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A&A
Volume 683, March 2024
Article Number A46
Number of page(s) 38
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202346443
Published online 06 March 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

Current and upcoming spectroscopic cosmological surveys, such as the Dark Energy Spectroscopic Instrument (DESI; Abareshi et al. 2022) and Euclid (Laureijs et al. 2012), rely on galaxies with strong spectral emission, or emission-line galaxies (ELGs), to build accurate and deep 3D cosmic maps and infer the cosmological composition and evolution of the Universe. According to the origin of their spectral lines, different types of ELGs might trace different regions of the cosmic web, or might be the result of a different evolution: for instance, quasars (QSOs) are more strongly clustered than star-forming (SF) galaxies (Zhao et al. 2021). Until now, the statistical errors of cosmological surveys have been larger than the uncertainties due to our lack of understanding of the galaxy formation and evolution processes (Avila et al. 2020; Raichoor et al. 2021). However, this might change with the new generation of Stage-IV cosmological surveys, such as DESI (Abareshi et al. 2022), Euclid (Laureijs et al. 2012), the 4-metre Multi-Object Spectroscopic Telescope (4MOST; de Jong et al. 2012), Subaru Prime Focus Spectrograph (PSF; Takada et al. 2014), or SphereX (Doré et al. 2014).

ELGs are also interesting as they have enabled us to reconstruct the cosmic star formation history (SFH) out to z ∼ 2 (e.g., Kennicutt 1998; Madau et al. 1998; Ascasibar et al. 2002; Kewley et al. 2002, 2004; Hopkins et al. 2003; Calzetti et al. 2007, 2010; Moustakas et al. 2006; Salim et al. 2007; Kennicutt et al. 2007, 2009; Rieke et al. 2009; Treyer et al. 2010). The study of star formation from emission lines has been possible thanks to an immense observational effort over the course of the last decades. In the past, high-sensitivity infra-red (IR) space telescopes, such as Spitzer1 or Herschel2, enabled the calibration of monochromatic star formation rate (SFR) indicators in nearby galaxies (Falcón-Barroso & Knapen 2013; Calzetti 2013), complementing the efforts in the UV and optical channels to map the SFR evolution of galaxies out to z ∼ 9 (Giavalisco et al. 2004; Bouwens et al. 2009, 2010).

While SF regions constitute the main origin of the spectral emission lines for ELGs (e.g., Kennicutt 1992; Sobral et al. 2013; Pirzkal et al. 2018; Xiao et al. 2018; Kewley et al. 2019), other origins are also possible, such as active galactic nuclei (AGN; e.g., Marziani et al. 2017; Lin et al. 2022), shocks (e.g., Hirschmann et al. 2023) and old stellar populations (e.g., Kennicutt 1992; Sansom et al. 2015; Byler et al. 2019; Nersesian et al. 2019; Clarke et al. 2021). Emission-line diagnostic ratios, such as the BPT diagram (Baldwin et al. 1981) or the Dn(4000) break index (Bruzual 1983; Balogh et al. 1999), have been used to separate SF ELGs from AGN, as well as older and younger stellar population contributions (e.g., Kewley et al. 2001, 2006; Kauffmann et al. 2003a,b; Gallazzi et al. 2005; Belfiore et al. 2016; Wu et al. 2018; Angthopo et al. 2020). The WHAN diagram, relating the equivalent width of the Hα line and the [N II]/Hα ratio (e.g., Stasińska et al. 2006; Cid Fernandes et al. 2011) provides additional information to discriminate between SF and active galaxies, and the relation between EWHα and the D4000 index (the so-called aging diagram) has been proposed to identify sudden changes in the recent star formation activity (Casado et al. 2015; Corcho-Caballero et al. 2020, 2021b, 2023).

Over the years, several studies have combined ELG observations both from spectroscopic and imaging surveys in order to constrain the emission-line luminosity functions. The Hα (Gallego et al. 1995; Tresse et al. 2002) and the [O II] (Gallego et al. 2002) LFs were among the first ones to be characterized in the local Universe. Fujita et al. (2003) at z = 0.24 and Ly et al. (2007) at 0.07 < z < 1.47 used broad-band galaxy colors to discriminate Hα from other lines, finding that the Hα LF evolution is stronger in the faint end than in the bright one. Gilbank et al. (2010) explored the [O II], Hα, and u-band luminosities as SFR indicators at z < 0.2, finding that, in the high-mass end (i.e., M⋆ > 1010 M⊙), [O II] needs a larger correction to compensate for the effects of metallicity dependence and dust extinction. Gunawardhana et al. (2013) studied the Hα LF and SFR density at z < 0.35, observing an increasing number of SF galaxies in the faint end. Sobral et al. (2013) studied the SFH and Hα LF evolution at 0.40 < z < 2.2, finding that the Hα line traces the bulk of star formation over the last 11 Gyr. In this period, the SF activity has produced ∼95 percent of the total stellar mass density observed locally, half of which was assembled within 2 Gyr between 1.2 < z < 2.2. Mehta et al. (2015) studied the bivariate Hα-[O III] LF at z ∼ 1 using galaxies from the WFC3 Infrared Spectroscopic Parallel (WISP; Atek et al. 2010) survey. They showed that the Hα LF can be determined by exclusively fitting [O III] data. Zhu et al. (2009) and Comparat et al. (2015) studied the [O II] LF evolution at 0.75 < z < 1.45 and 0.1 < z < 1.65, respectively. Comparat et al. (2016) measured the [O II], [O III], and, for the first time, the Hβ LFs over the last nine billion years. They found that both the characteristic luminosity and the density of all LFs increase with redshift. Saito et al. (2020) used photometric data to model galaxy spectral energy distributions (SEDs) and emission-line fluxes and used them to derive accurate predictions for the Hα and [O II] LF up to z = 2.5.

All the studies above show that, so far, the focus has been mainly on Hα, [O II], and [O III] lines. Here we propose a novel analysis aimed at exploring also other lines, namely Hβ, [N II], and [S II]. We want to split the different galaxy contributions to the ELG production to understand the impact of each one on the line LF. This work will be directly relevant to future high-redshift studies (see e.g., Gonzalez-Perez et al. 2020; Zhai et al. 2019). In particular, the aim of our work is twofold: (i) to measure the Hα, Hβ, [O II], [O III], [N II], and [S II] luminosity functions in the nearby Universe with high accuracy, using a uniform procedure to select our galaxy sample and account for statistical incompleteness; (ii) to establish the contribution of different ELG types to the total LF.

For this study we use a subsample of the SDSS DR7 main galaxy sample (Strauss et al. 2002) at 0.02 < z < 0.22, with spectral properties from the MPA-JHU3 release, where the SFR were computed from the Hα line luminosity as described in Brinchmann et al. (2004). We classify the selected ELGs based on their specific star formation rate (sSFR, star formation rate divided by the stellar mass), and their position in the BPT and WHAN diagrams. These diagnostics allow us to classify galaxies beyond the star-forming and passive split, to distinguish composite galaxies from those with spectral emission lines produced in jets or shocks, which, in many cases, host active galactic nuclei, that is, Seyfert galaxies.

The paper is organized as follows. In Sect. 2 we describe the SDSS main galaxy sample, its MPA-JHU spectral properties, the sample selections performed, and their incompleteness effects. In Sect. 3 we present a generalized 1/Vmax LF estimator capable of simultaneously correcting from spectroscopic, r-band magnitude, and emission-line incompleteness. In Sect. 4 we explain the methods adopted to classify ELGs. In Sect. 5, we present the measured LFs, both observed (i.e., dust attenuated) and intrinsic ones (i.e., corrected from dust extinction). Our findings are summarized in Sect. 6.

Throughout the paper we adopt the MultiDark Planck 2 cosmology consistent with Planck Collaboration XIII (2016). Our parameters are: Ωm = 0.3071, Ωb = 0.0482, ΩΛ = 0.6928, h = 0.6777, σ8 = 0.8228 and ns = 0.96.

2. Observational data

In this work we aim at characterizing the luminosity functions for a range of spectral emission lines in the local Universe. In particular, we study the following lines: Hαλ 6563 Å, Hβλ 4861 Å, [O II]λ 3727, 3729 Å, [O III]λ 5007 Å, [N II]λ 6584 Å, [S II]λ 6717, 6731 Å. Here we describe how we generate a sample of ELGs with adequate fluxes and signal-to-noise ratios (S/N) to then study their completeness and measure their LFs.

2.1. The parent-ELG sample

We select galaxies with good spectra, (i.e., with ZWARNING=0) from the SDSS DR7 main sample (Strauss et al. 2002) using the NYU-Value Added Galaxy Catalog4 (Blanton et al. 2005b). We spectroscopically match these galaxies to the MPA-JHU DR73 spectral release to obtain further properties, such as star formation rates, stellar masses, spectral emission-line fluxes and equivalent widths (Brinchmann et al. 2004; Tremonti et al. 2004).

The SDSS main galaxy sample covers an effective area of 7300 deg2 and is limited in r-band petrosian magnitude at rp < 17.77. The SDSS spectra span wavelengths of 3800–9200 Å, with a resolution that varies from R = 1500 at λ = 3800 Å, to R = 2500 at λ = 9000 Å (Stoughton et al. 2002). We limit our sample to the redshift range 0.02 < z < 0.22. The lower redshift cut ensures that we are studying galaxies beyond the local group, reducing the cosmic variance in our sample. The upper limit is chosen to mimic the SDSS main selection in Favole et al. (2017) and Guo et al. (2015), minimizing the effect of k-corrections and cosmic evolution. This matched sample, hereafter “parent-ELG”, is composed of 426 625 galaxies.

We calculate the observed (i.e., dust attenuated) luminosities of the parent-ELG sample from the observed fluxes F provided in the MPA-JHU catalog as (e.g., Hopkins et al. 2003; Favole et al. 2017):

L [ erg s − 1 ] = 4 π D L 2 ( z ) F , $$ \begin{aligned} L[\mathrm{erg\,s}^{-1}]=4\pi D_{\rm L}^2(z) F, \end{aligned} $$(1)

where DL(z) is the luminosity distance as a function of redshift and cosmology, and the fluxes are given in units of erg s−1 cm−2.

The SDSS fluxes were measured by fitting the spectra using Bruzual & Charlot (2003) stellar population synthesis models, accounting for stellar absorption. We note that, in the case of the [O II]λ 3727, 3729 Å, and [S II]λ 6717, 6731 Å doublets, the flux is the sum of the individual line fluxes.

2.2. Fiber aperture correction

The observed fluxes in Eq. (1) need to be corrected for fiber aperture to take into account that only the portion of the flux within each SDSS fiber (∼3″ diameter) was detected by the spectrograph (Strauss et al. 2002). Following Hopkins et al. (2003) and Gilbank et al. (2010), we estimate the aperture-correction factor for each parent-ELG that is not classified as a candidate active galactic nuclei (AGN; see Sect. 4) from its total and fiber magnitudes. The aperture-corrected line luminosity Lap − corr is related to the measured luminosity L, given in Eq. (1), as follows:

L ap − corr [ erg s − 1 ] = 10 − 0.4 ( m p − m fib ) L , $$ \begin{aligned} L^\mathrm{ap-corr}[\mathrm{erg\,s}^{-1}]=10^{-0.4(m_{\rm p}-m_{\rm {fib}})}\,L\,, \end{aligned} $$(2)

where the exponent (mp − mfib) represents the aperture correction as a function of the SDSS petrosian magnitude mp, used as a proxy for the total magnitude of the galaxy (Blanton et al. 2001), and the fiber magnitude mfib that accounts for the light enclosed within the diameter of the fiber.

