4. Analysis

We have performed a standard Local Thermodynamic Equilibrium (LTE) analysis, strictly differential with respect to the Sun, to derive chemical abundances from the measured equivalent widths.

4.1. Model atmospheres

We used the MARCS program, first described by Gustafsson et al. (1975), to generate the model atmospheres. Since then, the program has been further developed in various ways and updated in order to handle the line blanketing of millions of absorption lines more accurately, Asplund et al. (1997). The following assumptions enter into the calculation of the models: the atmosphere is assumed to be plane-parallel and in hydrostatic equilibrium, the total flux (including mixing-length convection) is constant, the source function is described by the Planck function at the local temperature with a scattering term, the populations of different excitation levels and ionization stages are governed by LTE. Since the analysis is differential relative to the Sun we have also used a solar model atmosphere calculated with the same program as the stellar models, in spite of the fact that the empirically derived Holweger-Müller model better reproduces the solar observed limb darkening; see Blackwell et al. (1995) for a discussion of this.

4.2. Fundamental parameters of model atmospheres

The effective temperature and surface gravity for each star were derived from photometry from Olsen (1983, 1993, 1994 and priv. comm.). We have used an extension of the calibration in Edvardsson et al. (1993a) and the calibration in Olsen (1984). The calibration by Edvardsson et al. (1993a) is valid for the parameter space and . This translates roughly to , and metallicity . The Edvardsson et al. (1993a) calibration was preferred for all stars to which it is applicable. For the three stars previously studied by Barbuy & Grenon (1990) photometry is not available, and we used the stellar parameters cited by them.

4.3. Surface gravity

Surface gravities were derived from the c₁ index, which primarily measures the Balmer jump and is sensitive to the surface gravity in solar type dwarf stars. In addition to surface gravities estimated from photometry we have also used the wings of the strong calcium line at 6162 Å (see Blackwell & Willis 1977 and Edvardsson 1988), to derive surface gravities. The results are given in Table 1 (click here). For these results we are indebted to Matthias Palmer and Mikael Nilsson, who carried out these laborious determinations. Edvardsson et al. (1993a) estimated the error in surface gravity determined from their calibration of the c₁ index to 0.2 dex. Olsen (1984) quotes a similar accuracy for his calibration. For the stars with trigonometric parallaxes in van Altena et al. (1991) we have also estimated surface gravities from parallaxes. This exercise was meant to be a consistency check on the photometric and spectroscopic determinations of the surface gravities. Assuming that the stars have masses of 0.8 and interpolating the bolometric corrections in the table given in Allen (1973) we derived, from the parallaxes, the surface gravities (see e.g. Gustafsson et al. 1974) shown in Fig. 1 (click here) and given in Table 1 (click here).

  
Figure 1: Surface gravities derived from parallaxes vs. surface gravities derived from photometry. The one-to-one relation is indicated by the dotted line. The error bars reflect the errors in the parallaxes. Note the different scales on x- and y-axis

   

