CLASSY V: The impact of aperture effects on the inferred nebular properties of local star-forming galaxies

Here we present new optical spectra for seven CLASSY galaxies using the Multi-Object Double Spectographs (MODS, Pogge et al. 2010) mounted on the LBT (Hill et al. 2010). The LBT spectra of two of these galaxies (J1044+0353 and J1418+2102) was already reported in Berg et al. (2021). The optical LBT/MODS spectra of the remaining five CLASSY galaxies were obtained on the UT dates of Feb 11th-12th and March 17th-18th, 2021, respectively. MODS has a large wavelength coverage from 3200 Å  to 10000 Å  with a moderate spectral resolution of $R\sim 2000$. The blue and red spectra were obtained simultaneously using the G400L (400 lines mm^-1) at $R\approx 1850$ and G670L (250 lines mm^-1) at $R\approx 2300$ gratings. The slit length was 60 arcsec with a width of 1 arcsec. To minimize flux losses due to atmospheric differential refraction (Filippenko 1982), the slit was oriented along the parallactic angle at half the total integration at airmasses ranging between 1.05 and 1.31. Each object was observed with a total exposure time of 45 min (3$\times$900s exposures). Fig. 1 shows the slit position and orientation of the LBT/MODS observations for J0808+3948, J0944-0038, J1148+2546 (SB 182), J1323-0132 and J1545+0858 (1725-54266-068). For comparison purposes, the LBT/MODS slit has been truncated (1″ $\times$ 2.5″ ) to show the extraction region of the observation. The slit was centered on the highest surface brightness knots of optical emission based on SDSS r-band images, following the position of HST/COS aperture of each CLASSY galaxy in the UV (Berg et al. 2022).

We use the CHAOS project’s data reduction pipeline (Berg et al. 2015; Croxall et al. 2016; Rogers et al. 2021) to reduce LBT/MODS observations. To correct for bias and flat field we apply the modsCCDRed²²2https://github.com/rwpogge/modsCCDRed Python programs to the standard stars, science objects and calibration lamps. The resulting CCD images are used in the beta version of the MODS reduction pipeline³³3http://www.astronomy.ohio-state.edu/MODS/Software/modsIDL/ which runs within the XIDL ⁴⁴4https://www.ucolick.org/ xavier/IDL/ reduction package. We perform sky subtraction, wavelength calibration and flux calibration using the standard stars Feige 34, Feige 67 and G191-B2B. In Fig. 2, we show the one-dimensional spectra for these galaxies. We have labeled the main emission line features. Note that with the exception of J0808+3948, the rest of the galaxies shows the very high ionization emission line He II $\lambda$4686 (Berg et al. 2021).

Berg et al. (2022) provide a detailed description of the optical observations for CLASSY, while the scaling of the optical data to UV data is presented in Mingozzi et al. (2022). Here, we give a brief summary of the main characteristics of the CLASSY galaxies relevant for this study. In Table 1, we list the optical observations of the selected galaxies. It includes the identification of the galaxy that we use in this work, the alternative names used in the literature, the coordinates, the observational ancillary, aperture size extraction of the observations and the optical size of each galaxy represented as the total galaxy radius, ($\sim$ $R_{100}$/2) (see Sec. 5.1).

APO/SDSS: SDSS sample comprises 12 observations of 3″ fiber diameter with a range in wavelength of 3800-9200 Å and spectral resolution of $R\approx 1500-2500$ (Eisenstein et al. 2011). This wavelength range allows to measure the main emission lines necessary for the analysis of the physical properties of these galaxies. We use this sample as reference to compare with the rest of the observations since the aperture size and center are similar to those of HST/COS data (Berg et al. 2022).

VLT/MUSE: we gathered archival VLT/MUSE IFU data for three CLASSY galaxies J0021+0052 (PI: Anderson), J1044 and J1418 (PI: Dawn Erb) (see Table 1). These observations cover a wavelength from 4300 Å  to 9300 Å  at a spectral resolution of $R\approx 2000-3500$, and a field of view (FoV ) of of 1’ $\times$1’. For the analysis of this sample, we have extracted one dimensional spectrum using the same 2.5″ HST/COS aperture. As an extra analysis, we have extracted one-dimensional spectra using different aperture sizes ranging from 1″to 4″  of diameter in steps of 0.5″. With such spectra, we study the variations of the physical properties with respect to the aperture size. This analysis is discussed in Section 5.5.

