3 Abundance analysis

We have used ATLAS9 (Kurucz 1993) model atmospheres as an input to the 1997 version of LTE line synthesis program MOOG first described in Sneden (1973). The procedure assumes plane-parallel atmospheres, hydrostatic equilibrium and LTE. The oscillator strength or gf value is an important atomic datum that affects the abundance calculations. For elements C, N and O we used gf values from Wiese et al. (1996). For Fe I, the values were taken in order of preference from; Table A1 of Lambert et al. (1996), Luck's compilation (1996, private communication), and Giridhar & Arellano Ferro (1989). For Fe II lines we used the Table A2 of Lambert et al. (1996), Giridhar & Arellano Ferro (1995) and Luck's compilation (1996, private communication).

For elements other than Fe, the large compilation by Luck (1996, private communication) was preferentially used and for some heavy s-process elements gf values were taken from the work of Thévenin (1989, 1990).

3.1 Determination of atmospheric parameters

In addition to abundances, the line strengths are strongly affected by atmospheric parameters like the effective temperature ( $T_{\rm eff}$), gravity (log g) and turbulent velocity ( $\xi_{\rm t}$). It is therefore necessary to determine these parameters before using line strengths for abundance determinations.

3.1.1 Effective temperature

Temperature calibrations exist that are valid for specific spectral type ranges. These methods are not only useful but also complement the spectroscopic efforts by providing initial values for the atmospheric parameters for calculating the atmospheric abundances. Here we briefly describe some of those calibrations that have been used for the stars of our sample. Later in Sect. 5, comparison with the finally adopted spectroscopic results is made in the discussion of each individual star.

Firstly, a rough estimate of $T_{\rm eff}$ can be made from the given spectral type and the calibration of Schmidt-Kaler (1982). However, more accurate values can be obtained from precise photometric colours. For our sample, we have used $uvby \beta$ photometric data and our own unpublished calibrations for F-G stars (HD 725, HD 9167, HD 172481). In addition, the calibration of Napiwotzki et al. (1993) for hotter stars like HD 172324, the 13-colour photometric system and the calibration of Bravo Alfaro et al. (1997), and the Geneva colour indices and the calibration of Cramer & Maeder (1979) were used as appropriate. These empirical calibrations provide $T_{\rm eff}$ with accuracies of $\pm 500$ K or better and serve as excellent starting values that are further refined by spectroscopic approaches. Any drastic difference between the two approaches deserves attention.

Yet another independent approach to estimate $T_{\rm eff}$ is from the Balmer lines profiles fitting (e.g. Arellano Ferro 1985; Venn 1995a). Theoretical Balmer profiles for grids of model atmospheres have been calculated by Kurucz (1993). For stars of intermediate temperature, this method does not lead to unique $T_{\rm eff}$, but rather it defines loci of possible temperatures and gravities. On the other hand, similar loci can be found from species where two states of ionization are well represented. Again, the solution is not unique but rather a locus on the $T_{\rm eff}$-$\log g$ plane is defined for each element. This approach will be illustrated in Fig. 3 for H$_\gamma$, H$_\delta$, Mg and Si for the star HD 218753. The above solution is of special importance for hot stars where no Fe I lines are present. For hotter stars, lines of Fe I are not only very weak but are also influenced by non-LTE effects. For A-F supergiants non-LTE effects could cause errors in the range of 0.2 to 0.3 dex in the iron abundance derived using Fe I lines (Boyarchuck et al. 1985). For example, in the well-known star Vega (A0V), the neglect of departure from LTE for Fe I lines leads to the underestimation of Fe abundance by 0.3 dex (Gigas 1986).

For stars cooler than 7500 K the lines of Fe I and Fe II with wide range in line strengths and lower excitation potential are adequate for estimating the effective temperature, microturbulence and gravity for any given star.

The finally adopted $T_{\rm eff}$ for our stars is that for which abundance consistency is obtained from neutral and ionized lines of well represented species such as Fe, Ti and Cr.

