---
abstract: 'We present observations with the Cosmic Origins Spectrograph onboard the [*Hubble Space Telescope*]{} of eight compact star-forming galaxies at redshifts $z$ = 0.02811 – 0.06540, with low oxygen abundances 12 + log(O/H) = 7.43 – 7.82 and extremely high emission-line flux ratios O$_{32}$ = \[O [iii]{}\]$\lambda$5007/\[O [ii]{}\]$\lambda$3727 $\sim$ 22 – 39, aiming to study the properties of Ly$\alpha$ emission in such conditions. We find a diversity in Ly$\alpha$ properties. In five galaxies Ly$\alpha$ emission line is strong, with equivalent width (EW) in the range 45 – 190Å. In the remaining galaxies, weak Ly$\alpha$ emission with EW(Ly$\alpha$) $\sim$ 2 – 7Å is superposed on a broad Ly$\alpha$ absorption line, indicating a high neutral hydrogen column density $N$(H [i]{}) $\sim$ (1 – 3)$\times$10$^{21}$ cm$^{-2}$. We examine the relation between the Ly$\alpha$ escape fraction $f_{\rm esc}$(Ly$\alpha$) and the Lyman continuum escape fraction $f_{\rm esc}$(LyC), using direct measures of the latter in eleven low-redshift LyC leakers, to verify whether $f_{\rm esc}$(Ly$\alpha$) can be an indirect measure of escaping LyC radiation. The usefulness of O$_{32}$, of the Ly$\alpha$ equivalent width EW(Ly$\alpha$) and of the Ly$\alpha$ peak separation $V_{\rm sep}$ as indirect indicators of Ly$\alpha$ leakage is also discussed. It is shown that there is no correlation between O$_{32}$ and $f_{\rm esc}$(Ly$\alpha$). We find an increase of $f_{\rm esc}$(Ly$\alpha$) with increasing EW(Ly$\alpha$) for EW(Ly$\alpha$)$<$100Å, but for higher EW(Ly$\alpha$)$\ga$150Å  the $f_{\rm esc}$(Ly$\alpha$) is nearly constant attaining the value of $\sim$0.25. We find an anticorrelation between $f_{\rm esc}$(Ly$\alpha$) and $V_{\rm sep}$, though not as tight as the one found earlier between $f_{\rm esc}$(LyC) and $V_{\rm sep}$. This finding makes $V_{\rm sep}$ a promising indirect indicator of both the Ly$\alpha$ and ionizing radiation leakage.'
author:
- |
    Y. I. Izotov$^{1,2}$, D. Schaerer$^{3,4}$, G. Worseck$^{5}$, A. Verhamme$^{3}$, N. G. Guseva$^{1,2}$,  T. X. Thuan$^{6}$, I. Orlitová$^{7}$ & K. J. Fricke$^{8,2}$\
    $^{1}$Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 14-b Metrolohichna str., Kyiv, 03143, Ukraine,\
    E-mail: yizotov@bitp.kiev.ua, nguseva@bitp.kiev.ua\
    $^{2}$Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany\
    $^{3}$Observatoire de Genève, Université de Genève, 51 Ch. des Maillettes, 1290, Versoix, Switzerland,\
    E-mail: daniel.schaerer@unige.ch, anne.verhamme@unige.ch\
    $^{4}$IRAP/CNRS, 14, Av. E. Belin, 31400 Toulouse, France\
    $^{5}$ Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany,\
    E-mail: gworseck@uni-potsdam.de\
    $^{6}$Astronomy Department, University of Virginia, P.O. Box 400325, Charlottesville, VA 22904-4325, USA,\
    E-mail: txt@virginia.edu\
    $^{7}$Astronomical Institute, Czech Academy of Sciences, Bočn[í]{} II 1401, 141 00, Prague, Czech Republic,\
    E-mail: orlitova@asu.cas.cz\
    $^{8}$Institut für Astrophysik, Göttingen Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany,\
    E-mail: kfricke@gwdg.de
date: 'Accepted XXX. Received YYY; in original form ZZZ'
title: 'Diverse properties of Ly$\alpha$ emission in low-redshift compact star-forming galaxies with extremely high \[O [iii]{}\]/\[O [ii]{}\] ratios'
---

\[firstpage\]

(cosmology:) dark ages, reionization, first stars — galaxies: abundances — galaxies: dwarf — galaxies: fundamental parameters — galaxies: ISM — galaxies: starburst

Introduction {#intro}
============

The extremely high O$_{32}$ = \[O [iii]{}\]$\lambda$5007/\[O [ii]{}\]$\lambda$3727 ratio in spectra of low-redshift dwarf star-forming galaxies (SFGs) indicates the presence of either an ionization-bounded compact H [ii]{} region with intense ionizing radiation from a very young star-forming region or a density-bounded H [ii]{} region losing its ionizing radiation, or both [e.g. @JO13; @NO14; @S15; @I17]. The ionizing photon production efficiency $\xi_{\rm ion}$ = $N_{\rm LyC}$/$L_\nu$ in these galaxies could be very high, where $N_{\rm LyC}$ is the Lyman continuum photon production rate and $L_\nu$ is the monochromatic UV luminosity at $\lambda$ = 1500Å. Therefore, they are considered as the local counterparts of the dwarf SFGs at high redshifts, which are likely the main source of the last phase transition of the matter in the Universe, namely its reionization, which ends at $z$ $\sim$ 6 [@O09; @WC09; @K11; @J13; @M13; @Y11; @B15a; @Sm18; @N18; @St18; @K19]. An alternative hypothesis is the dominant role of active galactic nuclei (AGN) in the reionization of the Universe, as proposed e.g. by @Madau15. However, in recent years, growing evidence for a small contribution of AGN to reionization has accumulated [e.g. @H18; @M18; @P18; @Mat18; @Ku19]. On the other hand, SFGs can be considered as an important source of ionization only if the product $\xi_{\rm ion}$$\times$$f_{\rm esc}$(LyC) is sufficiently high, where $f_{\rm esc}$(LyC) is the escape fraction of Lyman continuum (LyC), i.e. the fraction of ionizing radiation emitted into the intergalactic medium (IGM). It has been estimated that $f_{\rm esc}$(LyC) should not be less than 10–20 per cent on average in order to accomplish reionization [e.g. @O09; @R13; @D15; @Robertson15; @K16].

