used for the LDR computation are labeled with their wavelength (in Å),
chemical element and ionization level. The lines, with low excitation potential, such as λ6210.67 Sc I or λ6266.33 V I,
increase their depth with decreasing temperature, while the λ6247.56 Fe II line, with high excitation potential, shows an
opposite behaviour. The lines with intermediate χ, such as λ6256.35 Ni I, don’t display any relevant variation in this
temperature range.
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org
Astron. Nachr. / AN () 5
have taken into account the gravity spread in each sample in
the following way:
i. for MS stars we have considered the difference ∆L be-
tween their luminosity and that of ZAMS stars of the
same color (Fig. 3) as a gravity index;
ii. for giant stars we have computed their gravity, log g,
according to the evolutionary tracks of Girardi et al.
(2000).
Then, the residuals ∆rMS,GIA of LDRs compared to the fits
in the (B − V )0 − r plane have been plotted against ∆L
and log g for MS and giant stars, respectively. A linear fit
to the data provides very small positive slopes, indicating
slightly increasing LDRs with gravity (Fig. 5). The linear
fit was obtained by means of POLY FIT, an IDL routine
using matrix inversion, which performs a weighted least-
square polynomial fit with error estimates. If a and b are the
intercept and the slope of these linear fits, respectively, the
gravity-corrected line-depth ratio, rc, is
rc = r − (a+ b∆L), (2)
for MS stars and
rc = r − (a+ b log g), (3)
for giant stars. In Eq. 2 and 3, r is the observed LDR. The
final polynomial fits to the corrected LDRs are of the type
Teff = c0 + c1rc + ...+ cnr
both for MS and giant stars, with c0, ..., cn coefficients of the
polynomial fits. An example of calibration is illustrated in
Fig. 6 and the polynomial fit coefficients are listed in Table
2 for the 15 different line pairs.
With the aim of verifying the internal consistency of
our method, we have computed the effective temperature
of each star coming from each rc − Teff calibration and we
have carried out the weighted average on all the 15 LDR.
The resulting < Teff > are plotted as a function of (B−V )0
in Fig. 7, together with the following polynomial fit on the
points (continuous line):
log < Teff > = 3.85478− 0.0582469(B− V )0
− 0.1883(B − V )2
+ 0.0823(B − V )3
In the range 0.5 <∼ (B−V )0
∼ 1.5, our< Teff > −(B−V )0
calibration is perfectly consistent with the one expressed in
Eq. 1 and obtained by Gray (2005). The data scatter is ob-
viously larger than the individual errors in < Teff > (origi-
nating from the LDR errors), due to the errors in the B − V
measurements and to the residual dependence of B − V on
the stellar parameters other than the effective temperature,
like metallicity and microturbulence.
The values of < Teff >, L and rc for all the standard
stars are listed in Table 51.
1 Table 5 is only available in electronic form at the Web site
http://cdsads.u-strasbg.fr/.
Fig. 5 Examples of the residuals of the LDR λ6252 V I-
λ6253 Fe I compared to the polynomial fit as a function of
the gravity index (dots). The continuous lines represent lin-
ear fits to the data of giants and MS stars, respectively.
3.4 Rotational broadening effect
In a moderately rotating star, the depth at the line center
decreases with increasing v sin i at a rate depending on the
line characteristics. Following Stift & Strassmeier (1995), in
a weak line for which the saturation effects are very small,
the residual intensity directly reflects the run of the opacity
profile with frequency. A strong line, in contrast, behaves
differently, because saturation leads to a contribution to the
intensity at the line center that remains fairly high over a
considerable part of the stellar disk, resulting in a slow de-
crease in the central line intensity with v sin i. This implies
that if two lines are of comparable strength and do not dif-
fer radically in the broadening parameters, the LDR will
not depend on rotation. Stift & Strassmeier (1995) investi-
gated the dependence of the LDR on rotation by synthesiz-
ing the spectral region containing the λ6252 V I and λ6253
Fe I lines in a grid of atmospheric models (Kurucz 1993)
for main-sequence stars with v sin i values ranging from 0.0
to 6.0 km s−1. They estimated that, for a fixed microturbu-
lence, the rotation dependence is always present at all tem-
www.an-journal.org c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
http://cdsads.u-strasbg.fr/
6 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Fig. 6 rc − Teff calibration for the line pair λ6211 Sc I-λ6215 Fe I+Ti I at different v sin i’s (open circles: v sin i=0 km
s−1; triangles: v sin i=15 km s−1; crosses: v sin i=30 km s−1) for giant stars (left panel) and MS stars (right panel).
