A two-zone photoionized H II region has been assumed for abundance determination; the electron temperature $T_{\rm e}$ (O III) for the high-ionization region has been derived from the observed flux ratio [O III] $\lambda$ 4363/( $\lambda$ 4959+5007), using a five-level atom model (Aller 1984) with atomic data from Mendoza (1983). The electron temperature $T_{\rm e}$ (O II) for the low-ionization region has been derived using the empirical relation between $T_{\rm e}$ (O II) and $T_{\rm e}$ (O III) from the H II region photoionization models by Stasinska (1990). The [S II] $\lambda$ 6717/ $\lambda$ 6731 ratio was used to derive the electron number density $N_{\rm e}$ (S II).

The spectra were corrected for interstellar extinction, where the extinction coefficient C(H $\beta$ ) was derived from the hydrogen Balmer decrement using the equations given in Izotov et al. (1994) and the theoretical hydrogen emission line flux ratios from Brocklehurst (1971).

The emission line fluxes were measured using a Gaussian profile fitting. The errors of the line fluxes measurements include the errors in the fitting of profiles and those in the placement of the continuum. We also take into account the errors introduced by uncertainties in the spectral energy distributions of standard stars. Standard star flux deviations for both standard stars Feige 34 and HZ 44 are taken to be 1% (Oke 1990; Bohlin 1996). These errors have been propagated in the calculations of the element abundance errors. The observed (F( $\lambda$ )) and extinction-corrected (I( $\lambda$ )) emission line fluxes relative to the H $\beta$ emission line fluxes, the equivalent widths EW of the emission lines, the extinction coefficient C(H $\beta$ ), the observed flux of the H $\beta$ emission line, and the equivalent width of the hydrogen absorption lines for region a, derived from Keck II and MMT spectra with the slit position PA = -41 $^{\circ }$ are listed in Table 2. The derived extinction coefficient C(H $\beta$ ) is small.

**Table 2:** Observed (F( $\lambda$ )), extinction-corrected (I( $\lambda$ )) fluxes and equivalent widths (EW) of the emission lines in the spectra of the brightest H II region in SBS 0940+544.
	Keck II			MMT

