QUANTITATIVE SPECTROSCOPY OF BLUE SUPERGIANTS IN METAL-POOR DWARF GALAXY NGC 3109

The model atmosphere grid used in this study contains LTE line-blanketed atmospheres with the detailed non-LTE line formation calculations of Przybilla et al. (2006), as discussed in Kudritzki et al. (2008). The grid contains temperatures from 7900–15,000 K (spaced at increments of 250 K from 7900–10,000 K and 500 K from 10,000–15,000 K) and gravities between log g = 0.8 and 3.0 (cgs, spaced at increments of 0.05 dex), where the lowest log g value at each T_eff is established by the Eddington limit. Metallicities are calculated relative to solar abundance for the following values of [Z] = log (Z/Z_☉): −1.30, −1.15, −1.00, −0.85, −0.70, −0.60, −0.50, −0.30, −0.15, 0.00, 0.15, 0.30, and 0.50 dex. For each grid point, a microturbulence velocity v_t is adopted based on the observed relationship between v_t and log g found in high-resolution studies of A-type BSGs in the Milky Way (Przybilla 2002; Przybilla et al. 2006; Firnstein & Przybilla 2012; Venn 1995a, 1995b; Venn et al. 2000, 2001, 2003; Kaufer et al. 2004). Figure 1 of Kudritzki et al. (2008) shows the distribution of the model atmosphere points in the (T_eff, log g) plane together with the information about the microturbulence velocities used.

Our original model grid assumes that He abundance increases slowly with metallicity (see Table 2) as indicated by H ii regions and nucleosynthesis studies (e.g., Peimbert & Torres-Peimbert 1974; Pagel et al. 1992). While these values reflect the average He abundances of the young stellar populations examined in these studies well, detailed high-resolution studies of late-B- and early-A-type BSGs in the Small Magellanic Cloud (SMC; Schiller 2010) and the Milky Way (Firnstein & Przybilla 2012) reveal that many objects have He abundances higher than those predicted for their metallicities. This He enhancement is usually accompanied by a strong increase of nitrogen and a depletion of carbon that is interpreted as the result of rotationally induced mixing during the advanced stages of stellar evolution. The grid takes this additional enrichment effect into account. We adopt a He abundance of y = (n_He/n_H + n_He) = 0.12 at solar metallicity, as is found for main sequence B stars in the solar neighborhood (Nieva & Przybilla 2012). This value is supported by Firnstein & Przybilla (2012), who find He abundances between y = 0.11 and 0.13 for nearly all of the 35 A- and B-type supergiants they studied.

However, the situation is somewhat more ambiguous at the lower metallicity of the SMC. Of the 31 objects studied by Schiller (2010), 18 have a helium abundance between y = 0.08 and 0.10, which is why we adopt y = 0.09 close to SMC metallicity. However, the remaining 13 objects have higher helium abundances, mostly between y = 0.11 and 0.13. Because the He lines are an important part of our analysis (at least for the hotter objects), the assumptions about the He abundance could affect our results. To test this, we create a second model atmosphere grid identical to the first but with a constant enhanced He abundance y = 0.13 for each metallicity and move forward in our analysis using both grids independently. In this way, we can assess the influence of the adopted helium abundance on the determination of effective temperature and metallicity in the anticipated low-metallicity regime of NGC 3109. As shown below, the effects turn out to be small.

Following Kudritzki et al. (2008, 2012), the first step in our analysis is to use the Balmer lines to constrain the possible values of log g for each object. The low-resolution profiles and equivalent widths of the Balmer lines depend primarily on effective temperature and gravity, and can be fitted equally well by models with low temperature and low gravity as well as high temperature and high gravity. This establishes a Balmer line fit isocontour in the (T_eff, log g) plane along which the observed profile and equivalent width agrees with the models (see Figure 5 and 8 of Kudritzki et al. 2008, or Figure 4 of Kudritzki et al. 2012). We evaluate multiple Balmer lines (H5, H6, H8, H9, and H10) to determine the gravity and assess accuracy. H4 is not used since it is usually contaminated by emission from stellar winds and surrounding H ii regions, which can also affect H5 in extreme cases. H7 is frequently blended with interstellar Ca ii absorption and therefore is not used in the analysis, as well. In cases where the H4 or even H5 fits indicate lower gravities than the remaining higher Balmer lines, we attribute this to the effects of winds or H ii emission and rely instead on the higher Balmer lines. The log g fit is typically good to ∼0.05–0.1 dex at fixed T_eff (Figure 2 and Figures 17 and 18 in the Appendix). Since T_eff is not yet determined, the final value of the gravity is still unknown. However, the resulting Balmer line fit isocontour in the (T_eff, log g) plane restricts the log g parameter space, greatly reducing the number of models to evaluate when determining T_eff and [Z].

