© The Authors 2026

1. Introduction

Studies of low-redshift compact star-forming galaxies (CSFGs) selected from the Sloan Digital Sky Survey (SDSS) have shown that they are low-mass and low-metallicity galaxies, with star formation occurring in short bursts of a few million years’ duration (Izotov et al. 2006a, 2011, 2018, 2021a; Amorín et al. 2010).

Their properties, together with the fact that CSFGs and high-redshift star-forming galaxies (SFGs) follow similar mass- and luminosity-metallicity relations, suggest that CSFGs are good local counterparts of high-redshift dwarf SFGs (e.g. Izotov et al. 2021a). The strong emission lines in the optical spectra of H II regions in CSFGs are powered by numerous O stars, which produce abundant ionising radiation. This makes CSFGs promising candidates for significant leakage of ionising radiation into the intergalactic medium (IGM). Dwarf SFGs with similar properties are thought to be responsible for the reionisation of the Universe at redshifts z = 5 − 10 (e.g. Ouchi et al. 2009; Mitra et al. 2013; Yajima et al. 2011; Bouwens et al. 2015; Atek et al. 2024).

Many CSFGs are characterised by high line ratios, O₃₂ = [O III]λ5007/[O II]λ3727, reaching values of up to 60 in some galaxies (e.g. Stasińska et al. 2015; Izotov et al. 2021b, 2024). Such high values may indicate that their H II regions are density-bounded, allowing ionising radiation to escape into the IGM, as suggested by Jaskot & Oey (2013), Nakajima & Ouchi (2014), and Nakajima et al. (2016). However, this is not the only explanation. High O₃₂ can also arise from low metallicity, a high ionisation parameter, or hard ionising radiation (Jaskot & Oey 2013; Stasińska et al. 2015). Direct measurements of Lyman continuum (LyC) emission are not possible for most CSFGs because of their low redshifts, including the galaxies considered in this paper. This limitation does not allow us to link high O₃₂ with either of the above mechanisms.

The properties of the vast majority of CSFGs derived in the optical range are based on low-resolution spectra with unresolved nebular emission lines. In contrast, higher-resolution spectroscopic data are needed to study the kinematic properties of the ionised gas in CSFGs. However, most of studies have mainly considered only the strongest lines, most commonly Hα, [O III] λ5007, and Hβ (e.g. Bordalo & Telles 2011; Chávez et al. 2014; Melnick et al. 2019; Amorín et al. 2012, 2024).

In this paper, we used the Xshooter spectrograph mounted on the Very Large Telescope (VLT) to obtain high signal-to-noise spectroscopic observations of 11 CSFGs at z < 0.085 with extremely high O₃₂ = 11–42. We derive their chemical composition and study the kinematics of the ionised gas using strong emission lines of ions of different elements and ionisation potentials. In Section 2 we describe the selection criteria of CFSGs and their global characteristics. In Section 3 we describe the observations and data reduction. We derive element abundances in Section 4. In Section 5 we study the kinematics of the ionised gas. We summarise our main results in Section 6.

2. Selection of CSFGs and their global characteristics

We selected the objects from the SDSS based on their compactness, strong emission lines, extremely high emission-line ratios O₃₂ = [O III]λ5007/[O II]λ3727, and absence of active galactic nucleus (AGN) spectral features. Additionally, the objects must have low declinations (≲20 degrees) to be accessible for observations with the VLT. The sample includes 11 relatively bright galaxies at z < 0.085 (Table 1). Studies have examined some of these galaxies in the UV range with the Hubble Space Telescope (HST) (emission in Lyα and other UV lines, e.g. Jaskot et al. 2017; Izotov et al. 2020; Berg et al. 2022; Xu et al. 2022), in the optical range (e.g. Izotov et al. 2011, 2017; Chávez et al. 2014; Yang et al. 2017; Kouroumpatzakis et al. 2024), and in the radio range (Filho et al. 2013). Their angular sizes in the images obtained with the HST are considerably smaller than those measured from the SDSS images (Table 2).

The location of the 11 selected galaxies in the [O III]λ5007/Hβ – [N II]λ6584/Hα diagnostic diagram (Baldwin-Phillips-Terlevich (BPT) diagram, Baldwin et al. 1981) in Fig. 1a indicates that most of these CSFGs are more extreme than the full CSFG sample (Izotov et al. 2016). For comparison, we also show a sample of SFGs by Chávez et al. (2014). The spectra of this sample were obtained with high spectral resolution, which was sufficient to derive the velocity dispersion of the ionised gas from the widths of the strong Hβ and [O III] λ5007 emission lines. The solid line derived by Kauffmann et al. (2003) separates SFGs from AGNs. All selected CSFGs are located in the SFG region, implying that their interstellar medium is ionised by hot stars in the star-forming regions.

Fig. 1. (a) Baldwin–Phillips–Terlevich (BPT) diagram (Baldwin et al. 1981). Galaxies from this paper and from Chávez et al. (2014) are shown as red and blue circles, respectively. Compact SFGs from the SDSS are represented by black dots (EW(Hβ) ≥ 100 Å) and grey dots (EW(Hβ) < 100 Å). The line separating SFGs from AGNs is taken from Kauffmann et al. (2003). (b) O32 – R23 diagram, where O32 = I([O III] λ5007)/I([O II] λ3727) and R23 = I([O II] λ3727 + [O III] λ4959 + [O III] λ5007)/I(Hβ). (c) Relation between the ionising-photon production efficiency, ξion, and O32. The canonical value of ξion from Robertson et al. (2013) is shown as a magenta-shaded region. The meaning of the symbols in (b) and (c) is the same as in (a).

In Fig. 1b we compare the locations in the O₃₂ – R₂₃ (R₂₃ = {[O II]λ3727 + [O III]λ4959 + [O III]λ5007}/Hβ) diagram of the high O₃₂ sample with those of the entire CSFGs from SDSS. The selected galaxies with high O₃₂ lie at the extreme of the SDSS galaxy distribution, implying that they may be good LyC-leaking candidates. In Fig. 1b, the CSFGs at z < 0.085 lie, on average, somewhat apart from other SFGs because of their lower metallicities and higher O₃₂.

