Mon. Not. R. Astron. Soc. 378, 617–624 (2007)
doi:10.1111/j.1365-2966.2007.11804.x
High-precision effective temperatures of 161 FGK supergiants from
line-depth ratios
V. V. Kovtyukh
Odessa Astronomical Observatory, Shevchenko Park, 65014, Odessa, Ukraine
Accepted 2007 March 26. Received 2007 March 17; in original form 2006 August 24
ABSTRACT
Precise effective temperatures (T eff ) are determined for 161 FGK supergiants using method of
line-depth ratios. We obtain a set of 131 relations for temperatures of supergiants as a function
of line depths. These relations have been calibrated against previously published accurate
temperature estimates. The application range of the method is 3600–7800 K (F0I–K5I). The
internal error of a single calibration is less than 110 K, while combination of all calibrations
reduces uncertainty to only 5–30 K (standard error). The error in the zero-point is estimated to
be less than 100–200 K. A significant advantage of the line ratio method is its independence of
the interstellar reddening, and only modest sensitivity to abundance, macroturbulence, rotation
and other factors.
Key words: star: fundamental parameters – supergiants – Cepheids.
1 INTRODUCTION
Spectral lines of high- and low-excitation potentials respond differently to the changes in T eff . Therefore, the ratio of their depths (or
equivalent widths) is a very sensitive temperature indicator. Gray &
Johanson (1991) demonstrated that the ratio of the central depth of
V I λ 6251.83 Å to that of Fe I λ 6252.57 Å is correlated very strongly
with B − V and T eff in main-sequence (MS) F7–K7 stars. Their work
was developed by Gray (1994) to include more line pairs. As a next
step we derived 105 calibrations for MS stars, with temperatures
4000–6150 K (Kovtyukh et al. 2003). In Kovtyukh, Soubiran &
Belik (2004), the discovery of a narrow gap (just 50 K wide, between 5560 and 5610 K) in the distribution of effective temperatures
for 248 MS stars served a nice confirmation of the precision of the
method. This gap is attributed to the jump in the penetration depth
of convective zone.
The line ratio method has also been used for giant stars. Most
recently, Strassmeier & Schordan (2000) applied 12 calibrations for
224 giants with T eff in the range 3200–7500 K, using R = 38 000,
λ 6380–6460 Å spectra; Gray & Brown (2001) derived temperatures for 92 giants using five calibrations with a typical 25 K error
for R = 100 000, 70 Å wide reticon spectra centred at 6250 Å.
Using 100 calibrations, Kovtyukh et al. (2006) derived precise temperatures for 215 giants with near-solar metallicity. The range of
application of the method is 3500–5700 K (G0III–K4III). For the
majority of giants, the internal accuracy of T eff is 5–20 K.
In Kovtyukh, Gorlova & Klochkova (1998) and Kovtyukh &
Gorlova (2000), 37 calibrations for T eff were derived from highdispersion spectra of supergiants with effective temperatures from
4500 to 7000 K. The original Kovtyukh & Gorlova (2000) calibra E-mail: [email protected]
C
C 2007 RAS
2007 The Author. Journal compilation tion relies on the excitation temperature analysis of Fry & Carney
(1997) combined with the photometric results of Kiss & Szatmary
(1998). Since then, we increased the number of calibrations to 55,
which further improved the precision of the derived temperatures.
We applied our calibrations to the sample of 192 Classical Cepheids
(about 350 spectra) with a large range of galactocentric distances
(Rg = 5–15 kpc) to determine very accurate metallicities. Even for
the faintest objects (V of 14–15 mag), the uncertainty in T eff was
not larger than 50–100 K, and only when the signal-to-noise ratio
(S/N) was less than 40, it increased to 200–300 K (see Kovtyukh,
Wallerstein, Andrievsky 2005b, and references therein). The method
yielded consistent results as a function of phase for numerous
Cepheids spanning periods from 3 to 47 d (Luck & Andrievsky
2004; Andrievsky, Luck & Kovtyukh 2005; Kovtyukh et al. 2005a).
Furthermore, we discovered in the galactic disc, at longitude l ≈
120◦ and a solar distance of about 3 kpc, a region of enhanced
metallicity: [Fe/H] ≈ +0.2 with respect to the local region (Luck,
Kovtyukh & Andrievsky 2006). Effective temperature obtained using this new technique currently presents one of the most precisely
determined fundamental stellar parameter, with relative precision of
the order of 0.1–0.2 per cent.
In the present paper, we increase the number of temperature calibrations for supergiants to 131, and extend the application range to
3600–7800 K.
2 O B S E RVAT I O N S
The spectra of the program stars were obtained using facilities of
the 1.93-m telescope of the Haute-Provence Observatoire (France)
equipped with echelle-spectrograph ELODIE (Soubiran, Katz &
Cayrel 1998). The resolving power was R = 42 000, wavelengths
range 4400–6800 Å and S/N > 100 (at 5500 Å). The initial
618
V. V. Kovtyukh
processing of the spectra (image extraction, cosmic ray removal,
flat-fielding, etc.) was carried out as described in Katz et al. (1998).
In addition, we employed spectra obtained with UVES at the VLT
unit Kueyen (Bagnulo et al. 2003). All supergiants were observed
with two instrumental modes Dichroic 1 and Dichroic 2 in order
to cover almost completely the wavelength interval from 3000 to
10 000 Å. The spectral resolution is about 80 000, and for most of
the spectra, the typical S/N is 300–500 in the V band.
