3 Emission line measurements

Figure 1: Example of Gaussian fit for the blended lines H$\alpha$+[N  II]6548, 6583. Three narrow Gaussian components are used. The crosses are observed spectral data.

3.1 Measurements

The prominent spectral features of SFGs and AGNs include some commonly found strong emission lines, such as [O  II]3727, H$\beta$4861, [O  III]4959,5007, H$\alpha$6563, [N  II]6583, [S  II]6716, 6731, and some less common emission lines, such as H$\gamma$4340, [O  III]4363, He  I5876, and [O  I]6300.

The rest-frame equivalent widths, EWs, and integrated fluxes, F, of the emission lines were measured by direct numerical integration, using the SPLOT program in IRAF. The continuum levels and integration limits for the lines were set interactively, with repeat measurements made in difficult case. For single emission lines such as H$\beta$4861, [O  III]5007, direct integral methods were used. This method allows the measurement of lines with asymmetric shapes (i.e. with deviations from Gaussian profiles). For blended lines such as H$\alpha$, [N  II]6548,6583, and the [S  II]6716, 6731 doublet, we used the Gaussian deblending program of SPLOT. In Fig. 1, as an example, we show the three narrow Gaussian components to fit of H$\alpha$, [N  II]6548,6583 of III Zw 43. Note that in these blended cases, the lines are only partly blended. The interactive method allows us to control by eye the level of the continuum, taking into account defects that may be present around the line measured. It does not have the objectivity of automatic measurements, but it does allow us to obtain reliable, accurate measurements.

The equivalent widths of various emission lines are listed in Table 1, for all SFGs and active galactic nuclei. The objects are ordered by increasing right ascension at the epoch 2000 ( $\alpha_{2000}$). Column 1 lists the galaxy name (same as Table 1 of Paper I). Columns 2-9 list the equivalent widths of the commonly found emission lines. Columns 10-13 list the equivalent widths of less commonly found emission lines. The second line for each entry lists an estimate of the error (see in Sect. 3.2). We use the convention that positive equivalent widths denote emission to conserve space and improve readability. A dash in the table indicates either that the corresponding segment of the spectrum is lacking or that the spectrum was too noisy in the region to give a reliable value of equivalent widths. We have chosen an equivalent width of 1.0 Å as the lower limit for true detection. The observed emission line fluxes (the Galactic foreground reddening were corrected, see Kong & Cheng 2002) are listed in Table 2.

3.2 Standard deviations

Figure 2: Log of the detection level of equivalent widths, EW i.e. log (EW/$\sigma$(EW)), versus log EW for 4 emission lines. The emission line name, the number (SFG + AGN, EW > 1.5 Å) of plotted data and the 2$\sigma$, 3$\sigma$ detection levels (dashed lines) are indicated in each panel. The plotting symbols are coded according to spectral classification, the asterisks correspond to SFGs, the triangles to AGNs.

For measurements of emission lines and absorption lines where the slope and curvature of the continuum are well defined, the main sources of random errors in the flux and equivalent width measurements are the uncertainty of the overall height of the continuum level, the individual intensity points within the interval of integration, the signal-to-noise ratio of the continuum, and the uncertainty in the choice of the best-fitting profile parameter. To estimate $1\sigma$ standard deviations of emission lines, we followed the method outlined in Tresse et al. (1999), based on the formulae of propagation of errors and Poisson statistics. The derivation of error formulae can also be found in Longhetti et al. (1998).

The error $\sigma_{F}$ in the flux F of an emission line can be expressed as (Tresse et al. 1999):

$$\sigma_{F} = \sigma_{\rm c} D \sqrt{2 N_{\rm pix} + EW / D }.$$ (1)

The error $\sigma_{EW}$ with equivalent width EW of the line can be expressed as:

$$\sigma_{EW} = \frac{EW}{F} \sigma_{\rm c} D \sqrt{EW / D + 2 N_{\rm pix} + (EW / D)^2 / N_{\rm pix} }$$ (2)

where $\sigma_{\rm c}$ is the mean standard deviation per pixel of the continuum on each side of the line, D is the spectral dispersion in Å per pixel (for our spectral sample, D=4.8) and $N_{\rm pix}$ is the number of pixels covered by the line. Because the signal-to-noise ratio for each pixel was estimated by scaling the continuum variance according to Poisson statistics, these are not exactly the formal statistical $1\sigma$ errors of F or EW. Our approximation slightly overestimates the errors, but in our analysis, we are mainly interested in the consistency of the estimation of errors.