We derived the global characteristics of the CSFGs from their SDSS spectra and Galaxy Evolution Explorer (GALEX) photometry, which are presented in Table 1. We transformed the observed fluxes into luminosities and absolute magnitudes, adopting luminosity distances (NASA/IPAC Extragalactic Database (NED), Wright 2006) derived using the cosmological parameters H₀ = 67.1 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.682, and Ω_m = 0.318 (Planck Collaboration XVI 2014). We derived the Hβ luminosities L(Hβ) from the extinction-corrected Hβ fluxes measured in the SDSS spectra. Additionally, we corrected L(Hβ) for aperture effects using the relation 2.512^r(ap)−r, where r and r(ap) are the SDSS r-band total magnitude and the magnitude within the round spectroscopic 3″ aperture for galaxies in the ninth data release and the 2″ aperture for galaxies in later SDSS releases. We also derived extinction-corrected absolute SDSS g-band and GALEX far-UV (FUV) band magnitudes.

We derived the galaxy stellar masses by fitting the spectral energy distribution (SED) of the SDSS spectra, corrected for extinction as derived from the observed hydrogen Balmer decrement and for the contribution of nebular emission in the same spectra (Izotov et al. 2011).

Table 1 shows that the selected galaxies are dwarf systems with low stellar masses, M_★ ≲ 10⁸ M_⊙. These extreme CSFGs have low extinction (average C(Hβ) = 0.084, Table B.1), are metal-poor and have oxygen abundances, 12+log(O/H), between 7.53 and 7.99, with an average value of 7.77 (see also Section 4). The high equivalent widths of the Hβ emission line in our CSFGs (see Section 3) imply a very high production efficiency of the ionising photons, ξ_ion (Fig. 1c). These properties are similar to those of high-redshift dwarf galaxies which are thought to be the main contributors to the reionisation of the Universe at redshifts z > 5.

3. Observations and data reduction

We obtained Xshooter spectrophotometric observations of the galaxies listed in Table 1 in the wavelength range 3200–24 000 Å, using a three-arm spectrograph that splits emission from the object into three beams: UVB in the near-ultraviolet and blue wavelength ranges, VIS in the visual wavelength range, and NIR in the near-infrared wavelength range. We used set-ups with slit sizes of 1″ × 11″ and resolving power R = 5400 for the UVB arm, 0$\stackrel{″}{.}$9 × 11″ and R = 8900 for the VIS arm, and 0$\stackrel{″}{.}$9 × 11″ and R = 5600 for the NIR arm (Table 2). We used spectra of spectrophotometric standard stars obtained during the same nights for flux calibration and for correcting telluric absorption lines in the red part of the spectra. We also obtained calibration frames for biases, flats, and thorium-argon comparison lamps during the same nights.

We performed bias subtraction in the UVB and VIS arms, dark subtraction in the NIR arm, flat field correction, wavelength and flux calibration, and night sky background subtraction using IRAF. We manually removed cosmic-ray hits from the background-subtracted frames and then flux-calibrated them. For each object, we co-added individual subexposures. Finally, we extracted one-dimensional spectra in apertures of 1$\stackrel{″}{.}$0 × 2$\stackrel{″}{.}$0 (UVB arm), 0$\stackrel{″}{.}$9 × 2$\stackrel{″}{.}$0 (VIS arm), and 0$\stackrel{″}{.}$9 × 2$\stackrel{″}{.}$0 (NIR arm) using the IRAF apall routine. All galaxies are very compact, with a full width at half maximum of ∼1″ in the r band in SDSS images (Table 2). Therefore, the extraction apertures for the one-dimensional spectra include almost all emission from the galaxies. Fig. A.1 shows an example of the resulting rest-frame spectra. Strong, narrow emission lines are present in the spectrum, suggesting active star formation.

We measured emission-line fluxes using the IRAF splot routine. We calculated the errors of the line fluxes from the photon statistics in the non-flux-calibrated spectra, adding a relative error of 1% in the absolute flux distribution of the spectrophotometric standards. We propagated the line flux errors into the calculations of the elemental abundance errors. The strong [O III] λ4363 emission line is present in all spectra, allowing reliable determinations of electron temperature and abundance.

We corrected the observed fluxes for extinction using the extinction coefficient C(Hβ), derived from the observed decrement of the hydrogen Balmer emission lines. We adopted the Cardelli et al. (1989) reddening law with R(V) = A(V)/E(B − V) = 3.1, where A(V) and E(B − V) are the total extinction in the V band and the selective extinction, respectively. For R(V) = 3.1, the total extinction is linked to C(Hβ) by the relation A(V) = 2.11 × C(Hβ). Table B.1 lists the extinction-corrected emission-line fluxes I(λ), relative to the Hβ fluxes, multiplied by 100; the extinction coefficients C(Hβ); the rest-frame equivalent widths, EW(Hβ); and the observed Hβ fluxes F(Hβ). We note that the EW(Hβ)s of the studied CSFGs are high, ∼200–390 Å (Table 1). Most of them are among the highest ever measured in spectra of SFGs, indicating the bursting nature of star formation and very young burst ages (< 3 Myr).

4. Element abundances

4.1. Heavy elements

To determine heavy-element abundances, we followed the procedures of Izotov et al. (2006a). We adopted a two-zone photoionised H II region model: a high-ionisation zone with the temperature T_e(O III), where [O III], [Ne III], and [Ar IV] lines originate, and a low-ionisation zone with the temperature T_e(O II), where [N II], [O II], [S II], and [Fe III] lines originate. The [S III] and [Ar III] lines originate in the intermediate zone between the high- and low-ionisation regions. We calculated the temperature T_e(O III) using the [O III] λ4363/(λ4959 + λ5007) ratio. To calculate the electron temperatures T_e(O II) and T_e(S III), we used the expressions of Izotov et al. (2006a). We note that uncertainties in the determination of T_e(O II) do not change the total oxygen abundance because the fraction of the O⁺ ion in our objects is low. We derived electron number densities N_e(O II) and N_e(S II) from the [O II] λ3726/λ3729 and [S II] λ6717/λ6731 emission line ratios, respectively. We propagated the emission-line errors in the determination of electron number density and electron temperature, ionisation correction factors, ionic and total element abundances, and emission-line velocity dispersions. However, they do not take into account systematic effects introduced, for example, by uncertainties in the determination of ionisation correction factors.