Further processing of spectra (continuum level location, measurement of line depths and equivalent widths) was performed with the
DECH20 software (Galazutdinov 1992). Line depths Rλ were measured by means of Gaussian fitting. The accuracy of line-depth determination was obtained by measuring lines in two or more spectra
of the same star, when available. The standard error obtained (0.01–
0.02) reflects the typical error of Rλ and is dominated by uncertainty
in continuum placement. The highest precision was achieved when
Gaussian fit is restricted to the core of the line. The typical observed
error in a single line-depth ratio r = Rλ1 /Rλ2 is 0.02–0.05. All sufficiently strong and very weak lines have been rejected automatically
from further analysis (see the next section).
Table 1. The calibration lines. For example, equivalent widths for HD 26630
(T eff = 5337 K, romanic type) and HD 45348 (T eff = 7557 K, italic type)
are given; T eff1 − T eff2 is a working temperature range of calibrations.
λ1
(Å)
5348.30
5348.30
5373.71
5410.91
5497.52
5501.46
5501.46
5501.46
5506.78
5506.78
5506.78
5578.72
5578.72
5670.86
5754.68
5754.68
5772.15
5772.15
5778.47
5793.08
5809.25
5809.25
5862.36
5862.36
5934.66
5934.66
5956.70
5987.05
6003.03
6003.03
6008.56
6021.79
6021.79
6039.73
6046.01
6046.01
6046.01
6046.01
6046.01
6046.01
6046.01
6046.01
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6052.68
6055.99
6055.99
6055.99
6055.99
6055.99
6062.89
6078.50
3 C O N S T R U C T I O N O F T H E T E M P E R AT U R E
C A L I B R AT I O N S
Based on our previous experience, we restricted line pool to the
iron-peak elements (such as Si, Ti, V, Cr, Fe, Ni) because they
show a negligible response to changes in surface gravity (log g)
and chemical composition on a star-to-star basis. With few possible
exceptions, supergiants in our sample have metallicity of −0.45 <
[Fe/H] < +0.30, which is close to solar. Using synthetic spectra
method, we find that within this range the effect of metallicity on
the line ratios is negligible for majority of our calibrations.
To start iteration process, initial temperature has to be assigned
to each star. Recently, a number of studies have been published concerning temperature scale of supergiants (Luck & Bond 1989; Luck
& Wepfer 1995; Bravo Alfaro, Arellano Ferro & Schuster 1997;
Fry & Carney 1997; Yong et al. 2006). Using temperatures in these
studies, we constructed the first set of Rλ1 /Rλ2 versus T eff calibrations. Each calibration was composed of lines with vastly different
excitation energies of the lower level. We visually examined scattered plots for every ratio and retained only those ratios that showed
a clear tight correlation with T eff . An analytic fit was performed for
these selected ratios to produce the initial relations. By averaging
temperatures calculated from these fits, we obtained a second T eff
approximation for each star. The random scatter has been reduced by
50–100 K. Once we established temperature scale for non-variable
supergiants (∼200 spectra), we applied it to derive temperatures for
350 spectra of Classical Cepheids (see Kovtyukh et al. 2005a, and
references therein). Then we merged these two data sets to perform
the final refinement of our calibrations. From the initial 600 calibrations, we selected 131 whose mean square deviation for each
calibration (standard deviation σ ) was smaller than 110 K.
Table 1 shows the final 131 line pairs, with wavelengths, elements,
excitation energies of the lower level (in eV), equivalent widths of
two stars (HD 26630 and HD 45348), for example, and working
temperature range (T eff1 , T eff2 ).
The average internal accuracy of a single calibration (1σ ) is 80–
100 K (ranging from 60 to 70 K for the best and 100 to 110 K
for the worst cases). Figs 1 and 2 show our typical calibrations. In
many cases, the dependence could not be fitted with a continuous
polynomial, therefore we tried other analytical functions as well,
for example: T eff = abr rc , ab1/r rc , ar b , abr and a + bln(r). Here,
C
El
EPL
EW
(eV) (mÅ)
Cr I
