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# J1046+4047: an extremely low-metallicity dwarf star-forming galaxy with O32 = 57

Y. I. Izotov, T. X. Thuan, N. G. Guseva

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## ► To cite this version:

Y. I. Izotov, T. X. Thuan, N. G. Guseva. J1046+4047: an extremely low-metallicity dwarf star-forming galaxy with O32 = 57. Monthly Notices of the Royal Astronomical Society, 2024, 527, pp.3486-3493. 10.1093/mnras/stad3421. insu-04851598

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https://insu.hal.science/insu-04851598v1

Submitted on 20 Dec 2024

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# J1046+4047: an extremely low-metallicity dwarf star-forming galaxy with $O_{32} = 57$

Y. I. Izotov<sup>1,★</sup> T. X. Thuan<sup>2,3</sup> and N. G. Guseva<sup>1</sup>

Accepted 2023 November 1. Received 2023 October 25; in original form 2023 August 12

## ABSTRACT

Using the optical spectrum obtained with the Kitt Peak Ohio State Multi-Object Spectrograph mounted on the Apache Point Observatory 3.5 m Telescope and the Sloan Digital Sky Survey spectrum, we study the properties of one of the most metal-poor dwarf star-forming galaxies (SFGs) in the local Universe, J1046+4047. The galaxy, with a redshift $z = 0.04874$, was selected from the Data Release 16 of the SDSS. Its properties are among the most extreme for SFGs in several ways. The oxygen abundance $12 + \log(O/H) = 7.082 \pm 0.016$ in J1046+4047 is among the lowest ever observed. With an absolute magnitude $M_g = -16.51$ mag, a low stellar mass $M_* = 1.8 \times 10^6 M_\odot$, and a very low mass-to-light ratio $M_*/L_g \sim 0.0029$ (in solar units), J1046+4047 has a very high specific star formation rate $\text{sSFR} \sim 430 \text{ Gyr}^{-1}$, indicating very active ongoing star formation. Another striking feature of J1046+4047 is that it possesses a ratio $O_{32} = I([O\,III]\,\lambda5007)/I([O\,II]\,\lambda3727) \sim 57$. Using this extremely high $O_{32}$, we have confirmed and improved the strong-line calibration for the determination of oxygen abundances in the most metal-deficient galaxies, in the range $12 + \log(O/H) \lesssim 7.65$. This improved method is applicable for all galaxies with $O_{32} \le 60$. We find the H$\alpha$ emission line in J1046+4047 to be enhanced by some non-recombination processes and thus cannot be used for the determination of interstellar extinction.

**Key words:** galaxies: abundances – galaxies: dwarf – galaxies: ISM – galaxies: starburst.

## 1 INTRODUCTION

The importance of finding of extremely metal-deficient (XMD) low-redshift star-forming galaxies (SFGs), with oxygen abundances $12 + \log(O/H)$ in the range $\sim 6.9–7.1$, is emphasized by the fact that they share many of the same properties with the dwarf galaxies at high redshifts (low metallicities and luminosities, high star formation rates, and high specific star formation rates) and thus may be considered as their best local counterparts. These high-redshift dwarfs are thought to be responsible for the reionization of the Universe and so it is crucial to study them in detail. However, until very recently, no galaxy with a definite oxygen abundance below $12 + \log(O/H) \sim 7.1$ is known at high redshifts, even if recent JWST observations of galaxies with $z$ larger than 6 are included (Ouchi et al. 2009; Wise & Cen 2009; Yajima, Choi & Nagamine 2011; Mitra, Ferrara & Choudhury 2013; Bouwens et al. 2015; Izotov et al. 2018c). Only lately, Atek et al. (2023) have reported the discovery by JWST of eight SFGs at $z \sim 6–8$ with $12 + \log(O/H)$ approaching the value of $\lesssim 7.0$ and stellar masses of $\lesssim 10^7 M_\odot$. These properties are similar to those of the most metal-deficient low-$z$ SFGs considered in this paper.