To implement the above correction, we use the magnitudes measured with the SDSS broadband filters (Gunn et al. 1998; Fukugita et al. 1996)5. Table 1 summarizes the wavelength λ0 of our emission lines of interest, emitted in the rest frame of the galaxy, as well as the value λz = λ0(1 + z) observed at the Earth at the minimum, mean, and maximum redshifts of the sample, together with the corresponding SDSS filter. For each galaxy, we select the appropriate band for each emission line based on the observed redshift and then use Eq. (2) to derive the aperture-corrected luminosity. Note that the [S II] line at z = 0.02 falls at the gap between the r and i filters; we choose the latter since it has higher transmission.

Table 1.

Wavelengths of our six emission lines of interest, together with the SDSS filter (in brackets) in which they fall for a selection of redshifts, for illustration.

The Hopkins et al. (2003) prescription implicitly assumes that the emission measured through the fiber is characteristic of the whole galaxy, that is, the line equivalent width (EW) remains constant across its surface. To quantify the uncertainty associated this simplification, we compare our approach with the method proposed by Iglesias-Páramo et al. (2016) and Duarte Puertas et al. (2017) to take into account variations of EW across a galaxy. They fit the growth curves (i.e., integrated flux inside an aperture as a function of radius) of the emission-lines as a function of the petrosian half-light radius, R50, enclosing half the petrosian flux. We have approximated the aperture correction based on the work from Duarte Puertas et al. (2017) by using their fifth-order polynomial fit as a function of R50 (i.e., X(α50) in their Eq. (4)). Figure 1 shows, as a function of redshift, the difference in the Hα luminosity of the parent-ELG sample between applying our default aperture correction (y-axis) and that of Duarte Puertas et al. (2017) (superscript “D”, x-axis). We overplot the median and 1 σ dispersion of our LHα in bins of L H α D $ L_{\mathrm{H}\alpha}^{\mathrm{D}} $, as well as the 1:1 relation to help the comparison.

thumbnail Fig. 1.

Parent-ELG Hα luminosity computed using our our default aperture correction based on Hopkins et al. (2003; y-axis) versus the same quantity computed using an approximation to the Duarte Puertas et al. (2017) correction (z-axis), color-coded by redshift. We randomly show only 30 percent of the parent-ELG sample to avoid saturation. We overplot the median and 1σ dispersion of our LHα in bins of L H α D $ L_{\mathrm{H}\alpha}^{\mathrm{D}} $, as well as the 1:1 relation for comparison.

This result shows that the two corrections are consistent in the luminosity range 1040 − 1041.5 erg s−1, while the largest discrepancies arise in both the faint and bright ends, where the lower- and higher-z emitters respectively concentrate. Our aperture correction factor has typical values in the range 2–10, and below 1039 erg s−1 (above 1042 erg s−1) it returns Hα luminosities up to 0.5 dex higher (lower) than those from Duarte Puertas et al. (2017). The scatter of LHα and L H α D $ L_{\mathrm{H}\alpha}^{\mathrm{D}} $ in Fig. 1 are comparable, suggesting that the aperture-correction has an associated uncertainty on the order of a factor ∼3. We thus conclude that our default aperture-correction, assuming EW is constant across a galaxy, is adequate for the purposes of the present study, within this level of uncertainty.

2.3. The main-ELG selection

We aim at selecting a complete population of bright ELGs with well measured fluxes in all of the following six emission lines: Hαλ 6563 Å, Hβλ 4861 Å, [O II]λ 3727, 3729 Å, [O III]λ 5007 Å, [N II]λ 6584 Å, and [S II]λ 6717, 6731 Å. To achieve this, we extract a subsample of the parent-ELG sample above, and then we impose a combination of cuts in emission-line flux and signal-to-noise (S/N) in all the six lines of interest. We define the signal-to-noise as the ratio between the observed flux and its error, σF, as given by the MPA-JHU DR7 catalogs: S/N = F/σF.

We cut the parent-ELG sample at F > 2 × 10−16 erg s−1 cm−2 and S/N > 2 in all the six lines above. Furthermore, we remove any spurious object with nonphysical flux uncertainty by limiting our selection at σF < 10−12 erg s−1 cm−2, and EW ≥ 0 Å in all the six lines under study. The resulting ELG sample, hereafter “main-ELG”, is composed of 162 733 emitters (about 38 percent of the parent sample). The characteristics of this sample are discussed in Sect. 2.4.

Figure 2 shows the effect of the main-ELG selection on the signal-to-noise – F plane for the Hα line, color-coded by specific star formation rate (sSFR, star formation rate divided by stellar mass); the effect on the other emission lines, color-coded by both sSFR and EW, is shown in Fig. A.1. In all cases, the marginal probability distributions of the measured flux and SN are observed to decay below our adopted thresholds, suggesting that completeness would be very difficult to guarantee beyond that point.

thumbnail Fig. 2.

parent-ELG signal-to-noise as a function of the Hα line flux, color-coded by sSFR. Here we are representing a random subset of the total population, 30 percent of it, to avoid crowding. The black-dashed lines in the main panel represent the flux and S/N cuts we impose on the parent-ELG sample to obtain our main-ELG sample: F > 2 × 10−16erg s−1 cm−2 and S/N > 2 (see Sect. 2.3). The top and right panels show the flux and S/N histograms of the parent-ELG (gray-dashed lines) and the main-ELG (green-solid lines) samples. The marginal distributions displayed both here and in Fig. A.1 for the other lines motivate the flux and S/N cuts chosen to select a complete ELG sample.

2.4. Main-ELG properties

Here we analyze the impact of the S/N and emission-line flux cuts performed in Sect. 2.3 on the sSFR, stellar mass, and EW distributions of the main-ELG sample. Figure 3, left panel, shows the main-ELG sSFR as a function of stellar mass (green lines and colorful dots), compared to the distribution of the parent-ELG sample (gray contours and dots). Individual galaxies are shown as dots and the contours correspond to the 1σ and 2σ density distribution. The green contours correspond to the main-ELG sample. The average sSFR and standard deviations in bins of stellar mass are shown by markers. Both the contours and the average values show that the main-ELG population is a fair sample of the parent-ELG one.

thumbnail Fig. 3.

Left panel: main-ELG sSFR as a function of stellar mass, color-coded by Hα EW. On the background we also show the parent-ELG distribution (silver triangles). Here we are representing random subsets of both populations, 30 percent of them, to avoid crowding. We overplot the corresponding 68 and 95 (inner and outer lines, respectively) percent contours as green and silver lines. In addition, we show in black the contours of the star-forming (SF) population selected at sSFR > 10−11 yr−1. The large markers with error bars display the corresponding sSFR means and 1 σ deviations in bins of stellar. The side histograms show the sSFR and M⋆ marginal distributions of the main-ELG (green) and SF populations (black lines), and compare them to the parent-ELG sample (gray), which has no cuts. Right panel: Hα luminosity as a function of stellar mass, color-coded by sSFR, and corresponding marginal distributions, with the same colors as in the left panel.

In Fig. 3, galaxies from the main-ELG sample are color-coded by the Hα EW. Here we can see that ELGs with a high sSFR are also those with higher EW. As expected, the three selections are consistent with each other up to stellar masses ∼ 1011 M⊙.

Similar trends are found for the other spectral lines under study. The corresponding plots are shown in Fig. A.3.

On each side of the figure we display the marginal sSFR and M⋆ distributions for the SF and main-ELG samples, and we compare them with the parent-ELG sample (silver). The main-ELG sample includes galaxies with relatively low sSFR values, that will not be considered as star-forming, neither in terms of their sSFR nor in relation with the so-called star formation main sequence. We quantify the numbers of these populations below.

The right panel in Fig. 3 displays the Hα luminosity as a function of stellar mass, color-coded by sSFR. Figure A.4 shows similar plots for the rest of lines under study. Here we notice that Hα ELGs with lower star-formation activity (i.e., sSFR ≲ 10−11 yr−1) are also the most massive and least luminous ones, whereas SF ELGs with sSFR ≳ 10−11 yr−1 tend to concentrate toward the low-mass and high-luminosity end of the distribution.

These results highlight that ELGs selected with a combination of cuts in signal-to-noise and line flux, that is, the main-ELG sample, are not equivalent to ELGs selected by using a sharp cut in sSFR or, similarly, in EW. This agrees with theoretical studies that have shown that the small-scale clustering is different for samples selected either based on SFR or emission line fluxes (Gonzalez-Perez et al. 2020). In fact, the selection based on flux and S/N returns a heterogeneous population of galaxies, covering a similar range in both sSFR and stellar mass as the parent-ELG sample. This guarantees that the number density of galaxies, in particular the fainter ones, is preserved, maximizing the completeness of the luminosity function.

2.5. Incompleteness effects and redshift evolution

Figure 4 displays the Hα luminosity of the main-ELG sample as a function of the r-band absolute magnitude, Mr, color-coded by redshift. We compare this distribution to that of the parent-ELG sample, selected at rp > 17.77. To better understand its evolution, we analyze the result in three redshift bins: the full sample at 0.02 < z < 0.22, the lower-z bin at 0.02 < z < 0.12, and the higher-z one at 0.12 < z < 0.22. Figure A.5 shows similar plots for the other lines under study.

thumbnail Fig. 4.

Main-ELG Hα luminosity as a function of the r-band absolute magnitude, color-coded by redshift. On the background we show in gray the parent-ELG sample distribution, which has no cuts in flux nor S/N. For both populations we display random subsets of 30 percent of the total to avoid saturation. From left to right, we show the full sample (0.02 < z < 0.22), the lower-z bin (0.02 < z < 0.12), and the higher-z (0.12 < z < 0.22) one. The horizontal lines represent our lower completeness limits in luminosity (see the text for details).

We find that the Hα flux cut is not independent of Mr and hence from the limit rp < 17.77 intrinsic to the parent-ELG sample. A similar result is found for the other lines. The impact of such dependency is stronger as the redshift increases. In other words, when we cut in flux or S/N, we are also removing a fraction of galaxies below a certain line luminosity that varies in a nontrivial way with redshift.

Our modified 1/Vmax method for ELGs (see Sect. 3) is capable of individually correcting from flux-limited selection effects, but not from statistical correlations between the line luminosities and broadband magnitudes. We therefore set a lower completeness limit for all emission-line luminosities in order to ensure that these correlations do not significantly affect the LF measurement. For the Hα line, we set this threshold to L = {1040.2,  1040,  1041.1} erg s−1 in the full sample, low-z, and high-z bin, respectively. These limits for the other emission lines are provided in Appendix D. All these values are chosen by eye, based on the completeness that the main-ELG sample shows in Figs. 4 and A.5. Specifically, we set as threshold the luminosity value where the density of ELGs in these figures starts to degrade, indicated as dotted, dot-dashed and dashed lines in Figs. 4 and A.5.

3. Volume correction

The differential luminosity function is defined as the number, N, of galaxies per unit luminosity interval and comoving volume, V, as:

Φ ( log L , z ) = d N d log L d V ( z ) , $$ \begin{aligned} \Phi (\log L,z)=\frac{\mathrm{d}N}{\mathrm{d}\log L\,\mathrm{d}V(z)}, \end{aligned} $$(3)

where V is a function of redshift. The 1/Vmax estimator (Schmidt 1968; Felten 1976) allows us to correct the LF from the Malmquist bias, that is, the fact that faint objects tend to be detected only in a small volume, while bright ones are observed in the entire sample volume (see e.g., Weigel et al. 2016). Other methods to estimate the galaxy LF are the C− method by Lynden-Bell (1971), the parametric maximum-likelihood STY method proposed by Sandage (1978), or the Stepwise Maximum Likelihood Method (SWML; Efstathiou et al. 1988; Norberg et al. 2002) that does assume any functional form.