The electron temperatures T_e(O III) in the studied CSFGs are high (Table B.2), ranging from ∼15 000 K to ∼20 000 K. The electron number densities N_e(O II) and N_e(S II), characteristic of the low-ionisation zone in the H II region, are in general agreement within the errors, and for some galaxies they are relatively high.

We derived ionic and total heavy element abundances using the Izotov et al. (2006a) relations, and present them in Table B.2 together with the ionisation correction factors (ICF) for unseen stages of ionisation. Fig. 2 shows the abundance ratios N/O, Ne/O, S/O, Cl/O, Ar/O, and Fe/O. Except for nitrogen and iron (Figs. 2a and 2f), the abundance ratios in the CSFGs in this work are similar to those derived for a sample of BCDs with high signal-to-noise-ratio spectra (Izotov et al. 2006a, 2014) and to those for SDSS galaxies in which the [O III] λ4363 emission line is detected at the level above 4σ. The nitrogen-to-oxygen and iron-to-oxygen abundance ratios in our sample of CSFGs are higher than in the comparison sample of galaxies from Izotov et al. (2006a), which show milder ionising radiation, indicated by lower O₃₂ ratios (< 10) and somewhat older starbursts, indicated by lower EW(Hβ).

Fig. 2. Dependence of element abundance ratios on oxygen abundance, derived using the prescriptions of Izotov et al. (2006a). Red symbols represent galaxies from this study. Blue symbols represent dwarf SFGs observed with various telescopes for the determination of the helium abundance (Izotov et al. 2014), and black symbols represent SDSS SFGs in which the [O III] λ4363 emission line is detected at the level above 4σ. Open magenta circles with error bars indicate solar values (Lodders 2010).

Several mechanisms may explain the enhanced N/O and Fe/O abundance ratios in our galaxies with extreme characteristics. Nitrogen-enriched clumps in inhomogeneous H II regions with a Wolf-Rayet stellar population are likely required to explain such high N/O abundance ratios at low metallicity (12+log(O/H) ∼ 8) (Izotov et al. 2006a). Charbonnel et al. (2023), Isobe et al. (2023) and Marques-Chaves et al. (2024) attribute the high N/O abundance ratios to the evolution of Wolf–Rayet stars or supermassive (10³–10⁵ M_⊙) stars. Isobe et al. (2022) and Watanabe et al. (2024) suggest that high N/O and Fe/O abundance ratios arise from nucleosynthesis in massive hypernovae and pair-instability supernovae, whereas Kojima et al. (2021) propose that nearly solar Fe/O abundance ratio in extremely metal-poor galaxies results from nucleosynthesis in very massive stars with masses above 300 M_⊙.

However, both nitrogen and iron abundances are derived from the low-ionisation [N II]λ6584 and [Fe III]λ4658, 4988 emission lines, respectively. The fractions of N⁺ and Fe²⁺ are low in our galaxies with extremely high O₃₂ ratios. Therefore, high ionisation correction factors ICF(N) and ICF(Fe) are needed to convert ion abundances to total element abundances (Table B.2). We determined these ionisation correction factors from ionisation-bounded models. We note that high O₃₂ ratios in our galaxies imply that the H II regions in these galaxies might be clumpy or density-bounded. We investigated how N/O and Fe/O abundance ratios can differ in clumpy or density-bounded H II regions. Clumpiness of the ionised gas is determined by the filling factor, whereas that of the neutral gas is defined by the covering factor, ranging from 0 to 1.

We used the CLOUDY v25.00 code (Gunasekera et al. 2025) to calculate a set of uniform, spherically symmetric photoionised H II region models with finite neutral hydrogen column densities ranging from 10¹⁷–10²⁰ cm⁻² or covering factor ranging from 0 (open geometry) to 1 (closed geometry), and compared them with ionisation-bounded H II region models. We also adopted an input oxygen abundance 12+log(O/H) = 7.6, which is typical for our galaxies, and starburst ages of 2 and 3 Myr. For the production rate of ionising photons we adopted two values, Q_ion = 10⁵²–10⁵³ s⁻¹, corresponding to recombination Hβ luminosity of ∼10⁴⁰–10⁴¹ erg s⁻¹, which is also typical for our galaxies. Two other parameters, which we varied over a wide range, are the electron number density, N_e, and the filling factor, f. Table 3 shows the entire range of input parameters. We note that the product N_ef determines the compactness of the H II region model.

Fig. 3a shows variations of the O₃₂ ratio with neutral hydrogen column density in our models. Several values of O₃₂ at fixed N(H I) correspond to different values of N_ef. The O₃₂ ratio decreases with increasing N(H I) for N(H I) in the range 10¹⁷–10¹⁹ cm⁻² but reaches constant values at higher N(H I). The model values of O₃₂ at N(H I) = 10¹⁷ cm⁻² are too high compared to the observed values. Therefore, translucent models with N(H I) > 10¹⁷ cm⁻² are more likely.

Fig. 3. (a) Dependence of O32 ratio on column density of neutral hydrogen, N(H I), in density-bounded H II region models. The N(H I) value is expressed in cm−2. (b) and (c) Relations between ionisation correction factors ICF(N+) and ICF(Fe2+), and the O+ abundance fraction. (d) Dependence of the N+/O+ abundance ratio on O+ abundance fraction. The horizontal black line indicates the input value of log(N/O) = –1.6 used in the CLOUDY calculations. Red, blue, and green symbols in panels (b)–(d) represent density-bounded and ionisation-bounded models of H II regions, and H II regions with varying covering factor, respectively.

In Figs. 3b and 3c we show ionisation correction factors for nitrogen and iron for density-bounded, clumpy, and ionisation-bounded models of H II regions. The small difference between the three sets of models suggests that applying ICFs for density-bounded models and the relations from Izotov et al. (2006a) for N⁺/H⁺ and Fe²⁺/H⁺ abundance ratios would result in small variations in N/H and Fe/H abundance ratios, not exceeding 0.10 and 0.15 dex, respectively, for O⁺/(O⁺ + O²⁺) > 0.05, compared to ionisation-bounded H II regions.