Fig. 7 < Teff > of the standards as a function of the de-
reddened B − V . The continuous and dashed lines are re-
ferred to our and Gray’s calibrations, respectively.
peratures (from 3500 to 6000 K) for a v sin i ≥ 4 − 5 km
We find similar results computing the LDRs obtained
from high-resolution synthetic spectra. In particular, we
have considered the Synthetic Stellar Library described and
made available by Coelho et al. (2005), which contains
spectra synthesized by adopting the model atmospheres of
Castelli & Kurucz (2003). These spectra are sampled at 0.02
Å, range from the near-ultraviolet (300 nm) to the near-
infrared (1.8 µm), and cover the following grid of param-
eters: 3500 ≤ Teff ≤7000 K, 0.0 ≤ log g ≤ 5.0,
−2.5≤[Fe/H]≤+0.5, α-enhanced [α/Fe]=0.0, 0.4 and mi-
croturbulent velocity vt=1.0, 1.8, 2.5 km s
−1. In Fig. 8 we
show, as an example, the behaviour of synthetic LDRs with
v sin i at three different Teff for the line pair λ6211 Sc I-
λ6215 Fe I+Ti I. The synthetic-LDR for this couple de-
creases with the increase in v sin i from 0 to about 20 km
s−1 and then remains nearly constant. This behaviour is ap-
parent in all the three temperatures displayed in Fig. 8, and
is more evident in the lowest one. Neglecting this effect, a
systematic error in the effective temperature can arise. For
instance, if we use the rc − Teff calibration obtained by us
at v sin i=0 km s−1 for a giant star with Teff=4750 K and
v sin i= 20 km s−1, we overestimate its effective tempera-
ture by about 80 K. As a consequence, this LDR appears to
be quite sensitive to the rotation velocity in the range 0–20
km s−1. Thus, the rotational broadening must be taken into
account to perform a reliable calibration for this as well as
for several other LDRs.
To study in detail the influence of rotational broadening
on LDRs, we have computed the LDRs of our star sample
broadening the corresponding spectra at different rotation
velocities from 0 to 30 km s−1 in steps of 5 km s−1. The
LDR calculation has been carried out with a simple code
written in IDL2. The code first convolves the spectrum with
the required rotational profile and then, automatically, com-
putes the 15 LDRs in the selected wavelength range.
An example of an rc − Teff calibration (λ6211 Sc I-
λ6215 Fe I+Ti I) both for giant and MS stars is displayed in
Fig. 6, where only the calibrations for three v sin i values (0,
15, and 30 km s−1) are shown. We find that for some LDRs
the effects of the broadening are already visible at 5 km s−1,
while some other LDRs are practically not affected by the
rotational broadening. The main characteristics of these cal-
ibrations can be summarized as follows.
– Because of blending problems, for some pairs it is not
possible to broaden the lines at any rotational veloc-
ity (e.g., λ6214 V I-λ6213 Fe I, λ6233 V I-λ6232 Fe I,
λ6242V I-λ6244 Si I, λ6252V I-λ6253 Fe I, λ6257 V I-
λ6255 Fe I, λ6257 V I-λ6256 Fe I+Ni I).
– Some LDRs seem not to suffer from rotational broaden-
ing effects in almost all the effective temperature ranges
2 IDL (Interactive Data Language) is a trademark of Research Systems
Incorporated (RSI).
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org
Astron. Nachr. / AN () 7
Fig. 8 Synthetic LDRs at 3 differentTeff as a function of v sin i for the line pair λ6211 Sc I-λ6215 Fe I+Ti I. The synthetic
spectra are referred to a star with log g=2.5, [Fe/H]=0.0, [α/Fe]=0.0, vt=1.8, and have been degraded to the same resolution
of ELODIE.
(for example λ6199 V I-λ6200 Fe I, λ6214 V I-λ6213
Fe I, λ6275 V I-λ6270 Fe I), as expected for weak lines.
– Some line pairs show variation due to rotational broad-
ening for a temperature lower than about 4500 K and
5000 K for giant and MS stars, respectively (e.g., λ6243
V I-λ6247 Fe II, λ6269 V I-λ6270 Fe I).
– Other couples display changes at any temperature (e.g.,
λ6211 Sc I-λ6215 Fe I+Ti I, λ6216 V I-λ6215 Fe I+Ti I,
λ6252 V I-λ6253 Fe I, λ6266 V I-λ6265 Fe I).
– The slope of rc − Teff calibration in some ratios de-
creases with the increase in the rotation (e.g., λ6243V I-
λ6246 Fe I), while in some other ratios increases with
the rotation (e.g., λ6216 V I-λ6215 Fe I+Ti I).