Here we focus on emission-line LFs. The galaxy counts need to include their observational incompletness, usually given as a weight. In the parent-ELG sample we have different sources of incompleteness to take into account. In fact, the main-ELG sample is a r-band magnitude limited sample, on top of which we have imposed a combination of cuts in flux and signal-to-noise for the six spectral lines under study. In this section we describe the methodology used to estimate the line LFs taking into account the incompleteness induced by the thresholds we have imposed.

In practice, Eq. (3) is evaluated by counting the number of galaxies in each Δlog L bin, Nk, and weighting it by the maximum volume Vmax in which each galaxy can be observed, given the survey limits and its luminosity. In the k−th bin of luminosity and for a sample of i = 1, …, Nk galaxies we have:

Φ 1 / V max k = 1 Δ log L k ∑ i = 1 N k 1 V max , i . $$ \begin{aligned} \Phi _{1/V_{\rm max}}^{k}=\frac{1}{\Delta \log {L}^k}\sum _{i=1}^\mathrm{N_k}\frac{1}{V_{\mathrm{max},\,i}}\,. \end{aligned} $$(4)

To estimate Vmax,  i we need to determine the maximum redshift, zmax,  i at which a galaxy could still be observed as part of the main-ELG sample, given its observational limits. Explicitly this is:

V max , i = A 3 ( π 180 ) 2 ( D c 3 ( z max , i ) − D c 3 ( z low ) ) , $$ \begin{aligned} V_{\mathrm{max},\,i}=\frac{A}{3}\left(\frac{\pi }{180}\right)^2\left(D_{\rm c}^3(z_{\mathrm{max},\,i})-D_{\rm c}^3(z_{\rm low})\right)\,, \end{aligned} $$(5)

where A = 7300 deg2 is the survey area, Dc(z) is the galaxy comoving distance depending on redshift and cosmology, and zlow = 0.02 is the lower redshift limit of the main-ELG sample.

We modify the standard 1/Vmax formulation in Eq. (4) to correct the main-ELG sample from the spectroscopic, r-band magnitude, and luminosity selection effects. To correct from spectroscopic incompleteness in the SDSS sample (i.e., the fact that SDSS did not obtain the spectra of all the targets above its magnitude limit), we weight Eq. (4) by w c, i = c i −1 $ {\it w}_{{\rm c},\,i}=c_i^{-1} $, that is, the inverse of the SDSS spectroscopic completeness. Explicitly we have:

Φ 1 / V max k = 1 Δ log L k ∑ i = 1 N w c , i V max , i . $$ \begin{aligned} \Phi _{1/V_{\rm max}}^{k}=\frac{1}{\Delta \log {L}^k}\sum _{i=1}^\mathrm{N}\frac{w_{\mathrm{c},\,i}}{V_{\mathrm{max},\,i}}\,. \end{aligned} $$(6)

This is a small correction, as the main-ELG sample is more than 80 percent complete in spectroscopy (Blanton et al. 2003).

To correct from the limits in r-band, line flux, and S/N, we define the maximum redshift, zmax,  i, of a galaxy in our sample as a function of the observational cuts imposed (see Sect. 2.3):

z max , i = min ( z max , i mag , z max , i F , z max , i S / N , z up ) , $$ \begin{aligned} z_{\mathrm{max},\,i}=\mathrm{min}\left( z_{\mathrm{max},\,i}^\mathrm{mag}, \,z_{\mathrm{max},\,i}^F, \,z_{\mathrm{max},\,i}^\mathrm{S/N},\,z_{\rm up}\right)\,, \end{aligned} $$(7)

where the superscripts indicate the contributions based on magnitude (mag), flux (F), and signal-to-noise (S/N) limits, while zup = 0.22 is the upper limit of the main-ELG sample. The flux and S/N are grouped vectors, F = (FHα, F[O II], F[O III], FHβ, F[N II], F[S II]) and S/N = (S/NHα, S/N[O II], S/N[O III], S/NHβ, S/N[N II], S/N[S II]).

As shown in the top panel of Fig. 5, the faintest r-band absolute magnitude that a main-ELG can have while being part of a sample limited at r p faint = 17.77 $ r_{\mathrm{p}}^{\mathrm{faint}}=17.77 $ is (Blanton et al. 2003):

M r , i faint = r p faint − DM ( z i ) − K ( z i ) , $$ \begin{aligned} M_{r,\,i}^\mathrm{faint}=r_{\rm p}^\mathrm{faint}-\mathrm{DM}(z_i)-K(z_i)\,, \end{aligned} $$(8)

thumbnail Fig. 5.

Vmax computation scheme for a galaxy from the main-ELG sample (star symbol). Top panel: we take into account the survey r-band magnitude limit r p faint = 17.77 $ r_{\mathrm{p}}^{\mathrm{faint}}=17.77 $; note that we are omitting the K-corrections (K(zi) = 0 in Eq. (8)) for this representation. Bottom panel: similar plot as the top one for a survey with a limit in the Hα line flux of F H α faint = 2 × 10 − 16 erg s − 1 $ F_{\mathrm{H}\alpha}^{\mathrm{faint}}=2\times 10^{-16}\,\mathrm{erg\,s}^{-1} $. For the [O II], [O III], Hβ, [N II], and [S II] lines the methodology is identical (see Sect. 2.3). The lower and upper redshift limits of the survey, zlow = 0.02 and zup = 0.22, are highlighted by dashed vertical red lines in both panels. The maximum redshifts that the galaxy can have and still be included in the sample, considering its magnitude and Hα flux limits, as well as the faintest luminosity, are shown by dotted vertical blue lines.

where DM(z) is the distance modulus estimated at redshift z in our fiducial cosmology, and K(z) is the K-correction. To calculate it we use KCORRECT V4_36 (Blanton & Roweis 2007). Figure 6 compares the SDSS Mr luminosity functions computed with and without K-corrections. In the redshift range under study, the effect of K-corrections is less than 7 percent at −22.5 < Mr < −18, while it grows up to 30 percent in the faintest galaxies in our sample. Note that K-corrections are not needed when dealing with emission-line luminosities for which the redshift is known. We choose not to apply any evolution correction, as this is negligible at 0.02 < z < 0.22 (Blanton et al. 2001), and would require optimizing the model template to our ELG selection.

thumbnail Fig. 6.

SDSS Mr luminosity functions including (full markers) and omitting (empty markers) K-corrections. The effect is less than 7 percent at −22.5 < Mr < −18, while it grows up to ∼30 percent in the faint and luminous tails of the distribution. The gray band highlights the 10 percent difference range.

The maximum redshift, zmax,  i, of a galaxy in our magnitude-limited sample, is found as the root of the following equation:

M r , i faint − r p faint + DM ( z max , i mag ) + K ( z max , i mag ) = 0 , $$ \begin{aligned} M_{r,\,i}^\mathrm{faint}-r_{\rm p}^\mathrm{faint}+\mathrm{DM}\left(z_{\mathrm{max},\,i}^\mathrm{mag}\right)+K(z_{\mathrm{max},\,i}^\mathrm{mag})=0\,, \end{aligned} $$(9)

which is solved iteratively by interpolating the Mr,  i(z) – redshift relation.

The faintest Hα ELG luminosity that a galaxy can have and still be in the sample, when this is limited in line flux, is obtained in a similar manner, as shown in Fig. 5. For a flux limit F H α faint $ F_{\mathrm{H}\alpha}^{\mathrm{faint}} $ (Sect. 2.3) we derive the corresponding faintest luminosity in that line as:

L H α , i faint [ erg s − 1 ] = 4 π D L 2 ( z i ) F H α faint , $$ \begin{aligned} L_{\mathrm{H\alpha },\,i}^\mathrm{faint}\,\mathrm{[erg\,s^{-1}]}=4\pi \,D_{\rm L}^2(z_i)\,F_{\mathrm{H}\alpha }^\mathrm{faint}\,, \end{aligned} $$(10)

where the luminosity distance DL(zi) = (1 + zi) Dc(zi) is measured in [Mpc], and the line flux in [erg s−1 Mpc−2]. The maximum redshift, zmax,  i, the galaxy can have in the Hα flux-limited sample is the root of the following equation:

( 1 + z max , i F H α ) D c ( z max , i F H α ) − L H α , i 4 π F H α faint = 0 . $$ \begin{aligned} \left(1+z_{\mathrm{max},\,i}^{F_{\mathrm{H}\alpha }}\right)\,D_{\rm c}\left(z_{\mathrm{max},\,i}^{F_{\mathrm{H}\alpha }}\right)-\sqrt{\frac{L_{\mathrm{H\alpha },\,i}}{4\pi \,F_{\mathrm{H}\alpha }^\mathrm{faint}}}=0\,. \end{aligned} $$(11)

This is solved by interpolating and inverting the Dc(z) – redshift relation. For the [O II], [O III], Hβ, [N II], and [S II] lines we adopt the same procedure with the corresponding flux limit chosen for each line. In our case we choose the same cut for all the lines: F > 2 × 10−16 erg s−1 cm−2 (see Sect. 2.3).

Finally, the faintest Hα flux a galaxy can reach in the main-ELG sample, when this is limited in S / N H α lim $ {S/N}_{\mathrm{H}\alpha}^{\mathrm{lim}} $ (Sect. 2.3), is:

F H α , i faint = S / N H α lim × F err , i , $$ \begin{aligned} F_{\mathrm{H}\alpha ,\,i}^\mathrm{faint}={S/N}_{\mathrm{H}\alpha }^\mathrm{lim}\times F_{\mathrm{err},\,i}\,, \end{aligned} $$(12)

where Ferr,  i is the line flux uncertainty. By substituting the above expression in Eq. (11), we obtain z max, i S/ N Hα $ z_{{\rm max},\,i}^{S/N_{{\rm H}\alpha}} $. Again, for the rest of the lines the procedure is identical, using fixed signal-to-noise limit in our sample: S/N > 2 (see Sect. 2.3).

4. ELG classification

Strong spectral emission lines can have different origins, the most common being the gas heated by newly forming stars. Galaxies hosting super massive black holes actively accreting mass, AGN and QSOs, also present strong emission lines produced in jets and shock regions. The number density of AGN and QSOs is lower than SF galaxies, and their line ratios are different (see e.g., Kewley et al. 2019). Old stellar populations can also produce strong emission lines (see e.g., Kennicutt 1992; Flores-Fajardo et al. 2011; Cid Fernandes et al. 2011; Sansom et al. 2015; Byler et al. 2019; Nersesian et al. 2019; Clarke et al. 2021).

One of the goals of this work is to understand the contribution to the LF of local ELGs classified according to the most likely origin of their emission lines. We split the main-ELG sample using two selection criteria: (i) a sharp cut in sSFR to separate SF from passively evolving galaxies (Sect. 4.1), and (ii) the line ratios in the BPT and WHAN diagrams (Sect. 4.2). In Sect. 5 we study the luminosity functions for each of these ELG types.

4.1. Classification using the sSFR

We select star-forming galaxies as those with sSFR > 10−11 yr−1 in the main-ELG sample. These galaxies constitute 84 percent of the sample, including the volume correction. The value chosen for this cut corresponds to the classical threshold adopted to separate SF from passive galaxies (e.g., Ilbert et al. 2015; Donnari et al. 2019; Corcho-Caballero et al. 2021a).

4.2. Classification with the BPT and WHAN diagrams

As illustrated in Fig. 7, we classify the origin of the main-ELG spectral lines using the emission-line ratios in the Baldwin-Phillips-Terlevich (BPT) and the EWHα versus [N II]/Hα (WHAN) diagnostic diagrams (e.g., Stasińska et al. 2006; Cid Fernandes et al. 2011).

thumbnail Fig. 7.