Cr I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Ni I
Ni I
VI
Ni I
Ni I
Si I
Si I
Fe I
Si I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Mn I
Mn I
VI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
SI
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
1.00
1.00
4.47
4.47
1.01
0.96
0.96
0.96
0.99
0.99
0.99
1.68
1.68
1.08
1.93
1.93
5.08
5.08
2.59
4.93
3.88
3.88
4.55
4.55
3.93
3.93
0.86
4.80
3.88
3.88
3.88
3.08
3.08
1.06
7.86
7.86
7.86
7.86
7.86
7.86
7.86
7.86
7.87
7.87
7.87
7.87
7.87
7.87
7.87
7.87
7.87
7.87
7.87
7.87
4.73
4.73
4.73
4.73
4.73
2.18
4.80
23
23
18
70
69
38
38
38
48
48
48
105
105
35
158
17
100
100
42
78
85
85
137
137
18
18
126
131
144
26
149
138
138
30
43
43
43
43
43
43
27
27
40
40
40
40
40
30
30
30
30
30
30
30
118
118
118
118
118
59
126
λ2
(Å)
5554.89
5565.71
5501.46
5501.46
5554.89
5554.89
5565.71
5633.97
5554.89
5565.71
5633.97
5645.62
5805.23
5690.43
5772.15
5772.15
5778.46
5778.46
5793.07
5793.92
6046.01
6052.68
5866.45
5866.45
6046.01
6052.68
5983.69
6216.37
6052.68
6052.68
6046.01
6046.01
6052.68
6046.01
6086.29
6108.12
6165.37
6180.20
6240.66
6258.10
6176.81
6215.15
6108.12
6151.62
6180.20
6240.66
6258.10
6108.12
6122.23
6136.61
6162.18
6176.81
6215.15
6219.28
6062.89
6062.89
6082.72
6085.27
6085.27
6078.50
6082.72
El
EPL
EW T eff1
(eV) (mÅ) (K)
T eff2
(K)
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Si I
Ni I
Si I
Si I
Si I
Fe I
Fe I
Si I
Fe I
SI
SI
Ti I
Ti I
SI
SI
Fe I
VI
SI
SI
SI
SI
SI
SI
Ni I
Ni I
Fe I
Fe I
Fe I
Ti I
Ni I
Fe I
Ni I
Fe I
Fe I
Fe I
Ti I
Ni I
Ca I
Fe I
Ca I
Ni I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
4.55
4.61
0.96
0.96
4.55
4.55
4.61
4.99
4.55
4.61
4.99
4.93
4.17
4.93
5.08
5.08
2.59
2.59
4.93
4.22
7.86
7.87
1.07
1.07
7.86
7.87
4.55
0.28
7.87
7.87
7.86
7.86
7.87
7.86
4.27
1.68
4.14
2.73
2.22
1.44
4.09
4.19
1.68
2.18
2.73
2.22
1.44
1.68
1.89
2.45
1.90
4.09
4.19
2.20
2.18
2.18
2.22
2.76
2.76
4.80
2.22
7800
7800
7800
7800
7800
7800
7800
7800
7800
7800
7800
6300
6750
6400
7000
7800
5000
6500
6400
6900
6900
6900
5000
6700
7800
7800
6900
5650
7000
7800
7000
7000
7000
5400
6800
6700
6500
6700
6700
6700
7800
7800
6800
6800
6700
6750
6750
7800
7800
7800
7800
7800
7800
7800
6000
4850
6800
6750
4900
6100
6700
35
35
38
38
35
35
35
23
35
35
23
71
70
95
100
21
42
42
78
64
43
40
88
88
27
30
126
67
40
30
43
43
40
43
77
134
84
124
104
98
14
16
134
104
124
104
98
9
92
57
99
14
16
21
59
59
74
88
88
126
74
7000
7000
7000
7000
7000
7000
7000
7000
7000
7000
7000
5400
5600
3700
5400
7000
3600
5000
3900
4600
5300
5450
3600
5000
7000
7000
3700
4300
5550
7000
5600
5700
5700
3700
4800
4800
4950
4950
4950
4750
7000
7000
5250
5000
5000
5050
5000
7000
7000
7000
7000
7000
7000
7000
5000
3700
5000
4900
3600
3700
5000
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation High-precision effective temperatures of 161 FGK supergiants
Table 1 – continued
C
El
EPL
EW
(eV) (mÅ)
Fe I
Fe I
Fe I
Fe I
Fe I
Fe I
VI
VI
VI
Si I
Co I
Ni I
Ni I
Ni I
Ni I
Si I
Si I
Si I
Ti I
Ti I
VI
Si I
Si I
Si I
Si I
VI
VI
Fe I
Si I
Si I
Fe I
Ni I
Fe I
Fe I
Fe I
Si I
Si I
Si I
Si I
Si I
Fe I
Fe I
Fe I
VI
VI
VI
VI
Si I
Si I
Ni I
Cr I
Fe I
Fe I
Fe I
Fe I
Fe I
Si I
Fe I
SI
Fe I
Fe I
Fe I
Fe I
4.80
4.80
4.80
2.76
2.76
2.76
1.08
1.08
1.08
5.87
1.74
1.68
1.68
1.68
1.68
5.61
5.61
5.61
1.07
1.07
1.05
5.61
5.61
5.61
5.61
0.30
0.30
2.18
5.62
5.62
4.80
4.09
2.73
2.61
2.20
5.61
5.61
5.61
5.61
5.61
2.22
2.22
2.22
0.30
0.30
0.30
0.30
5.61
5.61
1.68
0.94
2.85
2.85
0.86
0.86
2.28
5.87
0.96
8.05
2.56
2.56
2.76
1.49
126
126
126
88
88
88
66
66
66
11
22
135
135
135
135
58
58
17
58
58
23
64
64
64
18
50
50
104
121
121
128
113
124
145
21
94
94
94
94
94
4
104
104
70
70
70
70
90
90
95
61
161
161
162
162
50
74
103
24
131
131
73
49
λ2
(Å)
El
EPL
EW
(eV) (mÅ)
T eff1
(K)
T eff2
(K)
λ1
(Å)
6082.72
6085.27
6085.27
6086.29
6091.92
6155.14
6091.92
6155.14
6330.86
6219.28
6093.66
6125.03
6145.02
6155.14
6237.32
6126.22
6151.62
6358.69
6155.14
6155.14
6142.49
6151.62
6180.20
6258.10
6151.62
6237.32
6380.75
6155.14
6180.20
6358.69
6180.20
6258.10
6237.32
6237.32
6414.99
6240.66
6240.66
6258.10
6258.71
6358.69
6414.99
6243.81
6244.48
6243.81
6243.81