We also note that the relation N/O ≈ N⁺/O⁺ is used in some studies (e.g. Berg et al. 2020; Arellano-Córdova et al. 2025) since the ionisation potential of N is slightly higher than that of O. Application of this relation results in ∼0.05–0.10 higher values of log N/O than those in Table B.2. An exception is the higher N⁺/O⁺ ratios in density-bounded models with very high O₃₂ values, due to the higher cutoff of the O⁺ zone compared to that of the N⁺ zone.

Thus, the variations in ICFs as well as in N/O and Fe/O abundance ratios lead us to the conclusion that the discussions about the possible origin of N and Fe in galaxies with extreme O₃₂ should be considered with caution if the N and Fe abundances are derived using low-ionisation [N II] λ6584, [Fe III] λ4658, and λ4988 emission lines. Furthermore, all of the above abundance determinations are based on the assumption of ionisation-bounded H II region models, whereas high O₃₂ values may indicate that H II regions can be density-bounded or clumpy, although the ionisation correction factors are similar in all models if O⁺/(O⁺ + O²⁺) > 0.05.

4.2. Helium

The determination of the He abundance in low-metallicity SFGs requires special, detailed consideration. This is because high precision in He abundances is needed to derive the primordial He abundance from these data. Until now, almost all He abundance determinations have been made using observations of low-redshift SFGs (e.g. Izotov et al. 2014; Matsumoto et al. 2022; Yanagisawa et al. 2026). However, with the advent of James Webb Space Telescope (JWST), He abundance determinations for high-redshift galaxies with 1.6 ≲ z ≲ 3.3 have become possible (Berg et al. 2026).

In this study, using Xshooter observations, we self-consistently derive the He abundance following the approach of Izotov et al. (1997), Izotov & Thuan (1998, 2004), Izotov et al. (2014). The method is based on minimisation of differences in the He mass fractions Y_i derived from different He I emission lines after correction of their intensities for collisional and fluorescent enhancement, using approximations for both effects on the optical depth, τ(λ3889), and the electron number density, N_e(He), in the zone of He I emission according to Benjamin et al. (1999, 2002), Porter et al. (2012, 2013), and Izotov et al. (2013). Alternative minimisation schemes have been developed by Aver et al. (2011, 2012, 2015), Yanagisawa et al. (2026), Berg et al. (2026). We note that the electron number density N_e(S II) is used in many papers to correct for collisional enhancement of He I emission lines. However, emission of [S II] λ6717, 6731 lines is produced in the outer region of the H II region and in the surrounding H I region. Therefore, N_e(S II) may not be appropriate for He abundance determination.

Apart from collisional and fluorescent enhancement of the He I emission lines, we took into account several other effects that deviate hydrogen and helium emission lines from recombination values, including the presence of underlying stellar absorption lines, interstellar extinction, and collisional excitation of hydrogen lines. Finally, we added the mass fraction of He in the He²⁺ stage, using the intensity of the He IIλ4686 emission line.

We considered two cases of weighted mean Y determination using two sets of He I emission lines: one set includes six lines, He Iλ3889, 4471, 5876, 6678, 7065, and 10830 Å, and the second set includes five lines, excluding the He Iλ10830 Å emission line. It is important to use the He Iλ10830 Å emission line because this line strongly depends on the electron number density.

Table 4 shows the ranges of the parameters T_e(He), N_e(He), and τ(λ3889) used in the He abundance minimisation, and Table B.2 shows their values for the minimum deviation of Ys for different He I lines from the weighted mean Y(mean). Table 5 shows the values of Y for different He I emission lines. They vary over a large range from line to line and from galaxy to galaxy, mainly because of large statistical uncertainties, but the weighted mean Y (mean) varies over a much narrower range and has small statistical errors. These values are similar to the values of Y (mean) derived, for example, by Izotov et al. (2014) for a large sample of galaxies with similar physical characteristics using the same minimisation technique (Fig. 4). We also note that the dispersion of Y values derived using six He I emission lines is somewhat lower than that derived using five He I emission lines (red and black symbols in Fig. 4, respectively). This fact was noted earlier by Izotov et al. (2014), who used a much larger sample of galaxies. The intensity of the He Iλ10830 emission line is affected by strong telluric absorption in the spectra of two galaxies, J0009+0234 and J1310+0852. Therefore, its intensity relative to Hβ in the spectra of these galaxies is unphysically low, below the recombination value of ∼0.2 (Table B.1). Consequently, the Y(10830) values in these galaxies are considerably lower than those for other galaxies. The intensity of this line might be reduced by dust absorption because of non-zero optical depth and multiple scattering. We cannot estimate this reduction, but it is likely not high because of the low metallicity in our galaxies.

Fig. 4. Dependence of the helium mass fraction, Y, on the oxygen abundance, O/H, for SFGs. Galaxies from Izotov et al. (2014) with Y derived using six He I emission lines are marked with blue symbols. Galaxies from this work are marked with red symbols for galaxies with Ys derived using six He I emission lines and by black symbols for galaxies with Y derived using five He I emission lines.

5. Ionised-gas kinematics

The large wavelength coverage, medium spectral resolution of the Xshooter spectrograph, and relatively high apparent brightness of our extreme galaxies allow us to derive velocity dispersions σ for a large number of emission lines from ions with various ionisation potentials originating in different parts of H II regions and to study the kinematics of the ionised gas. Previous studies have investigated the kinematics of ionised gas in a large sample of low-redshift high-excitation H II regions, for example by Chávez et al. (2014), using various telescopes and spectroscopic observations with a resolving power R > 10 000. They aimed to derive the relation between the extinction-corrected Hβ luminosity L(Hβ) and the velocity dispersion σ(Hβ) to determine the Hubble constant H₀. However, Chávez et al. (2014) only considered two strong lines, Hβ and [O III] λ5007 Å.