Diagnostic diagrams used to provide our BPT classification (see Sect. 4.2). Top and middle panels: main-ELG [N II] and [S II] BPT diagrams. Galaxies are color-coded by their sSFR; here we show only 60 percent, randomly sampled, of each population to avoid saturation. We overplot the Kewley et al. (2001), Kauffmann et al. (2003a) and Kewley et al. (2006) demarcation lines (black solid, dot-dashed, and thick dotted lines, respectively) separating the SF, AGN, LINER, and Seyfert contributions (see Sect. 4.2). Ambiguous objects are represented as stars. Bottom: Seyfert, passive, and ambiguous components of the main-ELG sample represented in the WHAN diagram, together with the EW cuts we use to select them: the EW = 6 Å limit (dot-dashed line) separating Seyferts from LINERs, and the EW = 0.5 Å cut (Cid Fernandes et al. 2011; solid) to isolate passive ELGs from the rest.

We build the BPT diagrams for the main-ELG [N II] and [S II] lines and adopt the demarcation criteria from Kewley et al. (2001) and Kauffmann et al. (2003a; “Kew01” and “Kau03”, hereafter) to separate ELGs into SF, Composite galaxies and AGN. The Kew01 line marks the upper envelope of the H II region in Kewley et al. (2001) photoionization models. Above this threshold, the origin of emission lines is expected to be different from young O and B stars (see also Belfiore et al. 2016). The Kau03 demarcation line is derived from an empirical relation to separate SF galaxies. Between this line and that from Kew01, the regions where emission lines originate may be due to star formation and/or other ionization sources.

For those galaxies above the Kew01 line in the BPT [S II] diagram, we further split the possible origin of their emission lines using the Kewley et al. (2006) criterion (“Kew06”, hereafter) coupled with the EW ≥ 6 Å condition from Cid Fernandes et al. (2011) in the WHAN diagram, that is, the plane defined by the Hα EW values as a function of log([N II]/Hα). This separation allows us to better distinguish AGN candidates into Seyfert galaxies and low-ionization narrow emission-line regions (LINERs; Heckman 1980).

LINERs are characterized by lower luminosities compared to Seyfert galaxies and QSOs. It is well known that most nearby AGN with [O II], [S II] or [O I] emission are dominated by LINERs (e.g., Ho et al. 1995, 1997; Kauffmann et al. 2003a; Kewley et al. 2006; Singh et al. 2013; Belfiore et al. 2016). Considering the intensity of their emissions, Seyfert sources and LINERs are often referred to as “strong” and “weak” AGN, respectively (see e.g., Cid Fernandes et al. 2011). On the other hand, these line ratios have also been observed in the outskirts of galaxies (e.g., González Delgado et al. 2014), and therefore it is unclear whether they may actually be produced by other mechanisms.

By adopting the above criteria, we finally classify the galaxies in our main-ELG sample into the following BPT classification: (i) Star-forming (SF): below Kau03 in [N II] BPT and Kew01 in [S II] BPT; (ii) Passive: EWHα < 0.5 Å as in Cid Fernandes et al. (2011; iii) Seyfert (Sy): above Kew01 in both BPT diagrams, above Kew06 in [S II] BPT, and EWHα ≥ 6 Å; (iv) LINERs: above Kew01 in both BPT diagrams, below Kew06 in [S II] BPT; (v) Composite: between Kau03 and Kew01 in [N II] BPT; (vi) Ambiguous: galaxies that either do not fall within any of the previous classifications (mostly Seyfert galaxies with EWHα < 6 Å), or that belong to more than one class at the same time.

The above classification is widely used in the literature, and it provides an ideal benchmark to characterize the contributions to emission line LFs from different physical origins.

4.3. Comparison of the classifications

Table 2 compares the volume-corrected percentages of galaxies, classified using the BPT+WHAN diagrams, with those that have a sSFR either above or below sSFR = 10−11 yr−1. It is clear from this table that, according to the BPT+WHAN classification, spectral emission lines originate from star-forming regions only for 63.3 percent of the main-ELG sample. Spectral emission lines are not originated in SF regions for an important fraction of ELGs with sSFR > 10−11 yr−1. The origin of these lines is likely to be shocks, as the combined total fraction of SF Seyfert, LINERs, and composite ELGs is 22.7 percent.

Table 2.

Volume-corrected percentages of the different types of ELGs as classified using the BPT+WHAN diagrams (second column) and percent split of the total fraction for each type based on sSFR = 10−11yr−1 (last two columns).

In Fig. 7 we show how the six main-ELG types distribute as a function of sSFR in the [N II] (top panel) and [S II] (middle) BPT planes. Composite and passive ELGs constitute 18 and 0.03 percent of the total, respectively, and show lower sSFR values compared to the SF population (i.e., sSFR ≲ 10−9.8 yr−1). LINERs (3.4 percent of the ELG) exhibit even smaller sSFR values, that is, sSFR ≲ 10−11.4 yr−1. Ambiguous galaxies make up 13.97 percent of the main-ELG sample. They also feature very small sSFR values, and they tend to preferentially occupy the AGN region of the BPT diagram. Finally, Seyfert ELGs are a mixed population in terms of sSFR. While most of them will be classified as star-forming, a nonnegligible fraction (i.e., 20.2 percent) of them display sSFR below our adopted threshold of 10−11 yr−1.

In the lower panel of Fig. 7, we display how Seyfert, passive, and ambiguous ELGs are located in the WHAN diagram. We overplot as horizontal lines the EW = 0.5 Å threshold (Cid Fernandes et al. 2011) used to separate passive ELGs from the rest, as well as the EW = 6 Å criterion used to separate Seyfert ELGs from LINERs.

Figure 8 shows the volume-weighted [N II]/Hα distributions of the ELG components resulting from our BPT classification. We overplot, as vertical dashed line, the Stasińska et al. (2006) log([N II]/Hα) = −0.4 criterion (“S06” hereafter) separating SF galaxies from the rest (see also Cid Fernandes et al. 2011). This condition is exclusively based on the Hα/[N II] line ratios and ignores the [O III]/Hβ ones. By looking at the distribution of SF ELGs, we propose log([N II]/Hα) = −0.3 as an alternative criterion to S06 to better separate SF main-ELG from the rest. Note, however, that we do not apply any of these two cuts in our analysis, as we select SF galaxies exclusively based on Kew01, Kew06 and Kau03 demarcation lines in the BPT diagrams. This result shows that a significant fraction (18.8 percent) of SF ELGs selected from BPTs spills into the non-SF region of the WHAN plane, as defined by S06, while only 2 percent of composite ELGs spills into the SF plane. If instead of S06 we applied our proposed criterion, the fraction of SF ELGs in the non-SF region would decrease to 0.8 percent, while that of composite in the SF plane would go up to 26 percent.

thumbnail Fig. 8.

Volume-weighted distributions of the [N II]/Hα line ratios resulting from our ELG BPT classification. The criteria to separate SF ELGs from the rest, solely based on the ratio [N II]/Hα proposed by Stasińska et al. (2006, S06) is shown by a vertical dashed line, log([N II]/Hα) = −0.4. Our sample is better separated by a slightly different value, log([N II]/Hα) = −0.3, also indicated by a vertical solid line. Note that we do not apply any of these two cuts in our analysis.

Figure 9 compares, in the sSFR – stellar mass plane, our ELG classification based on BPT+WHAN with the one based on sSFR (black contours). Both SF ELG classifications overlap well and concentrate in the upper region of the sSFR – stellar mass plane, that is, at higher sSFR and lower mass values. In particular, while LINERs and passive ELGs mainly inhabit the lower tail of the distribution, toward lower sSFR values, composite and Seyfert galaxies populate the entire sSFR range. In terms of stellar mass, while SF ELGs span smaller values, down to 108 M⊙, the other ELG types concentrate above 1010 M⊙.

thumbnail Fig. 9.

sSFR as a function of stellar mass for all the main-ELG contributions, each one represented by contours. In each set of contours, the inner line (outer shade) represents the 68 (95) percent confidence regions. The contours of the SF population at sSFR > 10−11 yr−1 (solid black) are broken due to the sharp sSFR cut; those of the passive component (dotted red) are broken due to the very low number density of this population (0.1 percent of the total; see Table 2).

4.4. Old populations

Galaxies that are passively evolving can present an excess of UV flux due to an old but hot stellar population, such as hot horizontal branch stars burning Helium (e.g., Phillipps et al. 2020). We find that 16.4 (0.03) volume-corrected percent of the sample are passive according to the sSFR (BPT+WHAN) classification used in this study (see Table 2).

To better understand the contribution of old stellar populations to the main-ELG sample, we study the 4000 Å break index, or Dn(4000), as a function of stellar mass and sSFR. The Dn(4000) index is reddening insensitive and traces SFRs on a time scale of 300–1000 Myrs. We employ the Dn(4000) values provided in the MPA-JHU catalog. These were estimated as the ratio of the flux in the red continuum to that in the blue continuum (see e.g., Balogh et al. 1999; Angthopo et al. 2020):

D n ( 4000 ) = ⟨ F c r ⟩ ⟨ F c b ⟩ , where $$ \begin{aligned} {D_n(4000)}=\frac{\langle F_{\rm c}^{ \mathrm r}\rangle }{\langle F_{\rm c}^{ \mathrm b}\rangle },\,\,\,\,\mathrm{where} \end{aligned} $$(13)

⟨ F c i ⟩ = 1 ( λ 2 i − λ 1 i ) ∫ λ 1 i λ 2 1 F c ( λ ) d λ , $$ \begin{aligned} \langle F_{\rm c}^{ i}\rangle =\frac{1}{(\lambda _2^i-\lambda _1^i)}\int _{\lambda _1^i}^{\lambda _2^1} F_{\rm c}(\lambda )\,d\lambda \,, \end{aligned} $$(14)

and ( λ 1 b , λ 2 b , λ 1 r , λ 2 r )=(3850,3950,4000,4100) $ (\lambda_1^{\rm b},\lambda_2^{\rm b},\lambda_1^{\rm r},\lambda_2^{\rm r})=(3850,3950,4000,4100) $Å.

Figure 10 compares the Dn(4000) index as a function of the galaxy stellar mass7, color-coded by sSFR, for the main-ELG sample and its different components.

thumbnail Fig. 10.

Dn(4000) break index as a function of the galaxy stellar mass, color-coded by sSFR. We compare the main-ELG sample (small dots on the background) with its SF population selected from sSFR (black contours, not including weights), and with the median ±σ results of the SF (light blue diamonds), composite (brown hexagons), Seyfert (navy blue stars), LINERs (orange squares), and passive (red triangles) ELG contributions selected using the BPT+WHAN diagrams. The points shown here are a random subset of the main-ELG sample, 60 percent of the total, to avoid saturation. The horizontal dotted line indicates the typical separation between younger and older stellar populations.

SF ELGs, no matter if selected from sSFR or from BPT+WHAN, are fully dominated by young stellar components. Considering the error bars, their Dn(4000) values range between 1 and 1.7, but most of them concentrate below 1.4. Above M⋆ ∼ 1010.5 M⊙, they also show some contributions from old stellar components, which are negligible (2.5 percent) for the SF ELGs based on BPT+WHAN, but significant (25.5 percent) for SF ELGs selected from sSFR. Here we are quantifying the portion of passive ELGs falling in the younger, SF region at Dn(4000) < 1.4 in Fig. 10. All these numbers are volume-corrected.