Because of the lack of many known XMDs in the early Universe, our strategy is to search for and use low-$z$ metal-poor SFGs as their

local proxies. A few such XMD objects have been found at low redshifts. Hirschauer et al. (2016) have reported $12 + \log(O/H) = 7.02 \pm 0.03$ for the galaxy AGC 198691. Izotov et al. (2018a) and Izotov, Thuan & Guseva (2019a, 2021a) have derived oxygen abundances in J0811+4730, J1234+3901, and J2229+2725 of $6.98 \pm 0.02$, $7.035 \pm 0.026$, and $7.085 \pm 0.31$, respectively. All these galaxies were selected from the Sloan Digital Sky Survey (SDSS). Kojima et al. (2020) have recently reported the discovery of the galaxy J1631+4426 with $12 + \log(O/H) = 6.90 \pm 0.03$. However, Thuan, Guseva & Izotov (2022) have derived a higher abundance $12 + \log(O/H) = 7.14 \pm 0.03$ for this galaxy, based on their own independent observations. In all these studies, the oxygen abundances have been derived by the direct $T_e$ method from spectra of the entire galaxy. Common characteristics of these XMD galaxies are their low stellar mass $M_* \lesssim 10^7 M_\odot$ and a very compact morphological structure. In addition to these galaxies, very low oxygen abundances of $7.01 \pm 0.07$, $6.98 \pm 0.06$, and $6.86 \pm 0.14$ have also been found by Izotov et al. (2009) in three individual H\,II regions of the XMD SBS 0335–052W. A value of $6.96 \pm 0.09$ has been obtained by Annibali et al. (2019) in one of the H\,II regions in the dwarf irregular galaxy DDO 68. However, other regions in SBS 0335–052W and DDO 68 do show oxygen abundances above 7.1.

In this paper, we present new spectroscopic observations of the XMD galaxy J1046+4047, obtained with the Kitt Peak Ohio State Multi-Object Spectrograph (KOSMOS), mounted on the Apache Point Observatory (APO) 3.5 m Telescope. We supplement the

<footnote n="1"><sup>1</sup>Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 14-b Metrolohichna str, Kyiv 03143, Ukraine</footnote>

<footnote n="2"><sup>2</sup>Astronomy Department, University of Virginia, PO Box 400325, Charlottesville, VA 22904-4325, USA</footnote>

<footnote n="3"><sup>3</sup>Institut d'Astrophysique de Paris (UMR 7095 CNRS & Sorbonne Université), 98 bis Bd Arago, F-75014 Paris, France</footnote>

<footnote>* E-mail: yizotov@bitp.kiev.ua</footnote>
<table><caption>**Table 1.** Observed and derived characteristics of J1046+4047.</caption><thead><tr><th>Parameter</th><th>J1046+4047</th></tr></thead><tbody><tr><td>RA (J2000)</td><td>10:46:09.23</td></tr><tr><td>Dec. (J2000)</td><td>+40:47:07.07</td></tr><tr><td>z</td><td>0.04874 ± 0.00006</td></tr><tr><td>GALEX FUV, mag</td><td>20.27 ± 0.24</td></tr><tr><td>GALEX NUV, mag</td><td>21.19 ± 0.28</td></tr><tr><td>SDSS <i>u</i>, mag</td><td>20.85 ± 0.06</td></tr><tr><td>SDSS <i>g</i>, mag</td><td>20.18 ± 0.02</td></tr><tr><td>SDSS <i>r</i>, mag</td><td>21.39 ± 0.07</td></tr><tr><td>SDSS <i>i</i>, mag</td><td>20.71 ± 0.04</td></tr><tr><td>SDSS <i>z</i>, mag</td><td>21.67 ± 0.27</td></tr><tr><td><i>D</i><sub>L</sub>, Mpc<sup>a</sup></td><td>217.8 ± 0.3</td></tr><tr><td><i>M</i><sub>g</sub>, mag<sup>b</sup></td><td>-16.51 ± 0.06</td></tr><tr><td>log <i>L</i><sub>g</sub>/<i>L</i><sub>g,⊙</sub><sup>c</sup></td><td>8.79 ± 0.44</td></tr><tr><td>log <i>M</i><sub>*</sub>/<i>M</i><sub>☉</sub><sup>d</sup></td><td>6.25 ± 0.15</td></tr><tr><td><i>M</i><sub>*</sub>/<i>L</i><sub>g</sub>, <i>M</i><sub>☉</sub>/<i>L</i><sub>g,⊙</sub></td><td>0.0029 ± 0.0001</td></tr><tr><td>L(Hβ), erg s<sup>-1</sup> e<sup>-1</sup></td><td>(3.5 ± 0.6) × 10<sup>40</sup></td></tr><tr><td>SFR, <i>M</i><sub>☉</sub>yr<sup>-1</sup> f</td><td>0.77 ± 0.13</td></tr><tr><td>sSFR, Gyr<sup>-1</sup></td><td>430 ± 180</td></tr><tr><td>12+logO/H<sup>g</sup></td><td>7.082 ± 0.016</td></tr></tbody></table>

Notes. <sup>a</sup>Luminosity distance.

<sup>b</sup>Absolute magnitude corrected for Milky Way extinction.

<sup>c</sup>log of the SDSS g-band luminosity corrected for Milky Way extinction.