All of our galaxies are very compact and unresolved in their SDSS images. Furthermore, HST imaging of some objects also reveals a very compact structure. This implies that their emission lines originate mainly in a single H II region and can thus be fitted by single Gaussians. However, very weak broad emission in the strongest lines is also present in some of our galaxies, most commonly of the [O III] λ5007 Å line. In these cases we applied two-Gaussian fitting and compared the widths of narrow components obtained by this method and by one-Gaussian fitting. We find that the widths of the narrow components derived by these two methods differ by less than 0.1%. This is because the fluxes of narrow components are about two orders of magnitude higher than those of the broad components. Therefore, single-Gaussian fitting is applicable to our galaxies and we adopt it in this paper, except for He Iλ10830 Å, for which we used two-Gaussian fitting because of broadening due to radiative transfer (see below). We note that the broad components are not central to this paper, and we do not present their analysis here.

Figs. 5 and 6 show single-Gaussian fits of the strong emission lines Hβ and Hα in all studied galaxies. It is clear from these figures that the emission lines are very well fitted with a single Gaussian, with only very slight deviations from the observed line profile in the weak wings. An exception is the galaxy J0240−0828, for which we adopted a three-Gaussian fit with one dominant Gaussian. The contribution of the other two Gaussians to the line emission is small. Therefore, for clarity, we adopted the simplest model with a single Gaussian for ten galaxies and a dominant Gaussian for J0240−0828.

Fig. 5. Profiles of the Hβ emission line in our galaxies. Solid black lines denote the observed profiles. All profiles are fitted by single Gaussians (dotted red lines) except that of J0240−0828, which is fitted by three Gaussians (dotted blue lines). The dotted red line denotes the total fitted profile. For the galaxy J0007+0226, the instrumental, thermal and macroscopic (turbulent) profiles are shown by blue, green, and magenta dashed lines, respectively.

Fig. 6. Same as in Fig. 5 but for the Hα profile.

We derived the observed velocity dispersion (σ_obs) from the relation σ_obs = FWHM/2.35, assuming that the line profile is Gaussian, where FWHM is the rest-frame full width of the line at half maximum.

We corrected σ_obs for thermal (σ_th) and instrumental (σ_in) broadening to derive the final dispersion, σ, characterising macroscopic turbulent motion, in accordance with Chávez et al. (2012), using the relation

$$\begin{array}{c}\hfill \sigma ={({\sigma }_{\mathrm{obs}}^2-{\sigma }_{\mathrm{th}}^2-{\sigma }_{\mathrm{in}}^2)}^{1/2}.\end{array}$$(1)

We derived the instrumental dispersion in each arm from the resolving power according to

$$\begin{array}{c}\hfill {\sigma }_{\mathrm{in}}=\frac{c}{2.35R},\end{array}$$(2)

where R is the resolving power and c is the speed of light. Adopting R = 5400, 8900, and 5600 for the UVB, VIS, and NIR arms, we obtain σ_in = 23.6 km s⁻¹, 14.3 km s⁻¹, and 22.2 km s⁻¹, respectively. We confirmed these values of σ_in from measurements of emission line widths of thorium-argon comparison spectra in all orders of the UVB and VIS arms and of night-sky spectra in all orders of the NIR arm, obtained with the same slit widths as those used to obtain spectra of the galaxies. Furthermore, very similar velocity dispersions σ of hydrogen Balmer and Paschen emission lines observed in all UVB, VIS, and NIR arms (see below) implies that the dispersions of instrumental profiles in different arms are derived correctly.

The thermal dispersion is derived from the relation

$$\begin{array}{c}\hfill {\sigma }_{\mathrm{th}}=\sqrt{\frac{k{T}_{\mathrm{e}}}{A{m}_p}},\end{array}$$(3)

assuming a Maxwellian velocity distribution, where k is the Boltzman constant, m_p is the proton mass, A is the atomic number of the ion, and T_e is the electron temperature derived from the spectrum (Table B.2). We adopted T_e(O III) for all emission lines considered below, except for [O II] λ3726 Å, λ3729 Å, and [S II] λ6717 Å, λ6731 Å, for which we used T_e(O II). The thermal dispersion is comparable to the instrumental dispersion for the VIS arm, but it is considerably smaller for the UVB and NIR arms.

There are two He I transitions from the metastable 2³S state, namely He Iλ3889 Å and λ10830 Å, which may be subject to resonant scattering due to non-zero optical depth. The He Iλ3889 Å emission line is usually used in He abundance determination as a measure of the optical depth (e.g. Benjamin et al. 1999, 2002). Recently Draine (2026) considered radiative transfer in the He Iλ10830 Å emission line. He predicts a complex He I 10830 Å profile for typical conditions in the H II regions, consisting of two strong peaks separated by ∼75–140 km s⁻¹ and additional weaker features. This mechanism causes the He Iλ10830 emission line in the Xshooter spectra somewhat broadened and asymmetric. Therefore, for this line we applied a two-Gaussian model to derive the separation between the peaks. Table 7 shows the results of this modelling. Fig. 7 shows an example of the fitting for the galaxy J0007+0226. Two-Gaussian fitting was not possible for four galaxies. In two galaxies, J0009+0234 and J1310+0852, the line is subject to telluric absorption and the profile is symmetric in two other galaxies. The table shows that the separation between the peaks in the spectra of other galaxies is consistent with the peak separation predicted by Draine (2026) for resonant scattering. For further comparison of the He Iλ10830 Å emission line with other emission lines, we adopted Gaussian characteristics only for its brightest component.

Fig. 7. Two-Gaussian fit (dashed lines) to the He Iλ10830 Å emission-line profile in the spectrum of J0007+0226 (solid black line).

Figs. 5 and 6 show details of the profile fitting for one galaxy. The observed wavelength of the Hβ emission line in the spectra of all our galaxies falls within the wavelength range of the UVB arm, whereas the Hα emission line was observed at wavelengths covered by the VIS arm. Therefore, the Hβ profile is only partly resolved because of the relatively broad instrumental profile (Fig. 5). The resolution is much better for the Hα profile because the instrumental profile is almost two times narrower (Fig. 6).

Table 6 lists the velocity dispersions σ of the 17 brightest lines in the spectra of all 11 selected galaxies. Some bright emission lines are not considered, for example, Pαλ18756 Å, [S III] λ9069 Å and λ9531 Å, because they are observed at wavelengths with relatively strong telluric absorption.