$\lambda_{0}$ (Å) Ion	F( $\lambda$ )/F(H $\beta$ )	I( $\lambda$ )/I(H $\beta$ )	EW (Å)	F( $\lambda$ )/F(H $\beta$ )	I( $\lambda$ )/I(H $\beta$ )	EW (Å)
3727 [O II]	$0.445 \pm 0.007$	$0.471 \pm 0.008$	$62.0 \pm 0.3$	$0.585 \pm 0.008$	$0.587 \pm 0.008$	$62.7 \pm 0.7$
3750 H12	$0.013 \pm 0.001$	$0.022 \pm 0.002$	$1.9 \pm 0.2$	$0.022 \pm 0.003$	$0.023 \pm 0.004$	$2.5 \pm 0.3$
3771 H11	$0.023 \pm 0.001$	$0.032 \pm 0.002$	$3.3 \pm 0.2$	$0.044 \pm 0.003$	$0.045 \pm 0.005$	$4.9 \pm 0.4$
3798 H10	$0.042 \pm 0.001$	$0.052 \pm 0.002$	$6.1 \pm 0.2$	$0.059 \pm 0.004$	$0.060 \pm 0.005$	$6.7 \pm 0.5$
3820 [He I]	$0.017 \pm 0.001$	$0.018 \pm 0.001$	$2.5 \pm 0.3$	...	...	...
3835 H9	$0.058 \pm 0.001$	$0.069 \pm 0.002$	$8.6 \pm 0.2$	$0.064 \pm 0.004$	$0.065 \pm 0.005$	$7.4 \pm 0.4$
3868 [Ne III]	$0.340 \pm 0.005$	$0.356 \pm 0.006$	$49.6 \pm 0.3$	$0.373 \pm 0.006$	$0.374 \pm 0.006$	$44.0 \pm 0.7$
3889 H8 + He I	$0.184 \pm 0.003$	$0.201 \pm 0.004$	$26.9 \pm 0.3$	$0.204 \pm 0.005$	$0.205 \pm 0.006$	$25.1 \pm 0.6$
3968 [Ne III] + H7	$0.259 \pm 0.004$	$0.278 \pm 0.005$	$38.3 \pm 0.3$	$0.288 \pm 0.005$	$0.290 \pm 0.006$	$39.8 \pm 0.7$
4026 He I	$0.014 \pm 0.001$	$0.014 \pm 0.001$	$2.1 \pm 0.2$	$0.019 \pm 0.004$	$0.019 \pm 0.004$	$2.7 \pm 0.5$
4068 [S II]	$0.009 \pm 0.001$	$0.009 \pm 0.001$	$1.4 \pm 0.2$	$0.007 \pm 0.003$	$0.007 \pm 0.003$	$1.0 \pm 0.4$
4101 H $\delta$	$0.244 \pm 0.004$	$0.259 \pm 0.004$	$39.3 \pm 0.3$	$0.267 \pm 0.005$	$0.269 \pm 0.006$	$40.0 \pm 0.7$
4340 H $\gamma$	$0.461 \pm 0.007$	$0.477 \pm 0.007$	$84.9 \pm 0.4$	$0.487 \pm 0.007$	$0.488 \pm 0.007$	$86.9 \pm 1.0$
4363 [O III]	$0.125 \pm 0.002$	$0.128 \pm 0.002$	$23.2 \pm 0.3$	$0.142 \pm 0.004$	$0.142 \pm 0.004$	$27.0 \pm 0.7$
4388 He I	$0.003 \pm 0.001$	$0.003 \pm 0.001$	$0.6 \pm 0.2$	...	...	...
4471 He I	$0.036 \pm 0.001$	$0.037 \pm 0.001$	$7.4 \pm 0.2$	$0.039 \pm 0.003$	$0.039 \pm 0.003$	$7.3 \pm 0.6$
4658 [Fe III]	$0.005 \pm 0.001$	$0.005 \pm 0.001$	$1.2 \pm 0.3$	$0.003 \pm 0.002$	$0.003 \pm 0.002$	$0.7 \pm 0.5$
4686 He II	$0.006 \pm 0.001$	$0.006 \pm 0.001$	$1.3 \pm 0.3$	...	...	...
4711 [Ar IV]+He I	$0.022 \pm 0.001$	$0.022 \pm 0.001$	$5.2 \pm 0.3$	$0.020 \pm 0.002$	$0.020 \pm 0.002$	$4.6 \pm 0.5$
4740 [Ar IV]	$0.013 \pm 0.001$	$0.013 \pm 0.001$	$3.0 \pm 0.2$	$0.012 \pm 0.003$	$0.012 \pm 0.003$	$2.9 \pm 0.6$
4861 H $\beta$	$1.000 \pm 0.015$	$1.000 \pm 0.015$	$241.1 \pm 0.8$	$1.000 \pm 0.011$	$1.000 \pm 0.011$	$250.1 \pm 1.9$
4922 He I	$0.010 \pm 0.001$	$0.010 \pm 0.001$	$2.4 \pm 0.3$	$0.010 \pm 0.002$	$0.010 \pm 0.002$	$2.6 \pm 0.6$
4959 [O III]	$1.415 \pm 0.021$	$1.402 \pm 0.021$	$348.8 \pm 1.0$	$1.436 \pm 0.014$	$1.435 \pm 0.014$	$381.3 \pm 2.3$
5007 [O III]	$4.251 \pm 0.061$	$4.204 \pm 0.061$	$1052.0 \pm 1.7$	$4.218 \pm 0.034$	$4.215 \pm 0.034$	$1154.2 \pm 3.9$
5199 [N I]	$0.003 \pm 0.001$	$0.003 \pm 0.001$	$0.9 \pm 0.2$	...	...	...
5271 [Fe III]	$0.004 \pm 0.001$	$0.004 \pm 0.001$	$1.2 \pm 0.3$	...	...	...
5876 He I	$0.102 \pm 0.002$	$0.097 \pm 0.002$	$39.0 \pm 0.5$	$0.097 \pm 0.003$	$0.097 \pm 0.003$	$39.2 \pm 1.1$
6300 [O I]	$0.011 \pm 0.001$	$0.010 \pm 0.001$	$4.9 \pm 0.4$	$0.007 \pm 0.002$	$0.007 \pm 0.002$	$3.4 \pm 0.7$
6312 [S III]	$0.012 \pm 0.001$	$0.011 \pm 0.001$	$5.3 \pm 0.3$	$0.010 \pm 0.002$	$0.010 \pm 0.002$	$4.7 \pm 0.9$
6363 [O I]	$0.004 \pm 0.001$	$0.004 \pm 0.001$	$1.9 \pm 0.3$	...	...	...
6563 H $\alpha$	$2.946 \pm 0.043$	$2.750 \pm 0.043$	$1409.0 \pm 2.5$	$2.761 \pm 0.024$	$2.733 \pm 0.025$	$1438.9 \pm 6.0$
6584 [N II]	$0.013 \pm 0.001$	$0.012 \pm 0.001$	$3.9 \pm 0.3$	$0.016 \pm 0.002$	$0.016 \pm 0.002$	$8.6 \pm 1.1$
6678 He I	$0.029 \pm 0.001$	$0.027 \pm 0.001$	$14.9 \pm 0.5$	$0.027 \pm 0.002$	$0.027 \pm 0.002$	$14.3 \pm 1.0$
6717 [S II]	$0.038 \pm 0.001$	$0.035 \pm 0.001$	$19.2 \pm 0.4$	$0.038 \pm 0.002$	$0.038 \pm 0.002$	$20.9 \pm 1.3$
6731 [S II]	$0.030 \pm 0.001$	$0.028 \pm 0.001$	$15.3 \pm 0.4$	$0.026 \pm 0.002$	$0.026 \pm 0.002$	$14.7 \pm 1.1$
7065 He I	$0.026 \pm 0.001$	$0.024 \pm 0.001$	$14.7 \pm 0.4$	$0.032 \pm 0.002$	$0.032 \pm 0.002$	$19.8 \pm 1.2$
7136 [Ar III]	$0.028 \pm 0.001$	$0.026 \pm 0.001$	$16.5 \pm 0.5$	$0.029 \pm 0.002$	$0.029 \pm 0.002$	$17.9 \pm 1.2$
7320 [O II]	$0.007 \pm 0.001$	$0.007 \pm 0.001$	$4.6 \pm 0.6$	...	...	...
7330 [O II]	$0.007 \pm 0.001$	$0.006 \pm 0.001$	$4.1 \pm 0.4$	...	...	...