Currently, direct observations of the LyC are available for only a limited number of galaxies at high and low redshifts. Searches for and confirmation of LyC emission from high redshift galaxies are difficult due to their faintness, contamination by lower-redshift interlopers and attenuation by residual H [i]{} in the highly ionized IGM. [e.g., @V10; @V12; @Inoue14; @Gr15]. They have resulted in the discovery of approximately three dozens of LyC leakers with reliably high escape fraction: [*Ion2*]{} [@Va15; @B16], Q1549-C25 [@Sh16], A2218-Flanking [@B17], [*Ion3*]{} [@Va18], SunBurst Arc [@RT19], 15 SFGs studied by @St18, and a dozen of galaxies at $z$ = 3.1 with strong \[O [iii]{}\] $\lambda$5007 emission [@F19].

At low redshifts, $z$ $\sim$ 0.3 - 0.4, @I16 [@I16b; @I18; @I18b] have detected LyC leaking emission in eleven compact SFGs with high O$_{32}$ $\sim$ 5 - 28 and derived $f_{\rm esc}$(LyC) ranging between 2 and 72 per cent. These values are higher than $f_{\rm esc}$(LyC) of $\la$ 1 per cent derived by @B14 and @C17 in SFGs with lower O$_{32}$, or by @He18 in SFGs with lower equivalent widths of the H$\beta$ emission line. There is hope that the number of low-$z$ LyC leakers will considerably be increased after the completion in 2020 of the [*HST*]{} Large Program GO 15626 (P.I. A. Jaskot), which includes more than 70 targets.

The [*Hubble Space Telescope*]{} ([*HST*]{})/Cosmic Origins Spectrograph (COS) sensitivity curve limits LyC observations to $z \ga 0.25$. At lower redshifts, only very bright targets are accessible [e.g. @L16]. Therefore, for low-redshift SFGs, reliable indirect indicators of LyC leakage are needed. @NO14 proposed that high O$_{32}$ can be an indication of density-bounded H [ii]{} region and thus of LyC leakage. However, O$_{32}$ depends on some other parameters, such as ionization parameter and hardness of radiation which in turn depend on metallicity.

@F16 has found a correlation between $f_{\rm esc}$(LyC) and O$_{32}$, using a small sample of galaxies which includes low-$z$ LyC leakers with O$_{32}$ $<$ 8. On the other hand, no correlation has been found by @I18b for eleven confirmed LyC leakers with O$_{32}$ in a wide range of $\sim$ 5 - 28. A similar conclusion was obtained by @N18 and @B19 [see also @R17]. However, this conclusion is based mainly on observations of galaxies with O$_{32}$ $\la$ 16. Only one observed galaxy has a higher value of O$_{32}$. It is thus important to observe LyC emission in more galaxies with higher O$_{32}$.

The He [i]{} emission-line ratios in optical spectra of galaxies can also be used to estimate the column density of neutral gas and thus to indirectly estimate $f_{\rm esc}$(LyC) [@I17]. However, deep spectra in the optical range are needed since these lines are weak with intensities $\la$10 per cent of the H$\beta$ emission line.

Finally, the properties of the Ly$\alpha$ emission line can serve as indirect indicators of escaping LyC emission. Its profile is double-peaked in the spectra of most of LyC leakers, with the separation between the peaks $V_{\rm sep}$ decreasing with decreasing neutral hydrogen column density $N$(H [i]{}) [e.g. @I16; @I16b; @I18; @I18b]. In rare cases, the Ly$\alpha$ profile is more complex and consists of three and more peaks [@RT17; @I18b; @Va18]. @V15 and @I18b have shown that there is a tight relation between the LyC escape fraction $f_{\rm esc}$(LyC) and the separation between Ly$\alpha$ peaks, making $V_{\rm sep}$ the most reliable indicator of escaping ionizing radiation. Furthermore, @V17 have shown for a limited sample of LyC leakers that the Ly$\alpha$ escape fractions $f_{\rm esc}$(Ly$\alpha$) are larger than the LyC escape fractions $f_{\rm esc}$(LyC), in accord with theoretical predictions of @D16.

In this paper we present new [*HST*]{}/COS observations of the Ly$\alpha$ in eight low-redshift ($z$ $<$ 0.07) compact SFGs with the highest O$_{32}$ $\sim$ 22 – 39 found in the Sloan Digital Sky Survey (SDSS), aiming to examine the properties of Ly$\alpha$ emission in these galaxies and to verify possible indirect indicators of escaping Ly$\alpha$ and LyC emission. The studied galaxies have lower stellar masses than previously observed Ly$\alpha$ emitting galaxies such as the “green pea” (GP) galaxies at $z$ $\sim$ 0.1 – 0.3 studied e.g. by @J17, @Y17, @MK19, and the confirmed LyC leakers at $z$ $\sim$ 0.3 – 0.4 [@I16; @I16b; @I18; @I18b]. The selection criteria and the properties of the selected galaxies derived from observations in the optical range are presented in Section \[sec:select\]. The [*HST*]{} observations and data reduction are described in Section \[sec:obs\]. The surface brightness profiles in the UV range are discussed in Section \[sec:sbp\]. Ly$\alpha$ emission is considered in Section \[sec:lya\]. In Section \[discussion\], our results are compared with the Ly$\alpha$ escape fractions obtained for other galaxies in some recent studies. We summarize our findings in Section \[summary\].

Selection criteria and the integrated properties of selected galaxies  {#sec:select}
======================================================================

Our galaxies were selected from the SDSS Data Release 14 (DR14) [@A18]. We adopted the following selection criteria for each galaxy:

1\) it has a very high O$_{32}$ $>$ 20, which is an indication of either a density-bounded H [ii]{} region or a high ionization parameter.

2\) it has a compact structure in the SDSS image in order to observe the total flux of the galaxy with the small 2.5 arcsec COS aperture.

3\) it is isolated from other sources to avoid contamination in the [*HST*]{}/COS spectra.

4\) it is sufficiently bright in the UV range ([*GALEX*]{} NUV magnitude brighter than 22 mag) to be acquired with COS.

In total, we selected the 8 brightest galaxies satisfying the above conditions.

The SDSS spectra of the selected galaxies reveal considerably lower oxygen abundances, in the range 12 + log(O/H) = 7.43 – 7.82 (see below), as compared to the confirmed LyC leakers [@I16; @I16b; @I18; @I18b]. They show comparably high rest-frame equivalent widths EW(H$\beta$) = 258 – 483 Å  (Table \[tab1\]), indicating very recent star formation.

