4 Analysis

We have performed a standard Local Thermodynamic Equilibrium (LTE) analysis, strictly differential with respect to the Sun, to derive chemical abundances from the measured values of $W_{\lambda }$. Spectrum synthesis was not employed in the present study.

4.1 Model atmospheres

To generate the model atmospheres we used the MARCS program, first described by Gustafsson et al. (1975). The program has been further developed and updated in order to handle the line blanketing of millions of absorption lines more accurately (Asplund et al. 1997). The following assumptions enter into the calculation of the models: the atmosphere is assumed to be plane-parallel and in hydrostatic equilibrium, the total flux (including mixing-length convection) is constant, the source function is described by the Planck function at the local temperature with a scattering term, the populations of different excitation levels and ionization stages are governed by LTE.

Since our analysis is strictly differential relative to the Sun, we have used a solar model atmosphere calculated with the same program as the stellar models - this in order to keep the analysis truly differential and thus in spite of the fact that the empirically derived Holweger-Müller model better reproduces the solar observed limb darkening (Blackwell et al. 1995).

4.2 Line data

Figure 2: Comparison of $\log gf$-values as derived in this study and in Neuforge-Verheecke & Magain (1997) study of $\alpha$ Cen A and B. Fe I lines are denoted by $\bullet$, Fe II by $\bullet$ and Ni I lines by $\diamond$

Since we did not have observations of the solar spectrum for all of the lines available in the stellar spectra, we measured solar line strengths in the Kurucz et al. (1984) Solar Flux Atlas. The spectrum from the Flux Atlas was first degraded by binnning and then convolved with a Gaussian profile to match the instrumental profile. To decide on the exact values of the convolution, we used three portions of a spectrum of reflected sunlight from Vesta. The Flux Atlas spectrum was convolved and then compared with the Vesta spectrum. The goodness of the fit was decided upon by inspection. The values of $W_{\lambda }$ for all our lines were measured in the degraded spectrum. They were then used to determine the astrophysical $\log gf$ values, Table 1.

We consider different line broadening mechanisms in our calculations; van der Waals damping, radiation damping, thermal Doppler broadening and broadening by microturbulence. The van der Waals broadening is calculated with the classical Unsöld formula. Enhancement factors to this value were compiled from the literature and are given in Table 1. For Fe we use values from Hannaford et al. (1992) and Holweger et al. (1991), for Ca, and for V from Neuforge (1992). For the remaining lines we use a value of 2.5, according to Mäckle et al. (1975). The values used for the enhancement factor do not, in general, influence the results, e.g. a change from 2.5 to 1.4 does not alter most abundances by more than 0.01 dex.

We have also compared our $\log gf$-values derived from the solar spectrum with those derived in a similar way, but using a Holweger-Müller solar model, by Neuforge-Verheecke & Magain (1997), Fig. 2. Our $\log gf$-values are 0.07 dex lower for Fe I lines and 0.04 dex lower for the Ni I lines than those derived by Neuforge-Verheecke & Magain (1997). Considering the different approaches to the derivation of the astrophysical $\log gf$-values we consider the agreement good. It is also reassuring that no trends are found either with wavelength or excitation potential, see Fig. 2.

4.2.1 Selection of lines

Selecting stellar lines which are free from blends is crucial for deriving accurate elemental abundances. To account for telluric lines we simply over-plotted each stellar spectrum with a spectrum of a hot star observed during the same night as the stellar spectrum was taken and discarded lines that were contaminated. To avoid blends from unidentified photospheric lines the solar spectrum was carefully inspected and the line-list by Moore consulted.

Care in the selection of lines is also of importance for the determination of surface gravities by means of ionization equilibrium (i.e., abundances derived from Fe I and Fe II lines give the same iron abundance). We have inspected the shape of the Fe II lines in all the stars when a line is observed in more than two stars. This inspection led us to discard the lines at 6386.72 and 7449.33 Å, Fig. 3. A line at 5823.15 Å was also discarded, although only measured in two stars, since it gave anomalously high iron abundances and clearly suffered from blends. The line at 6416.91 Å gave rather high iron abundances in HD 10780, HD 32147 and HD 145675. From our spectra we could not, however, conclude that this line is compromised by a blend (see Fig. 3) and it was therefore kept in the analysis, but only in those stars where it did not diverge significantly. Our final selection of lines, as well as the parameters used in the abundance analysis, are given in Table 1.