– In any case, the variation of the slope with v sin i seems
to be more evident for giant stars compared to MS stars
(e.g., λ6243 V I-λ6246 Fe I and λ6269 V I-λ6270 Fe I).
This behaviour can be due to the fact that the giants
have narrower lines compared to MS stars, due to their
lower atmospheric density. As a consequence, they ap-
pear to be sensitive to the rotational broadening, while
the gravity broadening in MS stars is comparable to the
rotational broadening at low rotational velocity and the
effect on LDR comes out to be less prominent.
3.4.1 Temperature sensitivity on LDR
In order to measure the temperature sensitivity of each LDR,
the slopes dT
of the polynomial fits have been calculated.
The dT
absolute values at a temperature of 5000 K are
listed in Table 2 for the calibrations of the giant and MS
stars not rotationally broadened. Values of about 10–30 K
and, in some case, even smaller, have been found for a 0.01
variation of rc, which represents the typical uncertainty for
the LDR determination in well-exposed spectra. Stars below
4000 K and above 6200 K have the most uncertain temper-
atures because of the influence of molecular bands in the
coolest stars and the very small depths of the low-excitation
lines in the hottest stars of our sample, respectively.
Thus, the temperature sensitivity changes from an LDR
to another one, but it is also a function of the rotational ve-
locity. Fig. 9 displays an example of the variation of the tem-
perature sensitivity with the rotational velocity of the cou-
ple λ6211 Sc I-λ6215 Fe I+Ti I obtained for the giant cali-
bration. For this ratio, the temperature sensitivity decreases
with the increasing rotational broadening. As we mentioned
before, other LDRs display different behaviours of the tem-
perature sensitivity as a function of v sin i.
The coefficients (c0, ..., cn) of the fits and the values of
and rms obtained at v sin i=0, 15, and 30 km s−1 are
listed in Tables 2, 3 4, respectively.
4 Conclusion
In this work we have performed LDR–Teff calibrations from
high-resolution spectra taking into account the corrections
for the gravity effect and the rotational broadening. To our
knowledge, this is the first work in which the dependence
of LDRs on rotational velocity has been considered on real
spectra. In previous studies, this dependence had not been
taken into account, also following Gray & Johanson’s
(1991) early suggestions that considered the effect of v sin i
to be negligible. Here we demonstrate that the rotational
broadening effect is already evident at 5 km s−1 both in
synthetic and real spectra of cool stars. Its effect can be ne-
glected only in particular temperature domains and for a few
line pairs. In other situations, the dependency of LDRs on
v sin i must be properly taken into account, at least at a spec-
tral resolution as high as 42 000. We show that neglecting
this effect can lead to temperature overestimates as high as
≈100 K.
www.an-journal.org c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
8 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Table 2 Coefficients of the fits Teff = c0 + c1rc + ...+ cnrnc for the ELODIE spectra not rotationally broadened.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5658.52 5630.37 5357.34 8808.49 4976.68 5328.31 5375.97 5435.02
c1 −1565.89 −2563.00 −846.737 −10484.1 697.119 −749.330 −292.110 −8.57992
c2 1384.63 2766.46 −176.810 10403.9 −849.779 −150.672 −25.7998 −654.941
c3 −807.719 −1384.76 −80.6700 −3804.58 184.978 −3.71716 0.715242
0.01 | dT
|5000 K 10.4 11.0 12.4 14.9 5.2 10.9 4.0 12.8
rms 0.080 0.060 0.070 0.071 0.081 0.078 0.085 0.068
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 5479.94 5630.09 5204.23 5407.48 5324.25 5346.80 5335.75
c1 −325.954 −1935.08 −53.5851 −2091.73 −1625.05 −1054.34 −327.402
c2 4.71410 2496.75 −325.674 2640.38 1431.70 619.856 −313.672
c3 1.43373 −1976.03 74.5653 −1956.14 −1193.13 −343.396 −42.0121
0.01 | dT
|5000 K 4.1 13.2 6.3 12.9 13.9 9.2 10.1
rms 0.070 0.054 0.068 0.062 0.063 0.081 0.081
DWARF STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 6592.19 6298.64 6303.41 8075.38 6181.66 6204.32 6122.76 6583.91
c1 −4053.01 −4813.87 −5018.31 −6053.31 −1077.50 −3855.13 −895.008 −3240.32
c2 4020.50 5670.56 6604.68 4843.37 197.649 3379.47 158.882 2763.93
c3 −1663.63 −2457.28 −3562.99 −1688.39 −7.73603 −1175.00 −8.65057 −1211.49
0.01 | dT
|5000 K 11.0 10.1 13.4 15.7 4.5 12.4 2.8 13.2
rms 0.065 0.060 0.040 0.057 0.085 0.047 0.087 0.049
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 6250.15 6486.68 6178.37 6210.10 6228.96 6120.07 6271.19
c1 −732.154 −5065.09 −1203.98 −5244.93 −6031.24 −2734.59 −1994.09
c2 143.714 7059.62 261.964 6959.06 9450.38 1909.74 716.031
c3 −9.97940 −4105.26 −19.2823 −3796.17 −5981.44 −559.915 −138.664
0.01 | dT
|5000 K 1.4 15.2 5.0 16.5 18.0 8.5 9.8
rms 0.074 0.043 0.067 0.047 0.053 0.067 0.076
This paper provides calibrations that can be used for
temperature determinations of stars with 0≤ v sin i <∼ 30
km s−1 and observed with ELODIE as well as with other
spectrographs at a similar resolution. We have shown that
all the LDRs examined in the present paper display a good
sensitivity to the effective temperature which allows us to
reach an uncertainty lower than 10–15 K at R = 42 000
for stars rotating up to v sin i=30 km s−1. The simultaneous
use of several LDRs allows us to improve the temperature
sensitivity and to fully detect and analyse effective tempera-
ture modulations produced by cool starspots in active stars,
as we have already shown in previous works (Frasca et al.