<sup>d</sup>Stellar mass derived from the extinction-corrected SDSS spectrum.

<sup>e</sup>H β luminosity derived from the extinction-corrected SDSS spectrum.

<sup>f</sup>Star formation rate derived from the Kennicutt (1998) relation using the extinction-corrected H β luminosity.

<sup>g</sup>Oxygen abundance derived from the SDSS spectrum.

KOSMOS observations with SDSS spectroscopic observations. The galaxy was selected from the SDSS Data Release 16 (DR16) data base (Ahumada et al. 2020) because its line ratios suggest it to be an extremely low-metallicity object. It also drew our attention because of its extremely high (extinction-corrected) $O_{32}$ value of 57, defined as the ratio $I([O III] \lambda 5007]/([O II] \lambda 3727)$. This high ratio indicates that the galaxy may contain density-bounded H II regions, and thus be a potential Lyman continuum leaker (e.g. Jaskot & Oey 2013) and a good local counterpart to the high-redshift dwarf galaxies. Its coordinates, redshift, and other characteristics obtained from the photometric and spectroscopic SDSS and the *Galaxy Evolution Explorer (GALEX)* data bases are presented in Table 1. We note that the galaxy was not detected by space *Wide-field Infrared Survey Explorer (WISE)* because in part of its low metallicity and thus low dust content.

## 2 OBSERVATIONS AND DATA REDUCTION

### 2.1 SDSS and APO/KOSMOS spectra

We show in Fig. 1(a) the SDSS spectrum of J1046+4047. It is seen from insets (1)–(3) that the signal-to-noise ratio of most weak emission lines is sufficiently high to derive extinction from the hydrogen Balmer emission lines and the element abundances. In particular, [O III] $\lambda 4363$ emission line [inset (2)] is strong. Another feature is the weak [O II] $\lambda 3727$ emission line that is partially blended with the hydrogen H13 and H14 emission lines. To derive its intensity, we apply the deblending procedure with fitting by Gaussians. However, the strongest emission lines H β, [O III] $\lambda 4959$ and most notably the [O III] $\lambda 5007$ emission lines, are clipped. The [O III] $\lambda 4959$ emission line is skewed because of clipping and the

[O III] $\lambda 4959/H \beta$ flux ratio is equal to 0.89 in the SDSS spectrum, whereas it is 1.06 in the KOSMOS spectrum. We also cannot exclude clipping of the H β emission line, because its intensity is similar to that of the [O III] $\lambda 4959$ emission line. Therefore, the SDSS spectrum alone cannot be used for the determination of the electron temperature and element abundances.

We attempted to observe this galaxy with the 8.4 m Large Binocular Telescope (LBT) to obtain a higher signal-to-noise spectrum and to derive intensities of the strong emission lines. However, due to a specific particularity of the Multi-Object Double Spectrograph (MODS) at the LBT, it was not possible to select a guide star for the observations. Therefore, we observed the blue part of the J1046+4047 spectrum with the KOSMOS at the 3.5 m APO telescope on 2023 April 19, with an exposure time of 900 s and a resolving power of ~2600. Observations were done at the relatively high airmass of 1.36, but with the slit oriented along the parallactic angle. Therefore, the effect of differential refraction was minimal (Filippenko 1982), at least in the wavelength range of ~4300–5000 Å, which is of main interest here. The seeing during the observations was 1.2 arcsec.

Our main aim is to obtain the intensities of the strong emission lines in the KOSMOS spectrum. This spectrum is shown in Fig. 1(b). It has a lower signal-to-noise ratio compared to the SDSS spectrum. Furthermore, the sensitivity of KOSMOS at $\lambda < 4000$ Å is low, making uncertain the determination of line intensities at these wavelengths, including the [O II] $\lambda 3727$ emission line. Therefore, for element abundance determination, we use the SDSS spectrum. The intensities of H β, [O III] $\lambda 4959$, 5007 emission lines in this spectrum are scaled from the KOSMOS spectrum with the use of the H γ emission line intensities in both the SDSS and KOSMOS spectra. The observed intensities of the H γ emission line in the SDSS and KOSMOS spectra differ only by ~5 per cent, indicating that aperture corrections for different spectroscopic apertures are small. We also note that the intensity of the H β emission line in the SDSS spectrum is ~10 per cent lower than in the KOSMOS spectrum and its equivalent width in the SDSS spectrum of ~390 Å is lower than the one of ~411 Å in the KOSMOS spectrum. These differences indicate some small clipping of the H β emission line in the SDSS spectrum.

