6 Chemical analysis

The abundance analysis was performed making use of a modified version of the ATLAS9 code (Kurucz 1993) in which the classical mixing length theory used for the treatment of convection has been replaced by the turbulent theory implemented by Kupka (1999) as described in Sect. 4.

Since the wavelength coverage of our spectra is quite extensive, we have been restrictive in the selection of lines for abundance analysis. Weak lines with large errors in equivalent width due to noise and strong lines with a high sensitivity to errors in microturbulence were discarded. Moreover, the typically high rotational velocities of the $\lambda$ Bootis stars produce a strong blending of the spectral lines and it is an additional limiting factor in the line selection. Only blended features formed by lines of the same element and ionization stage were considered (Fig. 2). The abundance of the different elements were computed line by line by linearly interpolating in the grid of metallicity values for a given $T_{\rm eff}$and $\log\,g$, the final abundance being the average value. Results are displayed in Table 4 and plotted in form of abundance patterns in Fig. 3. For those program stars in common with Stürenburg (1993), abundances have been also displayed, showing good agreement.

Microturbulence was calculated in an independent way for each individual spectrum by making abundance results of weak and strong lines agree. We have used the iron lines since they are the most numerous and are spread over a wide range in equivalent width. In those cases where the scarcity of Fe I lines prevents from using this method, a value of $\xi = 3.0$ kms^-1 was adopted (Stürenburg 1993).

6.1 Estimated uncertainties

One source of uncertainty is the quality of the oscillator strengths values. To avoid using lines with $\log\,gf$ values of poor quality, a careful selection has been made using the most recent papers in the literature and the VALD database (Kupka et al. 1999). An average value was adopted. As a further test we compared, for every spectrum, the abundance value derived from every single line with the average value. Lines with abundance values clearly discrepant (which could be attributed to a wrong $\log\,gf$) were discarded.

Another source of uncertainty results from the errors of the input atmospheric parameters. To get an estimation of how sensitive our results are to these errors we have derived the abundances of a synthetic spectrum with $T_{\rm eff}$: 7500 ${\rm K}$, $\log\,g$: 4.0, [M/H]: -1.0 varied by $\Delta$ $T_{\rm eff}$ $=\pm200$ ${\rm K}$, $\Delta$ $\log\,g$ $= \pm 0.3$ dex. Errors in metallicity of $\Delta\rm [M/H] = 0.2$  dex are obtained on average. As expected, the abundance of ions changes with changes in $\log\,g$  whereas the neutral species tend to have negligible changes. On the contrary, changes in $T_{\rm eff}$produce changes in the abundances derived from neutral species while the abundances derived from ions remain unchanged.

Uncertainties in the abundance values due to NLTE effects should also be included. However, according to Heiter et al. (1998), corrections due to non-LTE effects are of the same order as the abundance error bars in the range of temperature of our program stars making the LTE approach perfectly valid.

Finally, it must be stressed that some abundances rely in only one or few spectral lines so that the uncertainty is high.

 

 

Table 4: Abundances of the program stars. In brackets is the number of spectra and the lines per spectrum used.

Identification	$v_{\rm mic}$	[MgI/H]	[CaI/H]	[ScII/H]	[TiII/H]	[MnI/H]
		[CrI/H]	[CrII/H]	[FeI/H]	[FeII/H]
Procyon	2.0	$0.21 \pm 0.03$ (2/2)	$-0.19 \pm 0.45$ (4/1)	-0.02 (1/1)	$0.17 \pm 0.07$ (4/3)	-0.03 (1/1)
		$-0.05 \pm 0.08$ (3/2)	$-0.08 \pm 0.14$ (2/1)	$-0.18 \pm 0.11$ (4/14)	$-0.07 \pm 0.09$ (4/1)
HD 68758	3.0
				-0.58 (1/1)
HD 75654	3.5	$-0.52 \pm 0.18$ (1/2)	$-0.75 \pm 0.08$ (1/2)		$-1.01 \pm 0.29$ (2/2)	$-1.0 \pm 0.42$ (2/1)
		$-1.13 \pm 0.23$ (1/2)	-1.07 (1/1)	$-1.04 \pm 0.14$ (2/14)	$-1.12 \pm 0.13$ (2/1)
HD 81290	3.0	$-1.07 \pm 0.08$ (2/2)	-0.89 (1/1)	-0.88 (1/1)	$-1.10 \pm 0.17$ (4/2)	$-0.73 \pm 0.23$ (2/1)
			-1.21 (1/1)	$-1.22 \pm 0.12$ (4/12)	$-0.93 \pm 0.22$ (3/1)
HD 83041	3.0	$-1.40 \pm 0.17$ (3/1)	-1.31 (1/1)	-0.86 (1/1)	$-1.24 \pm 0.16$ (6/1)
				$-1.14 \pm 0.11$ (6/5)	-1.33 (1/1)
HD 107233	4.0				$-1.15 \pm 0.15$ (2/2)
			-0.96 (1/1)		$-1.14 \pm 0.21$ (2/8)	$-1.13 \pm 0.14$ (2/1)
HD 109738	3.0
				$-0.83 \pm 0.32$ (2/2)	-1.25 (1/1)
HD 111005	3.0				$-0.13 \pm 0.12$ (3/2)
				$-0.39 \pm 0.09$ (4/5)	$-0.33 \pm 0.15$ (3/1)
HD 142703	3.0	$-0.76 \pm 0.06$ (1/2)			$-1.13 \pm 0.1$ (1/2)
				$-1.10 \pm 0.12$ (2/4)	$-1.17 \pm 0.08$ (2/1)
HD 142994	3.0
				$-0.56\pm0.19$ (4/1)
HD 156954	2.5		$-0.56 \pm 0.07$ (2/2)		$-0.26\pm0.10$ (3/2)
			-0.76 (1/1)	$-0.75\pm0.10$ (3/11)	$-0.57 \pm 0.12$ (3/1)
HD 168740	3.0				$-0.70\pm0.08$ (2/2)
				$-0.84\pm0.06$ (2/4)	-0.73 (1/1)
HD 184190	3.0	0.20 (1/1)	-0.18 (1/1)		$0.55 \pm 0.12$ (1/2)
		$0.39\pm0.05$ (1/3)	0.0 (1/1)	$0.17 \pm 0.19$ (1/16)
HD 193281	4.0	$-0.11 \pm 0.07$ (2/2)			$-0.61 \pm 0.09$ (3/2)
				$-1.13\pm0.07$ (3/3)	$-0.84 \pm 0.03$ (2/1)
HD 204041	3.0	$-1.06\pm0.09$ (1/2)			$-1.47 \pm 0.1$ (3/2)
			-1.08 (1/1)	$-1.00\pm.13$0 (3/6)	$-0.80 \pm 0.13$ (3/1)
HD 210111	3.0	$-0.98\pm0.12$ (1/2)	$-0.85\pm0.12$ (1/2)		$-1.10\pm0.06$ (3/2)
		$-1.33\pm0.10$ (2/1)	-1.15 (1/1)	$-0.88\pm0.12$ (3/9)	$-0.82 \pm 0.08$ (3/1)

Figure 4: Relation between physical parameters.