These galaxies are located at the extreme upper tip of the SFG branch in the Baldwin-Phillips-Terlevich (BPT) diagram (filled circles in Fig. \[fig2\]a) implying the presence of high-excitation H [ii]{} regions. They are considerably more extreme than the confirmed LyC leakers shown by open circles. It is seen in Fig. \[fig2\]b, which shows the O$_{32}$ – R$_{23}$ diagram, that the selected SFGs (filled circles) have the highest O$_{32}$ ratios among all SDSS SFGs, and that they are offset to low R$_{23}$ values compared to the main sequence of SFGs (grey dots) because of their lower metallicities. On the other hand, most of the confirmed LyC leakers with higher metallicities are located in the upper part of the main sequence (open circles).

The SDSS spectra were used to derive the interstellar extinction from the hydrogen Balmer decrement and ionized gas metallicity using the prescriptions of @ITL94, @I06 and @G13.

The extinction-corrected emission-line flux densities, the extinction coefficients $C$(H$\beta$), the rest-frame equivalent widths of H$\beta$, \[O [iii]{}\]$\lambda$5007 and H$\alpha$ emission lines, and the observed H$\beta$ flux densities are shown in Table \[taba1\]. We note that the H$\alpha$ emission line in the SDSS spectra of J0820$+$5431 and J1032$+$4919 and the \[O [iii]{}\]$\lambda$5007 emission line in the SDSS spectrum of J1032$+$4919 are clipped. Therefore, for J1032$+$4919, $I$(\[O [iii]{}\]$\lambda$5007) = 3$\times$$I$(\[O [iii]{}\]$\lambda$4959) is used to derive O$_{32}$, the electron temperature $T_{\rm e}$(O [iii]{}) and oxygen abundance. Furthermore, the H$\alpha$ emission line in this galaxy and in J0820$+$5431 is excluded in the calculation of extinction. The He [ii]{} $\lambda$4686Å emission line is detected in seven out of eight galaxies implying hard ionizing radiation.

The flux densities from Table \[taba1\] and the direct $T_{\rm e}$ method are used to derive the electron temperature, electron number density and the element abundances in the H [ii]{} regions. These quantities are shown in Table \[taba2\]. The oxygen abundances of our galaxies are on average $\sim$ 0.2 - 0.3 dex lower than those in known low-redshift LyC leakers [@I16; @I16b; @I18; @I18b]. Four galaxies from our sample have been observed with the Large Binocular Telescope (LBT) by @I17. Those authors derived oxygen abundances that are in good agreement with the present determinations from SDSS spectra. The neon, sulfur and argon to oxygen abundance ratios (Fig. \[fig3\]) are similar to those in dwarf emission-line galaxies [e.g. @I06; @G13] and in confirmed LyC leakers, with similar small dispersions. On the other hand, the N/O ratios are scattered over a large range (Fig. \[fig3\]a) which can not be explained by N/O errors (Table \[taba2\]). Compared to SDSS SFGs (shown by grey dots), they tend to have systematically higher values both for the galaxies in our sample and for the confirmed LyC leakers.

The emission-line luminosities and stellar masses of our galaxies were obtained adopting a luminosity distance [NED, @W06] with the cosmological parameters $H_0$=67.1 km s$^{-1}$Mpc$^{-1}$, $\Omega_\Lambda$=0.682, $\Omega_m$=0.318 [@P14]. Using these parameters and apparent magnitudes, we also derived absolute magnitudes $M_g$ and $M_{\rm FUV}$ in the SDSS $g$ and [*GALEX*]{} FUV bands (Table \[tab3\]), assuming negligible bandpass corrections and neglecting dust extinction.

The H$\beta$ luminosity $L$(H$\beta$) and corresponding star-formation rates SFR shown in Table \[tab3\] were obtained from the extinction-corrected H$\beta$ flux densities using the relation by @K98 and adopting the value of 2.75 for the H$\alpha$/H$\beta$ flux ratio. They are one order of magnitude lower than the respective values for LyC leakers. Specific star formation rates sSFR = SFR/$M_\star$ of $\sim$ 100 Gyr$^{-1}$ are similar to sSFRs for LyC leakers [@I16; @I16b; @I18; @I18b] and are among the highest known for GPs and luminous compact galaxies [@Ca09; @I11], and dwarf SFGs at $z < 1$ [@I16c]. On the other hand, they are several orders of magnitude higher than the sSFRs of $\sim$ 0.01 - 1 Gyr$^{-1}$ of the SDSS main sequence galaxies.

The extinction-corrected SDSS spectra of our galaxies were used to fit the spectral energy distribution (SED) of both the stellar and nebular components and to derive their stellar masses, starburst ages and the modelled intrinsic absolute magnitudes $M_{\rm FUV}^{\rm SED}$ in the FUV range. The fitting method, using a two-component model, is described in @I18. We find that the stellar masses and FUV luminosities of our galaxies are $\sim$ 2 orders of magnitude lower compared to the confirmed LyC leakers (Table \[tab3\]), but their extinction-corrected absolute FUV magnitudes are similar to those of the faintest detected galaxies at $z$ = 6 – 8 [e.g. @L17; @Bo17b].

[*HST*]{}/COS observations and data reduction {#sec:obs}
=============================================

[*HST*]{}/COS spectroscopy of the eight galaxies was obtained in program GO 15136 (PI: Y. I. Izotov) during the period January 2018 – February 2019. The observational details are presented in Table \[tab4\]. The galaxies were acquired by COS near ultraviolet (NUV) imaging. Since our targets are compact but faint, as based on shallow [*GALEX*]{} imaging, a considerable fraction of one orbit was spent per object for deep NUV imaging and reliable acquisition. The NUV-brightest region of each target was centered in the 2.5arcsec diameter spectroscopic aperture (Fig. \[fig4\]). We note that acquisition observations failed for J1242$+$4851. We do not know the reason for that. The acquisition image has a flag raised in the header: EXPFLAG=‘INVALID CHECK IMAGE’. Possibly, something went wrong during one of the two acquisition exposures. Therefore, the imaging data for J1242$+$4851 are not present in this paper. However, the spectroscopic observations were not affected. For the other galaxies, some structure with an extended low-surface-brightness (LSB) component is seen. However, their sizes are smaller than the central unvignetted $0.8$arcsec diameter region of the spectroscopic aperture. Hence, the galaxy quantities derived from the COS spectra here do not require corrections for vignetting. In fact, most of the NUV continuum in these galaxies is concentrated in much smaller central regions, with full widths at half maximum $\la$ 0.1 arcsec.

