4 Analysis

We utilize the three-step analysis developed by and extensively discussed in Gummersbach et al. (1998) and Paper I. In short, log g is derived from the profile of H$\beta$, $T_{\rm eff}$ by balancing two adjacent ionization stages of silicon as a function of $\varepsilon$(Si) and $\xi$, with $\xi$ being concordantly determined between silicon and a set of oxygen lines. In all three steps, the metallicity of the underlying atmosphere (and with it the strength of the background opacities for the NLTE calculation) is varied in a self-consistent manner. This was shown to have a non-negligible effect on the abundances to be derived. In the simultaneous determination of $T_{\rm eff}$, log g, $\xi$, $\varepsilon$(Si) and $\varepsilon$(O) the average underabundance of Si and O is taken to be indicative of the overall metallicity [m/H]. Due to the [$\alpha$/Fe] ratio inherent to the MCs (see Sect. 5.2), this procedure results in slightly underestimated atmospheric metallicities. The residual discrepancy between [m/H] and [Fe/H] is, however, only of the order of 0.1dex. Thus this approach is clearly superior to assuming [m/Fe] to be solar, as it is still often found in the literature.

With regard to the NLTE line formation, new input physics was implemented in the model atoms for C, N and Mg. Here we only give a brief account of the expected reliability and refer the reader to the publications of Przybilla & Butler (2001) and Przybilla et al. (2001a,b).

We refer the reader to Paper I for an error analysis and references to the original publication of the other model atoms.

4.1 Carbon

With equivalent widths of 160$\pm$10 mÅ the strong C II feature at 4267Å (multiplet 6, cf. Fig. 3) is clearly visible in the spectra of our MS B stars (we don't have access to the two strong lines (multiplet 2) in the blue wing of H$\alpha$). While it became clear relatively early on (Hardorp & Scholz 1970) that this line yields artificially low carbon abundances in LTE, a reliable NLTE modelling was only achieved in the 1990s (Sigut 1996). Our model atom closely resembles that of Sigut and we follow Sigut's argumentation showing that the abundances derived with it are reliable to typically 0.2dex.

4.2 Nitrogen

The model atom has been extended to be applicable to early B-type stars. It includes the lowest 3 levels of N I, 77 of N II, the lowest 11 levels of N III and the ground state of N IV. Photoionization cross-sections and oscillator strengths in N III are adopted from the Opacity Project (Fernley, Hibbert, Kingston & Seaton; available only from the TOPBASE database at http://cdsweb.u-strasbg.fr/topbase.html) and electron collisions from $\bf R$-matrix calculations by Stafford et al. (1994).

The spectrum of nitrogen lines is far less pronounced than that of carbon. In fact, the strongest line at 3995Å has equivalent widths below 50 mÅ in our MS programme stars (cf. Fig. 3). In combination with projected rotation rates up to 70 km s^-1 a clear detection requires S/N ratios of around 100. The situation is less critical in stars which are more evolved and/or whose nitrogen abundance is higher, e.g. NGC 2004/B30 (125 mÅ) or NGC 1818/D1 (74 mÅ, cf. Fig. 4).

As far as the modelling is concerned, we note that the subordinate lines at 4621 and 4630Å yield abundances fully compatible with those derived from N II 3995. As in the case of carbon, these abundances are expected to be accurate to 0.2dex.

4.3 Magnesium

The only Mg line we have access to in the B-star temperature regime is the Mg II doublet at 4481Å (cf. Fig. 3). Departures from LTE are found to be $\simeq$-0.1dex, the absolute abundances have not changed in going from the old to the new model atom.

 

 

Table 3: Derived stellar parameters and abundances for the four programme stars plus NGC1818/D1 from Paper I. Solar System composition from Grevesse & Sauval (1998), LMC H II-region abundances from Garnett (1999). The customary notation $\varepsilon$(X):=log( $n_{X}/n_{\rm H}$)+12 is employed. Representative error estimates are assigned to the individual abundances determinations.

object	$T_{\rm eff}$	$\log g$	$\xi$	$v \sin i$	$\varepsilon$(He)	$\varepsilon$(C)	$\varepsilon$(N)	$\varepsilon$(O)	$\varepsilon$(Mg)	$\varepsilon$(Si)	$\varepsilon$(Fe)
	[K]		[km s-1]	[km s-1]							LTE
$\odot$					10.99	8.52	7.92	8.83	7.58	7.55	7.50
NGC2004/D15	22500	3.80	0	45	10.95	8.04	6.95	8.29	7.35	7.04	7.30
$\qquad \ \pm$	1000	0.20	2	10	0.2	0.2	0.2	0.2	0.2	0.2	0.3
NGC2004 /C16	24600	3.95	4	60	10.94	8.10	7.05	8.43	7.29	7.10	7.30
$\qquad \ \pm$	1000	0.20	2	10	0.2	0.2	0.2	0.2	0.2	0.2	0.3
NGC2004/D3	23900	4.15	1	70	11.00	8.15	7.05	8.40	7.43	7.20	7.35
$\qquad \ \pm$	1000	0.20	2	10	0.2	0.2	0.2	0.2	0.2	0.2	0.3
NGC2004/C9	24000	4.35	0	60	10.93	7.95	7.00	8.34	7.40	7.05	7.35
$\qquad \ \pm$	1000	0.20	2	10	0.2	0.2	0.2	0.2	0.2	0.2	0.3
$\bar{\varepsilon}{(X)}_{\rm 2004}$					10.96	8.06	7.01	8.37	7.37	7.10	7.33
$\qquad \ \pm \,\sqrt{\sum\frac{(x_i - \bar{x})^2}{n-1}}$					0.03	0.09	0.05	0.06	0.06	0.07	0.03
H II $_{\rm\,LMC}$					10.95	7.90	6.90	8.40	--	6.70	--
$\qquad \ \pm$					0.2	0.2	0.2	0.2	--	0.2	--
NGC1818/D1	24700	4.00	0	30	11.04	7.80	7.40	8.46	7.35	7.10	7.37
$\qquad \ \pm$	1000	0.20	2	10	0.2	0.2	0.2	0.2	0.2	0.2	0.3

Figure 2: The loci of the programme stars with respect to evolutionary tracks of non-rotating stars for Z=0.008 (Schaerer et al. 1993). Also shown are the two luminosity class III objects NGC2004/B30 and B15 from Paper I. No evolution of chemical elements is detected in comparing the MS stars, whereas B30 from Paper I is clearly enriched in nitrogen and depleted in carbon.

Figure 3: Profile fits for H (gravity determination), Si II/III/IV (temperature and microturbulence indicator), C II, N II, O II (microturbulence indicator) and Mg II. The observed noise level can fully account for the difference between theory and observation. Note that the He abundance is not based on He I 4121Å, since the observed profile seems to contain unidentified blend contributions other than from helium and oxygen.