6244.48
6244.48
6261.10
6358.69
6414.99
6414.99
6414.99
6419.98
6414.99
6419.98
6414.99
6498.95
6597.61
6609.12
6748.84
6757.17
6721.84
6721.84
Fe I
Fe I
Fe I
Ni I
Si I
Si I
Si I
Si I
Fe I
Fe I
Fe I
Si I
Si I
Si I
Si I
Ti I
Fe I
Fe I
Si I
Si I
Si I
Fe I
Fe I
Ti I
Fe I
Si I
Fe I
Si I
Fe I
Fe I
Fe I
Ti I
Si I
Si I
Si I
Fe I
Fe I
Ti I
Ti I
Fe I
Si I
Si I
Si I
Si I
Si I
Si I
Si I
Ti I
Fe I
Si I
Si I
Si I
Fe I
Si I
Fe I
Si I
Fe I
Fe I
Fe I
SI
SI
Si I
Si I
2.22
2.76
2.76
4.27
5.87
5.62
5.87
5.62
4.73
2.20
4.61
5.61
5.61
5.62
5.61
1.07
2.18
0.86
5.62
5.62
5.62
2.18
2.73
1.44
2.18
5.61
4.19
5.62
2.73
0.86
2.73
1.44
5.61
5.61
5.87
2.22
2.22
1.44
1.46
0.86
5.87
5.61
5.61
5.61
5.61
5.61
5.61
1.43
0.86
5.87
5.87
5.87
4.73
5.87
4.73
5.87
0.96
4.80
2.56
7.87
7.87
5.86
5.86
3600
3600
4900
4200
3700
4200
3700
3700
3700
7000
3700
5600
4000
3700
5400
5100
5600
7000
3700
5050
3700
3700
3700
3700
7000
3700
3700
3700
3700
3700
5150
3700
3700
5300
7000
5050
3800
4700
4800
4700
7000
3700
4500
4950
5450
5000
5500
3700
3700
3700
3700
3700
3700
4400
3700
3700
3700
4850
5600
5000
4600
3800
3700
4900
4950
6800
6700
7000
7000
5800
5750
5550
7800
6200
7000
7000
7000
7000
5900
6600
7800
5000
6150
5300
6700
5000
6700
7800
4900
4800
7000
6800
6700
6850
6200
7000
6900
7800
6800
4950
6700
6700
6700
7800
6900
6900
5450
6150
5500
6150
5600
7000
6900
6000
7000
7000
7000
7000
6200
7000
6600
7000
7000
7000
7000
6200
6710.31
6717.69
6717.69
6748.84
6748.84
6750.15
6757.17
74
88
88
77
63
121
63
121
62
21
54
58
64
121
94
58
104
10
121
121
61
104
124
98
3
94
90
121
124
162
124
98
94
94
16
104
104
98
98
162
16
90
87
90
90
87
87
95
162
74
74
74
146
74
146
74
103
60
131
49
61
73
73
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation El
EPL
EW
(eV) (mÅ)
Fe I
Ca I
Ca I
SI
SI
Fe I
SI
1.49
2.71
2.71
7.87
7.87
2.42
7.87
49
45
209
49
49
155
61
λ2
(Å)
El
EPL
EW
(eV) (mÅ)
T eff1
(K)
T eff2
(K)
6767.77
6757.17
6757.17
6750.15
6767.77
6757.17
6767.77
Ni I
SI
SI
Fe I
Ni I
SI
Ni I
1.83
7.87
7.87
2.42
1.83
7.87
1.83
3700
7000
5300
4900
5000
4700
4800
6000
7800
6800
6800
6800
7000
6700
165
45
61
155
165
61
165
7000
Fe I 6085.27 / Si I 6155.14
6500
6000
Te ff, K
6078.50
6078.50
6078.50
6085.27
6085.27
6085.27
6090.21
6090.21
6090.21
6091.92
6093.14
6108.12
6108.12
6108.12
6108.12
6125.03
6125.03
6125.03
6126.21
6126.21
6135.36
6145.02
6145.02
6145.02
6145.02
6150.16
6150.16
6151.62
6155.14
6155.14
6170.49
6176.81
6180.20
6200.32
6219.28
6237.32
6237.32
6237.32
6237.32
6237.32
6240.66
6240.66
6240.66
6243.11
6243.11
6243.11
6243.11
6243.81
6243.81
6327.60
6330.13
6355.04
6355.04
6358.69
6358.69
6392.55
6414.99
6498.95
6538.60
6609.12
6609.12
6703.57
6710.31
Table 1 – continued
5500
5000
4500
4000
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
R1/R2
Figure 1. Example of the typical temperature calibration derived in this
work. The scatter is dominated by line-depth measuring errors and by real
differences among stars, e.g., differing abundances, log g, etc. The typical
error in line ratio is 0.02–0.05.
7000
Fe I 5987.05 / V I 6216.37
6500
6000
Te ff, K
λ1
(Å)
619
5500
5000
4500
4000
3500
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
R1/R2
Figure 2. Another example of the temperature calibration. This calibration
is applied only in the temperature range (T eff < 5650 K) where it provides
a precision better than 110 K.
a, b, c are constants and r is the line ratio, Rλ1 /Rλ2 . The choice
of the particular approximation was done according to the leastsquare deviation. The typical uncertainty of the ratio r = Rλ1 /Rλ2
is 0.02–0.05, resulting in temperature error of 10–50 K. This observational error in the line-depth measurement accounts for about
half of the 100 K dispersion obtained for a given star from one calibration. The other half results from unaccounted parameters like
620
V. V. Kovtyukh
metallicity, non-LTE effects, gravity, macroturbulence, etc. In cases
where Rλ1 /Rλ2 was a non-monotonic function (i.e. a given value
of Rλ1 /Rλ2 corresponded to more than one value of T eff ), we have
limited the application range of the latter to exclude this ambiguity.