We refer to this sample as VLT/MUSE or IFU to distinguish from long-slit spectra. Note that we have extracted the integrated flux using an aperture size of 2.5″ resulting in one-dimensional spectra.

Keck/ESI: This sample comprises six CLASSY galaxies with high spectral resolution using the Echellette Spectrograph and Imager (ESI) on Keck II. These spectra cover a rest frame wavelength from 3800 Å  to 10000 Å  approximately, at a spectral resolution of $R\approx 4700$ at 1″ slit width. The long-slit spectra of these galaxies were obtained from Senchyna et al. (2019) and Sanders et al. (2022).

To prepare the spectra for emission line measurements, the optical spectra were corrected by Galactic extinction using the Green et al. (2015) extinction maps included in the Python dustmaps package (Green 2018), and the Cardelli et al. (1989) reddening law. Next, since the Balmer lines are affected by stellar absorption, we model the stellar continuum using Starlight⁵⁵5www.starlight.ufsc.br spectral synthesis code (Cid Fernandes et al. 2005) and subtract it. To do so, we follow the successful continuum-subtraction method of the CHAOS survey (Berg et al. 2015) and assume the stellar population models of Bruzual & Charlot (2003) with an initial mass function (IMF) of Chabrier (2003). We use a set of simple stellar populations that span 25 ages (1 Myr–18 Gyr) and six metallicities ($0.05\,Z_{\odot}<$ Z $<2.5\,Z_{\odot}$).

Using the continuum-subtracted spectra, we fit the emission lines with Gaussian profiles using the Python package LMFIT⁶⁶6Non-Linear Least-Squares Minimization and Curve-Fitting: https://github.com/lmfit/lmfit-py. Specifically, we simultaneously fit sections of nearby lines ($<200$ Å), while constraining the offset from line centers and the line width. This method also allows us to simultaneously fit weak and blended lines with a higher degree of accuracy. Since the [O II] $\lambda$$\lambda$3726, 3729 lines are blended in LBT and SDSS observations, we have fitted two Gaussian profiles to constrain the flux measurements in such lines. The errors in the flux were calculated using the expression reported in Berg et al. (2013) and Rogers et al. (2021). Note that for the LBT/MODS spectra of J1044+0353 and J1418+2102, we have adopted the line fluxes reported in Berg et al. (2021). To ensure significant emission line detections, we only use lines with S/N$>3$.

The auroral emission lines used to measure temperatures are intrinsically faint and so require careful consideration. Therefore, we inspected the [O III] $\lambda$4363, [N II] $\lambda$5755, [S III] $\lambda$6312, and [O II] $\lambda$$\lambda$7320,7330 auroral lines fits to ensure a well-constrained flux measurement. As a secondary check, we measured these faint $T_{e}$-sensitive lines by hand using the integration tool in iraf⁷⁷7IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. Both the python and iraf methods produced consistent flux values. Additionally, for high-metallicity star-forming galaxies (12+log(O/H) $>$ 8.4) the [O III] $\lambda$4363 emission line can be contaminated by [Fe II]$\lambda$4359 (Curti et al. 2017; 12$+$log(O/H)$>8.4$). Recently, Arellano-Córdova et al. (2020) analyzed the effect of using [O III] $\lambda$4363 blended with [Fe II] in the computation of temperature and metallicity in a sample of Milky Way and Magellanic Cloud H II regions. These authors concluded that the use of a contaminated [O III] $\lambda$4363 line can lead differences in metallicity up to 0.08 dex. However, most of objects in the present sample are metal-poor galaxies, but, we have taken into account the possible contamination of [O III] $\lambda$4363 by [Fe II]$\lambda$4359 in each spectrum of the sample as a precaution.

In Fig. 3, we show the resulting spectrum for SDSS, LBT and ESI of J0944-0038 (or SB 2). We have subtracted the continuum from the underlying stellar population, and we have added a small offset for a better comparison of the different spectra.

