5 Emission line analysis for SFGs

The main goal of this series of papers is to study the current star formation rates, stellar components, metallicities, and star formation histories and evolution of BCGs. For this purpose, we are mostly interested in the SFGs. Therefore, in present section, we do not consider the galaxies with Seyfert nuclei and the non-emission line galaxies in our BCG sample. In the following, the sample will refer to the 74 SFGs. We investigate the emission line trends in spectra of those SFGs in this section.

5.1 Equivalent widths of emission lines

5.1.1 EWs versus M_B

It is interesting to explore how the equivalent widths of emission lines depend on the galaxy absolute blue magnitude M_B (Col. 6 of Table 1 in Paper I). The equivalent widths of [O  II]3727, H$\beta$, and H$\alpha$ are well correlated with M_B, the other emission lines are also correlated with M_B, but the spread in equivalent widths at a given luminosity is large. Lower luminosity systems tend to have larger equivalent widths for most of emission lines, except for [N  II]6583.

In the top panel of Fig. 6, we plot the H$\alpha$ emission equivalent width as a function of M_B for the SFGs in our sample. A pronounced trend towards larger equivalent widths at lower luminosities can be found, galaxies with the strongest H$\alpha$ lines are of low luminosity. EW(H$\alpha$) is the ratio of the flux originating from UV photoionization photons (<912 Å) to the flux from the old stellar population emitted in the rest-frame R passband, which forms the continuum at H$\alpha$. Thus, a large equivalent widths is due either to a large UV flux (or B absolute magnitude since they are correlated), or to a low continuum from old stars. In either case, this implies a blue continuum color. Hence, the observed trend of larger EW(H$\alpha$) for fainter galaxies implies that the faint SFG population is dominated by blue galaxies, while the bright SFG population is dominated by redder galaxies.

In the bottom panel of Fig. 6, we plot the [N  II]6583  emission line equivalent width as a function of M_B for the SFGs in our sample. Its equivalent width behaves in the opposite way, lower luminosity systems tend to have smaller equivalent widths. Such a trend has also been found in other studies of nearby galaxies (Jansen et al. 2000). The global behavior of [N  II]6583  EW reflects intrinsic differences in the nitrogen abundance in BCGs, on average luminous BCGs are likely to be enhanced in nitrogen abundance. This suggests that, in faint, low-mass, BCGs, nitrogen is a primary element, whereas in brighter, more massive BCGs it comes from a secondary source.

Figure 6: The logarithm of integrated H$\alpha$ and [N  II]6583  emission line EWs plotted versus absolute B filter magnitude. A tendency towards larger H$\alpha$ EWs and smaller [N  II] EWs in lower luminosity systems is seen.

5.1.2 EW([N II])/EW(H$\alpha$) versus EW(H$\alpha$+ [N II])

In deep large optical surveys, low-resolution spectroscopy or narrowband H$\alpha$ imaging is often used. H$\alpha$ and [N  II]6548, 6583 lines are often blended, so it is important to recover the flux solely in H$\alpha$ to measure for instance the H$\alpha$ luminosity function, hence to derive a star formation rate. Figure 7a shows that the [N  II]6583/H$\alpha$ EW ratio decreases as a function of EW(H$\alpha$). All the spectra in this figure have EW([N  II]) and EW(H$\alpha$) > 10 Å, which can be measured very accurately. The [N  II]6583/H$\alpha$ equivalent widths ratio is strongly correlated with EW(H$\alpha$). A least-squares fit of this relation yields: log EW([N  II]6583)/EW(H$\alpha$) = $(1.01 \pm 0.14) - (0.85 \pm 0.07)$ log EW(H$\alpha$).