Figure 3: Two portions of the stellar spectra, showing the regions around the two Fe II lines at 6416.91 and 6432.68 Å. The spectra have been arbitrarily displaced in intensity and also along the x-axis to the laboratory wavelengths. The positions of the Fe II lines are marked with dotted lines. Note the different scales on the x-axes

4.3 Fundamental parameters of model atmospheres

In order to construct the stellar model atmospheres we need the effective temperature, surface gravity, metallicity and microturbulence for each star. These were all derived from the stellar spectra themselves.

Effective temperature

Initial estimates of effective temperatures for the stars were determined using the photometric calibrations by Alonso et al. (1996). These estimates were iterated until excitation energy equilibrium was achieved. The plots from which the final temperatures were derived are shown in Fig. 4, and the final adopted temperatures are given in Table 1.

 

 

Table 1: Stellar parameters for the program stars. Magnitudes, colours and parallaxes are from the Hipparcos catalogue (ESA 1997). The spectral types are from the SIMBAD database. Effective temperatures, surface gravities, [Fe/H] and microturbulence parameters as determined in this study

		Sp.T.	V	B-V	$\pi$	$\sigma_{\pi} (\sigma_{\pi}/\pi)$	$T_{\rm eff}$	log g	[Fe/H]	$\xi_{\rm t}$
					mas					km s$^{\rm -1}$
HD 10780	HR 511	K0V	5.63	0.804	100.24	0.68(0.007)	5300	4.13	-0.02	1.00
HD 32147	HR 1614	K3V	6.22	1.049	113.46	0.82(0.007)	4680	4.00	0.28	0.50
HD 99491	HR 4414A	K0IV	6.49	0.778	56.59	1.40(0.025)	5300	4.12	0.20	1.00
HD 104304	HR 4587	G9IV	5.54	0.760	77.48	0.80(0.01)	5400	4.12	0.16	1.15
HD 121370	HR 5235	G0IV	2.68	0.580	88.71	0.75(0.008)	6000	3.66	0.25	2.00
HD 145675		K0V	6.61	0.877	55.11	0.59(0.011)	5300	4.50	0.47	1.00
HD 182572	HR 7373	G8IV	5.17	0.761	66.01	0.77(0.012)	5400	4.00	0.35	1.10
HD 196755	HR 7896	G5IV+	5.07	0.702	33.27	0.82(0.02)	5700	4.00	0.02	1.50
$\alpha$ Cen A							5830	4.34	0.24	1.09
$\alpha$ Cen B							5225	4.51	0.23	1.00
1. $T_{\rm eff}$, $\log g$ and $\xi_{\rm t}$ from Neuforge-Verheeke & Magain (1997).

Figure 4: Excitation equilibrium. Fe I lines are denoted by $\bullet$, Fe II by $\bullet$ and Ni I lines by $\bigtriangleup$. [X/H] denote the abundance relative to solar as derived from Fe I, Fe II and Ni I lines, respectively. Note the different ranges on the y-axes

Surface gravity

Surface gravities were determined by requiring ionization equilibrium for Fe abundances derived from Fe I and Fe II lines. We adjusted $\log g$ until the iron abundance derived from Fe I and Fe II lines gave the same Fe abundance, compare Fig. 4.

Metallicity

Our first estimates were taken from Taylor (1996). The [Fe/H] were iterated until the metallicity used in constructing the atmosphere and the derived [Fe/H] agreed.

Microturbulence

The microturbulence parameter, $\xi_{\rm t}$, which is introduced to account for unknown line broadening mechanisms, affects strong and weak absorption lines differently. For weak lines only the shape, and not the $W_{\lambda }$ is affected, but for strong lines the line strength increases when $\xi_{\rm t}$ is increased. We use these trends to constrain the value of $\xi_{\rm t}$.