The different observations for J0944-0038 show the main emission lines used to compute the physical conditions of the nebular gas, namely the electron density and temperature and metallicity. These spectra contain significant He II $\lambda$4686, [Ar IV] $\lambda$$\lambda$4711,4740, and [Fe V] $\lambda$4227 emission, indicative of a very-high-ionization gas in this galaxy (see dashed lines in Fig. 3). Such very-high-ionization conditions of the gas were reported by Berg et al. (2021) for J1044+0353 and J1418+2102. Additionally, 11 galaxies in our sample have He II and [Ar IV] line detections, but no [Fe V] $\lambda$4227 detections. Note that for J0944-0038 (see Fig. 3), there is an odd artefact at $\approx$5100 Å in the SDDS spectrum that is not detected in the LBT or ESI spectra. This feature is likely an artefact of the SDSS reduction process, but it does not affect our emission-line flux measurements.

Before calculating nebular properties, emission lines must first be corrected for reddening due to dust with the galaxy. To do so, we calculate the color-excess, $E(B-V)$, for three Balmer decrements (H$\alpha$/H$\beta$, H$\gamma$/H$\beta$, and H$\delta$/H$\beta$) using the expression:

where $\kappa$($\lambda$) is the value of the attenuation curve at the corresponding wavelength, and $(I_{\lambda}/I_{{\rm H}\beta})_{\rm theo.}$ and $(I_{\lambda}/I_{{\rm H}\beta})_{\rm obs.}$ are the theoretical and observed Balmer ratios, respectively. We adopt the reddening law of Cardelli et al. (1989) to calculate $\kappa$($\lambda$).

To calculate the color excesses, we use three Balmer ratios, H$\alpha$/H$\beta$, H$\gamma$/H$\beta$, and H$\delta$/H$\beta$, for each galaxy, with a few exceptions (see Sec. 2):

• •

  For the MUSE spectra of J1044+0353 and J1418+2102, the limited spectral coverage limits the $E(B-V)$ calculations to only the H$\alpha$/H$\beta$ ratio.

• •

  For the SDSS spectra of J0944-0038, the H$\alpha$ emission line shows an asymmetric odd extension previously reported by Senchyna et al. (2017), which is not visible in MUSE and ESI spectra.

• •

  For the ESI spectra of J1129+2034, the H$\alpha$ emission line is saturated and so cannot be used.

• •

  For the ESI spectra of J1148+2546, the H$\gamma$ emission line is affected by a detector artifact and so cannot be used.

• •

  For the ESI spectra of J1024+0524, both the H$\gamma$ and [O III] $\lambda$4363 emission lines are affected by a detector artifact and so cannot be used.

• •

  For the LBT spectra of J1148+2546, the H$\delta$ is affected by an artifact and so cannot be used.

We calculate $E(B-V)$ values following the approach of (Berg et al. 2022), which iteratively calculates the electron temperature and density and $E(B-V)$ values. We calculate the initial electron temperature using $T_{\rm e}$[O III] [O III] ($\lambda$$\lambda$4959,5007)/$\lambda$4363 when measured, and other available temperature diagnostics when not (e.g., $T_{\rm e}$[S III] for MUSE). Using this temperature, and assuming the [S II] densities reported in Berg et al. (2022) and Case B recombination, we calculated the theoretical ratios of H$\alpha$, H$\beta$, H$\gamma$ and H$\delta$ relative to $H\beta$. The iterative process stops when the difference in $T_{\rm e}$ $\leq 20$ K. Note that in each iteration, the line intensities used to calculate temperature and density were corrected for reddening. For comparison, we have also calculated the $E(B-V)$ values for the SDSS sample assuming an unique value of $T_{\rm e}$ = 10000 K and $n_{\rm e}$ = 100 cm^-3 to derive the theoretical H$\alpha$/H$\beta$, H$\gamma$/H$\beta$, and H$\delta$/H$\beta$ ratios (a typical approach for star-forming regions). We find that the difference between this approach and our iterative procedure are up to $\sim$0.04 dex, in particular, when $T_{\rm e}$ ¿ 10000 K. The uncertainties of the $E(B-V)$ values were estimated using a Monte Carlo simulation, generating 500 random values and assuming a Gaussian distribution with a sigma equal to the uncertainty of the associated Balmer ratio. The final adopted value of $E(B-V)$ for each spectrum is the weighted mean after discarding any negative $E(B-V)$.