We obtained spectra of the Ly$\alpha$ emission lines with the COS G130M grating positioned at the central wavelength 1222Å and a small wavelength coverage of $\sim$ 300Å at COS Detector Lifetime Position 4, yielding a spectral resolving power $\lambda/\Delta\lambda\simeq 14,000$ in the wavelength range of interest. All four focal-plane offset positions were employed to correct grid wire shadows and detector blemishes.

The individual exposures were reduced with the CALCOS pipeline v3.3.4, followed by accurate background subtraction and co-addition with custom software [@W16]. Apart from adjustments of the rectangular extraction aperture due to the wide spatial profile of the G130M 1222Å setup (57 pixels) and adjustments in the detector pulse-height thresholds to reflect the current detector state, the reduction procedures were analogous to @I16. We verified in the two-dimensional spectra that the extraction aperture contains all visible Ly$\alpha$ flux and preserves the spectrophotometry of the continuum. The estimated background uncertainties of a few per cent do not affect our analysis. The homogeneous reduction enables a fair comparison to our previous results [@I16; @I16b; @I18; @I18b].

Surface brightness distribution in the NUV range {#sec:sbp}
================================================

Using the COS NUV acquisition images and the routine [*ellipse*]{} in [iraf]{}[^1]/[stsdas]{}[^2] we obtain the surface brightness (SB) profiles of our galaxies in the UV continuum. The [*GALEX*]{} NUV magnitudes were used to express the profiles in the units mag arcsec$^{-2}$. For this, we have scaled the total NUV flux of the galaxy measured in the acquisition image to the flux corresponding to the [*GALEX*]{} NUV magnitude. The shape of the SB profiles (Fig. \[fig5\]) in our galaxies is similar to those of confirmed LyC leakers [@I16; @I16b; @I18; @I18b] with a sharp increase in the central part because of the presence of the bright star-forming region(s) and a linear decrease (in magnitudes) in the outer part, reminiscent of a disc structure.

However, the scale lengths $\alpha$ of our galaxies in the range $\sim$ 0.09 – 0.48 kpc (Fig. \[fig5\]) are considerably lower than $\alpha$ = 0.6 – 1.8 kpc in LyC leakers [@I16; @I16b; @I18; @I18b], presumably because of their considerably lower stellar masses. The scale lengths of our galaxies are among the lowest found for local blue compact dwarf galaxies [@P02]. On the other hand, the corresponding surface densities of SFR in the studied galaxies $\Sigma$ = SFR/($\pi \alpha^2$) are comparable to those of LyC leakers. Because of the compactness of the bright star-forming regions, the half-light radii $r_{50}$ of our galaxies in the NUV are considerably smaller than $\alpha$ (see Table \[tab3\]). Adopting $r_{50}$ as a measure of the size of these galaxies (Table \[tab3\]), the corresponding $\Sigma$s are typically two orders of magnitude larger, and comparable to those found for low-redshift LyC leakers and SFGs at high redshifts [@CL16; @PA18; @Bo17].

Ly$\alpha$ emission {#sec:lya}
===================

The LyC emission can not be directly observed in our galaxies because of their low redshifts. Therefore, we wish to use the Ly$\alpha$ profiles in their spectra to derive information about possible leaking LyC radiation for galaxies with much lower stellar masses than those of confirmed LyC leakers. @D16 and @V17 have proposed that the presence of a double-peaked Ly$\alpha$ profile, with a small peak separation, would be a good indicator of LyC leakage. According to the models of @V15, the peak separation decreases with decreasing column density of the neutral gas. This in turn would result in a higher escape fraction of the LyC radiation. Additionally, the role of the blue Ly$\alpha$ peak in the LyC escape has been discussed by e.g. @H15 and @O18. They found that the escape fraction of the Ly$\alpha$ radiation increases when the blue peak velocity decreases.

The Ly$\alpha$ profiles in the medium-resolution spectra of the 8 observed galaxies are shown in Fig. \[fig6\]. In the upper panel for each object, both the flux and the wavelength are scaled so that the continuum behaviour can be seen over a broader wavelength range around the Ly$\alpha$ line, while in the lower panel both the flux and the wavelength scales are adjusted to examine the profile of the Ly$\alpha$ emission line. A strong Ly$\alpha$ $\lambda$1216Å emission-line without any evidence for an absorption profile is detected in five galaxies (Fig. \[fig6\]b,c,f,g,h), similarly to the low-$z$ LyC leakers [fig. 7 in @V17]. In the remaining 3 galaxies, the weak Ly$\alpha$ emission line is superposed on a broad absorption component (Fig. \[fig6\]a,d,e). The fraction of galaxies with a detected Ly$\alpha$ absorption line is similar to that obtained by @MK19. However, the intensity at the bottom of the absorption lines is above zero in these galaxies, indicating that the covering factor of the H [i]{} cloud surrounding the ionizing source is less than unity, allowing for some Ly$\alpha$ emission and some continuum emission in this wavelength range to escape. The full widths at zero intensity of the Ly$\alpha$ emission lines in all our galaxies are FWZI = 3 – 4Å  (Fig. \[fig6\]). On the other hand, the widths of the absorption lines at the bottom of their profiles are considerably broader, $\sim$ 10 – 20Å in the three galaxies J0007$+$0226, J0926$+$4504 and J1032$+$4919. Therefore, it is unlikely that the emission above zero at the bottom of the absorption profiles is due to the Ly$\alpha$ emission line.

Six out of eight observed galaxies show double-peaked Ly$\alpha$ emission profiles with the peak separations much larger than the nominal COS spectral resolution of $\sim$ 20 km s$^{-1}$ for the G130M grating. The Ly$\alpha$ emission line in J0926$+$4504 is too weak to definitely derive its profile. The two-peak shape is similar to that observed in known LyC leakers [@I16; @I16b; @I18; @I18b; @V17] and in GP galaxies [@JO14; @H15; @Y17; @MK19]. The Ly$\alpha$ emission-line profile of J1032$+$4919 is more complex and consists of three peaks, similar to that of one low-$z$ LyC leaker [@I18b], and two $z$ $>$ 2 LyC leakers [@Va18; @RT17]. However, at variance with J1032$+$4919, all other triple-peaked spectra in the literature do not show clear signs of underlying Ly$\alpha$ absorption.

