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Astron. Astrophys. 341, 539-546 (1999)

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3. Stellar parameters

3.1. Temperatures

The crucial issue in the detailed analysis of these cool and metal-rich giants is the determination of their effective temperatures [FORMULA]. We obtained very high quality V and I colours using the Hubble Space Telescope (HST) and J and K colours using the detector IRAC2 at the 2.2m telescope of ESO (Ortolani et al. 1995; Guarnieri et al. 1998).

In Table 2 are given the magnitudes: V from Hartwick (1975), BVR from Ortolani et al. (1990), VI from Ortolani et al. (1995) and JK from Guarnieri et al. (1998). It is interesting to note the large offsets in the V magnitudes between Hartwick (1975), Ortolani et al. (1990) and Ortolani et al. (1995) values. This clearly reveals the improvement of the photometry in crowded fields, which occurred along the years from photographic, to ground-based CCD, and HST data. HST calibration of V and I was tied to the Cousins system. The calibration of our old Danish data (Ortolani et al. 1990) showed an offset of about 0.28 mag, very probably due to crowding. A revised calibration of the Ortolani et al. (1990) data done with the more accurate crowding compensation showed excellent agreement with the new HST data.


Table 2. Magnitudes of the program stars

A further step in the derivation of temperatures, is the reddening value adopted. In Guarnieri et al. (1998) we derived a colour excess of [FORMULA] for NGC 6553. Assuming a ratio [FORMULA] (Dean et al. 1978) the resulting [FORMULA] is 0.7. Assuming E(V-K)/E(B-V) = 2.744 and E(J-K)/E(B-V) = 0.527 (Rieke & Lebofsky 1985), the available colours were dereddened. In Table 3 are given the observed and dereddened colours. In order to derive temperatures we used several methods:


Table 3. Observed/dereddened colours

(i) Infrared flux method: Based on absolute measurements of stellar monochromatic fluxes in the infrared region for a sample of 80 solar metallicity stars, Blackwell & Lynas-Gray (1994) established the relation T(V-K) = 8862-2583(V-K)-353.1(V-K)2.

(ii) Relations by McWilliam (1990): Based on a sample of 671 giants of about solar metallicity McWilliam (1990): derived the relations between the (B-V), (V-K), (V-I) and (J-K) colours and effective temperatures. The resulting temperatures obtained with the use of relations (i) and (ii) are given in Table 4; it has to be noted however that in both cases (McWilliam 1990 and Blackwell & Lynas-Gray 1994) the samples on which the relations are based did not contain a significant number of stars with effective temperatures around 4000 K and below, so that such relations should be valid only for T[FORMULA] [FORMULA] 4000 K, at the edge of validity for our sample stars.


Table 4. Derived temperatures using relations by McWilliam (1990) and Blackwell & Lynas-Gray (1994), and using Table 5 of Bessell et al. (1998) adopting [Fe/H] = -0.3 and log g = 1.0.

(iii) tables by Bessell et al. (1998): these calibrations based on NMARCS models of Plez (1995, unpublished) were obtained by linear interpolation in their Table 5; these temperatures are also reported in Table 4.

We have adopted T[FORMULA] = 4000 K for the 2 sample stars, based essentially on the calibrations by Bessell et al. (1998) (Table 4).

3.2. Gravities

The classical relation [FORMULA] was used (adopting [FORMULA] = 5770 K, M* = 0.8 [FORMULA] and [FORMULA] = 4.74 cf. Bessell et al. 1998). For deriving [FORMULA] we adopted [FORMULA](HB) = 1.06 (following Buonanno et al. 1989), V(HB) = 16.92 and E(B-V) = 0.7 (Guarnieri et al. 1998) and bolometric magnitude corrections BCV = -0.90 cf. Bessell et al. (1998); the resulting [FORMULA] values are given in Table 6. Due to an overionisation effect, as discussed in Pilachowski et al. (1983), a corrected value for log g, lower by 0.6 dex is adopted (values in parenthesis in Table 6). The ionisation equilibrium with these gravities was checked by verifying if the curves-of-growth of FeI and FeII give the same Fe abundance.


Table 6. Stellar parameters adopted. The log g values in parenthesis are the corrected values taking into account overionisation effects.

3.3. Metallicity

For comparison purposes, in Table 5 are given the metallicity values reported in the literature for NGC 6553, together with indication of the method employed in each case. Notice the spread in the metallicities reported, which we believe can be explained by a combination of overabundances of [FORMULA]-elements, to a moderate metallicity as deduced from Fe lines (Sect. 5).


Table 5. Metallicity of NGC 6553 given in the literature. References to Table: 1 Zinn (1980); 2 Bica & Pastoriza (1983); 3 Cohen (1983); 4 Zinn & West (1984); 5 Pilachowski (1984); 6 Webbink (1985); 7 Bica & Alloin (1986); 8 Barbuy et al. (1992); 9 Harris (1996); 10 Origlia et al. (1997); 11 Rutledge et al. (1997b) - the first value corresponds to the Zinn & West (1984) scale and the second one to the Carretta & Gratton (1997) scale; 12 Carretta & Gratton (1997)

3.3.1. Model atmospheres

We have adopted the photospheric models for giants of Plez et al. (1992) and their extended grid kindly made available to us by B. Plez (1997, private communication).