In table 2, we list the galaxy ID, the observational data, the $E(B-V)$ values for each Balmer line ratio (Columns 3–5), and the adopted $E(B-V)$ value (Column 6). In Section 5, we discuss the differences in $E(B-V)$ implied by the different Balmer lines with respect to H$\beta$ and other physical properties of CLASSY galaxies.

Finally, emission lines relative to H$\beta$ ($I_{\lambda}/I_{H_{\beta}}$) were corrected for reddening using the final $E(B-V)$ values reported in Table 2 and the reddening function $f({\lambda})$ normalized to H$\beta$ by Cardelli et al. (1989). Note that at optical wavelengths, the variation of extinction with $\lambda$  are small (Shivaei et al. 2020; Reddy et al. 2016). Therefore, our results are not affected by our choice of the extinction law selected for this sample. The final errors are the result of adding in quadrature the uncertainties in the measurement of the fluxes and the error associated with the fits. We report the resulting emission line intensities for optical spectra analyzed in this work in Table 3. Note that the optical emission lines are reported for the entire CLASSY sample in Mingozzi et al. (2022), but only for a single spectrum per galaxy. Given the comparison of multiple spectra per galaxy in this work, we have remeasured the emission lines of spectra in Mingozzi et al. (2022) for consistency.

To compute the electron density ($n_{\rm{e}}$), we use [S II] $\lambda$6717/$\lambda$6731 for all the set of observations and [O II] $\lambda$3726/$\lambda$3727 for LBT spectra and for four SDSS spectra. We calculate the electron temperature using the line intensity ratios: [O II] ($\lambda$$\lambda$3726,3729)/($\lambda$$\lambda$7319,7320 + $\lambda$$\lambda$7330,7331)⁸⁸8 Due to low spectral resolution it is not possible to resolve these lines. Hereafter referred to as [O II] $\lambda$3727 and [O II] $\lambda$$\lambda$7320,7330., [N II] ($\lambda$$\lambda$6548,6584)/ $\lambda$5755, [S III] ($\lambda$$\lambda$9069,9532)/$\lambda$6312, and [O III] ($\lambda$$\lambda$4959,5007)/$\lambda$4363, when they are available. The [S III] $\lambda$$\lambda$9069,9532 and [O II] $\lambda$$\lambda$7320,7330 ratios can be affected by telluric and absorption features (Stevenson 1994). We carefully check the different spectra for the presence of emission/absorption features that can affect those lines. For LBT spectra, we measured the flux of both [S III] $\lambda$9069 and [S III] $\lambda$9532 and compared the observed ratio to the theoretical ratio of [S III] $\lambda$9532/$\lambda$9069=2.47 from PyNeb test for contamination by absorption bands. If the observed ratio of [S III] $\lambda$9532/$\lambda$9069 is within its uncertainty of the theoretical ratio, we use both lines to compute $T_{\rm e}$([S III]). For [S III] ratios that are outside this range, we discarded [S III] $\lambda$9069 when the observed ratio is larger than the theoretical ratio, and discarded [S III] $\lambda$9532 when the theoretical one is lower following Arellano-Córdova et al. (2020); Rogers et al. (2021). Since it was only possible to measure [S III] $\lambda$9069 for most of the other spectra, we used it with the [S III] theoretical ratio to estimate [S III] $\lambda$9532.

We also inspected [O II] $\lambda$$\lambda$7320,7330 for possible contamination by telluric absorption bands (Stevenson 1994). For the observations considered here, absorption bands were not detected around the red [O II] lines. Note that due to the redshift of these galaxies, some other lines can also be affected by absorption bands. The [S II] $\lambda$6731 line of J1323-0132 of LBT is contaminated by a telluric absorption band, which might impact the results of $n_{\rm e}$ measurement (see Sec 5 for more discussion). Additionally, the strongest emission lines in the optical spectra are at risk of saturating. We, therefore, carried out a visual inspection of the [O III] $\lambda$5007 line and also compared its flux to the theoretical ratio of [O III] $\lambda$5007/$\lambda$4959 for our sample. If [O III] $\lambda$5007 is saturated, we instead used [O III] $\lambda$4959 to estimate [O III] $\lambda$5007 using the theoretical ratio of 2.89 from PyNeb.

In Table 4, we present the results of $n_{\rm e}$ in columns 2-3 and $T_{\rm e}$ in columns 3-7 for the whole sample. The uncertainties were calculated using Monte Carlo simulations in the similar way as $E(B-V)$.