Some parameters of the Ly$\alpha$ emission profile are presented in Table \[tab5\]. The Ly$\alpha$ emission-line fluxes in the spectra of galaxies with detected broad Ly$\alpha$ absorption are measured placing the continuum at the bottom of the absorption profiles. For J1032$+$4919, two separations (blue peak - centre peak and centre peak - red peak) are given. It is seen that the separation between the peaks is in a narrow range $\sim$ 240 – 310 km s$^{-1}$, indicating low neutral hydrogen column densities $N$(H [i]{}) and implying considerable fractions of escaping LyC emission. However, in the spectra of three galaxies, J0007$+$0226, J0926$+$4504 and J1032+4919, strong Ly$\alpha$ absorption is present as well. The flux in the central part of absorption profiles is above zero, although their shape indicates that they are clearly saturated. This appearance is in contrast to expectations for a single source surrounded by an uniform neutral gas cloud with high $N$(H [i]{}). We derive $N$(H [i]{}) using the relation $$I(\lambda)=I_{\rm cont} \exp{[-\tau(\lambda)]},  \label{profile}$$ where $I_{\rm cont}$ and $I(\lambda)$ are the flux of the continuum and the flux in the line at the wavelength $\lambda$, respectively, after subtraction of the flux at the bottom of the Ly$\alpha$ absorption line. The optical depth $\tau$($\lambda$) in the Ly$\alpha$ profile at the wavelength $\lambda$ is defined by the relation of @B75 $$\tau(\lambda) = 4.26\times 10^{-20} \frac{N({\rm H~I})}{6.04\times 10^{-10} + (\lambda - \lambda_0)^2}, \label{Lya}$$ where $N$(H [i]{}) is in cm$^{-2}$, $\lambda$ is in Å, $\lambda_0$ = 1215.67 Å, Using Eqs. \[profile\] and \[Lya\] we find $N$(H [i]{}) = 1.8$\times$10$^{21}$ cm$^{-2}$, 1.0$\times$10$^{21}$ cm$^{-2}$ and 3.0$\times$10$^{21}$ cm$^{-2}$ from the fit of wings of absorption Ly$\alpha$ profiles in the spectra of J0007$+$0226, J0926$+$4504 and J1032$+$4919, respectively (grey lines in the upper panels of Fig. \[fig6\]a, \[fig6\]d, and \[fig6\]e). We note that only the blue damped wing was used for fitting because the red wing is contaminated by the stellar N [v]{} $\lambda$1240Å  line with a P Cygni profile. Then the superposition of the Ly$\alpha$ absorption and emission lines could be explained by the emission of two star-forming regions, where the fainter one, with a flux in the continuum corresponding to the one at the bottom of the absorption profile, is surrounded by neutral gas with low $N$(H [i]{}), and the brighter one is surrounded by a neutral optically thick cloud. The flux of the continuum for the brighter region is determined by the difference between the observed flux outside the absorption profile and the flux at its bottom. The presence of Ly$\alpha$ emission in galaxies with broad Ly$\alpha$ absorption could also be explained by low-column-density holes in a thick cloud of neutral hydrogen.

Discussion
==========

Comparison with other galaxy samples
------------------------------------

We compare our galaxies with those studied in other recent papers. All galaxies from the sample in this paper are dwarf systems with SDSS $g$ absolute magnitudes $M_g$ $\sim$ –16 to –18 mag. Their absolute FUV magnitudes $M_{\rm FUV}$, in the range –14 to –16, compare well with the average $M_{\rm FUV}$ $\sim$ –15 mag of the faintest spectroscopically confirmed LAEs at redshifts 2.9 - 6.7, similar to those of the sources believed to reionize the Universe [@Ma18]. Our galaxies are much more compact in the NUV continuum (Fig. \[fig5\]) and have lower metallicities (Table \[tab1\]) than most Ly$\alpha$ emitters (LAEs) and LyC leakers. They have high ionizing photon production efficiencies $\xi_{\rm ion}$ (Table \[tab3\]), above the canonical value in log scale of $\log\xi_\mathrm{ion}\sim 25.2$ in units of log Hz erg$^{-1}$ adopted in high-$z$ studies [e.g. @R13] and similar to the values in LAEs at $z$ $\sim$ 3 - 7 [@Ha18; @Na18]. These high values are a natural consequence of a very young starburst age (Table \[tab3\]). High $\xi_{\rm ion}$ in our galaxies are also similar to those in confirmed low-$z$ LyC leakers [e.g. @S16]. If applicable to all high-$z$ galaxies, such $\xi_{\rm ion}$ values would suffice to reionize the Universe with a constant escape fraction $f_{\rm esc}$(LyC) $\sim$ 10 per cent [e.g. @O09; @R13; @D15; @Robertson15; @K16]. However, we note that the $\xi_{\rm ion}$ values in Table \[tab3\] should be considered only as lower limits, as including possible escaping LyC radiation, which is not taken into account, would somewhat increase these values.

The high-$z$ LAEs show a tight relation between the Ly$\alpha$ luminosity $L$(Ly$\alpha$) and the absolute magnitude $M_{\rm FUV}$ at $\lambda$ = 1500Å(small open grey circles in Fig. \[fig7\]a). The confirmed LyC leakers [open black circles, @I16; @I16b; @I18; @I18b] follow the same relation. On the other hand, GPs at redshifts $\la$ 0.3 (grey asterisks) are offset to lower $L$(Ly$\alpha$) by one order of magnitude. This offset can be caused by aperture effects because GPs are on average closer to us and have larger angular sizes. Furthermore, the EW(Ly$\alpha$)s in GPs are considerably lower than in low-$z$ LyC leakers (Fig. \[fig7\]a), indicating older burst ages and thus lower Ly$\alpha$ luminosities. We note that for the LyC leakers and GPs we do not use the published values for Ly$\alpha$ in @I16 [@I16b; @I18; @I18b], @JO14, @H15, @J17 and @Y17. Instead for the sake of data homogeneity, we measured Ly$\alpha$ fluxes and equivalent widths using the public [*HST*]{} data, correcting the fluxes for Milky Way extinction and converting them to luminosities. As for the absolute FUV magnitudes, we derived them from the apparent [*GALEX*]{} FUV magnitudes.