With the gravities constrained, we use a χ² analysis with the model atmosphere grid to simultaneously fit T_eff and [Z] for our objects. We define a set of spectral windows for the late-B and early-A BSGs which are free of Balmer lines, nebular/interstellar contamination, and can be easily matched to the synthetic spectra (Table 3). These windows contain lines of various metal species (Fe i/II, Ti ii, Cr ii, Mg ii, etc) and He i (typically only present for the hotter late-B type objects). Each spectral window is inspected and boundaries adjusted to avoid cosmic rays and other spectral defects which could affect the analysis. To accurately determine the continuum level of the windows, we define a region near each boundary that is free of spectral lines and take the median value as the continuum for that edge. A discrepancy between the boundary continuum levels is likely caused by a residual spectral slope after the flux-normalization, and is fit to first order by linear interpolation. We find these discrepancies to be small, if present at all.

With the spectral windows and continuum levels defined, we do a wavelength point-by-wavelength point comparison between the observed and model spectrum (with the model resolution degraded to match that of the observed spectrum) and calculate the χ² statistic for each spectral window:

$$\begin{equation} \chi ^{2}(T_{{\rm eff}}, [Z]) = \sum _{j=1}^{n_{w}} \frac{\left(F_j^{{\rm obs}} - F_j^{{\rm model}}\right)^2}{\sigma ^2_s}, \end{equation} \tag{ 1 }$$

$$\begin{equation*} \sigma _s = \frac{1}{({\rm S/N})_s}\quad\ \ \ \end{equation*}$$

where n_w is the number of wavelength points for a given window, (S/N)_s is the average signal-to-noise ratio across the spectrum, and $F_{j}^{{\rm obs}}$ and $F_{j}^{{\rm model}}$ are the normalized fluxes of the observed and model spectrum, respectively. We produce a grid of χ² values for each spectral window across the full range of possible temperature and metallicity models, with the log g of each model constrained by the Balmer fit. These individual windows show the temperature–metallicity degeneracy (Figure 3, top). However, the 1σ isocontours of different windows cover different regions of the (T_eff, [Z]) plane (Figure 3, middle). By adding the χ² values of the individual windows at each grid point, we combine this information to break the temperature–metallicity degeneracy. The He lines are especially valuable in this regard as their individual degeneracies are nearly perpendicular to those of the metal lines. All windows free of spectral defects are included in this analysis regardless of the position of their contours in the (T_eff, [Z]) plane, including those that do not appear to coincide with the other windows. This is done to safeguard against bias and to provide a conservative error estimate on the final stellar parameters. The overall T_eff and [Z] of the object can then be found from the minimum in the combined χ² grid (Figure 3, bottom). To accurately determine the minimum and plot the surrounding Δχ² isocontours (see below), we carry out a careful parabolic interpolation of the χ² values at the model atmosphere grid points to a significantly finer grid. As discussed above, we do this in parallel for both the normal He abundance and enhanced He abundance models.

