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Astron. Astrophys. 323, 909-922 (1997)

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5. Application to other F and G stars

In a next step, we now apply the strong line method to other stars of the same temperature/gravity range and compare the stellar parameters to the ones we would obtain from the ionization equilibrium.

As in the case with Procyon, we first need to know both, the rotational and macroturbulence velocities for subsequent line profile analyses. To a very good approximation we treat all stars of our sample as slow rotators. This especially holds true for the metal-poor stars, which may be as old as or even older than the Galactic disk. In addition the instrumental profile (a Gaussian of [FORMULA] km s-1) acts as the dominant contributor to the convolution profile for most objects of our sample. Therefore elaborate Fourier techniques are not considered here. Instead we make reasonable assumptions with respect to the rotational velocities (e.g. [FORMULA] km s-1 for HD 19445 and HD 140283) and, along with the known instrumental profile, deduce the macroturbulence from the observed line shape. Note also that [FORMULA] and [FORMULA] do compensate each other to some extent. A star that actually rotates some 3 - 4 km s-1 faster than assumed, will merely receive a higher macroturbulence parameter, whereas the other stellar parameters are practically unchanged. As has been suggested from time to time there are also observational hints that the values adopted for micro- and macroturbulence are correlated; thus, knowing the microturbulence parameter, one can estimate the macroturbulence to a first approximation. For the Sun we have [FORMULA], whereas Procyon shows a ratio of [FORMULA]. All other objects in Table 3 roughly fit to this assumption, with [FORMULA] and [FORMULA] as lower and upper limits.


Table 3. Stellar parameters derived from Balmer lines ([FORMULA]), the strong line method ([FORMULA]) and singly ionized iron lines ([Fe/H], [FORMULA]). For comparison purposes, the surface gravity and iron abundance deduced from the ionization equilibrium (I.E.) of Fe I/Fe II are listed in columns (8) and (9), with the number of Fe I and Fe II lines used in columns (10) and (11). The values in column (5) and (6) are, however, based on Fe II lines only. For all Fe I lines [FORMULA] eV is taken as a lower limit, except for Procyon, where [FORMULA] eV is adopted. The Moon spectrum (bottom row) - treated as a star - serves for comparison and to obtain the instrumental profile, which is found to be a Gaussian of [FORMULA] km s-1. Rotational and macroturbulence velocities for the line profile analyses are given in columns (12) and (13). The last column indicates, whether models with scaled-solar abundances ([FORMULA]), or [FORMULA] -elements enhanced by +0.4 dex ([FORMULA]) were employed. For HR 1545 both results are shown

A very important test for the accuracy of our analyses and the performance of the spectrograph is the investigation of the Moon spectrum from the reflected sunlight. For this purpose, three short exposures were obtained and added to a combined spectrum. The Kitt Peak Solar Flux Atlas degraded by a Gaussian of [FORMULA] km s-1 shows the great similarity of both spectra (cf. Fig. 3). Comparing the equivalent widths of iron lines one obtains [FORMULA] mÅ, with an 1  [FORMULA] rms error of [FORMULA]  mÅ. Due to the somewhat lower effective temperature (cf. Fig. 5 and 6), [FORMULA] is changed as well, if derived from the ionization equilibrium; the strong line method, on the other hand, results in the solar value [FORMULA] (cf. Table 3, Fig. 11). The iron abundance derived from 9 Fe II lines is found to be slightly too high by 0.05 dex, which reflects the uncertainties from the strong line blanketing in the solar spectrum. This tendency may also be present in the spectra of Procyon and o  Aquilae, but is negligible in the metal-poor stars. Nevertheless, the analysis shows that, to within the error bars, the parameters derived from the Moon spectrum, reproduce the actual solar values.

[FIGURE] Fig. 11. The spectroscopic surface gravity determination of the Moon (= reflected sunlight) spectrum (cf. Fig. 10). Left column: [FORMULA] derived from the ionization equilibrium. Right column: [FORMULA] from the analysis of Mg I lines

In analogy to the analysis of Procyon, Fig. 12 displays the surface gravity determination of HR 1545, a metal-poor star 200 K cooler than Procyon. The discrepancy of the iron ionization equilibrium vs. the strong line method amounts to 0.22 dex and, again, leads to a higher [FORMULA]. Table 3 indicates that this star is also enriched in the [FORMULA] -element magnesium by [Mg/Fe]=+0.14 dex. We therefore repeated the analysis on a grid of model atmospheres with [FORMULA] -elements enhanced by +0.4 dex. As a result, the iron abundance is changed from -0.48 to -0.42 and the surface gravity increases to [FORMULA]. Hence the final parameters for this star should be obtained from interpolation within these two limiting cases.