On the other extreme, ELGs classified as LINERs or passive exhibit higher Dn(4000) values, mostly between 1.4 and 2. These ELGs are thus not only characterized by small sSFR values, as we have seen in the previous section, but they are also located outside the contour defined by the galaxies with sSFR > 10−11 yr−1 on the Dn(4000) – logM⋆ plane. According to their Dn(4000) values, 99.1 percent of the BPT+WHAN ELGs classified as passive are dominated by an old stellar component, with their Dn(4000) indices ranging between 1.6 and 2. LINERs also exhibit very high Dn(4000) values. About 99 percent of LINERs are dominated by older stars, with Dn(4000) between 1.4 and 2. The sources of the ionizing photons in LINERS are expected to be different from star forming regions. The origins could be hot low-mass evolved stars (e.g., Flores-Fajardo et al. 2011), diffuse ionized gas (e.g., Mannucci et al. 2021), and X-ray busters (e.g., Mineo et al. 2012). As the EW of LINERs are low, the origin of the emission lines is expected to be less energetic than AGN or shocks.

The situation is much more complex for Seyfert galaxies. Note that the sSFR values and stellar masses of these objects cover the whole range 10−11.4 − 10−9.5 yr−1 and 108.5 − 1012 M⊙, respectively. 66.6 percent of Seyfert galaxies are dominated by old stellar components, with Dn(4000)∼1.5, and the relation between Dn(4000) and stellar mass is in between the trends observed for SF and passive systems.

Composite ELGs, on the other hand, are consistent with the high-mass end of the main sequence of star formation (stellar masses above 1011 M⊙, and sSFRs in the range 10−10.6 − 10−10.2 yr−1). Only 34.9 percent of them are dominated by old stars, with Dn(4000) only slightly above 1.4, and they follow the same scaling relation as the SF population.

5. Luminosity functions

We have obtained observed and dust-corrected luminosity functions for the six emission lines of interest in 3 redshift bins. All these luminosity functions are available in Appendix B and at the CDS.

Figure 11 presents our main-ELG luminosity functions for Hα, Hβ, [O II], [O III], [N II], and [S II] emission lines in the whole redshift range, 0.02 < z < 0.22. Note that all these LFs are observed (i.e., dust attenuated). It is important to also highlight that we only trust our measurements at luminosities higher than the completeness thresholds established in Sect. 2.5 and indicated in Fig. 11 by the shaded yellow regions. Those emission lines for which we do not show the shaded region have the completeness limit falling outside the luminosity range displayed in the figure.

thumbnail Fig. 11.

From top to bottom and from left to right: Hα, Hβ, [O II], [O III], [N II], and [S II] observed (i.e., dust extincted) luminosity functions of the main-ELG sample (full black dots). The contributions of ELGs classified in different ways are shown by empty colored markers, with colors as indicated in the legend. We compare our results – both tabulated in Appendix B and at the CDS – with several observed published measurements in the local Universe: Hα ELGs from Ly et al. (2007) at z = 0.07 − 0.09, Gilbank et al. (2010) at 0.032 < z < 0.2, Pirzkal et al. (2013) at 0 < z < 0.5, and Hα AGN from Schulze et al. (2009) at z < 0.3; Hβ ELGs from Comparat et al. (2016) at z = 0.3, Hβ AGN from Schulze et al. (2009) at z < 0.3; [O II] ELGs from Gilbank et al. (2010) at 0.032 < z < 0.2, Gallego et al. (2002) at z ≤ 0.045, Comparat et al. (2015) at z = 0.17, and Pirzkal et al. (2013) at 0.5 < z < 1.5; [O III] ELGs from Comparat et al. (2016) at z = 0.3, from Pirzkal et al. (2013) at 0.1 < z < 0.9, and [O III] AGN from Bongiorno et al. (2010) at 0.15 < z < 0.92. We overplot our Saunders fits as lines; the parameters are in Table 3 and were obtained considering only the points above the luminosity completeness thresholds discussed in Sect. 2.5 and Appendix A and represented as cyan shades in the panels (for those lines whose completeness limit falls within the L range shown in the figure). The error bars are computed from 50 jackknife resamplings (see Sect. 5.2).

Our main-ELG LF measurements are in good agreement with several published results in the local Universe. However, in this work we are able to measure the main-ELG LFs beyond the limit 1043 erg s−1 that previous studies show. This is thanks to the high statistics and large volume that the main-ELG sample offers, as well as the particular redshift selection performed.

Our Hα LF is consistent up to LHα ∼ 1042erg s−1 with results from Gilbank et al. (2010) at 0.032 < z < 0.2, and from Ly et al. (2007) at z = 0.07 − 0.09. The latter only spans the faint tail of our distribution around 1040erg s−1. Our Hα Seyfert LF shows good consistency with the AGN LF from Pirzkal et al. (2013) at 0 < z < 0.5.

The main-ELG [O II] LF is in good agreement with the results from Gilbank et al. (2010) at 0.032 < z < 0.2 up to ∼1042.3erg s−1. Below 1041erg s−1, our measurements are consistent with the results from Gallego et al. (2002) at z ≤ 0.045. In the L[O II] range between 1041 − 1042.3erg s−1 our measurements are consistent with the results from Comparat et al. (2015) at z = 0.17, and with the LF from Pirzkal et al. (2013) at 0.5 < z < 1.5 in the range 1040.2 − 1042.3erg s−1.

The main-ELG Hβ LF agrees, up to ∼1041 erg s−1, with the results from Comparat et al. (2016) at slightly higher redshift, z = 0.3. Our Hβ Seyfert LF is in reasonable agreement with the AGN LF from Schulze et al. (2009) at 0.1 < z < 0.9 only in the luminosity range 1041.2 − 1041.5 erg s−1, while at higher luminosities we obtain up to 0.5 dex less AGN.

Our main-ELG [O III] LF is in good agreement with the result from Comparat et al. (2016) at z = 0.3 and Pirzkal et al. (2013) at 0.1 < z < 0.9 below 1041.5 erg s−1. Above this luminosity, we find about 1 dex more luminous [O III] emitters than Comparat et al. (2016). Our LF trend is smoother with no bump around 1041.5 erg s−1.

5.1. Fitting the emission-line LFs

For each measurement in Figs. 12 and C.1, we overplot the best fit obtained using the Saunders et al. (1990) function:

Φ ( L ) = Φ ⋆ ( L L ⋆ ) α exp [ − ( log ( 1 + L / L ⋆ ) 2 σ ) 2 ] . $$ \begin{aligned} \Phi (L)= \Phi _\star \left(\frac{L}{L_\star }\right)^\alpha \exp \left[-\left(\frac{\log (1+L/L_\star )}{\sqrt{2} \sigma }\right)^2\right]\,. \end{aligned} $$(15)

thumbnail Fig. 12.

LFs compared for the six emission lines under study. Top panel: best Saunders fit to the observed (solid lines) and dust-corrected (dashed lines) line LFs, for the six studied emission lines, as indicated in the legend. Bottom panel: ratios between the observed and the intrinsic (dust-corrected) LF, for each emission line. In both panels the error bars are obtained from 50 jackknife realizations (Sect. 5.2).

depending on four parameters. For each emission line, we fit the quantity log(Φ(L)) considering only the points above the luminosity completeness threshold established in Sect. 2.5. The optimal parameters for each line LF are reported in Table 3 and they are overall consistent within the error bars with those provided by Comparat et al. (2016) as a function of redshift. Our reduced χ2 values indicate that the Saunders model statistically provides a very good fit both to the main-ELG LFs and their different contributions.

Table 3.

Saunders best-fit model parameters to the observed LFs shown in Fig. 11.

In Fig. 12 we compare the best Saunders models for the main-ELG LFs of the six studied emission lines. We do not find a clear trend with metallicity, however the [O III] LF is flatter than the rest.

Beyond Saunders, we also fit the ELG LFs using a single Schechter function (Schechter 1976):

Φ ( L ) = Φ ⋆ ( L L ⋆ ) α exp ( − L L ⋆ ) , $$ \begin{aligned} \Phi (L)= \Phi _\star \left(\frac{L}{L_\star }\right)^{\alpha }\exp {\left(-\frac{L}{L_\star }\right)}\,, \end{aligned} $$(16)

a double Schechter one (e. g. Blanton et al. 2005a):

Φ ( L ) = [ Φ 1 ⋆ ( L L ⋆ ) α 1 + Φ 2 ⋆ ( L L ⋆ ) α 2 ] exp ( − L L ⋆ ) , $$ \begin{aligned} \Phi (L)= \left[\Phi _1^\star \left(\frac{L}{L_\star }\right)^{\alpha _1}+\Phi _2^\star \left(\frac{L}{L_\star }\right)^{\alpha _2}\right]\exp {\left(-\frac{L}{L_\star }\right)}\, , \end{aligned} $$(17)

and a double power law. Their best-fit parameters and results are tabulated at the CDS.

The reduced χ2 values in Table E.1 indicate that a single Schechter function provides a poor fit to the observational data. The measured line LFs do show an excess in the very bright end, as already observed by Blanton & Roweis (2007) and Montero-Dorta & Prada (2009), who justified this excess by the presence of AGN and QSOs.

The double Schechter model statistically provides a good fit to the main-ELG LF, as shown in Table E.2, but it produces a bump in the bright end that seems to suggest overfitting rather than a physical feature of the LF. Moreover, in Fig. 11, when splitting the main-ELG LF in its different components, we see no evidence that the LF can be explained as the combination of two or more Schechter functions representing distinct galaxy populations. On the contrary, we argue that the bright end of both the individual and the combined LFs decrease more slowly than the exponential decay assumed by the Schechter parametric form.

The exact asymptotic behavior of very luminous galaxies is fundamental in order to make extrapolations at higher redshift, and it has profound implications on the expected duration of reionization and the type of galaxies contributing to it (see e.g., Mason et al. 2015; Sharma et al. 2018). Therefore, we further test a double power law model (e.g., Pei 1995) with five parameters, that is, slightly more flexible than the Saunders function:

Φ ( L ) = Φ 0 ( L L 0 ) − α 0 [ 1 + ( L L 0 ) β ] ( α 0 − α 1 ) / β . $$ \begin{aligned} \Phi (L)= \Phi _0 \left(\frac{L}{L_0}\right)^{-\alpha _0}\left[1+\left(\frac{L}{L_0}\right)^\beta \right]^{(\alpha _0-\alpha _1)/\beta }\,. \end{aligned} $$(18)

As shown in Appendix E, our power-law fit reaches the same level of agreement with the observations as the Saunders model, both for the main-ELG population as well as its different components. Therefore, in our analysis we choose to adopt a Saunders functional form for the fit, as it performs significantly better than any Schechter model and at a similar level than a model with more free parameters.

5.2. LF uncertainties

The uncertainties in the LFs are computed from 50 jackknife resamplings using the method presented in Favole et al. (2021). We split the SDSS footprint into a grid of 5 × 10 = 50 cells, with 5 RA and 10 Dec bins. Each cell spans ∼146 deg2 and contains about 3500 main-ELG galaxies. We then estimate 50 times the LF of the main-ELG sample removing a different cell each time. From these estimates we compute the jackknife covariance matrix as (e.g., Favole et al. 2016):

C ij = ( N res − 1 ) N res ∑ a = 1 N res ( Φ i a − Φ ¯ i ) ( Φ j a − Φ ¯ j ) , $$ \begin{aligned} C_{ij}=\frac{(N_{\rm res}-1)}{N_{\rm res}}\sum _{a=1}^{N_{\rm res}}(\Phi _i^a-\bar{\Phi }_i)(\Phi _j^a-\bar{\Phi }_j)\,, \end{aligned} $$(19)

where the indices i and j run over the bins in luminosity, and a runs over the number of resamplings, Nres = 50. The Φ ¯ $ \bar{\Phi} $ term represents the mean of the Nres LFs, and the multiplicative factor outside the sum takes into account that, in each jackknife configuration, (Nres − 2) copies are not independent from each other (see Norberg et al. 2011). The 1σ jackknife uncertainties are obtained as the square root of the diagonal elements of the covariance matrix.

