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Astron. Astrophys. 364, 674-682 (2000)

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3. Calculations

An updated version of the code by Spite (1967), extended to include molecular lines by Barbuy (1982), where LTE is assumed, is used for the spectrum synthesis calculations.

Oscillator strengths by Wiese et al. (1969), Fuhr et al. (1988) and Martin et al. (1988) were used whenever available, otherwise they were obtained by inverse solar analysis, using the solar atmospheric model by Holweger & Müller (1974) and the solar atlas by Delbouille et al. (1973). Solar abundances are adopted from Grevesse & Sauval (1998). The molecular lines of C2 ([FORMULA]-[FORMULA]), CN red ([FORMULA]-[FORMULA]) and TiO [FORMULA] ([FORMULA]-[FORMULA]) are taken into account in the calculations.

Model atmospheres employed have been interpolated in tables computed with the MARCS code by Plez et al. (1992, 1997). The calculations for two objects of our sample (HD 19745 and HD 95799) could not be done by using the grids from Plez et al., due to their higher temperatures, and for these two stars, the grid of Gustafsson et al. (1975) was adopted.

3.1. Stellar parameters

3.1.1. Temperature

A first guess of temperature is derived from colours. The photometric data are indicated in Table 2, except for one object of our sample (IRAS 19038-0026), since photometry is not available for this star.


Table 2. Johnson-Cousins UBVRI photometric data for the program stars. Average values were used for objects with different sources of data. The references are indicated in the last column.
Notes - (*) R from WBVR photometric system; (**) HD 146850 has been included to compare previous results (Castilho et al. 1995) with the parameters obtained from colours.
References: 1 - Hoffleit & Warren (1991); 2 - Castilho & Lorenz-Martins (2000); 3 - CDS; 4 - Clariá & Lapasset (1988); 5 - Corben (1966); 6 - Corben (1971); 7 - Cousins (1964); 8 - Cousins et al. (1966); 9 - Cousins & Stoy (1963); 10 - Dachs et al. (1978); 11 - Eggen (1992); 12 - Eggen (1989a); 13 - Eggen (1974); 14 - Eggen (1981); 15 - Eggen (1989b); 16 - Eggen (1968); 17 - Eggen & Stokes (1970); 18 - Gregorio-Hetem et al. (1992); 19 - Irwin (1961); 20 - Johnson et al. (1966); 21 - Kornilov et al. (1991); 22 - Lake (1963); 23 - Lloyd Evans & Koen (1987); 24 - MacConnell (1974); 25 - Nicolet (1979); 26 - Olsen (1993); 27 - Roman (1955); 28 - Rybka (1969); 29 - Wesselink (1962).
a (refs. 1, 7, 12, 15, 16, 19, and 20); b (refs. 1, 8, 9, 20, 22, and 25); c (refs. 1, 6, 17, 20, 21, 24, 25, and 27); d (refs. 4, 14, and 26); e (refs. 1, 5, 10, 11, and 13); f (refs. 1, 6, 21, 25, and 28).

We obtained additional UBVRI photometry at the LNA 60cm Zeiss telescope with the FOTRAP photometer (Jablonski et al. 1994), thus providing data for 8 stars of our sample. For stars with data from several sources, we used a weighted average. The LNA photometric data (Castilho & Lorenz-Martins 2000) are included in Table 2. The derived stellar parameters are reported in Table 3. We have corrected the colours with the Bond (1980) extinction law, where the distances were derived from parallaxes given in the Hipparcos catalogue when available (Column 2 in Table 3); for the other stars the distances were estimated from a Colour Magnitude Diagram for Hipparcos field stars (Perryman et al. 1995).


Table 3. Hipparcos Parallax, distance, and parameters determined from photometry. [Fe/H] and microturbulent velocity ([FORMULA]) adopted were obtained from curves of growth (Columns 10 and 11). The adopted atmospheric models are shown in the three last columns.
(a) The calculations for HD 19745 and HD 95799 were carried out employing the Gustafsson et al. models. For the other stars we used Plez et al.; (b) parameters obtained from the excitation equilibrium of the Fe I lines; (c) IRAS19038-0026 has no available photometry; (d) HD 146850 was analysed in Castilho et al. (1995): parameters obtained from photometry are compared here to those previously obtained.