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To verify our method and to assess the χ² uncertainties for our derived parameters, we analyze synthetic spectra with typical parameters for late-B and early-A BSGs (late-B: T_eff = 11,500 K, log g = 1.75, [Z] = −0.7; early-A: T_eff = 8750 K, log g = 1.05, [Z] = −0.7). We generate two sets of 1000 individual spectra for both types, adding Gaussian Monte Carlo noise to simulate S/N = 50 for one set and S/N = 100 for the other, and degrade the resolution to match that of our observed spectra. For each set, we run the individual spectra through our analysis, calculating a combined χ² grid for each and determining the location of the minimum in the (T_eff, [Z]) plane. We also calculate a mean χ² grid by averaging the 1000 individual χ² grids and determine the location of the corresponding minimum $\overline{\chi ^2_{{\rm min}}}$. We then calculate [$\overline{\chi ^2_{{\rm min}}}$ + Δχ²] isocontours and identify the isocontours that encompass 68% and 95% of the 1000 individual minimum locations (Figure 4). In this way we establish the 1σ and 2σ χ²-fit uncertainties of our results (Press et al. 2007). We find that Δχ² = 3.0 corresponds to a conservative estimate of the 1σ uncertainty. This is slightly higher than predicted by χ² theory (Δχ² = 2.3 when fitting two parameters), but this can be explained by uncertainties in the calculated spectral S/N and the fact that an average value is adopted over the entire spectral range, which affects the χ² calculation (see Equation (1)). We also find that the Δχ² -value is independent of the number of wavelength points and S/N, also in agreement with χ²-theory (Press et al. 2007). The Δχ² = 3.0 isocontour is then used to assess the 1σ uncertainty in the stellar parameters of the observed spectra by taking the maximum and minimum parameter values within the isocontour. See Figure 19 in the Appendix for the Δχ² isocontours of the stars not presented in Figure 3.

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The simulations show that our $\chi ^2_{{\rm min}}$-finding routine works well in recovering the parameters of both late-B- and early-A-type objects. The temperature-metallicity degeneracy for the late-B stars is broken completely, since these stars are hot enough for the He i lines to provide meaningful constraints. These lines are weak in the spectra of the cooler early-A stars, which as a result suffer from a partial degeneracy even after the combination of the spectral windows. This manifests itself as an elongated minimum "valley" in the combined χ² grid (see Figure 3 and the Appendix).

There are several additional sources of error which must be taken into account for the derived stellar parameters. The effect of uncertainty in the continuum level is evaluated by performing a χ² analysis using the highest and lowest possible values for each continuum region, calculated from the standard error of the median, and comparing the resulting stellar parameters to those determined in the original analysis. This uncertainty mainly affects [Z], and is added in quadrature with the 1σ errors from the original χ² fit to produce the final uncertainties reported. The total uncertainty in log g is determined by combining the inherent uncertainty of the Balmer line fit with the change in the final log g value caused by adopting the 1σ maximum and minimum T_eff values, which changes the log g value according to the Balmer equivalent width isocontour.

Two measures of stellar mass can be calculated from the stellar luminosity: a spectroscopic mass (M_spec) using the stellar radius and gravity derived from the spectrum, and an evolutionary mass (M_evol) using the BSG mass–luminosity relationship derived by Kudritzki et al. (2008) from evolutionary tracks with SMC metallicity (for the determination and discussion of metallicity, see the following subsection and subsection 4.3.2). A comparison of these masses provides an additional test of our results, identifying stars perhaps affected by binary star or blue loop evolution (e.g., Kudritzki et al. 2008; U et al. 2009), and, in our case, a confirmation of the parameters for early-A stars still affected by a weak temperature–metallicity degeneracy. It also offers a method of examining the systematics between evolutionary tracks and model atmospheres. Past studies have found that the spectroscopic masses of massive stars are often systematically lower than their evolutionary masses (e.g., Herrero et al. 1992), though recent studies with improved model atmospheres have shown that this effect has been significantly reduced (Kudritzki et al. 2008; Urbaneja et al. 2008; U et al. 2009; Kudritzki et al. 2012).

The absolute bolometric magnitudes, luminosities, radii, and spectroscopic/evolutionary masses calculated for each object are presented in Table 8. The spectroscopic masses are more uncertain than the evolutionary masses because they incorporate uncertainties in both T_eff and log g, though the evolutionary masses are prone to systematic errors in the evolutionary

tracks. A comparison of the masses shows that while M_spec is typically ∼0.05 dex lower than M_evol, they generally agree within uncertainties (Figure 9). No clear trend is found between the mass discrepancy and luminosity, and no obvious outliers exist. This indicates that single star evolution can explain the objects well and that additional mass-loss processes caused by blue-loop evolution back from the red supergiant branch or binary mass exchange are not important. This is in good agreement with the previous studies of BSGs analyzed using this grid of model atmospheres and serves as an affirmation of our derived stellar parameters.