HD HR Name V Spec.class [Fe/H] [M/H] U V W Q

30562 1536 5.77 F8V 5876 4.00 4.00 3.9 0.19 0.14 1.4 40.8 -70.9 -10.7 82.5

36130 7.76 G0M 5986 4.34 4.40 4.0 0.15 0.15 1.1 -14.3 -52.5 -43.7 69.8

37088 8.51 G0 5856 4.26 4.35 0.10 0.31 1.8 -17.4 -12.4 -43.0 48.0

37216 7.84 G5M 5527 4.47 4.90 -0.02 0.17 1.1 9.8 1.0 -4.3 10.7

49178 8.07 G0E 5683 4.37 4.45 0.01 0.06 1.2 32.3 10.3 -10.5 35.5

54322 8.40 G5 5894 4.50 4.55 0.15 0.33 0.9 -20.2 -0.7 7.1 21.4

55693 7.18 G5M 5845 4.15 4.40 0.26 0.24 1.3 33.9 3.3 -5.0 34.4

67228 3176 5.30 GIVB 5831 4.14 3.90 3.6 0.16 0.22 1.4 -41.9 16.6 -9.2 46.0

68988 8.20 G0 5956 4.03 4.25 0.37 1.4 -94.1 -8.8 11.8 95.2

69582 7.56 G5 5652 4.34 4.74 0.08 0.06 1.2 -20.0 11.5 10.5 25.3

69830 3259 5.96 G7.5V 5484 4.30 4.95 4.5 -0.03 0.10 1.1 -41.3 -51.7 -4.4 66.3

71479 7.18 G0 6036 4.18 4.48 0.25 0.32 1.5 34.8 -40.4 -9.1 54.1

72946B 3396 7.20 G5V 5911 4.40 5.00 0.24 0.40 1.3 15.0 -18.0 -3.4 23.7

75782 7.08 G0 5930 3.87 3.77 0.18 0.11 1.5 12.3 -23.0 -9.1 27.7

76780 7.64 G5M 5869 4.30 4.80 0.21 0.30 1.3 22.3 -6.7 10.1 25.3

80607A 9.15 G5R 5457 4.28 0.27 0.30 1.1 -16.9 15.0 19.3 29.7

87646 8.07 G0 5961 4.06 4.41 0.30 0.39 1.4 21.9 -11.4 2.6 24.8

91204 7.82 G0 5864 4.05 4.00 0.17 0.24 1.4 -19.6 9.7 3.6 22.2

94835 G058-030 9.11 K0/G0 5896 4.06 0.13 0.04 1.4 -65.1

101242 7.61 G5 5790 4.28 4.68 0.07 0.19 1.3 45.2 -50.0 -2.6 67.4

106156 7.92 K0 5437 4.27 4.77 0.13 0.20 1.1 -61.9 -13.0 -11.3 64.3

110010 7.01 G0 5965 4.08 4.58 4.7 0.35 0.34 1.4 9.0 -14.1 -6.6 17.9

117243 8.35 G0/G5III¹ 5902 4.01 4.36 0.24 0.33 1.0 13.2 -59.9 4.6 61.5

125968 7.77 G0/G5IV-V¹ 5868 4.12 4.32 4.7 0.15 0.25 1.4 22.6 -89.6 -27.7 96.5

126511 8.37 G5 5472 4.28 4.70 0.06 0.10 1.3 -14.5 -47.6 -9.9 50.7

128987 7.24 G5 5588 4.35 5.00 0.05 0.10 0.9 14.7 2.9 -7.1 16.6

130087 7.52 F5 6023 4.01 4.41 0.25 0.25 1.5 13.0 -16.6 4.9 21.7

134474 8.88 G5 5375 4.46 5.06 0.16 0.33 1.0 7.7 22.8 -27.1 36.2

134987 5657 23Lib 6.47 G4V 5833 4.11 4.31 4.0 0.36 0.58 1.3 10.3 -24.9 26.9 38.1

137510 5740 6.27 G0IV-V 5929 3.91 3.91 0.25 0.28 1.5 -0.2 2.0 7.6 7.9

144585 5996 6.31 G4IV-V 5831 4.03 4.38 0.27 0.26 1.4 23.6 -17.5 33.6 44.6

171999A 8.33 G5 5249 4.32 4.65 4.0 0.40 0.06 0.9 7.6 -61.3 -3.3 61.9

175518 K0IV-V ¹ 5713 3.93 4.73 4.3 0.32 0.67 1.5 14.6 -99.8 12.6 101.7

178911A 7272 6.73 G5R 5910 4.24 4.44 4.0 0.06 0.35 35.1 -8.8 6.0 36.7

180890 8.35 G5 5530 4.23 4.53 0.14 0.09 1.5 16.9 -50.0 -9.4 53.6

182572 7373 31Aql 6.36 G8IV² 5739 3.83 4.43 4.1 0.42 0.50 1.4 -1.0 123.2

183263 7.87 G5/G2IV 5837 4.05 4.40 0.15 0.22 1.5 18.6 -32.2 8.6 38.2

186427 7504 16CygB 6.23 G3V 5773 4.17 4.42 0.06 0.21 1.3 -27.9 -17.9 5.8 33.6

187055 9.00 G5 5298 4.56 4.96 3.9 0.16 0.25 0.9 83.0 5.3 -12.7 84.1 K dwarf stars