C(H $\beta$ ) dex	$0.085 \pm 0.019$			$0.005 \pm 0.011$
F(H $\beta$ )^a	$1.21 \pm 0.01$			$1.22 \pm 0.01$
EW(abs) Å	$1.1 \pm 0.1$			$0.1 \pm 0.3$

^a In units 10^-14 erg s^-1 cm^-2.

The ionic abundances of O⁺², Ne⁺², Ar⁺³, He⁺ and He⁺² were obtained using the electron temperature $T_{\rm e}$ (Oiii). The electron temperature $T_{\rm e}$ (Oii) is adopted to calculate the O⁺, N⁺, S⁺ and Fe⁺² ionic abundances, while the intermediate value of the electron temperature $T_{\rm e}$ (Siii) was used to derive the ionic abundances of Ar⁺² and S⁺² (Garnett 1992).

The total heavy element abundances were obtained using ionization correction factors (ICF) following Izotov et al. (1994, 1997c) and Thuan et al. (1995). For oxygen the total abundance is the sum of O⁺, O⁺² and O⁺³ ion abundances. Although emission lines of O⁺³ are absent in the optical spectrum, this ion resides in the He⁺² region. Therefore, we derive the O⁺³ ion abundance using the He II $\lambda$ 4686 Å emission line intensity as described by Izotov & Thuan (1999). The ionic and heavy element abundances for the brightest Hii region in SBS 0940+544 together with electron temperatures and electron number densities are given in Table 3 along with the adopted ionization correction factors.