Several stellar properties are expected to limit the precision of the
line-depth method, like rotation, macroturbulence, chemical abundance, gravity, etc. Note also that the precision of a given calibration
varies with T eff . For example, the low-excitation lines weaken at high
temperatures, which increases the measurement error for the line ratio and hence the error of the inferred T eff . Therefore, we provide for
each calibration an allowed range of temperatures where it should
be used (see Table 1). They were chosen such that uncertainties did
not exceed 110 K. This allowed to naturally eliminate all strong
(and also very weak) lines and lines sensitive to metallicity, log g,
rotation, macroturbulence and other effects for a given temperature
(see Fig. 2).
The averaging of temperatures obtained from 70 to 100 line ratios significantly reduces the uncertainty from a single calibration.
The final precision we achieve is 5–30 K (standard error, σ mean ) for
the spectra of R = 42 000 and S/N = 100–150. This can be further improved with higher resolution and larger S/N. For the vast
majority of stars, the errors are better than 30 K. We note that we
only have few stars hotter than 7000 K, therefore we expect a larger
systematic error at the hot end of our scale. For a number of supergiants, temperature was estimated independently from two or
more ELODIE spectra. The difference between these estimates is
within 2–3σ , where σ is a temperature error from a single spectrum
(σ mean ).
Our data set consists of spectra of two different resolutions, with
only one star in common: HD 210848. The estimated values of
T eff for this star are 6171 ±23 (51 calibrations) from ELODIE
spectrum (R = 42 000) and 6163 ±17 (77 calibrations) from VLT
(R = 80 000). As one can see, these determinations are very close,
despite a factor of 2 difference in resolution. Unlike in MS stars,
lines in supergiants are strongly broadened by rotation, micro- and
macroturbulence, resulting in intrinsic full width at half-maximum
(FWHM) of about 0.5–0.7 Å and more. Therefore, line depths do not
depend on resolution beyond R ∼ 35 000, and so does precision of
T eff . To investigate this effect at lower resolutions, we compare determinations of T eff from ELODIE spectra with determinations from
echelle-spectrometer LYNX (R = 25 000; Panchuk et al. 1999) at
Table 2. Comparison temperatures determined from spectra with different
resolution (R = 42 000 and 25 000).
Star
Teff
(K)
HD 020902
HD 026630
HD 194093
HD 209750
ELODIE
R = 420 000
σ mean
(K)
6541
5337
6202
5210
±11
±7
±12
±6
N
61
69
82
66
LYNX
R = 250 000
Teff
σ mean
(K)
(K)
6555
5358
6267
5229
±33
±20
±15
±10
N
26
46
52
46
the 6-m telescope of the Special Astrophysical Observatory (Russia)
(see Table 2). The decrease of resolution to R = 25 000 results in increase of T eff error to 30–50 K and reduces the number of unblended
lines available for temperature calibration. This effect is particularly
relevant for supergiants, whose lines are broadened by large macroturbulence and v sin i as compared to MS stars and giants. Similarly,
the number of calibrations is reduced at low S/N. For example, for
S/N ∼ 100 the depth of a weak line (Rλ ∼ 0.05) is comparable with
uncertainty of its measurement, ∼20 per cent, making it ineligible
for use in temperature determination.
Table 3 provides analytical fits for 15 most precise calibrations,
together with wavelengths (λ1 , λ2 ) and excitation potentials (in eV)
for the corresponding line pair, and working temperature range. All
calibrations are available in the electronic form from the author upon
request.
Table 4 lists T eff for 161 supergiants derived from our calibrations.
Each entry includes the name of the star, mean T eff , the mean square
deviation for each determination (σ ), number of calibrations used
(N) and the error of the mean (σ mean ).
4 C O M PA R I S O N W I T H OT H E R
T E M P E R AT U R E S C A L E S
We want to compare our line ratio based temperatures with temperatures derived from traditional colour method. V–K is regarded the
best photometric temperature indicator in F–K supergiants. Unfortunately, it has only been measured for a few stars in our sample,
Table 3. The 15 most precise temperature calibrations (r = Rλ1 /Rλ2 ).
λ1
(Å)
El
EPL
(eV)
λ2
(Å)
El
EPL
(eV)
T eff1
(K)
T eff2
(K)
T eff =
6039.73
6055.99
6085.27
6090.21
6108.12
6126.21
6135.36
6150.16
6237.32
6243.11
5348.30
5410.91
5506.78
6003.03
6125.03
VI
Fe I
Fe I
VI
Ni I
Ti I
VI
VI
Si I
VI
Cr I
Fe I
Fe I
Fe I
Si I
1.06
4.73
2.76
1.08
1.68
1.07
1.05
0.30
5.61
0.30
1.00
4.47
0.99
3.88
5.61
6046.01
6062.89
6155.14
6091.92
6237.32
6155.14
6142.49
6237.32
6240.66
6243.81
5554.89
5501.46
5565.71
6052.68
6358.69
SI
Fe I
Si I
Si I
Si I
Si I
Si I
Si I
Fe I
Si I
Fe I
Fe I
Fe I
SI
Fe I
7.86
2.18
5.62
5.87
5.61
5.62
5.62
5.61
2.22
5.61
4.55
0.96
4.61
7.87
0.86
3700
5000
3700
3700
5400
3700
3700
3700
5050
4950
7000
7000
7000
7000
7000
5400
6000
7000
5800
7000
5000
5300
4900
6800
5450
7800
7800
7800
7800
7800
5.36966r2 − 345.093r + 5569
−21.6837r2 + 418.865r + 4532
5839.37(0.855011r )(r−0.090522 )
−11.2669r3 + 185.711r2 − 1215.97r + 6585
283.413r2 − 1908.86r + 7549
161.954r2 − 1389.19r + 6007
35.5005r2 − 656.539r + 5575
−770.29r + 5505
6779.2 (0.8148941/r )(r0.0541857 )
−618.234r + 5845
−919.996r + 8120
463.441r + 6748
−968.498r + 8986
−551.182r + 8037
−505.937r + 8295
C
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation High-precision effective temperatures of 161 FGK supergiants
621
Table 4. Effective temperatures of the programme stars.