Our galaxies with extreme O$_{32}$ extend the range of $M_{\rm FUV}$ to appreciably lower FUV brightesses. Their low Ly$\alpha$ luminosities ($L$(Ly$\alpha$)$\la$10$^{42}$ erg s$^{-1}$) make the $L$(Ly$\alpha$)-$M_{\rm FUV}$ relation bend downwards at low $M_{\rm FUV}$ (Fig. \[fig7\]a)). We note that LAEs with low Ly$\alpha$ luminosities, similar to those of our galaxies, are also detected in the high-$z$ Universe [e.g. @L19]. A notable feature of the four galaxies with the highest EW(Ly$\alpha$) and highest $L$(Ly$\alpha$) in our sample is that their Ly$\alpha$ luminosities are lower by a factor $>$ 2 than the value derived from the extrapolation of the relation for high-$z$ galaxies to fainter absolute FUV magnitudes (dashed line). While they are consistent with the extrapolation of the trend defined by the GPs to fainter absolute UV magnitudes, the Ly$\alpha$ equivalent widths of the galaxies with extreme O$_{32}$ are similar to those of the low-$z$ LyC leakers [@I16; @I16b; @I18; @I18b] and are much higher than those of GPs.

It was shown e.g. by @Wi16 [@Wi18] that high-$z$ galaxies at $z$ $>$ 3 are surrounded by extended diffuse Ly$\alpha$-emitting haloes tracing neutral gas up to several tens of kpc and contributing 40 – 90 per cent of the total Ly$\alpha$ flux. These extended haloes are seen even in low-mass SFGs with stellar masses down to 10$^{8}$ – 10$^{9}$ M$_\odot$ [@E18; @E19]. @Y17b have shown that Ly$\alpha$ emission in Ly$\alpha$-emitting galaxies at lower redshifts $z$ $\la$ 0.3 is spatially more extended compared to that of the UV continuum.

The difference between our high-EW(Ly$\alpha$) and high-$z$ galaxies may possibly be caused by a low-intensity diffuse Ly$\alpha$ emission in our galaxies extending outside the extraction aperture used to obtain the one-dimensional spectrum. In this case, an aperture correction is needed for comparison of the Ly$\alpha$ flux with fluxes of other hydrogen emission lines. However, we do not expect a large aperture correction for $L$(Ly$\alpha$) ($>$ 2) because the adopted aperture for the extraction of one-dimensional spectra includes nearly all light from our galaxies. Additionally, we have compared Ly$\alpha$ fluxes in one-dimensional spectra obtained with different extraction apertures and reduced with the same custom and pipeline data reduction packages. We find that they differ by not more than 5 per cent. Ly$\alpha$ imaging of the lowest-mass SFGs, with stellar masses $\la$ 10$^{8}$ M$_\odot$, is needed to verify the importance of aperture corrections.

Other factors may play a role in reducing $L$(Ly$\alpha$) in our low-mass galaxies, e.g. unaccounted contribution of underlying Ly$\alpha$ absorption, enhanced UV extinction due to a larger fraction of dust and/or a steeper reddening law in the UV range than in LyC leakers and high-$z$ galaxies. But these factors are unlikely to be enough to explain the observed large offset of our galaxies from the extrapolated value (dashed line in Fig. \[fig7\]a). We note that the H$\beta$ luminosities in our galaxies are more than one order of magnitude smaller than in the LyC leakers, corresponding to a smaller number of massive stars by the same factor. Probably, dynamical processes such as large-scale outflows due to the evolution of massive stars in our galaxies are considerably less energetic and may result in a reduced escaping Ly$\alpha$ emission.

The distribution of the Ly$\alpha$ rest-frame equivalent widths EW(Ly$\alpha$) for the same samples of galaxies as in Fig. \[fig7\]a is shown in Fig. \[fig7\]b. The range of EW(Ly$\alpha$) for our objects is larger than that for LyC leakers with four galaxies having EW(Ly$\alpha$) smaller than those for LyC leakers, and four galaxies with EW(Ly$\alpha$) greater than the average value for LyC leakers. On the other hand, GPs from the literature have in general considerably lower EW(Ly$\alpha$). Comparing to high-$z$ galaxies we note that the EW(Ly$\alpha$)s of our galaxies are several times lower than of high-$z$ galaxies, due to the same reasons (i.e possible aperture effects) as for Ly$\alpha$ luminosities.

@Ha17 found a trend of increasing EW(Ly$\alpha$) with decreasing UV luminosity. They attributed this trend to the lower metallicities of lower-luminosity galaxies. However, the distribution of our galaxies which extend the EW(Ly$\alpha$)-$M_{\rm FUV}$ relation to lower UV luminosities does not support the existence of this trend. Although a dependence of EW(Ly$\alpha$) on metallicity is not excluded, the relation in Fig. \[fig7\]b can also be explained by increasingly higher EW(Ly$\alpha$) errors at their high values for high-$z$ galaxies and by the fact that only galaxies with high EW(Ly$\alpha$) at high redshifts can be selected. The presence of many low-$z$ GPs with low EW(Ly$\alpha$) favours this selection effect.

The Ly$\alpha$ escape fraction
------------------------------

An important quantity to consider is the escape fraction $f_{\rm esc}$(Ly$\alpha$). In this paper we define $f_{\rm esc}$(Ly$\alpha$) as the ratio of the extinction-corrected Ly$\alpha$ to H$\beta$ flux ratio to its Case B value of 23.3, corresponding to that at a low electron number density, $N_{\rm e}$ $\sim$ 10$^2$ cm$^{-3}$ [@SH95]: $$f_{\rm esc}({\rm Ly}\alpha) = 
\frac{1}{23.3}\frac{I({\rm Ly}\alpha)}{I({\rm H}\beta)}, \label{fesc}$$ where $I$(Ly$\alpha$) is the flux density corrected for the Milky Way extinction, and $I$(H$\beta$) is the flux density corrected for both the Milky Way and internal galaxy extinction. At higher electron densities, for example at $N_{\rm e}$ $\sim$ 10$^3$ cm$^{-3}$, the Case B Ly$\alpha$/H$\beta$ ratio is higher by $\sim$ 10 per cent, resulting in a lower $f_{\rm esc}$(Ly$\alpha$). Using Eq. \[fesc\], we calculate $f_{\rm esc}$(Ly$\alpha$) for the eleven LyC leakers from @I16 [@I16b; @I18; @I18b] and compare them with their directly measured $f_{\rm esc}$(LyC) in Fig. \[fig8\]. It is seen that there is a general trend of increasing $f_{\rm esc}$(LyC) with increasing $f_{\rm esc}$(Ly$\alpha$). That trend can be approximated by the maximum likelihood relation (solid line) $$\log f_{\rm esc}({\rm LyC})=(2.67\pm 0.51)\times \log f_{\rm esc}({\rm Ly}\alpha) 
+ (0.40\pm 0.29), 
\label{LyC-Lya}$$ but with large uncertainties. The distribution of the data points in Fig. \[fig8\] is somewhat different from that of the dusty, clumpy interstellar medium models of @D16 (shaded region in Fig. \[fig8\]). Their models predict $f_{\rm esc}$(Ly$\alpha$) $\ga$ 2$\times$$f_{\rm esc}$(LyC) and a wide range of $f_{\rm esc}$(Ly$\alpha$) at fixed $f_{\rm esc}$(LyC), depending on the covering factor of the neutral gas. The observational data show a much narrower range of $f_{\rm esc}$(Ly$\alpha$) at fixed $f_{\rm esc}$(LyC), with some galaxies lying outside the model prediction regions. A relatively small dispersion of the data points in the observed relation in Fig. \[fig8\] gives hope that $f_{\rm esc}$(Ly$\alpha$) can be used to indirectly derive $f_{\rm esc}$(LyC). However, the number of confirmed LyC leakers is still very small and larger statistics are needed to verify the relation given by Eq. \[LyC-Lya\]. There is also the possibility that there exist sources with significant Ly$\alpha$ escape but with no leaking LyC radiation which would flatten the relation shown by the solid line.