In Fig. 8 we compare velocity dispersions σ(Hβ) and various other characteristics of our extreme galaxies observed with the Xshooter and galaxies by Chávez et al. (2014). Fig. 8 shows that the sample of Chávez et al. (2014) is characterised by low O₃₂ ratios that do not exceed a value of four for most galaxies. In contrast, galaxies observed with Xshooter are much more extreme, with the O₃₂ ratio extending to very high values, from ten to more than 40. The EWs of the Hβ emission line in most galaxies of the Chávez et al. (2014) sample are also much lower than those in galaxies of our sample (Fig. 8b). The EW(Hβ) is a characteristic of the H II region age. Therefore, lower EW(Hβ) values indicate older ages of H II regions in the vast majority of galaxies studied by Chávez et al. (2014). In addition, the contribution of the underlying older stellar population to emission in the H II region of most galaxies from the Chávez et al. (2014) sample is higher. At fixed σ(4861) our galaxies are systematically less massive (Fig. 8c) and more metal-poor (Fig. 8d). It is worth emphasising that all our galaxies have low velocity dispersion of the Hβ emission line, and for such low dispersion we increase the statistics in the range of low metallicity, low stellar mass, and high Hβ EW. We find that σ(Hβ) increases with stellar mass and oxygen abundance and slightly decreases with O₃₂. In contrast, there is no correlation between σ(Hβ) and EW(Hβ).

Fig. 8. Relations between the velocity dispersion of the Hβ emission line (in km s−1) and (a) O32 = [O III]5007/([O II]3726 + [O II]3729), (b) EW (Hβ), (c) log(M★/M⊙), and (d) oxygen abundance 12+log(O/H). Filled red circles represent our galaxies, and filled blue circles represent galaxies by Chávez et al. (2014).

The Xshooter observations allowed us to derive velocity dispersions not only of Hβ, Hα, and [O III]λ5007 Å emission lines, but also of several other strong recombination and collisionally excited emission lines of ions with different ionisation potentials. This enabled an investigation of the kinematic properties in various parts of H II regions. Similar studies were previously performed for some blue compact dwarf and green pea galaxies (e.g. James et al. 2009; Amorín et al. 2012; Firpo et al. 2011; Hägele et al. 2012). However, no such study has been performed before for CSFGs with extremely high O₃₂ ratios. For convenience, to compare velocity dispersions σ(λ) of different emission lines, we used the ratio of the velocity dispersion of a particular line to that of the Hβ emission line, σ(λ)/σ(4861). Figs. 9, A.2, A.3 and A.4 show the dependence of σ(λ)/σ(4861) on O₃₂ ratios, stellar masses, Hβ emission line EWs, and oxygen abundances. We also show data for galaxies from Chávez et al. (2014) in panel (i) of these figures. We note that O₃₂ is a proxy for the ionisation parameter and varies over a wide range. The ratios σ(λ)/σ(4861) are nearly constant and equal to ∼ 1 for [Ne III] λ3868 Å, [O III] λ4363 Å, and λ5007 Å emission lines, as well as for most He I and all hydrogen lines. This indicates that these lines originate in the same parts of H II regions. In contrast, the ratios σ(λ)/σ(4861) considerably deviate from unity for [O II]λ3726 Å, λ3729 Å, [S II]λ6717 Å, λ6731 Å, He IIλ4686 Å, and He Iλ10830 Å emission lines.

Fig. 9. Ratios of velocity dispersions of various lines to that of Hβ as a function of O32 ratios (filled red circles), with typical errors shown in the lower right corners. Filled blue circles in panel (i) represent galaxies from Chávez et al. (2014).

The most deviant is the He IIλ4686 Å emission line, with a velocity dispersion that is on average ∼1.5 times larger than σ(4861) of the Hβ emission line (Figs. 9h, A.2h, A.3h, and A.4h). The He IIλ4686 Å emission line is likely produced in the inner part of the H II region and can be broadened by dynamical processes such as stellar winds of massive stars, massive X-ray binaries, and/or shocks in expanding supernova remnants from current and/or past bursts of star formation. However, the presence of an AGN can likely be excluded because the high-ionisation emission line [Ne V] λ3426 Å is detected in the spectra of only two galaxies, J0009+0234 and J0240−0828, with the I([Ne V] λ3426 Å)/I(He IIλ4686 Å) ratios of ∼0.4 and ∼0.1. These low ratios are typical of SFGs with detected [Ne V] emission, in contrast to the high ratios of ∼1–3 in Seyfert 2 galaxies (e.g. Izotov et al. 2012, 2021c; Thuan & Izotov 2005).

A similar appearance of the He IIλ4686 Å emission line was found, for example, by Izotov et al. (2006b) in the blue compact dwarf galaxy SBS 0335−052E. They found that the width of this line in the galaxy was 1.5–2 times greater than the width of other lines. Furthermore, Thuan & Izotov (2005) detected a weak [Ne V] λ3426 Å emission line in SBS 0335–052E with an intensity typical of SFGs. However, at present the origin of high-ionisation He II and [Ne V] emission lines in SBS 0335−052E (and other SFGs with detected [Ne V] emission) remains unsolved, despite considerable efforts (e.g. Mingozzi et al. 2025).

Conversely, the σ([O II] 3726)/σ(Hβ 4861), σ([O II] 3729)/σ(Hβ 4861), σ([S II] 6717)/σ(Hβ 4861), and σ([S II] 6731)/σ(Hβ 4861) ratios are systematically lower than unity and likely do not depend on O₃₂ (Figs. 9a, 9b, 9l, and 9m) and EW(Hβ) (Figs. A.3a, A.3b, A.3l, and A.3m). This can be explained by the fact that the low-ionisation ions O⁺ and S⁺ reside in the outer parts of the H II region, which are likely less disturbed by dynamical processes caused by massive stars in the central cluster, resulting in relatively low velocity dispersions. Similarly, these ratios do not depend on the stellar mass (Figs. A.2a, A.2b, A.2l, and A.2m) and oxygen abundance (Figs. A.4a, A.4b, A.4l, and A.4m). We note that the [N II] λ6584 emission line in our galaxies is generally weaker than the [S II] emission lines (Table B.1). We derived velocity dispersions σ for this line in only six galaxies with the highest signal-to-noise ratios in the continuum and with the [N II] λ6584 profiles that can be fitted by a single Gaussian. We find that σ([N II] λ6584)/σ(Hβ) in these galaxies is systematically lower than unity, similar to that for [O II] and [S II] emission lines, meaning that they are emitted in nearly the same outer zones of the H II region.