The oxygen abundance derived from the Keck II and MMT spectra are 12 + log(O/H) = 7.50 $\pm$ 0.01 and 7.46 $\pm$ 0.02 respectively. For comparison, Izotov et al. (1991) derived 12 + log(O/H) = 7.52 $\pm$ 0.12, while Izotov et al. (1994) obtained 12 + log(O/H) = 7.37 $\pm$ 0.02. The former value was calculated using a three-level atom model. If the five-level atom model is adopted instead then the oxygen abundance is decreased by $\sim$ 0.04 dex (Izotov & Thuan 1999). The latter value is significantly lower than the previous ones. However, Izotov & Thuan (1998b) noted that Izotov et al. (1994) used an erroneously low [O III] $\lambda$ 5007 emission line intensity. They rederived the oxygen abundance using the data of Izotov et al. (1994) and found 12 + log(O/H) = 7.43 $\pm$ 0.01. Thus, all 12 + log (O/H) values are confined in the narrow range 7.43-7.50, or $Z_\odot$ /31- $Z_\odot$ /26.

The ratios of other heavy element abundances to the oxygen abundance derived from the Keck II and MMT observations (Table 3) are mutually consistent and they are also in agreement with the heavy element abundance ratios derived earlier in SBS 0940+544 and in other low-metallicity BCDs (Izotov & Thuan 1999).

The very low metallicity of SBS 0940+544 and the presence of very strong emission lines in its spectrum makes it one of the best galaxies for the determination of the primordial helium abundance. For this, we use the five strongest He I $\lambda$ 3889, $\lambda$ 4471, $\lambda$ 5876, $\lambda$ 6678 and $\lambda$ 7065 emission lines in both Keck II and MMT spectra. The first and last He I emission lines are more sensitive to collisional and fluorescent enhancement mechanisms. They are used to correct other He I emission lines for these effects (Izotov et al. 1994, 1997c). The helium abundance is derived from the corrected intensities of the He I $\lambda$ 4471, $\lambda$ 5876, $\lambda$ 6678 emission lines and is shown in Table 3. The mean values of the ⁴He mass fraction Y = 0.247 $\pm$ 0.003 (Keck II) and $Y = 0.244 \pm 0.006$ (MMT) (see Table 3) are consistent with the previously derived value Y = 0.247 $\pm$ 0.007 (Izotov & Thuan 1998b) and they are close to the primordial ⁴He mass fraction $Y_{\rm p}$ = 0.244 $\pm$ 0.002 derived by extrapolating the Y vs. O/H linear regression to O/H = 0 (Izotov & Thuan 1998b), or to $Y_{\rm p}$ = 0.245 $\pm$ 0.002 derived in the two most metal-deficient BCDs I Zw 18 and SBS 0335-052 (Izotov et al. 1999).

It was pointed out in Sect. 2.2 that atmospheric dispersion may introduce some uncertainties in the abundance determination. To estimate these uncertainties we measure the fluxes of the [O II] $\lambda$ 3727 and [O III] $\lambda$ 4363 emission lines in an aperture 1 $^{\prime \prime }$ $\times$ 1 $^{\prime \prime }$ placed on the maximum in the flux distribution, and those in an aperture with the same size but displaced along the slit by 0 $.\!\!^{\prime\prime}$ 4 and 0 $.\!\!^{\prime\prime}$ 1 respectively for the [O II] and [O III] lines. We obtain relative flux differences of $\sim$ 7% and $\sim$ 1% for the [O II] and [O III] emission lines. The effect of the atmospheric dispersion results in an uncertainty not exceeding 1% of the total oxygen abundance, because oxygen in the H II region is mainly O⁺² (see Table 3). However, because the H II region is much more extended than the size of the aperture used for analysis of the atmospheric dispersion, and of the large apertures used in the extraction of spectra for the abundance analysis, the effect of atmospheric dispersion is expected to be smaller for the [O II] $\lambda$ 3727 emission line and negligible compared to the statistical errors for the [O III] $\lambda$ 4363 emission line. Therefore, we decided not to include it in the error budget.