We started with $\xi_{\rm t} = 1.00$ kms^-1 and, after inspecting plots of [Fe/H] and [Ni/H] as a functions of $W_{\lambda}/\lambda$ (reduced equivalent width), varied the value of $\xi_{\rm t}$ until all lines, weak and strong, yielded the same abundance. The final values used in the abundance analysis are given in Table 1.

4.4 Comparison/verification with calibrationsof ${\mathsfsl u}{\mathsfsl v}{\mathsfsl b}{\mathsfsl y}-\beta$ photometry

As a further check of our final stellar parameters we have derived $T_{\rm eff}$, $\log g$, and [Fe/H] from the self-consistent calibration of $T_{\rm eff}$, $\log g$ and [Fe/H] by Olsen (1984), Table 2. The agreement is in general good.

   
4.5 Comparison with other studies

The stars in our study have been included in few, if any, abundance studies. However, HD 32147 and HD 182572 have been extensively studied. HD 32147 has been especially difficult to analyze, because it is a cool K dwarf star with strong lines. This is amply exemplified by the comparison of our $W_{\lambda }$ measurements and abundances with those of Feltzing & Gustafsson (1998). In Table 3 we compare our results to theirs. As expected (from the comparison of $W_{\lambda }$) the abundances for HD 32147 are larger in our study than in theirs. In this work we impose ionization equilibrium in order to derive the surface gravity of the star. This affects in particular the abundances derived from HD 32147, but also some of the species, i.e. Fe, Co and Ni, for HD 182572. For a discussion of stellar abundances in K dwarf stars, that for HD 32147 supersedes the current analysis, we refer the reader to Thorén & Feltzing (2000).

 

 

Table 2: Strömgren photometry and stellar parameters derived from the photometry thorough the calibration by Olsen (1984). References; O93 = Olsen (1993), O94a = Olsen (1994a), O94b = Olsen (1994b), GO = Gronbech & Olsen(1997)

ID	b-y	m1	c1	ref.	Olsen (1984)
					$T_{\rm eff}$	$\log g$
HD 10780	0.468	0.316	0.327	O93	5431	4.27
HD 32147	0.601	0.634	0.236	O94a	4614	4.57
HD 99491	0.484	0.335	0.362	O93	5347	4.12
HD 104304	0.469	0.313	0.345	O94a	5437	4.19
HD 121370	0.370	0.202	0.533	GO	6205	3.92
HD 145675	0.537	0.336	0.438	O93	4852	4.55
HD 182572	0.465	0.299	0.381	O93	5495	4.07
HD 196755	0.432	0.220	0.381	O94b	5642	3.98

 

 

Table 3: Comparison of results from this study with those of Feltzing & Gustafsson (1998), FG98, for HD 32147 and HD 182572

	HD 32147		HD 182572
	This work	FG98	This work	FG98
Al I	0.48	0.25	0.55	0.53
Si I	0.36	0.48	0.49	0.51
Ca I		0.01		0.42
Sc II	-	0.49	0.36	0.36
Ti I	0.66	0.11	0.32	0.50
V I	0.95	-0.18
Cr I	0.50	0.10	0.40	0.43
Fe I	0.28	0.22	0.34	0.42
Fe II	0.24	0.61	0.32	0.08
Co I	0.56	0.39	0.47	0.58
Ni I	0.29	0.57	0.36	0.46

Gonzalez et al. (1999) found HD 145675 (14 Her) to have [Fe/H] of $0.50\pm0.05$, using a spectrum with nearly twice the resolution as ours. Nevertheless, it is in good agreement with our 0.47 dex estimate with a line-to-line scatter of 0.11 dex derived using 30 lines.

For HD 104304 François (1988) found [Fe/H] = 0.16 and [S/H] = 0.59; our estimate of [Fe/H] = 0.17 is in excellent agreement. We derive an [S/H] value lower by 0.10 dex, but since our result is based on one fairly weak S I line, we consider this to be a good agreement.