32147 1614 6.21 K3V 4625 4.57 4.55 4.4 0.28 0.17 1.0 -11.5 -36.1 -3.7 38.0

61606A 7.17 K2V 4833 4.55 4.85 4.6 -0.08 0.11 1.0 -34.9 9.4 -1.0 36.1

103932 6.95 K5V 4510 4.58 4.85 4.6 0.16 0.21 1.0 9.9 -59.9 0.4 60.7

131977A 5568 5.72 K4V 4585 4.58 4.70 4.6 0.04 0.18 1.0 -57.2 -9.5 -26.1 63.6

136834 8.26 K0 4765 4.56 4.47 4.5 0.19 0.23 1.0 9.6 -44.3 -8.7 46.2 Stars in common with Barbuy & Grenon (1990)

37986³ 7.37 G5/K0IV 5455 4.50 4.40 4.3 0.27 0.47 1.0

77338³ 8.63 K0IV 5290 4.50 4.90 0.22 0.45 1.0

87007³ 8.81 K2 5300 4.50 4.70 0.27 0.43 1.0 40.3⁴ -42.5⁴ -14.2⁴

The agreement between surface gravities determined with the different methods is in general good. We note, however, that there is in the mean an offset in the surface gravities determined from the wings of the strong CaI line as compared to the surface gravities determined from photometry, see Table 1 (click here), of about +0.27 dex. The reason for this offset is not clear but, a corresponding uncertainty in surface gravity is of minor significance for the abundance results, see Table 3 (click here). A tendency for the trigonometric determiantions to agree closer with the photometric than with the spectroscopic ones may also be traced. It is interesting to note that the K dwarf stars in our study have derived from parallaxes that are in good agreement with those determined from photometry.

On the basis of these comparisons we found no reason to change the surface gravities to be used in the abundance analysis but kept those determined from photometry.

4.4. Microturbulence parameters

 

We have determined microturbulence parameters, , from both the CaI lines and the FeI lines for 12 of the stars with enough calcium and iron lines measured. For the determination from the CaI lines, abundances from the individual lines were derived with ranging from 0.10 to 1.90 km s^-1. The microturbulence parameter for each star was then determined as the value which gave the smallest abundance scatter (the inflexion point, see e.g. Smith 1981). The microturbulence parameters were also determined by plotting the iron abundance versus the reduced equivalent widths, , derived for each line. If the correct microturbulence parameter is used the slope of a fit to the data points should be zero. Both methods agreed well for these 12 stars.

Using the values obtained we derived a relation between effective temperature, surface gravity and the microturbulence parameter, which was then used to determine microturbulence parameters for the rest of the stars: and predicts, with and adopted, values to an accuracy of km s^-1 for the 12 stars. This relation is valid for and . For a few stars just outside the validity range we extrapolated the relation to calculate approximative microturbulence parameters. This procedure was checked to yield consistent abundances for individual iron lines of different strengths. For five stars a somewhat lower microturbulence parameter was preferred (HD 36130, HD 134474, HD 171999, HD 182572, HD 187055). Our relation for microturbulence parameters yield slightly higher values than the relation presented by Edvardsson et al. (1993a).

For the K dwarf stars none of the described methods seemed to yield definite values for the microturbulence parameter. A microturbulence parameter of 1.0 km s^-1 was adopted for these stars.