The filled circles in Fig. \[fig8\] show the galaxies from our sample with the exclusion of the three galaxies with Ly$\alpha$ absorption. For these galaxies, $f_{\rm esc}$(LyC) is derived using the velocity separation between the peaks of Ly$\alpha$ emission lines. It is seen that, for a given $f_{\rm esc}$(LyC), the galaxies are offset from the confirmed LyC leakers to lower $f_{\rm esc}$(Ly$\alpha$). Possible aperture corrections for Ly$\alpha$ emission would be too small to account for those offsets. On the other hand, corrections for unaccounted Ly$\alpha$ absorption would increase $f_{\rm esc}$(Ly$\alpha$). Overall, these corrections do not appear to be enough to account for the offsets. Alternatively, parts of the offsets could be due to an overestimation of the indirect value of $f_{\rm esc}$(LyC), as determined by eq. 2 of @I18b.

It was suggested by @NO14 that the fraction of escaping ionizing radiation from galaxies correlates with the O$_{32}$ ratio. However, @I18b found that the O$_{32}$ – $f_{\rm esc}$(LyC) correlation for the confirmed LyC leakers is rather weak and a high O$_{32}$ does not garantee a high $f_{\rm esc}$(LyC). Adopting the correlation between the Ly$\alpha$ and LyC escape fractions (Fig. \[fig8\]), we investigate whether O$_{32}$ can be used as indirect indicator of escaping ionizing radiation for galaxies with the highest O$_{32}$. We show in Fig. \[fig9\]a the O$_{32}$ – $f_{\rm esc}$(Ly$\alpha$) diagram for the same galaxies as in Fig. \[fig7\], excluding the high-$z$ LAEs. The galaxies discussed in this paper (filled circles) extend the range of O$_{32}$ up to $\sim$ 40, a factor of two higher than in previous studies. However, no correlation is found. Thus, we confirm and strengthen the conclusion of @I18b that O$_{32}$ is not a reliable indicator of escaping Ly$\alpha$ emission and likely also of escaping LyC radiation. This conclusion is in agreement with the models of @B19 who have shown that galaxies with various metallicities and ionization parameters fill all the $f_{\rm esc}$(LyC) – O$_{32}$ space. However, we note that $f_{\rm esc}$(Ly$\alpha$) for our galaxies (filled circles in Fig. \[fig9\]) could be somewhat higher because of unaccounted possible aperture corrections for Ly$\alpha$ emission and underlying absorption.

We discuss other possible indicators of $f_{\rm esc}$(Ly$\alpha$). A possible candidate is the rest-frame equivalent width EW(Ly$\alpha$). The diagram EW(Ly$\alpha$) – $f_{\rm esc}$(Ly$\alpha$) is shown in Fig. \[fig9\]b. This diagram is somewhat puzzling. At low EW(Ly$\alpha$), the Ly$\alpha$ escape fraction $f_{\rm esc}$(Ly$\alpha$) increases with increasing EW(Ly$\alpha$). However, no such dependence is found at high EW(Ly$\alpha$) $\ga$ 60Å for four of our galaxies and three confirmed LyC leakers with the highest EW(Ly$\alpha$). One possible explanation for that behavior has been proposed by @SM19. They have shown that the EW(Ly$\alpha$) – $f_{\rm esc}$(Ly$\alpha$) relation flattens considerably in the presence of dust absorption and is nearly independent of EW(Ly$\alpha$), given a varying ionizing photon production efficiency $\xi_{\rm ion}$. In particular, our data, in the flat part of the diagram at EW(Ly$\alpha$) $\ga$ 150Å, can be reproduced adopting $E(B-V)$ $\sim$ 0.2 mag, corresponding to $C$(H$\beta$) $\sim$ 0.3, given that log $\xi_{\rm ion}$ increases from $\sim$ 25.0 to $\sim$ 25.7 with increasing EW(Ly$\alpha$) (solid line in Fig. \[fig9\]b). This value of $C$(H$\beta$) is somewhat higher than the values derived from the SDSS spectra (Table \[tab5\]), but is consistent with the values obtained from the high signal-to-noise ratio LBT spectra for J0159$+$0751, J1032$+$4919, J1205$+$4551 and J1355$+$4651 [@I17].

Another indirect indicator of escaping radiation is the velocity separation between Ly$\alpha$ peaks $V_{\rm sep}$. @I18b have found a tight correlation between $f_{\rm esc}$(LyC) and $V_{\rm sep}$. Fig. \[fig9\]c shows a possible correlation between the peak separation $V_{\rm sep}$ and the Ly$\alpha$ escape fraction $f_{\rm esc}$(Ly$\alpha$), described by the maximum likelihood relation (solid line in Fig. \[fig9\]c): $$f_{\rm esc}({\rm Ly}\alpha)=6.56\times 10^{-7} V_{\rm sep}^2
-1.25\times 10^{-3}V_{\rm sep}+0.607. \label{fesc1}$$ The large scatter of the data around the relation found between an integrated property of Ly$\alpha$ ($f_{\rm esc}$(Ly$\alpha$)) and a characteristic of the Ly$\alpha$ profile ($V_{\rm sep}$) is probably to be expected, since several physical properties, such as dust content, H [i]{} column density, H [i]{} kinematics and geometry affect the Ly$\alpha$ radiative transfer [see e.g. @S11; @V15].