5.3. Contributions to the luminosity functions

We find that the main-ELG LFs at z ∼ 0.1 are dominated by star-forming galaxies, independently from the emission line considered. This is true for the two classifications we have made, based on sSFR and the BPT+WHAN diagrams. For most spectral lines, the second contributing population is that classified as “composite”, which could actually be mostly massive SF galaxies with weaker emission lines. The shape of the composite component of each emission line is similar to the full and SF results, but its amplitude is about one order of magnitude lower.

Our measurements of the LFs for the Seyfert and LINER components are in reasonable agreement with results in the literature (see e.g., Bongiorno et al. 2010; Ermash 2013). In particular, the Seyfert contributions to the Hα and Hβ main-ELG LFs are consistent with the AGN LFs at z < 0.3 measured by Schulze et al. (2009). The Seyfert contribution to the [O III] line is in agreement, up to ∼1041.8 erg s−1, with the [O III] AGN LF at 0.15 < z < 0.92 from Bongiorno et al. (2010), but it drops by about 1 dex at 1042.5 erg s−1.

In general, Seyfert galaxies contribute significantly to the main-ELG LFs only in the bright end, while passive galaxies and LINERs are nonnegligible only in the faint end. One may notice in Fig. 11 that the Seyfert contribution to [O III] at 1042 erg s−1 is higher than that from composite galaxies by ∼1 dex. For the other lines (e.g., [N II] and [S II]), the contribution from Seyfert ELGs is either subdominant or similar to that of composite galaxies. This is somewhat expected to happen by construction, as in the BPT diagram we are requiring that these emission lines are strong for a galaxy to be assigned to the Seyfert class.

5.4. LF evolution

We further explore the evolution of the observed main-ELG LFs by separating the sample into two redshift bins: low-z, 0.02 < z ≤ 0.12, and high-z, 0.12 < z < 0.22. Fig. 13 shows that our main-ELG results are consistent with observations from Ly et al. (2007) at z = 0.08 and Sobral et al. (2013) at z = 0.4. Other lines are presented in Appendix D. Similar consistency is found for the other lines compared to observations.

thumbnail Fig. 13.

main-ELG observed LF in the low (top) and high (middle) redshift bins, together with their Saunders fits. The markers, lines and colors are the same as in Fig. 11. The cyan shades indicate where the incompleteness starts to dominate and our LF measurements cannot be trusted. The lower completeness limits are set to LHα = 1040,  1041.1 erg s−1 for the lower-z and higher-z, respectively (see Appendix D). We compare them to the LF results at slightly higher redshift from Ly et al. (2007; z = 0.08) and Sobral et al. (2013; z = 0.4). The bottom panel shows the ratios of the low- to high-z LF Saunders fits. We compare these ratios to better understand the change in the line luminosity functions. At z > 0.12, there are no passive galaxies above the completeness threshold considered: LHα = 1041.1 erg s−1.

We fit our LFs in the two redshift bins using a Saunders model and compare them. The Hα best-fit Saunders parameters in both z bins are reported in Table 4; those for the rest of lines are in Tables D.1 and D.2.

Table 4.

Best-fit Saunders parameters of the observed Hα LF fits in two redshift bins, 0.02 < z < 0.12 (top) and 0.12 < z < 0.22 (bottom), to better understand their evolution.

The global increase with redshift of the number of the main-ELG is clear from Figs. 13, D.1 and D.2. The differences are larger for the brightest objects, except when low number statistics appear to affect the observations. Such a trend is expected, as the main-ELG are predominantly star-forming galaxies and the star formation density increases with redshift (i.e., decreases with cosmic time since the Big Bang) within the range considered.

In terms of ELG contributions, SF, LINERs, and composite ELGs follow similar trends to those reported for the main-ELG, with some differences mostly happening at the brightest end. There are no passive ELGs brighter than L ∼ 1041.5 erg s−1 in the low-z bin. In the high-z bin, we do not have enough statistics to measure the passive contributions to the Hα, Hβ, and [S II] LF.

From the low- to the high-z bin, the luminosities of the full ELG sample increase by 0.2 − 0.3 dex (a factor of ∼0.5). Part of the decrease in numbers is due to the effect of dust attenuation. However, there is also an expected decline in the star formation rates at lower redshifts, consistent with that reported for star-forming main sequence (Speagle et al. 2014). A similar behaviour is found for the different types of ELGs, although number statistics start to become a problem for Seyfert galaxies at low luminosities. The evolution of Seyfert ELGs is not trivial and will be worth examining in more detail in the future.

5.5. Dust effect in the luminosity functions

The analysis carried out so far shows observed (i.e., dust attenuated) emission-line luminosities. In this section we study the effect that dust extinction has on the LFs. We correct the line fluxes from dust attenuation using the Balmer decrement as implemented in Corcho-Caballero et al. (2020) and assuming a Calzetti et al. (2000) extinction curve. The intrinsic Balmer decrement remains roughly constant for typical gas conditions in star-forming galaxies (Osterbrock & Ferland 1989). Therefore, we assume the standard intrinsic value of (HαHβ)int = 2.86, commonly used in the literature for star forming galaxies8. For the small fraction of galaxies, 5.3 percent, with an observed ratio Hα/Hβ below the theoretical value of 2.86, no correction is applied.

The intrinsic (i.e., dust extinction corrected) main-ELG luminosity functions for the six lines of interest are presented in Fig. C.1 and tabulated in Tables C.1–C.3. Their best-fit Saunders parameters are shown in Table 5 to facilitate the comparison with the observed LF parameters in Table 3.

Table 5.

Same result as Table 3, but for the intrinsic (i.e., dust corrected) LFs.

Our intrinsic LFs are consistent with several published results in the literature, with different levels of agreement. In particular, beyond LHα1041 erg s−1, our LFs are in good agreement with Gunawardhana et al. (2013) and James et al. (2008) results at z < 0.1, while at fainter luminosities they measure up to 3 times more Hα ELGs than us. Our LFs agree with the results from Sullivan et al. (2000) at z < 0.4 above LHα1042 s−1 erg. Below this value, we measure 2 times less Hα emitters. The result by Ly et al. (2007) at z = 0.07 − 0.09 only spans the very faint end of the Hα LF, at LHα1040 s−1 erg, where it is consistent with our findings. Our Hα LFs are consistent with those from Fujita et al. (2003) at z = 0.24 around 1042 erg s−1 Hα, but at fainter luminosities our LFs are lower by about 0.8 dex. With Gallego et al. (1995) Hα LF at z ≤ 0.045 we agree around 1042 erg s−1, while at lower (higher) LHα our LF is higher (lower) by about 2 dex.

In the [O II] line, our main-ELG LF is in between those from Sullivan et al. (2000) and Gallego et al. (2002).

Figure 12 compares the observed and intrinsic main-ELG LFs for the six studied emission lines. We find that the effect of dust increases with luminosity. As shown by Duarte Puertas et al. (2017), this is motivated by the fact that the actual amount of dust increases with stellar mass and SFR, which correlate strongly with line luminosity. Similar results were found also by Gilbank et al. (2010), Lumbreras-Calle et al. (2019) and Vilella-Rojo et al. (2021).

For the six lines, the number of galaxies is affected by less than a factor of 10 up to L ≳ 1042 erg s−1. For brighter galaxies there is a clear decline in numbers beyond a factor of 10 for Hβ, [N II], and [S II]. Since the impact of the extinction corrections on the LFs is significant only at L ≳ 1042 erg s−1, for the intrinsic LFs we maintain the same luminosity completeness thresholds of the observed ones (see Sect. 2.5).

Dust attenuation changes the slope of the Saunders fits to the line LFs. Observed LFs are systematically steeper (i.e., smaller α values) than the intrinsic ones. However, most of the best fit α values are compatible with zero both with or without dust attenuation. This indicates a small variation.

6. Summary and conclusions

We have studied the properties of emission-line galaxies (ELGs) selected from the SDSS DR7 main galaxy sample (Strauss et al. 2002) at 0.02 < z < 0.22 (i.e., 2.4 Gyrs). We have obtained the spectral properties of these galaxies from the MPA-JHU catalog3. Here we only study galaxies with a line flux of F > 2 × 10−16 erg s−1 cm−2 and error σF < 10−12 erg s−1 cm−2, a signal-to-noise S/N > 2, and an equivalent width EW ≥0 Å in the six lines of interest: Hα, Hβ, [O II], [O III], [N II], and [S II]. The resulting main-ELG is composed of 174572 ELGs (see Sect. 2.3). The performed cuts guarantee the line luminosity function (LF) to be complete up to certain luminosity threshold.

We have measured the main-ELG luminosity function (LF) – both observed and corrected from dust extinction (i.e., intrinsic) – of the Hα, Hβ, [O II], [O III], and, for the first time, of the [N II], and [S II] emission lines. To this purpose, we have developed a generalized 1/Vmax weighting scheme to account for the different incompleteness effects in the LF due to the sample selection: the one due to the SDSS r-band magnitude limit, the spectroscopic selection, and those related to the thresholds imposed to each studied spectral line in our main-ELG sample. However, we have not taken into account the effect that the correlations between the different sources of incompleteness might have. In fact, when selecting galaxies based on emission-line flux, we are implicitly removing a fraction of objects fainter than a given Mr (see Fig. 4). Neither the standard 1/Vmax estimator nor our modified method are capable of correcting from this source of incompleteness.

We have fit the Hα, Hβ, [O II], [O III], [N II], and [S II] LFs using several functional forms (Sect. 5): Saunders (Saunders et al. 1990), Schechter (Schechter 1976), double Schechter (e.g., Blanton et al. 2005a), and a double power law (e.g. Pei 1995). Globally, the smallest reduced χ2 are achieved using double power laws, however this function has five free parameters. Comparable values of reduced χ2 are obtained using Saunders models, with four free parameters. We therefore conclude that Saunders functions are the most appropriate ones to describe the emission-line LFs.

We have investigated the contributions of different ELG types to the emission-line LFs, both observed and intrinsic, and we also explored their redshift evolution. Our main-ELG sample has been classified both according to the specific star formation rate, sSFR > 10−11 yr−1 for SF galaxies, and using the line ratios (Sect. 4). In particular, we have measured the [N II] and [S II] BPT diagrams, as well as the WHAN one. Using these three diagrams, we have separated the main-ELG sample into SF, passive, LINER, Seyfert, and composite galaxies. We have also used the Dn(4000) break index to quantify the contribution of older stellar components to the main-ELG sample.

Our main findings on the ELG types and their contributions to the line LFs are summarized below:

  • The main-ELG sample is dominated by star-forming galaxies, independently from how they are selected and from the specific emission line considered. Including the volume correction, we find that 84 (63.3) percent of the sample are SF when selected from sSFR (BPT+WHAN).

  • ELGs selected using a combination of line flux and signal-to-noise cuts are not equivalent to ELGs selected using a sharp cut in sSFR. In order to minimize the incompleteness in the faint end of their luminosity function, it is preferable to select ELGs based on line flux and S/N.

  • Besides the SF population, composite galaxies and LINERs are the ones that contribute the most to the ELG production below 1041 erg s−1.

  • The Seyfert contribution is nonnegligible only in the bright end of the line LF for the [O III] and [N II] lines, L[N II] > 1042 erg s−1, L[O III] > 1043 erg s−1.

  • The effect of dust in the LFs becomes significant only at L ≳ 1042 erg s−1, independently from the emission line chosen. Correcting from dust extinction does not change the LF shape, and both observed and intrinsic LFs are best fitted using Saunders functions.

  • The number of ELGs decline with redshift, with the exception of passive ELGs and Seyfert ELGs. Most of the passive ELGs are detected at z < 0.12. The evolution of Seyfert ELGs is not trivial and needs a more detailed study.