4.5. Atomic line data

The oscillator strengths were determined by requiring that the abundances calculated for the solar model (=
5780 K, , [Me/H]=0.00, =1.00) should reproduce the observed equivalent widths of the solar spectrum. The resulting values are given in Table 2 (click here).

Different line broadening mechanisms, van der Waals damping, radiation damping, thermal Doppler broadening and microturbulence were considered in the calculations of equivalent widths and abundances. Enhancement factors for the van der Waals damping were compiled from the literature. For iron lines values from Hannaford et al. (1992) and Holweger et al. (1991) were used, for calcium values from Smith (1981) and references therein, for sodium values from Holweger (1971) and for scandium values from Neuforge (1992). For the remaining lines a correction factor of 2.5 was adopted to the classical Unsöld value, according to #M&Mäckle et al. (1975). For the (unimportant) radiation damping parameter values from Kurucz (1989) were adopted for lines from calcium through nickel.

 

Note Note

[Å] [eV] [s^-1] [mÅ] [Å] [eV] [s^-1] [mÅ]

6300.31 0.0 -9.84 2.5 1.0+8 4.6 6452.31 1.19 -0.81 2.5 4.0+7 8.9

6156.80 10.74 -0.43 2.5 1.0+8 4.1 6504.18 1.18 -0.47 2.5 3.9+7 27.0

6158.17 10.74 -0.65 2.5 1.0+8 2.6

7771.95 9.14 0.29 2.5 1.0+8 72.2 5303.22 2.28 -2.02 2.5 2.7+8 4.1

7774.18 9.14 0.14 2.5 1.0+8 61.5 5384.87 2.28 -2.50 2.5 2.7+8 1.4

7775.39 9.14 -0.05 2.5 1.0+8 50.9

5220.91 3.38 -1.01 2.5 8.1+7 10.9

6160.75 2.10 -1.30 2.1 1.0+8 58.8 5238.96 2.71 -1.43 2.5 2.5+8 16.7

6154.23 2.10 -1.62 2.1 1.0+8 37.2 5304.18 3.46 -0.79 2.5 2.5+8 14.9

5312.86 3.45 -0.69 2.5 2.5+8 18.5

6319.24 5.11 -2.20 2.5 1.0+8 31.7 5318.77 3.44 -0.78 2.5 2.5+8 15.7

7759.37 5.93 -1.76 2.5 1.0+8 17.8 5480.51 3.50 -0.90 2.5 7.4+7 11.1

7930.82 5.94 -1.04 2.5 1.0+8 56.6 5574.39 4.45 -0.70 2.5 6.7+7 2.5

6630.03 1.03 -3.56 2.5 2.4+7 7.1

6696.03 3.14 -1.58 2.5 1.0+8 38.1 6636.33 4.14 -1.20 2.5 4.4+7 1.6

