4 Non-LTE calculations for Vega

The Vega model atmosphere is the same as used in the non-LTE abundance analysis of nitrogen (Rentzsch-Holm 1996). It was generated with the ATLAS9 code (Kurucz 1992), adopting $T_{\rm eff} = 9500$ K, $\log g = 3.90$, $[{\rm M}/{\rm H}] = -0.5$, and a depth-independent microturbulence $\xi = 2.0$kms^-1. The adopted subsolar metallicity is in accordance with recent non-LTE analyses (see Rentzsch-Holm 1996), e.g. $[{\rm C}/{\rm H}] = -0.30 \pm 0.18$ for carbon (Stürenburg & Holweger 1991). The applied model atom is the same as for the Sun.
The resulting departure coefficients of Si I (Fig. 6) show that low-lying energy levels are strongly underpopulated with respect to LTE,

Figure 6: Departure coefficients of Si I in Vega.

implying substantial overionisation. Most of the silicon is in the singly ionized stage. The two lowest energy levels of Si II are almost perfectly in LTE (Fig. 7) but most of the excited Si II levels are overpopulated with respect to LTE. The ground state of Si III is also illustrated in Fig. 7.

Figure 7: Departure coefficients of Si II in Vega. The dashed line represents the ground state of Si III.

Again, strong overpopulation is obvious. However, the fraction of silicon present as Si III is still small compared to Si II.

4.1 Abundance analysis

The abundance analysis of Vega is based on low-noise high-resolution photographic spectra kindly provided by R. Griffin (Griffin & Griffin 1977) covering the visible spectral region. Seven Si II lines (Table 5) were found to be suitable for a reliable abundance determination,

 

 

Table 5: Si II line list used for the abundance analysis in Vega: Wavelength, excitation potential $\chi _i$ of lower level, equivalent width $W_{\lambda }$, silicon abundances and non-LTE corrections $\Delta \log \epsilon = \log \epsilon_{\rm NLTE} - \log \epsilon_{\rm LTE}$. Oscillator strengths: VALD.

$\lambda$	mult.	$\chi _i$	$\log gf$	$W_{\lambda }$	$\log \epsilon$	$\Delta \log \epsilon$
(Å)	nr.	(eV)		(mÅ)
3862.595	1	6.8575	-0.817	89	6.980	+0.050
4128.054	3	9.8367	0.316	67	6.911	-0.093
4130.872	3	9.8388	-0.824	84	6.928	$-0.106\;^a$
4130.894	3	9.8388	0.476	a	6.928	$-0.106\;^a$
5041.024	5	10.0664	0.291	43	6.980	$-0.062\;^b$
5055.984	5	10.0739	0.593	77	6.970	$-0.062\;^c$
5056.317	5	10.0739	-0.359	c	6.970	$-0.062\;^c$

a,c	Si II blend, combined equivalent width.
b	Blend with Fe I.

whereas all Si I lines are much too weak. Equivalent widths were measured directly from the tracings. Line broadening is treated in the same way as in the foregoing solar abundance determination. As for the Sun, the oscillator strengths compiled by Wiese et al. (1969) and Fuhr & Wiese (1998) produce a larger abundance scatter ( $\sigma = 0.094$ dex) than the values taken from VALD ( $\sigma = 0.029$ dex). For this reason the latter set is used. The lines marked with ^a and ^c in Table 5 are close blends of Si II lines. Consequently, the listed equivalent widths refer to the entire blend, and these blends are only considered with half weight. The line marked with ^b is also weighted half because it is blended with a Fe I line.
The non-LTE corrections are all negative with values between -0.062and -0.106 with the exception of $\lambda 3862$. For this particular line the non-LTE correction is positive (+0.05) because the departure coefficient of the upper level exceeds that of the lower level, contrary to the other lines.
From these 7 lines a weigthed LTE abundance of $\log \epsilon_{\rm LTE} = 7.005$ was derived. The small mean non-LTE correction of $\Delta \log \epsilon = -0.054$ finally leads to a silicon abundance of $\log \epsilon_{\rm NLTE} = 6.951$ with a standard deviation of 0.029 dex. The estimated error limits, including uncertainties in the equivalent widths, are $\approx$0.1 dex. Table 6 shows the influence of the line broadening parameters and the microturbulence on the mean non-LTE abundance compared to the described standard Vega model.

 

 

Table 6: Abundance differences due to different model assumptions for the abundance determination of Vega. Silicon non-LTE mean abundances, mean non-LTE corrections and deviations $(\Delta \log \epsilon)_{\rm d}$ from the result for the standard model.

model assumption	$\log \epsilon$	$\Delta \log \epsilon$	$(\Delta \log \epsilon)_{\rm d}$
standard model	$6.951 \pm 0.029$	-0.054
$\Delta\log \gamma_{\rm rad} = -1.0$	$6.952 \pm 0.029$	-0.054	0.001
$\Delta\log \gamma_{\rm rad} = +1.0$	$6.935 \pm 0.028$	-0.054	-0.016
$\Delta\log C_4=-0.5$	$7.014 \pm 0.017$	-0.062	+0.063
$\Delta\log C_4=+0.5$	$6.861 \pm 0.052$	-0.044	-0.090
no Stark broadening	$7.096 \pm 0.047$	-0.083	+0.145
$\Delta\log C_6=1.5$	$6.951 \pm 0.029$	-0.053	0.000
$\xi= 1.5\,{\rm km}\,{\rm s}^{-1}$	$7.179 \pm 0.077$	-0.089	+0.228

For a smaller microturbulence of $\xi= 1.5\,{\rm km}\,{\rm s}^{-1}$, the resulting non-LTE abundances increases by +0.228 dex. Unlike the Sun, van der Waals broadening is less important than Stark broadening, as expected for an A star. Completely neglecting the Stark broadening causes an abundance deviation of +0.119 dex from the standard model.
For comparison, Hill (1995) and Lemke (1990) obtained values of $\log \epsilon_{\rm Si} = 6.86$ and $\log \epsilon_{\rm Si} = 6.94$, respectively, which is in good agreement with the result of this work.
The abundance of silicon in Vega differs by -0.599 dex from the solar value, confirming the deficiency of Si found by other authors.