The main-ELG sample can be considered as a low-redshift laboratory to test the robustness of our ELG selection methods and our ability to correct for survey incompleteness. The ongoing DESI (Schlegel et al. 2015); desi and near future Euclid (Laureijs et al. 2012; Sartoris et al. 2016), 4MOST (de Jong et al. 2012) or Rubin (LSST Science Collaboration 2009; LSST Dark Energy Science Collaboration 2012) surveys will target millions of galaxies out to z ∼ 2 with strong emission spectral lines. These will be used as tracers of the dark matter field, in an attempt to build the most detailed 3D maps of the Universe to date. The methods used in cosmological surveys for validating different inference pipelines are based on model catalogs of galaxies, and the results of this study, together with the Hα main-ELG clustering and bias results from Favole et al. (in prep.), can be used as guidelines to prepare these and other future science cases at higher redshifts. A detailed comparison of the results presented here with those from a range of semi-analytic galaxy models will be instrumental in order to constrain their parameters and make realistic predictions of the statistics of the galaxy population at earlier cosmic epochs.

5

From Fukugita et al. (1996), we see that the u filter peaks at about 3500 Å, with a full width at half maximum (FWHM) of 600 Å, and covers the range 3000–4000 Å; g peaks at ∼4800 Å, with a FWHM of 1400 Å, and covers the range 4000–5500 Å; r peaks at about ∼6250 Å, with a FWHM of 1400 Å, and covers the range 5500–7000 Å; i peaks at about 7700 Å, with a FWHM of 1500 Å, and covers the range 7000–8500 Å; z peaks at about 9100 Å, with a FWHM of 1200 Å, and covers the range 8500–10 000 Å.

7

We have investigated the evolution of the Dn(4000) – log M⋆ relation, finding no significant variation over the redshift range 0.02 < z < 0.22.

8

This corresponds to a gas temperature of T = 104 K and an electron density of ne = 102 cm−3 for Case B recombination (Osterbrock & Ferland 1989).

Acknowledgments

The observational samples were selected from the SDSS NYU–VAGC (http://sdss.physics.nyu.edu/vagc/) and spectroscopically matched to the MPA-JHU DR7 spectral relase (http://www.mpa-garching.mpg.de/SDSS/DR7/) to obtain the emission-line properties. G.F. is supported by a Juan de la Cierva Incorporación grant n. IJC2020-044343-I. G.F. acknowledges the MICINN “Big Data of the Cosmic Web” research grant (P.I. F.-S. Kitaura) for additional support, as well as the SNF 175751 “Cosmology with 3D Maps of the Universe” research grant and the LASTRO group at the Observatoire de Sauverny for hosting and supporting the first stage of this project. She further thanks Andrés Balaguera for insightful discussion on the computational aspects of this work. V.G.P. is supported by the Atracción de Talento Contract no. 2019-T1/TIC-12702 granted by the Comunidad de Madrid in Spain. V.G.P. and A.K. are also supported by the Ministerio de Ciencia e Innovación (MICINN) under research grant PID2021-122603NB-C21. Y.A. and P.C. acknowledge financial support from grant PID2019-107408GB-C42 of the Spanish State Research Agency (AEI/10.13039/501100011033). A.K. and further thank Dan Lacksman for the flamenco moog. S.A.C. acknowledges funding from Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, PIP-2876), Agencia Nacional de Promoción de la Investigación, el Desarrollo Tecnológico y la Innovación (Agencia I+D+i, PICT-2018-3743), and Universidad Nacional de La Plata (G11-150), Argentina. A.D.M.D. thanks Fondecyt for financial support through the Fondecyt Regular 2021 grant 1210612. G.F. and coauthors are thankful to the anonymous referee for comments that have improved the quality and scope of the paper. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

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Appendix A: Selection effects and ELG properties for all the six lines of interest

In Fig. A.1 below we show the impact of the line flux and SN selection cuts in all six lines of interest, color-coded by sSFR (upper 6 panels) and EW (lower 6 panels). The results of the different lines are overall consistent, with [O II] spanning larger EW values compared to the rest of the lines.

thumbnail Fig. A.1.

Same result as Fig. 2 but for the rest of the lines of interest, color-coded by sSFR. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.

thumbnail Fig. A.2.

Same result as Fig. A.1 but color-coded by EW.

Fig. A.3 displays the main-ELG sSFR as a function of stellar mass color-coded by EW for the six lines of interest. The contours change in each panel as they are weighted by the Ew of each line. Overall the results are all consistent. The [O II] line is the one showing higher EW values, while the [O III] and Hβ EW are more concentrated toward smaller values.

thumbnail Fig. A.3.

Same result as shown in the left panel of Fig. 3 for the other lines of interest. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.

thumbnail Fig. A.4.

Same result as shown in the right panel of Fig. 3 for the rest of the lines. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.

In Fig. A.5 we show the emission line luminosity, in the six lines of interest, as a function of the r-band absolute magnitude, color-coded by redshift. From left to right we show our result in three redshift bins to better analyze their evolution: the full sample at 0.02 < z < 0.22, the lower 0.02 < z < 0.12, and the upper 0.12 < z < 0.22 bins. We overplot as horizontal lines the completeness limits chosen by eye as the luminosity below which the galaxy number density falls significantly. This threshold changes for each one of the six emission lines as a function of redshift. These thresholds for the full, low-z and high-z samples are summarized in Table A.1.

thumbnail Fig. A.5.

Same result as Fig. 4 for all the six lines of interest. The horizontal lines indicate the luminosity completeness threshold we establish by eye as the L value where the distribution starts to degrade (see Sect. 2.5).

Table A.1.

Emission-line luminosity completeness limits, in units of s−1 erg, for the full (left column), low-z (center) and high-z (right) samples.

This result tells us that, when selecting ELGs by cutting in line flux (i.e., in luminosity), we are implicitly removing a fraction of the sample fainter than a given r-band magnitude, meaning that we are making our sample incomplete in Mr. Our 1/Vmax LF estimator is not able to correct from this incompleteness effect.

Appendix B: Main-ELG luminosity function values

The numerical values of the Hα, Hβ, [O II], [O III], [N II], and [S II] main-ELG luminosity functions and its different components are provided in Tables B.1 - B.3.

Table B.1.

Hα and Hβ luminosity functions of the main-ELG sample and their different components.

Table B.2.

[O II] and [O III] luminosity functions of the main-ELG sample and their different components.

Table B.3.

Observed [N II] and [S II] luminosity functions of the main-ELG sample and their different components.

Appendix C: Main-ELG intrinsic LFs

The intrinsic (i.e., dust corrected) Hα, Hβ, [O II], [O III], [N II], and [S II] main-ELG luminosity functions are shown in Figure C.1. The numerical values are provided in Tables C.1 - C.3 and the best-fit Saunders parameters are given in Table 5.

thumbnail Fig. C.1.

Intrinsic emission-line LFs. From top to bottom and from left to right: Hα, Hβ, [O II], [O III], [N II], and [S II] intrinsic (i.e., dust corrected) luminosity functions of the main-ELG sample (full black dots). The contribution of ELGs classified in different ways are shown by empty colored markers, with colors as indicated in the legend. We overplot the Saunders fits as thick black lines; the parameters are tabulated in Table 5 and were obtained considering only the points above the luminosity completeness threshold established in Sec. 2.5. For those lines having the lower completeness limit in the L range of the figure, we highlight with a yellow shade the region of incompleteness, where our LFs cannot be trusted. The error bars are computed from 70 jackknife resamplings.

Table C.1.

Hα and Hβ intrinsic luminosity functions of the main-ELG sample and their different components.

Table C.2.

[O II] and [O III] intrinsic luminosity functions of the main-ELG sample and their different components.

Table C.3.

[N II] and [S II] intrinsic luminosity functions of the main-ELG sample and their different components.

Appendix D: Evolution of the LFs in all the lines of interest

thumbnail Fig. D.1.

From top left to bottom right we show the observed Hβ, [O II], [O III] and [N II] LFs and their different ELG components in the low-z (top panels) and high-z (middle panels) bins, together with their Saunders fits. The bottom panels in each figure displays the ratios between the high- and low-z LF fits. The shaded cyan regions indicate where the incompleteness starts to dominate and our LF results cannot be trusted. The completeness limit value for each line is provided in Table A.1. For those lines for which the shade is not visible, the completeness limit is at lower L, outside the figure range.

thumbnail Fig. D.2.

Same as Fig. D.1, but for the [S II] line.

Table D.1.

Best-fit Saunders parameters of the observed Hβ, [O II] and [O III] LF fits shown in Fig. D.1 in the two redshift bins, 0.02 < z < 0.12 and 0.12 < z < 0.22.

Table D.2.

Same as previous Table, but for [N II] and [S II].

Appendix E: Other functional forms for the LF fits

In Tables E.1–E.3 we present the best-fit parameters of the LF fits using the models beyond Saunders, as described in Sec. 3. The corresponding results are shown in Fig. E.1.

Table E.1.

Best-fit Schechter parameters to the measured luminosity functions shown in Tables B.1 and B.2.

Table E.2.

Best-fit double Schechter parameters to the measured luminosity functions in Tables B.1 and B.2.

Table E.3.

Best-fit parameters of our double power law fits to the measured luminosity functions in Tables B.1 and B.2.

thumbnail Fig. E.1.

SF BPT+WHAN and Seyfert contributions to the six ELG luminosity functions of interest. We compare the performance of the Saunders fits already shown in Fig. 11 (solid curves), with the Schechter (dashed), double Schechter (dot-dashed), and double power-law (dotted) functions.

All Tables

Table 1.

Wavelengths of our six emission lines of interest, together with the SDSS filter (in brackets) in which they fall for a selection of redshifts, for illustration.

In the text
Table 2.

Volume-corrected percentages of the different types of ELGs as classified using the BPT+WHAN diagrams (second column) and percent split of the total fraction for each type based on sSFR = 10−11yr−1 (last two columns).

In the text
Table 3.

Saunders best-fit model parameters to the observed LFs shown in Fig. 11.

In the text
Table 4.

Best-fit Saunders parameters of the observed Hα LF fits in two redshift bins, 0.02 < z < 0.12 (top) and 0.12 < z < 0.22 (bottom), to better understand their evolution.

In the text
Table 5.

Same result as Table 3, but for the intrinsic (i.e., dust corrected) LFs.

In the text
Table A.1.

Emission-line luminosity completeness limits, in units of s−1 erg, for the full (left column), low-z (center) and high-z (right) samples.

In the text
Table B.1.

Hα and Hβ luminosity functions of the main-ELG sample and their different components.

In the text
Table B.2.

[O II] and [O III] luminosity functions of the main-ELG sample and their different components.

In the text
Table B.3.

Observed [N II] and [S II] luminosity functions of the main-ELG sample and their different components.

In the text
Table C.1.

Hα and Hβ intrinsic luminosity functions of the main-ELG sample and their different components.

In the text
Table C.2.

[O II] and [O III] intrinsic luminosity functions of the main-ELG sample and their different components.

In the text
Table C.3.

[N II] and [S II] intrinsic luminosity functions of the main-ELG sample and their different components.

In the text
Table D.1.

Best-fit Saunders parameters of the observed Hβ, [O II] and [O III] LF fits shown in Fig. D.1 in the two redshift bins, 0.02 < z < 0.12 and 0.12 < z < 0.22.

In the text
Table D.2.

Same as previous Table, but for [N II] and [S II].

In the text
Table E.1.

Best-fit Schechter parameters to the measured luminosity functions shown in Tables B.1 and B.2.

In the text
Table E.2.

Best-fit double Schechter parameters to the measured luminosity functions in Tables B.1 and B.2.

In the text
Table E.3.

Best-fit parameters of our double power law fits to the measured luminosity functions in Tables B.1 and B.2.