HD
000371
000611
000725
001457
003421
004362
004817
005747
007927
008906
008992
009167
009900
009973
010494
010806
011544
015784
016901
017506
017905
017958
017971
018391
020123
020902
025056
025291
026630
031910
032655
033299
034248
036673
036891
037536
038808
039949
042454
042456
044391
045348
045829
047731
048329
048616
048640
050372
052005
052220
052497
053003
054605
057146
061227
072722
074395
075276
077912
079698
084441
090452
092125
C
Name
φ Cas
14 Per
η Per
α Per
µ Per
β Cam
α Lep
NO Aur
α Car
25 Gem
ω Gem
δ CMa
37 LMi
Teff
(K)
σ
(K)
N
σ mean
(K)
5085
5431
6793
7636
5302
5325
3839
5024
7341
6710
6278
7632
4529
6654
6672
5051
5126
6467
5555
4050
6352
3974
6822
5871
5165
6541
5752
7497
5337
5441
6653
4574
6101
7500
5082
3918
5112
5248
5277
4754
4599
7557
4459
4989
4510
6413
3908
4794
3954
5661
5090
5540
6443
5134
7433
3774
5264
7487
4957
5252
5296
6688
5354
35
125
99
57
96
92
138
147
163
63
92
135
119
113
253
77
68
102
67
142
172
110
99
130
47
84
157
38
55
98
130
53
159
48
65
241
79
85
93
103
51
35
63
66
77
76
140
93
206
77
83
118
83
57
37
143
54
60
75
111
90
106
89
28
87
46
26
90
86
24
29
15
43
68
8
58
64
66
28
55
28
93
26
25
22
18
64
58
61
36
22
69
94
48
34
66
27
85
10
81
83
81
68
43
29
43
66
51
55
22
55
30
97
46
76
67
82
28
33
84
16
63
84
66
74
86
6.6
13.4
14.6
11.2
10.1
9.9
28.1
27.3
42.2
9.7
11.1
47.7
15.6
14.1
31.2
14.6
9.2
19.3
7.0
27.9
34.3
23.5
23.4
16.3
6.2
10.7
26.2
8.0
6.6
10.1
18.8
9.1
19.6
9.2
7.1
76.2
8.8
9.4
10.3
12.5
7.8
6.4
9.6
8.1
10.8
10.3
29.8
12.5
37.6
7.8
12.2
13.6
10.1
6.3
7.0
24.9
5.9
14.9
9.5
12.1
11.1
12.4
9.6
Remarks
emiss
NGC 654
Double
var
Cluster
SB
Double
var
var
var
var?
SB
Double
Double
Double
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation HD
Name
Teff
(K)
σ
(K)
N
σ mean
(K)
099648
104452
109379
114988
117440
125728
125809
134852
136537
139862
146143
147266
151237
152830
159181
161074
161149
164136
165435
171237
171635
171874
172365
173638
174104
178524
179784
180028
180583
182296
182835
183864
185018
185758
186155
187203
187299
187428
188650
189671
190113
190323
190403
190405
191010
192713
193370
194069
194093
194951
195295
195432
195593
195617
196725
199394
200102
200805
200905
202109
202314
204022
204075
τ Leo
1 Com
4942
5704
5117
4985
4683
4972
4837
6488
4960
5091
6077
5091
5825
6603
5220
4008
6505
6483
7400
6792
6201
6275
5978
7444
5657
6710
4956
6251
6043
5072
6912
5323
5451
5390
6560
5710
4566
5911
5669
4891
4784
6155
4894
6358
5269
5028
6369
4883
6202
7392
6575
5872
6625
3949
4165
5085
5364
6865
3980
4976
5004
5375
5287
109
218
111
182
98
90
58
155
72
91
87
110
162
156
52
167
330
161
168
116
71
197
163
50
181
147
42
127
121
50
120
45
72
92
184
110
167
119
212
65
160
64
57
132
81
67
50
40
104
75
58
105
52
159
200
104
94
121
194
107
56
66
91
62
25
80
21
58
26
65
28
65
30
85
29
33
26
64
38
40
21
19
26
79
55
27
22
16
44
55
72
92
77
26
82
28
68
13
53
27
53
78
24
60
22
57
12
81
48
79
23
82
25
68
89
8
37
39
26
29
6
34
65
47
84
77
13.8
43.6
12.4
39.8
12.9
17.6
7.1
29.2
8.9
16.7
9.5
20.5
28.2
30.7
6.5
27.0
52.1
35.0
38.5
22.7
7.9
26.6
31.4
10.6
45.3
22.2
5.7
15.0
12.6
5.7
23.5
5.0
13.6
11.2
51.0
15.1
32.1
16.4
24.0
13.2
20.6
13.7
7.6
38.0
9.0
9.6
5.6
8.4
11.5
15.0
7.0
11.1
18.3
26.2
32.1
20.4
17.5
49.3
33.3
13.3
8.2
7.2
10.4
46 Her
V644 Her
β Dra
83 Her
ν Her
45 Dra
V473 Lyr
32 Aql
α Sge
QS Vul
44 Cyg
θ Del
ξ Cyg
ζ Cap
Remarks
SB
Irregular
SB
Double
SB
Double
in nebula
Double
SB
622
V. V. Kovtyukh
Table 4 – continued
HD
204509
204867
205114
205603
206731
206778
206859
207089
207119
207489
207647
207991
208606
209750
210745
210848
211153
214714
Name
β Aqr
Peg
12 Peg
α Aqr
ζ Cep
Teff
(K)
σ
(K)
N
σ mean
(K)
6510
5466
5224
4994
5030
4108
4876
4428
3946
6350
5127
3777
4702
5210
4180
6163
5130
5424
217
64
61
101
60
176