Morell et al. (1992) derived Fe and Th abundances for a group of stars in order to estimate their ages. For HD 182572 and HD 196755 they derived [Fe/H] = +0.3 and +0.1 dex, respectively. This is in reasonable agreement with our results.

 

 

Table 4: Comparison for HD 121370 of results from this study with those of Edvardsson et al. (1993). The second line for Fe II give the iron abundance derived if the line at 6416.91 Å is excluded

	This work	Edv.93
Na I	0.50	0.45
Si I	0.40	0.31
Ca I		0.23
Ti I	0.22	0.32
Fe I	0.24	0.19
Fe II	0.19	0.25
	0.22
Ni I	0.31	0.30

Edvardsson et al. (1993) analyzed 189 dwarf and subgiant stars with [Fe/H] up to +0.25 dex, including HD 121370. The agreement between the two studies is very good, Table 4. Also, the stellar parameters agree well. These different comparisons give us confidence that our analysis is satisfactory.

   
4.5.1 $\alpha$ Cen A and B

As a final test of our analysis method and its compatibility with the analysis procedures adopted by other groups, we derived elemental abundances for the stars in the nearby triple system $\alpha$ Centauri from the equivalent widths published by Neuforge-Verheecke & Magain (1997). They observed the two stars (components A and B) with the CAT-telescope at La Silla with a resolution of 100000 and a final $S/N \sim$ 550 and derived stellar abundances as well as stellar parameters self-consistently from the spectra. Using their published equivalent widths as well as their $\log gf$ and damping parameters with our set of model atmospheres and programs, we derive almost the same abundances for all elements with lines that are not affected by hyperfine splitting, see Table 5. In fact for most of those elements taking the hyperfine structure in the line profile into account makes very little difference in the derived abundances. This is true in particular for Al.

 

 

Table 5: Comparison of abundances for $\alpha$ Cen A and B derived by Neuforge-Verheeke & Magain (1997) and in this work using their equivalent widths and models as described in Sect. 4.5.1

	$\alpha$Cen A			$\alpha$Cen B
El.	# lines	This work	NVM97	# lines	This work	NVM97
		${\rm [X/H]}\pm {\rm sc.}$	${\rm [X/H]}\pm {\rm error}$		${\rm [X/H]}\pm {\rm sc.}$	${\rm [X/H]}\pm {\rm error}$
O I	3	0.20 0.07	0.21 0.06
Al I	1	0.23 0.00	0.24 0.04	1	0.27 0.00	0.24 0.05
Si I	3	0.26 0.02	0.27 0.03	3	0.30 0.00	0.27 0.04
Ca I	5	0.21 0.05	0.22 0.03	5	0.23 0.05	0.21 0.05
Sc II	1	0.35 0.00	0.25 0.05	1	0.36 0.00	0.26 0.04
Ti I	15	0.22 0.04	0.25 0.03	13	0.26 0.07	0.27 0.06
V I	4	0.22 0.04	0.23 0.05	4	0.40 0.07	0.32 0.08
Cr I	11	0.20 0.03	0.24 0.02	12	0.25 0.03	0.27 0.04
Cr II	2	0.25 0.02	0.26 0.03	1	0.29 0.00	0.26 0.09
Fe I	69	0.24 0.06	0.25 0.02	65	0.23 0.05	0.24 0.03
Fe II	4	0.25 0.03	0.25 0.02	4	0.27 0.04	0.25 0.02
Co I	3	0.29 0.04	0.28 0.04	3	0.39 0.02	0.26 0.04
Ni I	26	0.29 0.05	0.30 0.03	25	0.31 0.06	0.30 0.02
Y II	1	0.36 0.00	0.20 0.05	1	0.30 0.00	0.14 0.05
Eu II	1	0.17 0.00	0.15 0.05	1	0.16 0.00	0.14 0.05

For the A component we derive in general abundances 0.01 dex less than Neuforge-Verheecke & Magain (1997) and for the B component 0.02-0.03 dex higher abundances, see Table 5. Iron is however 0.01 dex lower for the B component. We find this level of agreement satisfactory considering that we use model atmospheres of slightly different construction.