6698.67 3.14 -1.89 2.5 1.0+8 22.4 6643.00 3.84 -1.20 2.5 7.4+7 3.1

6796.49 4.40 -0.29 2.5 1.6+8 7.3

6518.74 5.95 -1.40 2.5 1.0+8 26.6

7415.96 5.61 -0.80 2.5 1.0+8 93.5 5305.86 3.83 -2.09 2.5 2.6+8 24.7

7760.64 6.20 -1.35 2.5 1.0+8 19.4 5308.42 4.07 -1.82 2.5 2.6+8 26.9 +

5310.69 4.07 -2.26 2.5 2.6+8 12.9

6166.44 2.52 -1.36 5.2 1.9+7 70.4 K

6455.60 2.52 -1.41 2.3 4.7+7 58.6 5388.50 3.37 -1.69 2.5 7.1+7 5.3

6508.85 2.53 -2.35 2.0 4.4+7 13.7 5399.47 3.85 -0.18 2.5 9.0+7 38.1

6709.87 2.93 -2.76 4.5 3.8+8 2.5 5470.64 2.16 -1.38 2.5 4.0+8 58.4

6798.47 2.71 -2.42 3.7 1.9+7 8.7 6440.93 3.77 -1.27 2.5 7.1+7 6.3

7764.66 5.37 0.17 2.5 9.8+7 5.9

5484.64 1.85 0.04 1.5 1.5+8 2.2

5308.69 4.26 -2.43 2.0 2.1+8 7.6 t

5239.82 1.45 -0.76 1.5 1.0+8 48.5 5315.07 4.37 -1.54 2.0 1.8+8 32.5 t

5318.36 1.36 -1.77 1.5 1.5+8 12.4 5223.18 3.63 -2.31 2.0 7.9+7 28.5 t

6300.69 1.51 -2.00 1.5 2.3+8 6.2 5308.69 4.26 -2.43 2.0 2.1+8 7.6 t

6320.84 1.50 -1.88 1.5 2.3+8 8.2 5315.07 4.37 -1.54 2.0 1.8+8 32.5 t

5320.03 3.64 -2.54 2.0 3.1+8 19.3

5219.70 0.02 -2.25 2.5 6.0+6 26.7 K 5321.11 4.43 -1.30 2.0 1.7+8 42.0 K

5299.98 1.05 -1.44 2.5 3.4+6 20.4 K 5322.04 2.28 -2.89 2.0 1.0+8 62.2 K

5389.16 0.81 -2.24 2.5 8.3+7 6.7 5386.34 4.15 -1.76 2.0 2.3+8 31.6 t

5471.20 1.44 -1.61 2.5 1.1+8 7.0 5395.22 4.44 -1.81 2.0 1.8+8 18.7 t

5473.55 2.33 -0.83 2.5 1.1+8 5.8 5398.28 4.44 -0.81 2.0 1.9+8 70.5 t

5474.23 1.46 -1.31 2.5 8.4+7 12.7 5473.16 4.19 -2.02 2.0 2.2+8 19.5 t

5474.46 2.34 -0.96 2.5 1.1+8 4.3 5483.10 4.15 -1.49 2.0 2.6+8 45.5 t

5490.15 1.46 -0.98 2.5 1.5+8 21.6 K 5560.22 4.43 -1.16 2.0 1.6+8 49.5 t

6303.76 1.44 -1.60 2.5 1.7+8 7.8 5577.02 5.03 -1.51 2.0 6.9+8 11.7 t

6312.24 1.46 -1.60 2.5 1.7+8 7.5 6165.36 4.14 -1.55 2.0 8.8+7 43.8 t

7440.58 2.26 -0.76 2.5 1.4+8 9.5 6303.46 4.32 -2.59 2.0 1.9+8 5.1

7949.15 1.50 -1.45 2.5 2.0+6 11.3 6380.75 4.19 -1.27 2.0 7.4+7 56.9

 

 

Note Note

[Å] [eV] [s^-1] [mÅ] [Å] [eV] [s^-1] [mÅ]