45
188
126
98
96
74
53
49
99
149
112
197
55
76
77
22
24
34
70
27
32
78
33
6
43
66
32
77
27
70
29.2
7.4
7.0
21.5
12.3
30.1
5.4
36.3
22.3
11.1
16.7
30.4
8.0
6.0
17.4
17.0
21.5
23.5
Remarks
HD
216206
216219
216756
218043
218600
219135
219978
220102
220819
221661
221861
223047
224165
225292
236433
249750
+60 2532
var
Flower
Castelli, logg=1.5
7000
Te ff, K
6000
5500
5000
4500
0.2
0.4
0.6
0.8
1.0
1.2
V809 Cas
ψ And
Sp
Teff
(K)
F0
F1
F2
F3
F5
F6
F7
F8
F9
G0
G1
7492
7392
6920
6699
6500
6268
6210
5979
5752
5561
5364
this paper
6500
4000
0.0
σ
(K)
N
σ mean
(K)
5003
5701
6526
6447
7458
5479
3928
6832
7495
5033
4417
4808
4804
4947
6541
5475
6268
31
233
142
145
99
82
238
103
78
111
66
62
59
81
93
115
149
53
64
36
37
5
91
26
35
7
24
34
56
50
27
35
41
70
4.3
29.2
23.6
23.8
44.2
8.5
46.7
17.5
29.4
22.7
11.4
8.3
8.3
15.6
15.7
17.9
17.9
Remarks
var
double
NGC 129
NGC 7654
Table 5. Effective temperatures of supergiants as a function of spectral type.
The number of used stars is given.
8000
7500
Teff
(K)
Name
1.4
1.6
(B-V)o
Figure 3. The correlation of (B − V)o colours and effective temperatures
for the program supergiants. Two colour–temperature relationships from the
literature also are indicated by lines in the figure: Flower (1996); Castelli
(model atmospheres of Castelli for log g = 1.5; see table 2 in Bessell et al.
1998).
σ mean
(K)
N
Sp
Teff
(K)
80
8
1
8
2
13
3
3
4
1
13
1
G2
G3
G4
G5
G8
G9
K0
K1
K2
K3
K5
5189
5124
5065
4955
4884
4689
4443
4180
3977
3944
3835
318
107
12
43
139
142
σ mean
(K)
N
140
74
62
97
113
264
15
4
2
8
8
3
2
1
5
2
3
69
84
In practice, spectral types are often used for a quick estimation of
T eff . In Table 5, we provide such relation for line ratio temperatures
derived for our sample. Spectral types for program stars have been
taken from SIMBAD.
Fig. 4 compares out temperature scale with four other studies
from the literature. Fry & Carney (1997) and Yong et al. (2006)
derive T eff by balancing iron abundance obtained from individual
lines with different excitation potentials. Fry & Carney used 101
high-resolution spectra of 23 Galactic Cepheids. Yong et al. (2006)
updated temperatures from Fry & Carney sample and added 24
new Cepheids. Comparison to our determinations gives a standard
deviation of 112 K (76 common spectra). The difference does not
appear to correlate with T eff (see Fig. 4a).
Bravo Alfaro et al. (1997) used 13-Colour photometry for the
determination of T eff for 71 supergiant stars with an average accuracy of about 300 K. Their temperatures are also in good agreement with that of ours. No clear correlation of the difference
with temperature is observed (Fig. 4b), and the mean dispersion
of 226 K (for 22 common stars) is within the uncertainty of that
study.
precluding accurate comparison. In Fig. 3, we plot our temperatures against another popular index – (B−V)0 . The dereddened B−V
colour is taken from Bersier (1996), who derived extinction based
on Geneva photometry. For comparison, colour–temperature relations from Flower (1996) and Castelli [colours have been computed
by Castelli; see table 2 in Bessell, Castelli & Plez (1998)] are also
shown. Flower obtained T eff from the literature, while Castelli determined colour indices and bolometric corrections from ATLAS9
no-overshoot Kurucz’s models. As one can see, in general our temperatures agree well with both scales, except at the hot end (T eff >
5500 K) where the former are ∼200 K hotter. Note that (B − V)0
values are very sensitive to metallicity, and (to a lesser degree) to
macroturbulence and other physical factors. Fig. 3 seems to be dominated by colour excess errors, with essential contribution from real
variations in (B − V)0 due to other physical parameters beside temperature.