The measured velocity dispersion of the infrared hydrogen line Pγ10941 Å may be affected by telluric absorption. However, in spectra of our galaxies this line is located at wavelengths with relatively low telluric absorption, resulting in σ(10941)/σ(4861) ∼1 (Fig. 9n).

We find interesting features for the He I emission lines. We present data only for emission lines that arise in transitions between triplet states of ortho-He (He I 4471, 5876, 7065, and 10830; Table 6, Figs. 9, A.2, A.3, and A.4). Emission lines arising in the transitions between singlet states (para-He), not blended with other lines, are also present in spectra of our galaxies (e.g. He I 4922, 5016, and 6678), but they are much weaker than the triplet lines. Therefore, their velocity dispersions are subject to higher uncertainties and we did not consider them.

Certain He I emission lines (λ7065 and λ10830) can be subject to telluric absorption. This is true for the He Iλ10830 emission line in two objects, J0009+0234 and J1310+0852. The intensities of the He Iλ10830 emission line in these two galaxies (Table B.1) are lower than the predicted recombination value (I(He I 10830)/I(Hβ) ∼ 0.2), whereas the intensities of the nearby hydrogen Pγλ10941 emission line are consistent with the recombination value (I(Pγ 10941)/I(Hβ) ∼ 0.07). However, in other galaxies the He I emission lines λ7065 and λ10830 are located at wavelengths free of telluric absorption. We also checked whether possible systematic uncertainties in the wavelength calibration influence the velocity dispersions. For this we compared the widths of particular emission lines, not only of He I but also of ions of other elements, measured in two adjacent orders of the echelle spectrum, where possible. We find that the differences in the widths of the same line in the two orders are in the range of 2–5%.

Figures 9g and A.2g show that the velocity dispersions of He Iλ4471, λ5876, and λ7065 are almost equal to that of the Hβ emission line, indicating that collisional and fluorescent enhancement has a minor effect on the broadening of these lines. In contrast, the He Iλ10830 emission line is on average ∼20% broader than the Hβ emission line. The higher σ(10830) is real and is not due to uncertainties in the data reduction because the velocity dispersion of the nearby Pγλ10941 emission line is the same as that of Hβ (Figs. 9o–A.2o). Part of this broadening is caused by radiative scattering in the He Iλ10830 emission line. Another emission line subject to radiative scattering is the He Iλ3889 emission line. However, this line is blended with the H Iλ3889 emission line. The line separation in the blend is 0.4 Å, corresponding to a velocity separation of ∼30 km s⁻¹, and the blend is characterised by a slightly asymmetric profile. We measured the velocity dispersion of the blend using a single-Gaussian fit and find that it exceeds 30 km s⁻¹ in all galaxies. Thus, the broadening of the blend is likely caused by the wavelength difference between the H I and He I lines. Additionally, the He Iλ10830 emission line is emitted in inner, higher-density regions compared to other He I emission lines.

Inner regions appear to be characterised by higher turbulent velocities. This difference between He Iλ10830 and other He I lines, though small, may potentially pose a problem in the determination of the He abundance weighted by several He I emission lines, because they are emitted in different parts of the H II region. The best lines for determining the He abundance are likely He Iλ4471 and He Iλ6678, as they are less dependent on collisional and fluorescent enhancement and their velocity dispersions are equal to those of Hβ, at least for the He Iλ 4471 line. However, these lines are weak (∼3–4% of the Hβ intensity); therefore, spectra with a high signal-to-noise ratio are needed to derive their intensities with good precision. Furthermore, the intensity of the He Iλ4471 Å emission line can be affected by the underlying stellar He I absorption line to a greater extent than of other He I emission lines.

6. Conclusions

In this paper we present VLT/Xshooter spectrophotometric observations of 11 low-mass compact star-forming galaxies (CSFGs) at z < 0.085 with extremely high O₃₂ = 11–42 (the ‘high O₃₂ sample’). Our goal was to study the physical conditions and chemical composition and to investigate the kinematic properties of galaxies using various hydrogen, helium, oxygen, neon, and sulphur emission lines. Our main results are as follows.

1. All spectra show strong emission lines, which imply the presence of a very young stellar population. This is supported by very high equivalent widths, EW(Hβ), of the Hβ emission line, with values of 200–390 Å, corresponding to a starburst age of < 3 Myr.

2. We detect a strong [O III] λ4363 Å emission line in all objects, allowing elemental abundance determination via the direct T_e-method. We find low oxygen abundances, 12+log(O/H), in the range 7.53–7.99. The Ne/O, S/O, Cl/O, and Ar/O abundance ratios in all our galaxies are similar to those found in low-metallicity blue compact dwarf (BCD) galaxies (Izotov et al. 2006a). In contrast, the N/O and Fe/O abundance ratios in our CSFGs at fixed 12+log(O/H) are higher by up to 0.5 dex and are almost independent of the adopted ionisation-bounded, density-bounded, or clumpy H II models, which determine the ionisation correction factors.

3. Using six He I 3889, 4471, 5876, 6678, 7065, and 10830 Å emission lines, and taking into account processes that deviate their intensities from the recombination values, we derive the He mass fraction Y in a self-consistent manner similar to that described by Izotov et al. (2014). The derived Ys in our 11 galaxies are similar to those in the compact SFGs sample used by Izotov et al. (2014) for the determination of the primordial helium abundance.

4. The presence of high-excitation H II regions with many strong permitted and forbidden emission lines in a wide range of wavelengths, and the compact structure of our galaxies with a single dominant H II region, results in line profiles that can be fitted by single Gaussians in ten out of eleven galaxies. This allows the study velocity dispersions using many lines of various ions originating in different parts of the H II region. This approach differs from many other spectroscopic studies, which considered only velocity dispersions of the brightest lines, Hβ, Hα, and [O III] λ5007 (e.g. Chávez et al. 2012, 2014). We find that σ(Hβ) increases with stellar mass and oxygen abundance and slightly decreases with O₃₂. On the other hand, there is no correlation between σ(Hβ) and EW(Hβ).