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Kudritzki et al. (2008) showed that individual BSGs can be used as reliable metallicity indicators within galaxies based on the many metal lines in their spectra, which vary strongly as a function of metallicity (see their Figure 11). The reliability of this method was further demonstrated by Bresolin et al. (2009), who found the BSG metallicities and subsequent abundance gradient derived for NGC 300 by Kudritzki et al. (2008) to be highly consistent with those determined from H ii regions via direct measurement using auroral lines. Moreover, they found that applying several strong-line calibrations to their H ii region sample produced significantly different metallicities, emphasizing the importance of BSGs when studying galaxy metallicities where auroral line measurements are not possible.

We determine an average metallicity for NGC 3109 from the weighted average of the metallicities of our late-B- and early-A-type objects:

$$\begin{equation} [\bar{Z}] = \frac{\sum _{i = 1}^{n_{s}}w_i [Z]_i}{\sum _{j = 1}^{n_{s}}w_j}, \end{equation} \tag{ 2 }$$

$$\begin{equation*} w_i = \frac{1}{\sigma ^2_i}\qquad\quad\ \ \end{equation*}$$

where n_s is the number of late-B and early-A stars in our sample while [Z]_i and σ_i are the metallicity and uncertainty in metallicity for a given star, respectively. The choice of He abundance has a small effect on this result due to the shift in metallicity for the late-B stars, which is driven by a slight change in T_eff. Because the strength of the He i lines increases with both T_eff and He abundance, the enhanced He model fits have slightly lower temperatures than the normal He abundance model fits. Since the metal line strengths increase with decreased temperature, lower metallicities can be used to fit the observed metal lines, and thus the enhanced He abundance models have lower metallicities than the normal He abundance models. This effect is not seen with the early-A stars since they do not have strong He i lines. If the normal He abundance models are used then we find $[\bar{Z}]$ = −0.63 ± 0.13, while if the enhanced He abundance models are used we find $[\bar{Z}]$ = −0.71 ± 0.14. The uncertainty on these values are calculated from the standard deviation of the sample. In both He abundance cases, all but two of the late-B and early-A stars (stars 5 and 25) agree with the associated average metallicity to within one sigma of their error. Interestingly, both of these average metallicities are greater than one sigma above than the value of $[\bar{Z}]$ = −0.93 ± 0.07 found by E07 from the early-B objects (Figure 10) and supported by H ii region studies (Lee et al. 2003a, 2003b; Peña et al. 2007). It is important to note that our metallicity is derived from Fe-group elements, while the E07 result is derived from the oxygen. We discuss this discrepancy in Section 4.3.2. Moving forward, we adopt a final metallicity of $[\bar{Z}]$ = −0.67 ± 0.13 for NGC 3109, the average of the normal and enhanced He abundance metallicities.

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Given that our late-B and early-A objects are fairly spread out along the galactic disk, we can use our results to test for a metallicity gradient in NGC 3109. The presence of such a gradient would indicate a changing star formation history with galactocentric distance, as commonly found in spiral galaxies (see references in Section 1). Past spectroscopic studies of BSGs have been used to investigate metallicity gradients in NGC 300 (Kudritzki et al. 2008), M33 (U et al. 2009), M81 (Kudritzki et al. 2012), and NGC 55 (Castro et al. 2012). We adopt the positional parameters of Jobin & Carignan (1990, Table 9) to calculate the de-projected galactocentric distance of each star. These distances should be treated cautiously, as the high inclination angle of NGC 3109 makes such calculations uncertain. Even so, we do not find evidence of a significant abundance gradient in NGC 3109 in either the normal or enhanced He abundance case (Figure 10). This is consistent with the low dispersion in oxygen abundances found in early-B BSGs and H ii regions (Evans et al. 2007; Peña et al. 2007) and indicates that NGC 3109 is fairly homogenous in terms of metallicity and star formation history.