[FIGURE] Fig. 12. The spectroscopic surface gravity determination of HR 1545 (cf. Fig. 10). Left column: [FORMULA] derived from the ionization equilibrium. Right column: [FORMULA] from the analysis of Mg I lines

HD 19445, in Fig. 13, is one of the standard halo stars, whose radial velocity and spectral appearance was found to be peculiar as early as 1914 by Adams & Kohlschütter. Later Chamberlain & Aller (1951) demonstrated that this star is underabundant in metals. Since then many analyses have been published on this object, not always without contradicting results. Our investigation of the ionization equilibrium shows a [FORMULA] and an iron abundance [Fe/H] [FORMULA]. The surface gravity derived from the Mg Ib lines increases this value to [FORMULA], whereas the iron abundance changes by [FORMULA] dex to [Fe/H] [FORMULA]. This value, as well as the microturbulence [FORMULA] km s-1, is however based on only three Fe II lines. On the other hand, repeating the analysis with Fe I lines only, would result in [Fe I/H] [FORMULA] and [FORMULA] km s-1. Our analysis therefore puts this object closer to the main sequence, whereas the value of the ionization equilibrium suggests a turnoff stage. Implications following these findings will be addressed in the final section. Note especially, that both Mg Ib lines are still strong enough to show pronounced wings, although HD 19445 is depleted in iron by a factor of 100. The same holds true for HD 140283, with [FORMULA] mÅ and [FORMULA] mÅ, for which we obtain similar systematics. Both halo stars reveal however considerable deficiencies in the line cores of [FORMULA] and [FORMULA] which may restrict the applicability of our LTE analysis.

[FIGURE] Fig. 13. The spectroscopic surface gravity determination of HD 19445 (cf. Fig. 10). Left column: [FORMULA] derived from the ionization equilibrium. Right column: [FORMULA] from the analysis of Mg I lines. Note in panel a and b [FORMULA] 5528 is used instead of [FORMULA] 5711, which is rather weak ([FORMULA] 10 mÅ) in HD 19445

Closer inspection of Table 3 indicates that all stars receive higher [FORMULA] values with the strong line method. The discrepancy is strongest for Procyon, the hottest star in our sample, and gets smaller the closer we come to the solar parameters, as expected for a differential analysis. HD 140283, for instance, is only slightly hotter than the Sun, but its evolved stage and metal-deficiency shifts this star to a region where the ionization balance is comparable to that of Procyon.

As a second result of Table 3 we mention a slightly increased metal abundance scale by [FORMULA] dex on average. Individual Fe I and Fe II abundances can however deviate by up to 0.2 dex. This is not immediately obvious from Table 3, where column (9) gives the mean abundance of neutral and ionized lines. Column (5) instead results from Fe II lines only, a different [FORMULA] and different [FORMULA]. The analysis of Procyon, e.g. leads to [Fe I/H]=-0.16 and [Fe II/H]=+0.01 for [FORMULA].

Reasonable error bars for the analyzed stars are similar to the ones mentioned for Procyon. The effective temperature can be fixed to [FORMULA] K from a single Balmer line. With both, H [FORMULA] and H [FORMULA], as well as redundant spectra, errors in the placement of the continuum can be estimated, and a formal error well below 50 K is achieved. On the other hand, the wings of the Balmer lines are the result of a temperature structure which in turn depends on the convective efficiency and the line blanketing. To assess the reliability of the Balmer line method we refer to the Sun and Procyon, where a small systematic effect (cf. Fig. 5 and 6) is indicated, at least for metal-rich stars. All other stars are based on the same kind of model atmosphere and show consistent results for all Balmer lines. We therefore estimate the true effective temperatures to be most probably within 100 K of the values given in column (3) of Table 3.

The determination of the surface gravity is not very much affected by the exact value of the effective temperature. From direct inspection of the pressure-broadened profiles of the Mg Ib lines, accuracies on the 0.05 dex scale can be achieved without doubt and redundancy is obtained from [FORMULA], [FORMULA] and repeated observations. The strong line method depends however on the adopted magnesium abundance value, which in turn is fixed from weak Mg I lines and brings velocity and turbulence parameters as well as the instrumental profile into play. Again, we estimate the resulting accuracies in combination with the individual data for the Sun and Procyon. Taking all uncertainties into account, an error less than [FORMULA] dex is expected.

Finally the iron abundance derived from Fe II lines is insensitive to a precise knowledge of the effective temperature, the temperature structure and NLTE effects. On the contrary, it depends on the surface gravity and, due to the paucity of useful Fe II lines (especially in metal-poor stars), on the microturbulence parameter. We estimate the Fe II abundance determinations to be better than 0.1 dex, but consider the microturbulence values to be erroneous by 0.2 to [FORMULA] km s-1.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998