Since $EW(\hbox{[N~{\sc ii}]}6583)=3EW(\hbox{[N~{\sc ii}]}6548)$, we also plot the relation $1.33EW(\hbox{[N~{\sc ii}]}6583)/EW(\hbox{H$\alpha$ })$ versus $EW(\hbox{H$\alpha$ })+1.33EW(\hbox{[N~{\sc ii}]}6583)$ in Fig. 7b. The trend is similar to that in Fig. 7a, log $1.33EW(\hbox{[N~{\sc ii}]}6583)/EW(\hbox{H$\alpha$ })$ = $(1.36 \pm 0.20) - (0.91 \pm 0.09)$ log $(EW(\hbox{H$\alpha$ })+1.33EW(\hbox{[N~{\sc ii}]}6583))$. Thus we can predict which value is expected for the ratio when observing the blend H$\alpha$ + [N  II]6548, 6583. For instance, if this latter, EW(H$\alpha$)+1.33EW([N  II]6583), is $\sim$100 Å, the ratio 1.33 $EW(\hbox{[N~{\sc ii}]}6583)/EW(\hbox{H$\alpha$ })$ should be $\sim$0.35. The value of the ratio [N  II]6548, 6583/H$\alpha$, as determined by Kennicutt (1992), is usually taken to be 0.5 to remove the contribution of [N  II] to (H$\alpha$+[N  II]) blended emission. This is slightly larger than the typical value for our star-forming galaxy sample trend, presumably because Kennicutt's sample contains a large fraction of early-type galaxies, which have systematically higher ratios (Tresse et al. 1999).

Figure 7: a) log EW([N  II]6583)/EW(H$\alpha$) versus log EW(H$\alpha$). b) log 1.33 $EW(\hbox{[N~{\sc ii}]}6583)/EW(\hbox{H$\alpha$ })$ versus log $EW(\hbox{H$\alpha$ })+1.33EW(\hbox{[N~{\sc ii}]}6583)$.

5.2 Fluxes of emission lines

Figure 8: The correlation of the intrinsic (reddening and underlying absorption were corrected) emission line fluxes as a function of the intrinsic H$\alpha$ emission line flux. The dotted line indicates a linear least-squares fit to the data points. Fluxes are in erg cm-2 s-1. a) [O  II]3727; b) H$\gamma$4340.

Emission line fluxes are primary traces of the star formation rate (SFR) in galaxies (Kennicutt 1998). For star-forming galaxies, the Balmer emission line luminosities scale directly with the ionizing fluxes of the embedded young stars, and this makes it possible to use the Balmer lines to derive SFRs in galaxies. H$\alpha$ is the best line for such applications, but beyond $z \simeq 0.2 {-} 0.3$, this line is redshifted into the near infrared. To find other tracers of SFR we analyze the fluxes of other emission lines as a function of the intrinsic H$\alpha$ flux.

Since the various prominent emission lines correlate with each other, any of them is likely to be a first order ranking indicator of SFR of star-forming galaxies, but the strongest correlations are found between [O  II]3727, H$\gamma$4340, H$\beta$ and H$\alpha$. [O  II]3727 is the most useful star formation tracer in the blue. In Fig. 8a, we show the flux of [O  II]3727 as a function of the intrinsic H$\alpha$ flux. We found, as expected, these two lines have a strong correlation.

From purely astrophysical considerations, the most reliable star formation tracers in the blue should be the higher order Balmer lines, since the fluxes of these lines scale directly with the massive star formation and are nearly independent of the temperature and ionization level of the emitting gas. Figure 8b shows the relation between the fluxes of H$\alpha$ and H$\gamma$. A strong, roughly linear correlation between H$\alpha$ and H$\gamma$ is apparent. This correlation confirms that the H$\gamma$ line can serve as a reliable star formation tracer in strong emission line galaxies, such as the SFGs in our BCG sample. In addition, the correlation between the intrinsic fluxes of H$\alpha$ and H$\beta$ is stronger than that between the fluxes of H$\alpha$ and H$\gamma$, H$\beta$ is another good star formation tracer for SFGs.