The observed emission-line intensities in both SDSS and KOSMOS spectra were measured using the IRAF *splot* routine. The emission-line errors in the SDSS spectrum are calculated using the pixel-by-pixel errors included in the file of the spectrum, whereas the emission-line errors in the KOSMOS spectrum are calculated using the pixel-by-pixel errors generated by the IRAF *apall* routine during extraction of the one-dimensional spectrum. We then use the ratio of the H γ emission line intensities in both SDSS and KOSMOS spectra to scale the intensities of the strong H β, [O III] $\lambda 4959$, 5007 emission lines in the KOSMOS spectrum. These intensities are employed instead of those of the clipped emission lines in the SDSS spectrum.

The intensities of emission lines in the SDSS spectrum were corrected iteratively for extinction and underlying stellar absorption, derived from comparison of the observed intensity ratios of the hydrogen Balmer emission lines H α, H β, H γ, H δ, H9, H10, H11, H12 with the theoretical recombination ratios, as described in Izotov, Thuan & Lipovetsky (1994). The theoretical ratios weakly depend on the electron temperature and electron number density. We obtain them, adopting the approximate electron temperature $T_e(\text{O III})$ from the observed [O III] $\lambda 4363/(\lambda 4959+\lambda 5007)$ intensity ratio, and the approximate electron number density from the observed [S II] $\lambda 6717/\lambda 6731$ intensity ratio. The equivalent widths of the
<figure><img src="image_4.png" /><figcaption>**Figure 1.** The rest-frame (a) SDSS spectrum and (b) APO/KOSMOS spectrum of J1046+4047. Three insets in (a) show expanded parts of the spectral regions for a better view of weak features. Some emission lines are labelled.</figcaption></figure>
<table><caption>**Table 2.** Extinction-corrected emission-line intensity ratios in J1046+4047.</caption><thead><tr><th rowspan="2">Line</th><th colspan="2">100 × I(λ)/I(Hβ)</th></tr><tr><th>C(H β) is derived including H α</th><th>C(H β) is derived excluding H α</th></tr><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>3722.00 H14</td><td>3.44 ± 1.05</td><td>2.67 ± 0.81</td></tr><tr><td>3727.00 [O II]</td><td>7.20 ± 1.22</td><td>5.61 ± 0.95</td></tr><tr><td>3735.00 H13</td><td>4.37 ± 1.38</td><td>2.85 ± 0.82</td></tr><tr><td>3750.15 H12</td><td>5.22 ± 1.27</td><td>3.56 ± 0.83</td></tr><tr><td>3770.63 H11</td><td>7.85 ± 1.25</td><td>5.72 ± 0.89</td></tr><tr><td>3797.90 H10</td><td>8.39 ± 1.28</td><td>6.15 ± 0.92</td></tr><tr><td>3835.39 H9</td><td>11.11 ± 1.37</td><td>8.33 ± 1.01</td></tr><tr><td>3868.76 [Ne III]</td><td>35.62 ± 2.07</td><td>28.43 ± 1.65</td></tr><tr><td>3889.00 He I + H8</td><td>27.52 ± 1.84</td><td>21.62 ± 1.44</td></tr><tr><td>3968.00 [Ne III] + H7</td><td>33.24 ± 1.99</td><td>26.60 ± 1.58</td></tr><tr><td>4026.19 He I</td><td>1.89 ± 0.84</td><td>1.56 ± 0.69</td></tr><tr><td>4101.74 H δ</td><td>35.02 ± 2.00</td><td>28.87 ± 1.64</td></tr><tr><td>4227.20 [Fe V]</td><td>1.50 ± 0.74</td><td>1.29 ± 0.63</td></tr><tr><td>4340.47 H γ</td><td>54.23 ± 2.38</td><td>47.71 ± 2.09</td></tr><tr><td>4363.21 [O III]</td><td>17.12 ± 1.32</td><td>15.27 ± 1.17</td></tr><tr><td>4471.48 He I</td><td>3.69 ± 0.79</td><td>3.38 ± 0.73</td></tr><tr><td>4685.94 He II</td><td>1.65 ± 0.59</td><td>1.59 ± 0.57</td></tr><tr><td>4712.00 [Ar IV] + He I</td><td>2.95 ± 0.66</td><td>2.86 ± 0.64</td></tr><tr><td>4740.20 [Ar IV]</td><td>1.94 ± 0.59</td><td>1.89 ± 0.58</td></tr><tr><td>4861.33 H β</td><td>100.00 ± 3.22</td><td>100.00 ± 3.21</td></tr><tr><td>4958.92 [O III]</td><td>103.92 ± 3.27</td><td>106.30 ± 3.33</td></tr><tr><td>5006.80 [O III]</td><td>309.65 ± 7.55</td><td>319.76 ± 7.77</td></tr><tr><td>5875.60 He I</td><td>7.76 ± 0.69</td><td>9.12 ± 0.81</td></tr><tr><td>6562.80 H α</td><td>281.88 ± 7.12</td><td>356.59 ± 8.98</td></tr><tr><td>6583.40 [N II]</td><td>&lt;0.41</td><td>&lt;0.53</td></tr><tr><td>6678.10 He I</td><td>2.04 ± 0.36</td><td>2.61 ± 0.46</td></tr><tr><td>6716.40 [S II]</td><td>0.34 ± 0.24</td><td>0.44 ± 0.30</td></tr><tr><td>6730.80 [S II]</td><td>0.36 ± 0.24</td><td>0.46 ± 0.31</td></tr><tr><td>7065.30 He I</td><td>2.92 ± 0.39</td><td>3.90 ± 0.52</td></tr><tr><td>7135.80 [Ar III]</td><td>0.64 ± 0.24</td><td>0.86 ± 0.32</td></tr><tr><td>7281.35 He I</td><td>0.86 ± 0.25</td><td>1.18 ± 0.35</td></tr><tr><td>C(Hβ)<sup>a</sup></td><td>0.520 ± 0.030</td><td>0.180 ± 0.030</td></tr><tr><td>F(Hβ)<sup>b</sup></td><td>41.13 ± 2.25</td><td>41.13 ± 2.25</td></tr><tr><td>EW(H β)<sup>c</sup></td><td>411.3 ± 22.0</td><td>411.3 ± 22.0</td></tr><tr><td>EW(abs)<sup>c</sup></td><td>1.1 ± 0.3</td><td>0.0 ± 0.0</td></tr></tbody></table>