Because of the systematic uncertainties affecting galaxy metallicities determined using strong-line measurements of H ii regions, Kudritzki et al. (2012) compiled a new galaxy mass–metallicity relation only using objects whose metallicities have been derived through quantitative spectroscopy of BSGs. While currently containing only 12 galaxies (Table 10), efforts are underway to expand this sample in order to test existing strong-line calibrations and their subsequent relations. In addition, the dwarf galaxies studied are an important probe of the low-mass regime of the mass–metallicity relation, which is important for our understanding of galaxy formation and evolution (Lee et al. 2006). NGC 3109 is one of these dwarf galaxies, and we adjust its position based on the average metallicities found in our study (Figure 15). Our result appears to be in better agreement than E07's result with the others in the sample, although the BSG-derived relation is still too sparse to make a definitive assessment at this point.

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Following Kudritzki et al. (2012), we compare the BSG-based galaxy mass–metallicity relation to those derived using H ii regions of star-forming galaxies in Sloan Digital Sky Survey (SDSS; Figure 15). We include the 10 mass–metallicity relations from Kewley & Ellison (2008), each one employing a different strong-line calibration on the same set of ∼25,000 galaxy spectra. The result is 10 distinctly different relations (demonstrating the uncertainties surrounding the calibrations), several of which are clearly discrepant with the BSG results. We also include the recent SDSS mass–metallicity relation presented by Andrews & Martini (2013), which has two major advantages: (1) galaxy metallicities are measured directly using auroral lines, eliminating the need for strong-line calibrations; and (2) the relation extends down to galaxy masses of log (M/M_☉) = 7.4, equivalent to the lowest mass galaxies studied using BSGs and significantly beyond the lower limits of the Kewley & Ellison (2008) relations. The authors achieve this by stacking spectra of galaxies with similar masses in order to obtain the S/N required to measure the faint auroral lines, creating an average spectrum for each mass bin from which metallicity can be directly measured. The Andrews & Martini (2013) relation appears to be qualitatively similar to that of the BSGs, though their metallicities appear to be systematically higher than ours. There could be several explanations for this, such as small-sample statistics in the BSG sample and differences in how the galaxy masses are determined. Clearly this requires further investigation.

The average metallicity of our late-B and early-A sample ($[\bar{Z}]$ = −0.67 ± 0.13) is notably higher than the metallicity found from early-B BSGs by E07 ($[\bar{Z}]$ = −0.93 ± 0.07). This seems to indicate a systematic difference between the two samples. The metallicities in our study are derived from different elements than in E07; we derive our metallicities primarily from Fe-group elements, such as Cr and Fe, and assuming a solar abundance pattern, while E07 derive their metallicities mostly from a set of isolated O lines (also one Mg and a few Si lines). The discrepancy between these results would seem to suggest that the Fe-group elements are enhanced compared to the α-group elements in NGC 3109. This is unusual because, at least for older stellar populations, the α-group elements are typically enhanced at lower metallicities (see review by McWilliam 1997). However, low α/Fe ratios for galaxies as metal-poor as NGC 3109 is not unheard of. Studies of low-metallicity dwarf irregular galaxies have revealed a wide range of α/Fe ratios, some lower than what is observed in the Milky Way (Figure 16, see review by Tolstoy et al. 2009). This is thought to reflect the different star formation histories of these galaxies, though the exact mechanisms are not yet known. We note that the assumption of a solar α/Fe ratio used in our model grid does not severely affect our metallicity determination, which is dominated by the Fe-group metal lines.

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There are several ways to investigate this interesting possibility further. A re-analysis of our sample using a significantly extended grid of model atmospheres with varying α/Fe ratios and focusing on spectral windows with α-element lines would require a substantial computational effort and careful testing of the accuracy of the method. A more direct and conventional method of determining the α/Fe ratio would be to conduct a detailed spectroscopic analysis of high quality/resolution spectra of a few of our targets. At the distance of NGC 3109 and the brightness of our targets such an approach would be feasible, but would require a substantial amount of 8 m telescope time.