In Fig. 2, we plot a logarithm of the detection level of equivalent widths, log ( $EW/\sigma (EW)$), versus log EW for 4 commonly found emission lines, [O  II]3727, H$\beta$, [O  III]5007, and H$\alpha$ with equivalent widths above 1.5 Å. The result shows our equivalent widths limit is at a $3\sigma$ confidence level for those commonly found emission lines, and the typical uncertainty in these measurements is less than 10%. For those less common lines, such as H$\gamma$4340, [O  I]6300, the measurements typically have confidence levels $\geq$2$\sigma$, and the typical uncertainty in these measurements is about 20%.

3.3 Stellar absorption correction

Fluxes of emission lines will be used to determine the internal reddening of emission line regions, the star formation rate, and the element abundance of galaxies. It is known that the measurements are an underestimate of the real flux of the spectral lines, because of the underlying absorption component. To correct the underlying stellar absorption, some authors (such as Popescu & Hopp 2000) adopt a constant equivalent width (1.5-2 Å) for all the hydrogen absorption lines. Because the real value of the absorption equivalent width is uncertain and dependent on the age of star formation burst and star formation history (Izotov et al. 1994; González Delgado et al. 1999), the other usual correction for the contamination by stellar absorption lines assumes absorption equivalent widths, and iterates until the color excesses derived from H$\alpha$/H$\beta$, H$\beta$/H$\gamma$, and H$\beta$/H$\delta$  ratios converge to the same value (Izotov et al. 1994).

To derive the absorption equivalent width for hydrogen lines, we have applied an empirical population synthesis method, which uses observed properties of star clusters as a base (Cid Fernandes et al. 2001), to our BCG spectra. This empirical population synthesis method can give the synthetic stellar population spectrum, so we can measure these underlying stellar absorption features for hydrogen lines. A full description of this application and equivalent widths of underlying stellar absorption lines will be presented in a forthcoming paper.

Emission line fluxes of H$\alpha$, H$\beta$, and H$\gamma$  are corrected for this underlying absorption effect as follows:

$$F^{\rm cor}_{\rm line}=F^{\rm obs}_{\rm line}(1 + EW^{\rm abs}_{\rm line}/EW^{\rm obs}_{\rm line}),$$ (3)

where $F^{\rm cor}_{\rm line}$ and $F^{\rm obs}_{\rm line}$ (see in Table 2, were corrected for Galactic extinction) are respectively the absorption corrected and the observed emission line fluxes, and $EW^{\rm abs}_{\rm line}$ and $EW^{\rm obs}_{\rm line}$ (see in Table 1) are, respectively, the equivalent widths of the underlying stellar absorption line and of the observed emission line.

3.4 Dust attenuation corrections

The extinction of interstellar dust in SFGs modifies the spectra of these objects. It is necessary to correct all observed line fluxes for this internal reddening. The most widely method used to correct the emission line spectra for the presence of dust is based on the relative strengths of low order Balmer lines. In order to have an internally consistent sample, we applied this method to each of our objects, using only the ratio of the two strongest Balmer lines, H$\alpha$/H$\beta$.

We used the effective absorption curve $\tau_{\lambda} = \tau_V(\lambda/5500~{\rm\AA})^{-0.7}$, which was introduced by Charlot & Fall (2000). The color excesses arising from attenuation by dust in a galaxy, $E^{\rm int}_{B-V}$, can be written:

$$E^{\rm int}_{B-V} = A_V/R_V = 1.086 \tau_V/R_V ,$$ (4)

$$\tau_V = -\frac{{\rm ln}[F(\hbox{H$\alpha$ })/F(\hbox{H$\bet... ...m H\alpha}/5500)^{-0.7} - (\lambda_{\rm H\beta}/5500)^{-0.7}]}$$ (5)

where $I(\hbox{H$\alpha$ })/I(\hbox{H$\beta$ })$ is the intrinsic Balmer flux ratio, $F(\hbox{H$\alpha$ })/F(\hbox{H$\beta$ })$ is the observed Balmer flux ratio (were corrected for Galactic extinction and underlying stellar absorption), $\tau_V$ is the effective V-band optical depth. $\lambda_{\rm H\alpha} =6563~{\rm\AA}$, $\lambda_{\rm H\beta} =4861~{\rm\AA}$, and R_V=3.1. We adopted $I(\hbox{H$\alpha$ })/I(\hbox{H$\beta$ }) = 2.87$ for SFGs, and $I(\hbox{H$\alpha$ })/I(\hbox{H$\beta$ }) = 3.10$ for the AGN-like objects (Dessauges-Zavadsky et al. 2000). For 4 galaxies, I Zw 18, Haro 43, II Zw 70, and, I Zw 123, their observed flux ratio, F(H$\alpha$)/F(H$\beta$), are less than the theoretical flux ratio 2.87, we set $E^{\rm int}_{B-V}$ to be zero. The results of color excesses $E^{\rm int}_{B-V}$ are listed in the last column of Table 3.