2005, Biazzo et al. 2007).
Acknowledgements. This work has been supported by the Italian
National Institute for Astrophysics (INAF), by the Italian Minis-
tero dell’Istruzione, Università e Ricerca (MIUR) and by the Re-
gione Sicilia which are gratefully acknowledged. We thank the ref-
eree for useful suggestions. We are also grateful to Mrs. Luigia
Santagati for the English revision of the text. This research has
made use of SIMBAD and VIZIER databases, operated at CDS,
Strasbourg, France.
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Table 3 Coefficients of the fits Teff = c0 + c1rc + ... + cnrnc for the ELODIE spectra rotationally broadened to 15 km
s−1. The empty columns relate to the line pairs completely blended at this rotational velocity.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5249.84 5559.50 8090.67 5453.71 5355.55 5662.56
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|5000 K 9.8 13.5 15.6 5.1 12.6 8.0
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c3 −4.27056 −3379.88 −8240.08 −1716.93 −483.352 −322.180
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|5000 K 1.0 18.6 16.4 18.7 6.9 10.1
rms 0.075 0.033 0.053 0.049 0.082 0.087
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http://obswww.unige.ch/gcpd/cgi-bin/photoSys.cgi
10 K. Biazzo et al.: Effective temperature vs line-depth ratio for ELODIE spectra
Table 4 Coefficients of the fits Teff = c0 + c1rc + ... + cnrnc for the ELODIE spectra rotationally broadened to 30 km
s−1. The empty columns relate to the line pairs completely blended at this rotational velocity.
GIANT STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 5481.25 5496.39 7025.27 5695.10
c1 −596.797 −2961.51 −5597.99 −800.163
c2 −43.7139 4228.71 5957.99 75.3450
c3 −48.3037 −3087.51 −2710.79
0.01 | dT
|5000 K 9.3 16.1 16.5 8.4
rms 0.095 0.058 0.061 0.075
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 5337.08 5150.51 5190.59 5357.17
c1 −166.813 −825.095 −500.186 −591.566
c2 8.35369 70.5176 28.5439 −202.882
c3 −0.153085 −989.250 6.34586 92.0652
0.01 | dT
|5000 K 1.7 15.1 7.5 9.5
rms 0.075 0.071 0.089 0.085
DWARF STARS
LDR 1/2 3/6 5/4 7/6 9/8 11/10 12/14 13/15
c0 6432.25 5999.97 7479.52 6874.46
c1 −3039.71 −4545.30 −3706.65 −3697.12
c2 2161.86 6247.09 1147.46 2312.46
c3 −692.710 −3573.28 −116.692 −595.265
0.01 | dT
|5000 K 10.3 11.6 18.9 11.1
rms 0.066 0.046 0.051 0.079
LDR 13/16 17/18 21/19 21/20 23/22 24/25 26/25
c0 6082.76 5895.59 5712.75 6039.12
c1 −329.412 −4065.13 −1362.68 −885.351
c2 30.3591 5641.78 931.915 −863.622
c3 −0.945513 −5297.51 −312.388 527.239
0.01 | dT
|5000 K 1.0 20.0 5.0 10.1
rms 0.080 0.033 0.085 0.090
c© WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org
	Introduction
	The star sample
	Sample selection
	Effective temperature and luminosity
	LDR analysis and results
	Line identification
	Metallicity effect
	Gravity effect
	Rotational broadening effect
	Temperature sensitivity on LDR
	Conclusion