C
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation High-precision effective temperatures of 161 FGK supergiants
5 Z E RO - P O I N T O F T E M P E R AT U R E S C A L E
400
0
a)
-400
3500
4000
4500
5000
5500
6000
6500
7000
7500
4000
4500
5000
5500
6000
6500
7000
7500
4000
4500
5000
5500
6000
6500
7000
7500
400
Te ff (other paper) - Te ff (this paper)
623
0
b)
-400
3500
400
0
c)
-400
3500
400
Values of T eff for a given star often differ between independent
sources in the literature by as much as 200–500 K. Yong et al. (2006)
discuss how non-LTE and other effects in the extended atmospheres
of supergiants may compromise precision of T eff determination. At
present, we cannot give preference to one method over the others
discussed in Sections 3 and 4, since all of them are prone to these
effects. Therefore, we do not attempt to constrain the zero-point
of our temperature scale further by tying it to any of the above
scales. Bravo Alfaro et al. (1997) used three independent methods to determine the effective temperatures for A0–K0 supergiants
from their 13-Colour photometry. The estimated uncertainties in T eff
by the three methods are comparable and are approximately 200–
300 K. According to compilative catalogue of Cayrel de Strobel et al.
(2001), the mean errors of T eff supergiant are 100–200 K. Hence,
we think that the possible zero-point error of our scale is less than
100–200 K.
0
-400
6 S U M M A RY
d)
3500
4000
4500
5000
5500
6000
6500
7000
7500
Te ff (this paper)
Figure 4. Comparison of our temperatures with estimates from the literature: (a) filled squares – Fry & Carney (1997), filled triangles – Yong et al.
(2006); (b) Bravo Alfaro et al. (1997); (c) Gray et al. (2001) and (d) Cayrel
de Strobel et al. (2001).
Gray, Graham & Hoyt (2001) derived T eff from the comparison
of classification-resolution spectra and fluxes from Strömgren photometry with a grid of synthetic spectra and fluxes computed from
Kurucz models. Comparison with our scale shows a trend of difference with T eff : the scales agree around T eff = 6500 K, but at 5200 K
our values are ≈300 K higher while at 7500 K ≈ 200 K lower
(Fig. 4c).
The most accurate determinations of T eff from the literature have
been compiled in catalogue by Cayrel de Strobel, Soubiran & Ralite
(2001). It is evident from Fig. 4(d) that our derived temperatures are
in good agreement with this catalogue but this figure also shows
a possible quadratic trend of difference with T eff . Note that this
compilation is very inhomogeneous.
Blackwell & Lynas-Gray (1998) have determined very precise
T eff of 420 stars using the Infrared Flux Method (IRFM). We derive
temperatures very close to theirs for three common stars (Table 6).
The average temperature difference is only −12 ± 9 K.
These tests demonstrate reliability of our scale. Note that some
supergiants may be photometrically variable, with associated temperature variations (see Table 4). Though we tried to avoid using
such supergiants, we cannot completely rule out the possibility of
variability in some of the stars considered.
Table 6. Comparison of our temperatures with those of Blackwell & LynasGray (1998).
Star
HD185758
HD204867
HD209750
C
Blackwell & Lynas-Gray
Teff
σ mean
(K)
(K)
5415
5474
5206
±38
±27
±30
(This paper)
Teff
σ mean
(K)
(K)
5390
5466
5210
±11
±7
±6
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation The traditional spectroscopic methods (e.g. using model atmospheres) do not always allow to derive certain atmospheric parameters with high precision. New methods are sought to improve the
accuracy and to automate the whole process. The line ratio method
presented in this work has been designed with these goals in mind.
We tested our method on a given star’s spectra obtained at different
times, on different telescopes and with different resolution R. For
R > 35 000, these estimates agree within 2–3 σ mean , where σ mean
is an accuracy of T eff from a single spectrum. Highly precise T eff
derived here for 161 supergiants can serve as T eff standards in the
3600–7800 K range. For the majority of the sample σ = 20–30 K,
being only slightly worse at the hot and cool ends of the scale, as
well as for a non-solar metallicity ([Fe/H] larger than ±0.5 dex).
We also tested our method on stars common between our sample and the independent studies from the literature. In all cases, our
method demonstrates a good match, except with Gray et al. (2001).
The difference with the latter study is a monotonic function of temperature, the origin of which is unclear.
The comparison with independent studies from the literature provides an approximate estimate for the accuracy of the zero-point of
our scale: 100–200 K. To determine this uncertainty precisely requires comparison with directly measured T eff . The direct method of
T eff definition relies on the measurement of stellar angular diameter
and bolometric flux.
For a given star, the line ratio technique allows to detect variations
in T eff as small as 10 K and less. Another important advantage of
this method is that it produces reddening-free estimates.
Summarizing the supergiant temperatures determined in this work
using line ratio technique has both the high internal precision and
agree well with the most accurate estimates from the literature.
AC K N OW L E D G M E N T S
This work is based on spectra collected with the 1.93-m telescope
of the OHP (France) and the ESO Telescopes at the Paranal Observatory under programme ID 266.D-5655. The author thanks Dr C.
Soubiran for kindly providing ELODIE spectra of some supergiants.
In addition, the author would like to thank Dr N. Gorlova for many
useful discussions. The author is also grateful to the anonymous
referee for the careful reading of the manuscript and the numerous
important remarks that helped to improve the paper.
624
V. V. Kovtyukh
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This paper has been typeset from a TEX/LATEX file prepared by the author.
C
C 2007 RAS, MNRAS 378, 617–624
2007 The Author. Journal compilation