 

 

Table 2: Physical and dynamical parameters derived for program stars

Star	$T_{\rm eff}$	$\log g$	$\xi_{\rm t}$	$V_{\rm r}$(hel)	V(LSR)	$\sigma_{V_{\rm r}}$	log $(L/L_{\odot })$
	(K)		(km s-1)	(km s-1)	(km s-1)	(km s-1)
HD 725	7000	1.0	4.65	-56.9	-48.8	0.8	4.2
HD 9167	7250	0.5	4.20	-45.7	-40.2	1.1	4.2
HD 158616	7300	1.5	4.6	+68.8	+78.6	2.1	4.5
				+63.7	+78.5	1.5
HD 172324	11000	2.5	5.0	-126.1	-106.4	1.1	2.7
	11500	2.5	7.5	-117.3	-97.5	2.5
HD 172481	7250	1.5	4.60	-73.1	-76.9	1.8	4.1, 4.5
	7250	1.5	5.10	-84.4	-74.0	2.1
HD 173638	7500	1.5	4.30	+11.6	+26.9	1.2	4.5
HD 218753	8000	2.0	3.35	+3.2	+13.9	1.0	1.6
HD 331319	7750	1.0	5.35	-2.5	+15.8	1.5	4.5
HDE 341617	23000	3.0	15.00	+67.9	+87.8	2.9	4.6

3.1.2 Gravity

A good discussion of atmospheric parameters determination for A type stars can be found in Venn (1995a), who points out that H$_\gamma$ and H$_\delta$, being very sensitive to temperature and gravity in A type stars, provide a locus of possible temperature-gravity pairs, and that ionisation equilibrium of Mg I and Mg II gives another useful locus of temperature-gravity pair as the non-LTE effects are expected to be very small in magnesium lines. Since ionisation equilibrium of Si I and Si II give a temperature-gravity pair very similar to that given by Mg I and Mg II, the latter can also serve as yet another indicator of these parameters. Intersection of the above mentioned loci could lead to reliable temperature and gravity for each star, as demonstrated in Fig. 3.

The hydrogen lines were distorted in many of the program stars due to underlying emission, and therefore could not be used to derive temperature-gravity loci. We used excitation equilibrium of Fe I lines to get a preliminary estimate of $T_{\rm eff}$. It was followed by ionisation equilibrium of Mg I/Mg II, Si I/Si II and Cr I/Cr II to arrive at a satisfactory estimate of $T_{\rm eff}$ and $\log g$. For HD 725, HD 9167, HD 158616, HD 172481 and HD 173638 the excitation equilibrium of Fe I lines (requiring derived abundances to be independent of the lower excitation energy of the lines) gave very good estimates of the temperature which were further verified using lines of other species, as mentioned above. Similarly, for gravities, the values giving a good consistency for neutral and ionised Mg, Ti, Cr and Fe were adopted.

The star HD 172324 required an altogether different approach as described in Sect. 5.4.

3.1.3 Microturbulence velocity

All our program stars turned out to be hotter than 7000 K (see Table 2). For hotter stars, Fe I lines were difficult to measure. The Fe II lines on the other hand, had good range in equivalent widths. We therefore relied upon Fe II lines to derive microturbulence. The microturbulence was derived by requiring that weak, medium and strong lines give a consistent value of abundance.

The final atmospheric parameters derived for the program stars are given in Table 2, along with their radial velocities relative to the Sun and to the Local Standard of Rest (LSR). The log $(L/L_{\odot })$ values in Table 2 were estimated from the effective temperatures determined spectroscopically, and the calibration of Schmidt-Kaler (1982). For HD 172481 a red spectrum obtained at McDonald Observatory in May, 2000, allowed us to measure the three components of the OI feature near 7774 Å. The combined equivalent width W(7774) = 1.3 Å and the calibration of Arellano Ferro et al. (1991) lead to $M_{\rm v}$ = -5.6 or log $(L/L_{\odot })$ = 4.1, which is in good agreement with the value 4.5 obtained from Schmidt-Kaler's calibration. For homogeneity we have adopted the latter value for our discussion about the evolutionary status of this object in Sect. 6.