The value of the color excess was then applied to the observed spectrum, and the final, intrinsic line fluxes relative to H$\beta$ for each galaxy can be expressed as:

$$\frac{I(\lambda)}{I(\rm H\beta)} =\frac{F(\lambda)}{F(\rm H\b... ...[(\lambda/5500)^{-0.7} - (\lambda_{\rm H\beta}/5500)^{-0.7}]},$$ (6)

where $F(\lambda)$ and $I(\lambda)$ are the dust-obscured (observed) and intrinsic line fluxes, respectively. The attenuation corrected line intensities relative to H$\beta$ are given in Table 3 for each star forming galaxy and AGN. The objects are ordered by increasing right ascension at the epoch 2000 ( $\alpha_{2000}$). Column 1 lists the galaxy name, Cols. 2-12 list the line intensities relative to H$\beta$, Col. 13 lists the intrinsic flux of H$\beta$, which was corrected for both internal and Galactic extinction, and underlying stellar absorption. Column 14 lists the color excesses $E^{\rm int}_{B-V}$ for each galaxy.

3.5 Comparison with previous works

Seven galaxies in our BCG sample - III Zw 43 (0211+038), II Zw 40 (0553+033), Mrk 5 (0635+756), I Zw 18 (0930+554), Haro 4 (1102+294), Haro 29 (1223+487), I Zw 123 (1535+554) - have been observed previously by Izotov, Thuan & Lipovetsky (1997, ITL97), Izotov & Thuan (1998, IT98), and Guseva et al. (2000, GIT00), with the Ritchey-Chretien spectrograph at the Kitt Peak National Observatory (KPNO) 4 m telescope, and with the GoldCam spectrograph at the 2.1 m KPNO telescope. These high signal-to-noise ratio spectrophotometric observations allow us to test the quality of our data. We perform a detailed comparison of these previous works in this subsection.

In III Zw 43, GIT00 did not detect [O  III]4363 line, the [S  II]6731 line intensity ratio is about 10% higher, and the other emission line ratios are in good agreement with ours. For II Zw 40 in GIT00, Haro 29 in ITL97, our data are in fairly good agreement with these works. In Mrk 5, our [O  I]6300 and [S  II]6717  line intensities are about 25% higher, and [O  II]  is $\sim$13% lower than that in IT98. In I Zw 18, our H$\gamma$, [O  III]4363, [S  II]  line intensities are stronger, but He  I5876 is weaker. In Haro 4, some less strong lines are not good agreement with IT98. Finally for I Zw 123, the agreement is not good as the other galaxies, our $I(\lambda)/I(\hbox{H$\beta$ })$ data have large differences with ITL97, but the $F(\lambda)/F(\hbox{H$\beta$ })$ are in good agreement with ITL97.

We now display this comparison in a more visible form in Fig. 3. The horizontal axis represent different spectral lines, the vertical axis shows the differences between our line intensities ( $[I(\lambda )/I(\hbox {H$\beta $ })]_{\rm OUR}$) and the values of GIT00, IT98 and ITL97 ( $[I(\lambda )/I(\hbox {H$\beta $ })]_{\rm IT}$). We found, our line intensity ratios are in good agreement with these previous works for most spectral lines of most galaxies, the difference between our sample and these works is less than 10% for those strong emission lines, and less than 15% for those less strong lines, such as H$\gamma$4340, [O  III]4363, [O  I]6300 of most galaxies.

The observed fluxes of H$\beta$ in our data are larger than those in previous works, the explanation could be: 1) the data in these previous works were not corrected for the Galactic extinction; 2) Our slit width is larger than that of previous works; 3) the position angle of slit is different between ours and those previous works. We will discuss the slit effect and derive an aperture correction for each galaxy in a future paper.

Figure 3: Difference between our line intensity ratios $[I(\lambda )/I(\hbox {H$\beta $ })]_{\rm OUR}$ and these of previous works $[I(\lambda )/I(\hbox {H$\beta $ })]_{\rm IT}$. The plotting symbols represent different galaxies, the dash lines outline the 15 per cent error window.