The temperatures are derived by using the tables of colours vs. temperatures for cool giants by Bessell et al. (1998) and Lejeune et al. (1998). An effect of intrinsic reddening may probably be important for the stars of our sample, considering their far-infrared excess. Different values of temperature were calculated based on the colours for both calibration tables mentioned above. A mean value showing a typical r.m.s. deviation of 65 K was derived, leading to the first guess [FORMULA] listed in Table 3.

These temperature values were checked and in some cases modified for reaching the excitation equilibrium of the Fe I lines in the curves of growth. The final effective temperatures adopted are indicated in Table 3.

3.1.2. Gravity

A first guess of the surface gravity is estimated by using the calibration of colour indices as a function of log g by Lejeune et al. (1998), corresponding to the evolutionary track of a giant star of solar metallicity with 1 [FORMULA] (Schaller et al. 1992). In order to compare this procedure with a different method, we also used the classical relations involving luminosity, mass and radius where the bolometric magnitudes were determined by assuming the visual-to-selective absorption R = 3.1, and bolometric corrections by Lejeune et al. (1998). By considering that most of the LRG has about 2 [FORMULA], this value was applied in the calculations of this second method. The r.m.s. deviation between both methods is about 0.21 dex, showing that errors in log g are not significant, when the mass variation is small. In Table 3 we give the log g obtained. Finally, the gravities were checked and modified if necessary, from the ionization equilibrium of the Fe I and Fe II lines. The adopted gravities are listed in Column 13 of Table 3. For the star HD 176588 no Fe II line could be identified in the observed region, and the log g determination comes only from the photometric data.

HD 146850 is included in Table 3 to illustrate the good agreement of the stellar parameters derived from photometry and those derived from spectroscopy ([FORMULA] = 4000 K, log g = 1.5, Castilho et al. 1995). Note that Jasniewicz et al. (1999) found different parameters which do not seem to be compatible with our data.

For the star HD 65750, Dachs et al. (1978) found a variability of [FORMULA] = 6.2 to 7.1, but it was not clear if this variation was regular or not. They estimated [FORMULA] = -2.4 from the spectral type, and assuming d = 400 pc, R = 3.5, E(B-V)= 0.28, [FORMULA] = 0.98, and (m-M) = 8.47, a mass of 5 [FORMULA] was obtained. These values are different from those obtained here, indicating the errors produced in a calibration based on the spectral type, as well as other sources of errors due to differences in distance (of about 35[FORMULA]), or the circumstellar envelope contribution in E(B-V).

HD 19754 and HD 31993 are RS CVn type stars. Objects of this class generally present an excess Li abundance with respect to the values typically observed in evolved stars of the same spectral type. Strassmeier et al. (1999) reported the VRI variability of HD 31993, probably due to rotational modulation of an asymmetrically spotted stellar surface. They found a maximal amplitude of 0.05 mag for this star. The errors due to this variability are not significant on the estimation of gravity based on the colour calibration.

3.2. Curves of growth: metallicity and [FORMULA]

Curves of growth were used to check the excitation equilibrium of Fe lines, to estimate the value of metallicity [Fe/H] and microturbulent velocity [FORMULA]. The Plez et al. (1992, 1997) grid of model atmospheres and the code RENOIR by M. Spite were used.

Fig. 1 shows the curves of growth of Fe I and Fe II lines, measured for one object (HD 95799) of our sample. Different symbols are used to represent three ranges of excitation potential, in this plot: their distribution shows that the excitation equilibrium is reached.

[FIGURE] Fig. 1. Curve of growth of Fe lines for the star HD 95799. Different symbols indicate three ranges of excitation potential. The Fe II lines are represented by filled circles. The full line is a theoretical curve of growth. [FORMULA] is the solar abundance of the element, gf the line transition probability of the line, and [FORMULA] is a function of the element and of the stellar model.

The parameters [Fe/H] and [FORMULA] are obtained by calculating a theoretical curve which gives the best fit of the data and compared to the solar value log N(Fe) = 7.50 in the usual scale where log N(H) = 12.0 (Grevesse & Sauval 1999). The dispersion of points displayed in Fig. 1 is quite the same for most of our stars. A larger dispersion is found only for those observed with lower resolution.

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Online publication: January 29, 2001