5. We compared the velocity dispersions of Hβ and various other emission lines. We find that all other hydrogen lines in the optical and near-infrared ranges have the same velocity dispersion as that of Hβ, indicating that all of these lines originate in the same volume of the H II region. We also note that [O II] λ3726, λ3729, [S II] λ6717, and λ6731 are narrower than Hβ, because they are produced in the outer layers of the H II region. In contrast, the velocity dispersion of the He IIλ4686 emission line is considerably higher than that of Hβ, indicating that this line is produced in the inner part of the H II region. An interesting case is provided by the He I emission lines. The He Iλ4471, λ5876, and λ7065 emission lines have velocity dispersions similar to those of Hβ. The λ10830 emission line is somewhat broader (by ∼20%), likely due to radiative scattering, implying that it is emitted in a somewhat different and denser region because of the strong dependence of its intensity on the electron number density compared to that for other He I emission lines.

Data availability

Tables B.1 and B.2 are available at the CDS via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/712/A19

Acknowledgments

YII and NGG acknowledge support from the National Academy of Sciences of Ukraine by its project no. 0126U000353. The activities underlying the published results were carried out in the framework of the project No. 224866 supported in the result of the Joint Call ‘Ukrainian-Swiss Joint Research Projects: Call for Proposals 2023’. RA acknowledges support of Grant PID2023-147386NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU, the Severo Ochoa award to the IAA CEX2021-001131-S.

References

Appendix A: Figures.

Fig. A.1. The rest-frame spectrum of one of our galaxies, J0825+1846.

Fig. A.2. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of stellar mass. Symbols are the same as in Fig. 9.

Fig. A.3. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of the Hβ equivalent width. Symbols are the same as in Fig. 9.

Fig. A.4. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of the oxygen abundance. Symbols are the same as in Fig. 9.

All Tables

All Figures

Fig. 1. (a) Baldwin–Phillips–Terlevich (BPT) diagram (Baldwin et al. 1981). Galaxies from this paper and from Chávez et al. (2014) are shown as red and blue circles, respectively. Compact SFGs from the SDSS are represented by black dots (EW(Hβ) ≥ 100 Å) and grey dots (EW(Hβ) < 100 Å). The line separating SFGs from AGNs is taken from Kauffmann et al. (2003). (b) O32 – R23 diagram, where O32 = I([O III] λ5007)/I([O II] λ3727) and R23 = I([O II] λ3727 + [O III] λ4959 + [O III] λ5007)/I(Hβ). (c) Relation between the ionising-photon production efficiency, ξion, and O32. The canonical value of ξion from Robertson et al. (2013) is shown as a magenta-shaded region. The meaning of the symbols in (b) and (c) is the same as in (a).

In the text

Fig. 2. Dependence of element abundance ratios on oxygen abundance, derived using the prescriptions of Izotov et al. (2006a). Red symbols represent galaxies from this study. Blue symbols represent dwarf SFGs observed with various telescopes for the determination of the helium abundance (Izotov et al. 2014), and black symbols represent SDSS SFGs in which the [O III] λ4363 emission line is detected at the level above 4σ. Open magenta circles with error bars indicate solar values (Lodders 2010).

In the text

Fig. 3. (a) Dependence of O32 ratio on column density of neutral hydrogen, N(H I), in density-bounded H II region models. The N(H I) value is expressed in cm−2. (b) and (c) Relations between ionisation correction factors ICF(N+) and ICF(Fe2+), and the O+ abundance fraction. (d) Dependence of the N+/O+ abundance ratio on O+ abundance fraction. The horizontal black line indicates the input value of log(N/O) = –1.6 used in the CLOUDY calculations. Red, blue, and green symbols in panels (b)–(d) represent density-bounded and ionisation-bounded models of H II regions, and H II regions with varying covering factor, respectively.

In the text

	Fig. 4. Dependence of the helium mass fraction, Y, on the oxygen abundance, O/H, for SFGs. Galaxies from Izotov et al. (2014) with Y derived using six He I emission lines are marked with blue symbols. Galaxies from this work are marked with red symbols for galaxies with Ys derived using six He I emission lines and by black symbols for galaxies with Y derived using five He I emission lines.
In the text

Fig. 5. Profiles of the Hβ emission line in our galaxies. Solid black lines denote the observed profiles. All profiles are fitted by single Gaussians (dotted red lines) except that of J0240−0828, which is fitted by three Gaussians (dotted blue lines). The dotted red line denotes the total fitted profile. For the galaxy J0007+0226, the instrumental, thermal and macroscopic (turbulent) profiles are shown by blue, green, and magenta dashed lines, respectively.

In the text

	Fig. 6. Same as in Fig. 5 but for the Hα profile.
In the text

	Fig. 7. Two-Gaussian fit (dashed lines) to the He Iλ10830 Å emission-line profile in the spectrum of J0007+0226 (solid black line).
In the text

	Fig. 8. Relations between the velocity dispersion of the Hβ emission line (in km s−1) and (a) O32 = [O III]5007/([O II]3726 + [O II]3729), (b) EW (Hβ), (c) log(M★/M⊙), and (d) oxygen abundance 12+log(O/H). Filled red circles represent our galaxies, and filled blue circles represent galaxies by Chávez et al. (2014).
In the text

	Fig. 9. Ratios of velocity dispersions of various lines to that of Hβ as a function of O32 ratios (filled red circles), with typical errors shown in the lower right corners. Filled blue circles in panel (i) represent galaxies from Chávez et al. (2014).
In the text

	Fig. A.1. The rest-frame spectrum of one of our galaxies, J0825+1846.
In the text

	Fig. A.2. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of stellar mass. Symbols are the same as in Fig. 9.
In the text

	Fig. A.3. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of the Hβ equivalent width. Symbols are the same as in Fig. 9.
In the text

	Fig. A.4. The ratios of velocity dispersions of various lines to the velocity dispersion of the Hβ emission line in function of the oxygen abundance. Symbols are the same as in Fig. 9.
In the text