In the text

All Figures

thumbnail Fig. 1.

Parent-ELG Hα luminosity computed using our our default aperture correction based on Hopkins et al. (2003; y-axis) versus the same quantity computed using an approximation to the Duarte Puertas et al. (2017) correction (z-axis), color-coded by redshift. We randomly show only 30 percent of the parent-ELG sample to avoid saturation. We overplot the median and 1σ dispersion of our LHα in bins of L H α D $ L_{\mathrm{H}\alpha}^{\mathrm{D}} $, as well as the 1:1 relation for comparison.
In the text
thumbnail Fig. 2.

parent-ELG signal-to-noise as a function of the Hα line flux, color-coded by sSFR. Here we are representing a random subset of the total population, 30 percent of it, to avoid crowding. The black-dashed lines in the main panel represent the flux and S/N cuts we impose on the parent-ELG sample to obtain our main-ELG sample: F > 2 × 10−16erg s−1 cm−2 and S/N > 2 (see Sect. 2.3). The top and right panels show the flux and S/N histograms of the parent-ELG (gray-dashed lines) and the main-ELG (green-solid lines) samples. The marginal distributions displayed both here and in Fig. A.1 for the other lines motivate the flux and S/N cuts chosen to select a complete ELG sample.
In the text
thumbnail Fig. 3.

Left panel: main-ELG sSFR as a function of stellar mass, color-coded by Hα EW. On the background we also show the parent-ELG distribution (silver triangles). Here we are representing random subsets of both populations, 30 percent of them, to avoid crowding. We overplot the corresponding 68 and 95 (inner and outer lines, respectively) percent contours as green and silver lines. In addition, we show in black the contours of the star-forming (SF) population selected at sSFR > 10−11 yr−1. The large markers with error bars display the corresponding sSFR means and 1 σ deviations in bins of stellar. The side histograms show the sSFR and M⋆ marginal distributions of the main-ELG (green) and SF populations (black lines), and compare them to the parent-ELG sample (gray), which has no cuts. Right panel: Hα luminosity as a function of stellar mass, color-coded by sSFR, and corresponding marginal distributions, with the same colors as in the left panel.
In the text
thumbnail Fig. 4.

Main-ELG Hα luminosity as a function of the r-band absolute magnitude, color-coded by redshift. On the background we show in gray the parent-ELG sample distribution, which has no cuts in flux nor S/N. For both populations we display random subsets of 30 percent of the total to avoid saturation. From left to right, we show the full sample (0.02 < z < 0.22), the lower-z bin (0.02 < z < 0.12), and the higher-z (0.12 < z < 0.22) one. The horizontal lines represent our lower completeness limits in luminosity (see the text for details).
In the text
thumbnail Fig. 5.

Vmax computation scheme for a galaxy from the main-ELG sample (star symbol). Top panel: we take into account the survey r-band magnitude limit r p faint = 17.77 $ r_{\mathrm{p}}^{\mathrm{faint}}=17.77 $; note that we are omitting the K-corrections (K(zi) = 0 in Eq. (8)) for this representation. Bottom panel: similar plot as the top one for a survey with a limit in the Hα line flux of F H α faint = 2 × 10 − 16 erg s − 1 $ F_{\mathrm{H}\alpha}^{\mathrm{faint}}=2\times 10^{-16}\,\mathrm{erg\,s}^{-1} $. For the [O II], [O III], Hβ, [N II], and [S II] lines the methodology is identical (see Sect. 2.3). The lower and upper redshift limits of the survey, zlow = 0.02 and zup = 0.22, are highlighted by dashed vertical red lines in both panels. The maximum redshifts that the galaxy can have and still be included in the sample, considering its magnitude and Hα flux limits, as well as the faintest luminosity, are shown by dotted vertical blue lines.
In the text
thumbnail Fig. 6.

SDSS Mr luminosity functions including (full markers) and omitting (empty markers) K-corrections. The effect is less than 7 percent at −22.5 < Mr < −18, while it grows up to ∼30 percent in the faint and luminous tails of the distribution. The gray band highlights the 10 percent difference range.
In the text
thumbnail Fig. 7.

Diagnostic diagrams used to provide our BPT classification (see Sect. 4.2). Top and middle panels: main-ELG [N II] and [S II] BPT diagrams. Galaxies are color-coded by their sSFR; here we show only 60 percent, randomly sampled, of each population to avoid saturation. We overplot the Kewley et al. (2001), Kauffmann et al. (2003a) and Kewley et al. (2006) demarcation lines (black solid, dot-dashed, and thick dotted lines, respectively) separating the SF, AGN, LINER, and Seyfert contributions (see Sect. 4.2). Ambiguous objects are represented as stars. Bottom: Seyfert, passive, and ambiguous components of the main-ELG sample represented in the WHAN diagram, together with the EW cuts we use to select them: the EW = 6 Å limit (dot-dashed line) separating Seyferts from LINERs, and the EW = 0.5 Å cut (Cid Fernandes et al. 2011; solid) to isolate passive ELGs from the rest.
In the text
thumbnail Fig. 8.

Volume-weighted distributions of the [N II]/Hα line ratios resulting from our ELG BPT classification. The criteria to separate SF ELGs from the rest, solely based on the ratio [N II]/Hα proposed by Stasińska et al. (2006, S06) is shown by a vertical dashed line, log([N II]/Hα) = −0.4. Our sample is better separated by a slightly different value, log([N II]/Hα) = −0.3, also indicated by a vertical solid line. Note that we do not apply any of these two cuts in our analysis.
In the text
thumbnail Fig. 9.

sSFR as a function of stellar mass for all the main-ELG contributions, each one represented by contours. In each set of contours, the inner line (outer shade) represents the 68 (95) percent confidence regions. The contours of the SF population at sSFR > 10−11 yr−1 (solid black) are broken due to the sharp sSFR cut; those of the passive component (dotted red) are broken due to the very low number density of this population (0.1 percent of the total; see Table 2).
In the text
thumbnail Fig. 10.

Dn(4000) break index as a function of the galaxy stellar mass, color-coded by sSFR. We compare the main-ELG sample (small dots on the background) with its SF population selected from sSFR (black contours, not including weights), and with the median ±σ results of the SF (light blue diamonds), composite (brown hexagons), Seyfert (navy blue stars), LINERs (orange squares), and passive (red triangles) ELG contributions selected using the BPT+WHAN diagrams. The points shown here are a random subset of the main-ELG sample, 60 percent of the total, to avoid saturation. The horizontal dotted line indicates the typical separation between younger and older stellar populations.
In the text
thumbnail Fig. 11.

From top to bottom and from left to right: Hα, Hβ, [O II], [O III], [N II], and [S II] observed (i.e., dust extincted) luminosity functions of the main-ELG sample (full black dots). The contributions of ELGs classified in different ways are shown by empty colored markers, with colors as indicated in the legend. We compare our results – both tabulated in Appendix B and at the CDS – with several observed published measurements in the local Universe: Hα ELGs from Ly et al. (2007) at z = 0.07 − 0.09, Gilbank et al. (2010) at 0.032 < z < 0.2, Pirzkal et al. (2013) at 0 < z < 0.5, and Hα AGN from Schulze et al. (2009) at z < 0.3; Hβ ELGs from Comparat et al. (2016) at z = 0.3, Hβ AGN from Schulze et al. (2009) at z < 0.3; [O II] ELGs from Gilbank et al. (2010) at 0.032 < z < 0.2, Gallego et al. (2002) at z ≤ 0.045, Comparat et al. (2015) at z = 0.17, and Pirzkal et al. (2013) at 0.5 < z < 1.5; [O III] ELGs from Comparat et al. (2016) at z = 0.3, from Pirzkal et al. (2013) at 0.1 < z < 0.9, and [O III] AGN from Bongiorno et al. (2010) at 0.15 < z < 0.92. We overplot our Saunders fits as lines; the parameters are in Table 3 and were obtained considering only the points above the luminosity completeness thresholds discussed in Sect. 2.5 and Appendix A and represented as cyan shades in the panels (for those lines whose completeness limit falls within the L range shown in the figure). The error bars are computed from 50 jackknife resamplings (see Sect. 5.2).
In the text
thumbnail Fig. 12.

LFs compared for the six emission lines under study. Top panel: best Saunders fit to the observed (solid lines) and dust-corrected (dashed lines) line LFs, for the six studied emission lines, as indicated in the legend. Bottom panel: ratios between the observed and the intrinsic (dust-corrected) LF, for each emission line. In both panels the error bars are obtained from 50 jackknife realizations (Sect. 5.2).
In the text
thumbnail Fig. 13.

main-ELG observed LF in the low (top) and high (middle) redshift bins, together with their Saunders fits. The markers, lines and colors are the same as in Fig. 11. The cyan shades indicate where the incompleteness starts to dominate and our LF measurements cannot be trusted. The lower completeness limits are set to LHα = 1040,  1041.1 erg s−1 for the lower-z and higher-z, respectively (see Appendix D). We compare them to the LF results at slightly higher redshift from Ly et al. (2007; z = 0.08) and Sobral et al. (2013; z = 0.4). The bottom panel shows the ratios of the low- to high-z LF Saunders fits. We compare these ratios to better understand the change in the line luminosity functions. At z > 0.12, there are no passive galaxies above the completeness threshold considered: LHα = 1041.1 erg s−1.
In the text
thumbnail Fig. A.1.

Same result as Fig. 2 but for the rest of the lines of interest, color-coded by sSFR. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.
In the text
thumbnail Fig. A.2.

Same result as Fig. A.1 but color-coded by EW.
In the text
thumbnail Fig. A.3.

Same result as shown in the left panel of Fig. 3 for the other lines of interest. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.
In the text
thumbnail Fig. A.4.

Same result as shown in the right panel of Fig. 3 for the rest of the lines. From top to bottom and from left to right we show the Hβ, [O II], [O III], [N II] and [S II] lines.
In the text
thumbnail Fig. A.5.

Same result as Fig. 4 for all the six lines of interest. The horizontal lines indicate the luminosity completeness threshold we establish by eye as the L value where the distribution starts to degrade (see Sect. 2.5).
In the text
thumbnail Fig. C.1.

Intrinsic emission-line LFs. From top to bottom and from left to right: Hα, Hβ, [O II], [O III], [N II], and [S II] intrinsic (i.e., dust corrected) luminosity functions of the main-ELG sample (full black dots). The contribution of ELGs classified in different ways are shown by empty colored markers, with colors as indicated in the legend. We overplot the Saunders fits as thick black lines; the parameters are tabulated in Table 5 and were obtained considering only the points above the luminosity completeness threshold established in Sec. 2.5. For those lines having the lower completeness limit in the L range of the figure, we highlight with a yellow shade the region of incompleteness, where our LFs cannot be trusted. The error bars are computed from 70 jackknife resamplings.
In the text
thumbnail Fig. D.1.

From top left to bottom right we show the observed Hβ, [O II], [O III] and [N II] LFs and their different ELG components in the low-z (top panels) and high-z (middle panels) bins, together with their Saunders fits. The bottom panels in each figure displays the ratios between the high- and low-z LF fits. The shaded cyan regions indicate where the incompleteness starts to dominate and our LF results cannot be trusted. The completeness limit value for each line is provided in Table A.1. For those lines for which the shade is not visible, the completeness limit is at lower L, outside the figure range.
In the text
thumbnail Fig. D.2.

Same as Fig. D.1, but for the [S II] line.
In the text
thumbnail Fig. E.1.

SF BPT+WHAN and Seyfert contributions to the six ELG luminosity functions of interest. We compare the performance of the Saunders fits already shown in Fig. 11 (solid curves), with the Schechter (dashed), double Schechter (dot-dashed), and double power-law (dotted) functions.
In the text

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