In H II regions, a temperature gradient is expected in the interior of the nebula, associated with its different ionization zones (low-, intermediate-, and high-ionization) based on the ionization potential energy (eV) of the ions present in the gas (Osterbrock 1989; Osterbrock & Ferland 2006). To characterize the temperature structure of the nebular gas, we use $T_{\rm e}$([O III]) as representative of the high-ionization region and $T_{\rm e}$([O II]) or $T_{\rm e}$([N II]) as representative of the low-ionization region. If both $T_{\rm e}$([O II]) and $T_{\rm e}$([N II]) are measured, we prioritize $T_{\rm e}$([O II]) to characterize the low ionization region. It is because at low metallicity the [N II] $\lambda$5755 line is too faint and the uncertainties associated to $T_{\rm e}$ are large in comparison to $T_{\rm e}$([O II]) (see Table 4). When $T_{\rm e}$([O II]), $T_{\rm e}$([N II]) or $T_{\rm e}$([O III]) is not detected, we use the temperature relation of Garnett (1992) to estimate those temperatures, which are based on photoionization models:

and,

For those cases where the only available temperature is $T_{\rm e}$([S III]), J1014 and J1418 of MUSE, we use the empirical relation from Rogers et al. (2021) to estimate $T_{\rm e}$([O II]):

Fig. 4 shows different temperature relation implied by the multiple apertures of CLASSY galaxies. In the left panel of this figure, we show the $T_{\rm e}$([O III])-$T_{\rm e}$([S III]) relation. The temperature relationships based on photoionization models of Garnett (1992) and Izotov et al. (2006) (for low metallicity regime) are indicated by solid and dashed lines, respectively. In principle, the sample of galaxies follows both temperature relations, in particular, the LBT and ESI sample. However, at low temperatures ($T_{\rm e}<14000$ K), the relationship of Garnett (1992) is consistent with our results for ESI and SDSS observations (although few galaxies are present in these low temperature regime). As such, we feel confident in using the temperature relation of Garnett (1992) to estimate $T_{\rm e}$([O III]) from $T_{\rm e}$([S III]) when a unique $T_{\rm e}$ is available.

Low ionization temperatures, $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]) are available for few CLASSY galaxies in this sample. However, in the middle and right panels of Fig. 4, we present the low ionization temperatures versus $T_{\rm e}$([O III]) and $T_{\rm e}$([S III]), respectively. The solid and empty symbols represent the results for $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]). For J0021+0051, it was possible to calculate both $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]) using the SDSS spectrum (see also Table 4). We find that $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]) show a difference of 900 K. However, the uncertainty derived to $T_{\rm e}$([N II]) is large with respect to $T_{\rm e}$([O II]). Such an uncertainty might be associated mainly to the measurement of the faint [N II] $\lambda$5755 auroral in the SDSS spectrum. On the other hand, $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]) are expected to be similar due to that those temperatures are representative of the low ionization zone of the nebula (see Eqs 2 and 4). Previous works have studied the behaviour of the $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]) relation using observations of H II regions and star-forming galaxies ( see e.g., Izotov et al. 2006; Pérez-Montero et al. 2007; Croxall et al. 2016; Rogers et al. 2021; Zurita et al. 2021). Such results show a discrepancy and large dispersion between $T_{\rm e}$([N II]) and $T_{\rm e}$([O II]), whose origin might be associated to the measurements of the [N II] $\lambda$5755 auroral in the case of $T_{\rm e}$([N II]). For $T_{\rm e}$([O II]), the [O II] $\lambda$$\lambda$7320, 7330 auroral lines have a small contribution of recombination, depend on the electron density and reddening, and those lines can be contaminated by telluric lines  (e.g., Stasińska 2005; Pérez-Montero et al. 2007; Rogers et al. 2021; Arellano-Córdova et al. 2020). Therefore, the impact of using $T_{\rm e}$([O II]) in the determination of $O^{+}$ and the total oxygen abundance might be more uncertain in low ionization objects, i.e., high metallicity environments (12+log(O/H) $\gtrsim 8.2$.) In Fig. 4, we find that those results for $T_{\rm e}$([O II]) (empty symbols) follow the relationships of Garnett (1992) and Izotov et al. (2006). As such, we also use Garnett (1992) to estimate the low ionization temperature, $T_{\rm e}$([O II]), when this temperature is not available.