Finally, we consider whether He [i]{} emission lines in the optical range can be indicators of Ly$\alpha$ emission. @I17 have argued that He [i]{} emission line ratios are promising diagnostics because some of these lines can be optically thick, indicating a high column density of the neutral gas. The He [i]{} $\lambda$3889Å emission line is most sensitive to this effect. This line is blended with the hydrogen H8 $\lambda$3889Å emission line, and its intensity can be obtained by subtracting the H8 intensity equal to 0.107$\times$$I$(H$\beta$).

The recombination intensity of the He [i]{} $\lambda$3889Å emission line is $\sim$ 0.1$\times$$I$(H$\beta$). This line can be enhanced by collisions with electrons but weakened if its optical depth is high. Therefore, the condition $I$(He [i]{} $\lambda$3889)/$I$(H$\beta$) $<$ 0.1, corresponding to $I$(H8 + He [i]{} $\lambda$3889)/$I$(H$\beta$) $<$ 0.2, would be an indication of high optical depth and high $N$(H [i]{}).

It is seen in Table \[taba1\] that $I$(H8 + He [i]{} $\lambda$3889)/$I$(H$\beta$) is considerably lower than 0.2 in only two galaxies, J0926$+$4504 and J1032$+$4919. Both of these show broad Ly$\alpha$ absorption line in their spectra (Fig. \[fig6\]d,e), indicating high $N$(H [i]{}). For the remaining galaxies, this technique predicts lower $N$(H [i]{}) and thus stronger Ly$\alpha$ in emission. The technique fails for only one galaxy, J0007$+$0226, which shows Ly$\alpha$ absorption in its spectrum (Fig. \[fig6\]a), but has $I$(H8 + He [i]{} $\lambda$3889)/$I$(H$\beta$) $\sim$0.2. Thus we conclude that the He [i]{} $\lambda$3889Å emission line is generally a good indicator of $N$(H [i]{}), and hence of Ly$\alpha$ emission.

Conclusions {#summary}
===========

We present here new [*HST*]{}/COS observations of eight low-redshift ($z$ $<$ 0.07) compact star-forming galaxies (SFG) with extremely high O$_{32}$ in the range $\sim$ 22 – 39. All studied objects are compact low-mass (log ($M_\star$/M$_\odot$) = 5.8 – 8.6) and low-metallicity (12$+$log(O/H)= 7.43 – 7.82) galaxies with strong nebular emission lines in their spectra (EW(H$\beta$) = 258 - 483Å), indicating very young starburst ages of 0.5 – 3.3 Myr. The Ne/O, S/O and Ar/O abundance ratios in our galaxies are similar to the values for the bulk of compact SDSS SFGs. On the other hand, similarly to confirmed LyC leakers, the N/O abundance ratios in our galaxies are higher than those of the most compact SDSS SFGs. We also study the Ly$\alpha$ emission and indirect indicators of the escaping Ly$\alpha$ and Lyman continuum (LyC) radiation of these SFGs. Our main results are summarized as follows:

1\. A strong Ly$\alpha$ emission line with two peaks was observed in the spectra of five galaxies, while a Ly$\alpha$ emission line with a low equivalent width on top of a broad Ly$\alpha$ absorption profile is present in the remaining three galaxies. Using the damped wings of these absorption profiles, we derive neutral hydrogen column densities $N$(H [i]{}) in the range (1 – 3)$\times$10$^{21}$ cm$^{-2}$.

2\. We discuss various indirect indicators of escaping Ly$\alpha$ and ionizing radiation, such as the O$_{32}$ ratio, EW(Ly$\alpha$) and the velocity separation between Ly$\alpha$ emission line peaks $V_{\rm sep}$, assuming that the strength of the Ly$\alpha$ emission line is a measure of LyC leakage. We found that there is no correlation between O$_{32}$ and the Ly$\alpha$ escape fraction $f_{\rm esc}$(Ly$\alpha$). The dependence of $f_{\rm esc}$(Ly$\alpha$) on EW(Ly$\alpha$) is such that at low EW(Ly$\alpha$) $\la$ 100Å, there is a linear increase of $f_{\rm esc}$(Ly$\alpha$), while at high EW(Ly$\alpha$) $>$ 150Å, $f_{\rm esc}$(Ly$\alpha$) is nearly constant with a value $\sim$ 0.25. This behavior may be explained by dust absorption. We find a trend of increasing of $f_{\rm esc}$(Ly$\alpha$) with decreasing of $V_{\rm sep}$. However, even galaxies showing double-peaked Ly$\alpha$ profiles exhibit a large scatter between the Ly$\alpha$ escape fraction and the separation of their peaks $V_{\rm sep}$. The latter quantity has been shown to correlate more strongly with the LyC escape fraction [@I18b].

3\. Bright compact star-forming regions are seen in the COS near ultraviolet (NUV) acquisition images. The surface brightness profile at the outskirts can be approximated by an exponential disc profile, with a scale length of $\sim$ 0.09 – 0.48 kpc. These scale lengths are several times lower than those of confirmed LyC leakers and are among the lowest ones found for local blue compact dwarf galaxies.

The global properties of the selected galaxies are very similar to those of the lowest-mass high-$z$ galaxies. They are thus ideal nearby laboratories for investigating the mechanisms responsible for the escape of Ly$\alpha$ and ionizing radiation from galaxies during the epoch of the reionization of the Universe.

Acknowledgements {#acknowledgements .unnumbered}
================

We thank the anonymous referee for valuable comments. These results are based on observations made with the NASA/ESA [*Hubble Space Telescope*]{}, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Support for this work was provided by NASA through grant number HST-GO-15136.002-A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. Y.I.I. and N.G.G. acknowledge support from the National Academy of Sciences of Ukraine (Project No. 0116U003191) and by its Program of Fundamental Research of the Department of Physics and Astronomy (Project No. 0117U000240) of the National Academy of Sciences of Ukraine. G.W. has been supported by the Deutsches Zentrum für Luft- und Raumfahrt (DLR) through grant number 50OR1720. I.O. acknowledges grants GACR 14-20666P and 17-06217Y of the Czech National Foundation. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration. GALEX is a NASA mission managed by the Jet Propulsion Laboratory. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space AdministrationGALEX is a NASA mission managed by the Jet Propulsion Laboratory. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Emission-line fluxes in SDSS spectra and element abundances
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