Recently, Charlot & Longhetti (2001) quantified the uncertainties in these SFR estimators. They found SFR estimates based purely on one of emission line luminosity of galaxies could be in error by more than an order of magnitude. On the other hand, with the help of other emission lines, these errors can be substantially reduced. Based on our high quality spectrophotometric data, we can derive star formation rate for each galaxy, using these different star formation rate estimators.

Figure 9: Intrinsic emission line flux ( $I_{\lambda }$, reddening and underlying absorption were corrected) ratios as a function of the galaxy absolute blue magnitude MB and the color excesses, $E^{\rm int}_{B-V}$. a) [N  II]6583/H$\alpha$; b) [N  II]6583/[O  II]3727; c) R23 = ([O  II]3727+[O  III]4959, 5007)/H$\beta$; d) [N  II]6583/H$\alpha$ as a function of $E^{\rm int}_{B-V}$.

5.3 Line ratios and metallicity

Numerous studies have claimed the existence of a metallicity-luminosity relation in a variety of classes of galaxies: dynamically hot galaxies, i.e. ellipticals, bulges, and dwarf spheroidals, dwarf H  II galaxies, irregular galaxies and spirals (Lequeux et al. 1979; Skillman et al. 1989; Stasinska & Sodré 2001). In Figs. 9a-c, we show the various metallicity indices, R₂₃=([O  II]3727+[O  III]4959, 5007)/H$\beta$ (Pagel et al. 1979), [N  II]6583/H$\alpha$ (van Zee et al. 1998) and [N  II]6583/[O  II]3727 (Dopita et al. 2000) as a function of the total absolute blue magnitude M_B. The line flux ratios were corrected for both internal (using the value of $E^{\rm int}_{B-V}$) and Galactic extinction, and underlying stellar absorption. Since the reddening correction becomes more uncertain for galaxies with small EW(H$\alpha$) and EW(H$\beta$), we only use those objects that have EW(H$\beta$) > 5 Å and thus the most reliable reddening corrections. We do find a good correlation between M_B and the metallicity indices [N  II]6583/H$\alpha$ and R₂₃. The correlation of the [N  II]6583/[O  II]3727 index with M_B is statistically significant, but at a rather low level. These metallicity indices show clear trends with galaxy absolute magnitude, confirming that indeed there is a relation in blue compact galaxies between the overall metallicity of the star forming regions and the galaxy luminosity. The higher the galaxy absolute magnitude, the higher the heavy element content. This relation suggests that the metallicity of faint, low mass BCGs is low.

We now examine whether there is a relation between the color excesses due to internal extinction, $E^{\rm int}_{B-V}$, and the overall metallicity of the galaxies. So far, there have been contradictory claims in this respect. Zaritsky et al. (1994) found no evidence for a systematic dependence between reddening and abundance in a sample of 39 disk galaxies. In other contexts, Stasinska & Sodré (2001) found that the nebular extinction as derived from the Balmer decrement strongly correlates with the effective metallicity of the emission line regions of spiral galaxies.

Figure 9d shows $E^{\rm int}_{B-V}$ as a function of the metallicity indicator [N  II]6583/H$\alpha$, which is less affected by the reddening correction. We find there is a clear correlation, ${\rm log}(I_{{\rm [NII]}6583}/I_{{\rm H}\alpha})_{\rm cor} = - (1.06 \pm 0.07) + (0.92\pm 0.17) E^{\rm int}_{B-V}$. [N  II]6583/H$\alpha$  tends to be larger for larger values of $E^{\rm int}_{B-V}$, when $E^{\rm int}_{B-V} > 0.1$. Internal extinction indeed correlates with the overall metallicity of BCGs, especially among the galaxies with large $E^{\rm int}_{B-V}$. Since the metallicity indices correlate with M_B, the correction between $I_{{\rm [NII]}6583}/I_{{\rm H}\alpha}$ and $E^{\rm int}_{B-V}$ also suggest the internal extinction of brighter, more massive BCGs is higher.