3.3.2. Oscillator strengths

We have used two sets of oscillator strengths gfs:

(i) Along the years we have fitted line-by-line the solar spectrum, by comparing synthetic spectra computed with the Holweger & Müller (1974) semi-empirical solar model to the observed solar spectrum at the center of the solar disk Delbouille et al. (1973), in the wavelength range [FORMULA] 4000-8700 Å (see for example Castro et al. 1995). This work has been carried out with the intent of applying spectrum synthesis to large wavelength regions (e.g. Barbuy 1994), in which case gfs for all lines are needed; we emphasize that there is no complete list of accurate laboratory gf values.

(ii) Laboratory oscillator strengths available in Fuhr et al. (1988), Martin et al. (1988) and Wiese et al. (1969) and compilations of laboratory gf values by MR.

For the curves of growth only the laboratory (ii) gfs were used, since they are more homogeneous, showing less spread. For the spectrum synthesis calculations the laboratory (ii) gfs are used where available, and our fitted gfs (i) are employed for the remaining lines.

3.3.3. Continuum definition

The equivalent widths have been measured using the detectable pseudo-continuum, as illustrated in Fig. 1. This procedure was adopted in order to minimize uncertainties in the equivalent width measurements, from one order to another, due to a non-homogeneous placement of the continuum. On the other hand, when overplotting the theoretical curve-of-growth on the observed points, we considered the upper metallicity envelope, as shown in Fig. 3. The metallicities so derived are reported in Table 6. Such metallicity values were then tested through direct comparison of synthetic to the observed spectra, confirming these values. We note that curves-of-growth computed with [FORMULA] = 4250 K give a metallicity of +0.2 dex relative to the values obtained with [FORMULA] = 4000 K.

[FIGURE] Fig. 3. Curve-of-growth of FeI for the star III-3, using stellar parameters ([FORMULA], log g, [Fe/H], vt) = (4000, 1.0, -0.6, 1.3), and adopting oscillator strengths by Wiese et al.

3.3.4. Curves-of-growth

The metallicities were derived by plotting curves of growth of FeI, where the equivalent widths of a selected list of lines were measured using IRAF, and the code RENOIR by M. Spite was employed for plotting the curves of growth. The FeI curve of growth for III-3 is shown in Fig. 3. The final stellar parameters adopted are shown in Table 6. The resulting metallicity for the cluster is [Fe/H] = [FORMULA]. The difference with respect to Barbuy et al. (1992) where [Fe/H] = -0.2 was derived for the star III-17 can be explained by the main reason that no equivalent widths of FeI had been measured, and only overall fits of synthetic spectra, using the gf's (i) (Sect. 3.3.2) in a region with many blends ([FORMULA] 5000-6000 Å) were carried out. That procedure was adopted in view of the low S/N of the spectrum, which we had to convolve further reducing the resolution.

3.3.5. Abundance ratios

In Table 7 are reported the lines used, together with oscillator strengths, and the abundance ratios found line-by-line.


Table 7. Line by line abundance ratios. Oscillator strengths values refer to `fit' = our fitting to the solar spectrum (Sect. 3.3.2); `MR' - McWilliam & Rich 1994; `W' = Wiese et al. 1969, Fuhr et al. 1988 and Martin et al. 1988

The calculations of synthetic spectra were carried out using the code described in Barbuy (1982) where molecular lines of CN A2[FORMULA]-X2[FORMULA], C2 A3[FORMULA]-X3[FORMULA] and TiO A3[FORMULA]-X3[FORMULA] [FORMULA] system are taken into account.

Abundance ratios were derived by computing synthetic spectra line-by-line. For this we have adopted laboratory gf-values (Sect. 3.3.2) for the lines studied. By the use of an homogeneous set of oscillator strengths, the abundance ratios present very low uncertainties.

In Figs. 4 to 10 are shown fits of synthetic to observed spectra for some of the lines indicated in Table 7.

[FIGURE] Fig. 4. III-3: MgI [FORMULA] 6765.450 Å line. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Mg/Fe] = 0.0, +0.4 and +0.6.

[FIGURE] Fig. 5. III-3: CaI [FORMULA] 6166.440, 6169.044, 6169.564 Å lines. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Ca/Fe] = 0.0, +0.4 and +0.6.

[FIGURE] Fig. 6a and b. III-3: a  TiI [FORMULA] 6743.127 Å line. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Ti/Fe] = 0.0, +0.4 and +0.6. b  TiII [FORMULA] 6559.576 Å line. Same as in a .

[FIGURE] Fig. 7. II-85: AlI [FORMULA] 6696.032, 6698.669 Å lines. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Al/Fe] = 0.0, +0.4 and +0.6.

[FIGURE] Fig. 8. II-85: TiI [FORMULA] 6554.238, 6556.077 Å lines. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Ti/Fe] = 0.0, +0.4 and +0.6.

[FIGURE] Fig. 9. II-85: YI [FORMULA] 6435.049 Å line. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Y/Fe] = -0.4, 0.0 and +0.4.

[FIGURE] Fig. 10a and b. II-85: a  BaII [FORMULA] 6141.727 Å line. Dashed line: observed spectrum; solid lines: synthetic spectra computed with [Ba/Fe] = -0.4, 0.0 and +0.4. b  BaII [FORMULA] 6496.910 Å line. Same as in a .

In Table 8 are given the final mean values of the abundance ratios.


Table 8. Final mean abundance ratios

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© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998