On the other hand, the right panel of Fig. 4 also shows the $T_{\rm e}$([N II]) - $T_{\rm e}$([S III]) relation for ESI and LBT ($T_{\rm e}$([O II])) observations. Such a relationship was previously presented for local star-forming regions by Croxall et al. (2016); Berg et al. (2020); Rogers et al. (2021) showing a tight relation between those temperatures. The LBT and ESI observations follow the relationship derived by Rogers et al. (2021) with some dispersion resulting mainly by the use of $T_{e}$([N II]) results. We stress again that $T_{e}$([N II]) are uncertain in the high-$T_{\rm e}$/low metallicity limits because [N II] $\lambda$5755 is weaker at such metallicities, for that reason we are more confident $T_{\rm e}$([O II]) given the general agreement with the temperature relation presented in Fig. 4. A future analysis of such relationships between $T_{\rm e}$([O II]) and $T_{\rm e}$([O III]) and $T_{\rm e}$([S III]) will be presented in Arellano-Cordova et al. (in prep.) using CLASSY galaxies, which cover a wider range of physical properties than local H II regions (Croxall et al. 2016; Arellano-Córdova & Rodríguez 2020; Berg et al. 2020; Rogers et al. 2021). In addition, we will use photoionization models to constrain the temperature relations.

The ionic abundances of O⁺ were calculated using the adopted $T_{\rm e}$([O II]) or $T_{\rm e}$([N II]) representative for low ionization zone. To derive O⁺, we use [O II] $\lambda$3727 when this line was available and the [O II] $\lambda$$\lambda$7320,7330 lines for the rest of the observations. For those spectra with both [O II] $\lambda$3727 and $\lambda$$\lambda$7320,7330 lines, we have compared the results obtained for O⁺. We find an excellent agreements with small differences of 0.02 dex.

For high ionization ions, O²⁺, we use $T_{\rm e}$([O III]) as representative of such an emitting zone. In Table 4, we list the adopted $T_{\rm e}$ associated to the low and high ionization zones in columns 8 and 9 ($T_{\rm e}$([O II]) (low) and $T_{\rm e}$([O III]) (high). In the same Table 4, we also list the ionic abundances of O in columns 10 and 11.

The total oxygen abundance was calculated by summing the contribution of O⁺/H⁺ + O²⁺/H⁺. We neglected any contribution of O³⁺/H⁺ to O/H at it is negligible (Berg et al. 2021). The uncertainties were calculated using Monte Carlo simulations by generating 500 random values assuming a Gaussian distribution with sigma associated with the uncertainty. In Table 4, we list the results of 12+log(O/H) in column 12 for the whole sample. In addition, in Table 5, we present the results of metallicity for the multiple apertures in columns 2-5, and the differences in metallicity, $\Delta{\rm O/H}={\rm O/H}_{\rm IFU,\,long-slit}-{\rm O/H}_{\rm SDSS}$ in columns 6-8.

We define O₃₂ = [O III] $\lambda$5007/[O II] $\lambda$3727 as proxy of the ionization parameter. We calculate O₃₂ for five galaxies of SDSS spectra (J0021+0052, J0808+3948, J1024+0524, J1148+2546 and J1545+0858) and for the whole LBT sample, whose [O II] $\lambda$3727 line was available.

For the rest of the sample (ESI and MUSE spectra and some SDSS spectra), we obtained O₃₂ using the emissivities of [O II] $\lambda$3727 and [O II] $\lambda$$\lambda$7320,7330 using PyNeb. Such emissivities were calculated using $T_{\rm e}$ (low) associated to the low ionization emitting zone (see Table 8). We derived a representative factor between both [O II] lines in the red and blue ranges for each galaxy. To estimate the intensity of [O II] $\lambda$3727_estimated, we used the observed emission lines of [O II] $\lambda$$\lambda$7320,7330 multiplied for the factor calculated from the emissivity ratio of $j$[O II] $\lambda$3727/$j$[O II] $\lambda$$\lambda$7320,7330, for each galaxy. In Table 6, we list the results of O₃₂ for our sample of galaxies. We have identified those galaxies of SDSS sample with estimates of [O II] $\lambda$3727 with an asterisk, ‘$*$’.