6436.41 4.19 -2.41 2.0 3.0+7 10.6 t

6501.67 4.83 -1.25 2.0 1.0+8 27.7 5220.29 3.74 -1.29 2.5 8.7+7 28.3

6696.32 4.83 -1.50 2.0 2.4+8 18.0 t 5388.35 1.94 -3.46 2.5 1.1+8 13.0

6699.13 4.59 -2.12 2.0 1.4+8 8.3 t 5392.33 4.15 -1.30 2.5 2.0+8 14.5

6703.57 2.76 -3.01 2.0 1.0+8 38.1 t 5468.11 3.85 -1.68 2.5 1.6+8 11.8 K

6704.50 4.22 -2.58 2.0 1.0+8 6.6 t 6175.37 4.09 -0.59 2.5 2.3+8 49.6 K

6710.32 1.48 -4.81 2.0 1.7+7 16.6 t 6176.81 4.09 -0.34 2.5 1.4+8 64.2 K

6713.04 4.61 -1.29 2.0 2.4+8 36.0 K 6316.58 4.15 -1.89 2.5 2.0+8 4.4

6713.74 4.79 -1.43 2.0 2.4+8 22.3 K 6502.22 3.40 -2.85 2.5 1.0+8 2.6

6796.12 4.14 -2.27 2.0 1.4+8 14.9 t 6635.13 4.42 -0.74 2.5 1.5+8 26.5

6806.85 2.73 -3.10 2.0 1.0+8 35.8 6813.61 5.34 -0.41 2.5 8.2+8 9.9

6810.26 4.61 -1.01 2.0 2.3+8 51.1 t 7110.90 1.94 -2.89 2.5 5.2+7 38.3

7107.46 4.19 -1.96 2.0 4.8+7 24.2 t 7126.71 3.54 -2.34 2.5 4.8+7 6.4

7114.57 2.69 -4.02 2.0 8.0+7 7.7 t 7414.51 1.99 -2.04 2.5 1.0+8 81.9

7120.58 4.14 -3.40 2.0 8.0+8 1.3

7127.57 4.99 -1.07 2.0 4.9+8 30.2 t 5220.08 3.82 -0.61 2.50 1.0+8 16.4

7130.92 4.22 -0.66 2.0 2.1+8 97.7 t 7933.12 3.78 -0.27 2.50 1.0+8 35.9

7418.33 4.14 -2.84 2.0 5.5+7 4.7 t

7418.67 4.14 -1.47 2.0 1.1+8 50.7 t 6435.04 0.07 -0.98 2.50 1.0+8 1.8

7421.55 4.64 -1.68 2.0 2.5+8 19.0 t 6687.50 0.00 -0.67 2.50 1.0+8 4.3

7440.91 4.91 -0.62 2.0 5.0+8 60.6 t

7751.11 4.99 -0.76 2.0 6.4+8 48.9 t 5402.78 1.84 -0.64 2.5 1.0+8 11.2

7941.09 3.27 -2.47 2.0 1.4+8 43.7 t 6795.42 1.70 -1.14 2.5 1.0+8 5.9

7955.71 5.03 -1.17 2.0 6.4+8 25.5 t 5473.39 1.74 -0.83 2.5 1.0+8 9.4

7959.14 5.03 -1.13 2.0 6.4+8 27.5 t

5385.12 0.52 -0.97 2.5 1.0+8 1.3

6416.93 3.89 -2.69 2.0 3.4+8 41.5 + 6506.35 0.63 -0.64 2.5 1.0+8 2.5

6432.68 2.89 -3.62 2.0 2.9+8 42.3 7439.87 0.54 -1.00 2.5 1.0+8 1.5

6456.39 3.90 -2.21 2.0 3.4+8 65.0

6516.08 2.89 -3.36 2.0 2.9+8 55.6 5570.39 1.33 0.43 2.5 1.0+8 9.6

5301.04 1.71 -1.89 2.5 1.2+8 21.7 6320.42 0.17 -1.39 2.5 1.0+8 5.2

5312.65 4.21 -0.02 2.5 2.5+8 7.7 6390.49 0.32 -1.47 2.5 1.0+8 3.2

5483.36 1.71 -1.25 2.5 1.9+7 50.6

6455.00 3.63 -0.24 2.5 7.4+7 16.2 5319.82 0.55 0.02 2.5 1.0+8 18.8

6632.47 2.28 -1.73 2.5 6.5+6 11.8

6814.96 1.96 -1.76 2.5 2.1+7 20.6 6645.12 1.38 0.28 2.5 1.0+8 5.7

7417.39 2.04 -2.00 2.5 2.2+7 11.9

7437.07 5.98 1.13 2.5 7.0+7 2.6 5311.63 1.78 0.13 2.5 1.0+8 4.4