**Table 3:** Physical conditions and element abundances in the brightest H II region of SBS 0940+544.
Value	Keck II	MMT
$T_{\rm e}$ (O III)(K)	$18\,830 \pm 220$	$20\,000 \pm 370$
$T_{\rm e}$ (O II)(K)	$15\,320 \pm 170$	$15\,690 \pm 260$
$T_{\rm e}$ (S III)(K)	$17\,330 \pm 190$	$18\,300 \pm 300$
$N_{\rm e}$ (S II)(cm^-3)	$170 \pm 60$	$10 \pm 10$
$N_{\rm e}$ (He II)(cm^-3)	$10 \pm 10$	$60 \pm 10$
$\tau$ ( $\lambda$ 3889)	0.0	$0.5 \pm 0.3$

O⁺/H⁺( $\times$ 10⁵)	$0.389 \pm 0.013$	$0.447 \pm 0.020$
O⁺²/H⁺( $\times$ 10⁵)	$2.727 \pm 0.081$	$2.438 \pm 0.102$
O⁺³/H⁺( $\times$ 10⁶)	$0.201 \pm 0.033$	...
O/H( $\times$ 10⁵)	$3.137 \pm 0.082$	$2.885 \pm 0.116$
12 + log(O/H)	$7.497 \pm 0.011$	$7.460 \pm 0.018$

N⁺/H⁺( $\times$ 10⁷)	$0.874 \pm 0.034$	$1.115 \pm 0.112$
ICF(N)^a	8.05	6.46
log(N/O)	$-1.649 \pm 0.021$	$-1.603 \pm 0.048$

Ne⁺²/H⁺( $\times$ 10⁵)	$0.476 \pm 0.015$	$0.436 \pm 0.020$
ICF(Ne)^a	1.15	1.18
log(Ne/O)	$-0.758 \pm 0.018$	$-0.748 \pm 0.028$

S⁺/H⁺( $\times$ 10⁷)	$0.608 \pm 0.015$	$0.583 \pm 0.031$
S⁺²/H⁺( $\times$ 10⁷)	$3.643 \pm 0.213$	$2.794 \pm 0.516$
ICF(S)^a	2.10	1.83
log(S/O)	$-1.546 \pm 0.025$	$-1.670 \pm 0.069$

Ar⁺²/H⁺( $\times$ 10⁷)	$0.744 \pm 0.021$	$0.751 \pm 0.050$
Ar⁺³/H⁺( $\times$ 10⁷)	$1.124 \pm 0.069$	$0.959 \pm 0.205$
ICF(Ar)^a	1.01	1.02
log(Ar/O)	$-2.219 \pm 0.020$	$-2.219 \pm 0.059$

Fe⁺²/H⁺( $\times$ 10⁷)	$0.934 \pm 0.212$	$0.547 \pm 0.384$
ICF(Fe)^a	10.1	8.07
log(Fe/O)	$-1.537 \pm 0.099$	$-1.815 \pm 0.313$
[O/Fe]	$0.103 \pm 0.099$	$0.395 \pm 0.313$

He⁺/H⁺( $\lambda$ 4471)	$0.0801 \pm 0.0023$	$0.0829 \pm 0.0066$
He⁺/H⁺( $\lambda$ 5876)	$0.0821 \pm 0.0015$	$0.0805 \pm 0.0024$
He⁺/H⁺( $\lambda$ 6678)	$0.0813 \pm 0.0023$	$0.0804 \pm 0.0055$
He⁺/H⁺(mean)	$0.0815 \pm 0.0011$	$0.0807 \pm 0.0021$
He⁺²/H⁺( $\lambda$ 4686)	$0.0005 \pm 0.0001$	...
He/H	$0.0820 \pm 0.0011$	$0.0807 \pm 0.0021$
Y	$0.2468 \pm 0.0034$	$0.2439 \pm 0.0066$

^a ICF is the ionization correction factor.

4 Chemical abundances