Notes. $^a$Extinction coefficient, derived from the observed hydrogen Balmer decrement.

$^b$Observed flux in units of $10^{-16}$ erg s$^{-1}$ cm$^{-2}$.

$^c$Rest-frame equivalent width in Å.

underlying stellar Balmer absorption lines are assumed to be the same for each hydrogen line.

The extinction-corrected fluxes together with the extinction coefficient $C(H\beta)$, the observed $H\beta$ emission-line flux $F(H\beta)$, the rest-frame equivalent width $EW(H\beta)$ of the $H\beta$ emission line, and the equivalent width of the Balmer absorption lines are shown in the left column of Table 2.

## 2.2 Enhancement of $H\alpha$ emission

We find the derived extinction coefficient $C(H\beta)$ to be abnormally high, equal to 0.520. This value is not typical for low-metallicity SFGs. Furthermore, the extinction-corrected intensities of $H\gamma$ and other higher order hydrogen lines in the blue part of the spectrum relative to the extinction-corrected intensity of the $H\beta$ line are ~20–30 per cent higher than the theoretical recombination values (e.g. Storey & Hummer 1995). It is clear that these emission-line

intensities were overcorrected for extinction. The likely reason for such an overcorrection may be that the $H\alpha$ emission line is enhanced by some non-recombination process. For example, an additional contribution of $H\alpha$ emission from massive stars and supernovae could produce such an effect. Such an enhancement has been detected in the spectra of several other SFGs, most notably in the galaxies J1320+2155 (Izotov & Thuan 2009), Haro 11C (Guseva et al. 2012), and J1154+2443 (Izotov et al. 2018b).

It is clear from the above considerations that the $H\alpha$ emission line should not be used for the determination of the extinction coefficient in J1046+4047. Excluding this line, we derive a much lower $C(H\beta) = 0.180$, more typical of low-metallicity SFGs. The intensities of all hydrogen emission lines relative to $H\beta$, corrected for extinction with the lower $C(H\beta)$ and underlying absorption (right column in Table 2), are now close to the theoretical recombination values (Storey & Hummer 1995).

## 2.3 A very young starburst and hard ionizing radiation

We note two features in the spectrum of J1046+4047, which are very rarely seen in the spectra of other SFGs, including those with the lowest heavy element abundances. First, the $O_{32}$ ratio of 57 is very high compared to the ones in most other SFGs from the SDSS (compare the position of another SFG, J2229+2725, with a similar $O_{32} = 53$, and the positions of SDSS galaxies in fig. 4 from Izotov, Thuan & Guseva 2021a). Second, the $H\beta$ equivalent width $EW(H\beta)$ of ~411 Å is also very large. J1046+4047 is very similar in these characteristics to J2229+2725 (Izotov, Thuan & Guseva 2021a). This indicates that the starbursts in both galaxies are very young, with an age $\le 1–2$ Myr.

The SDSS spectrum of J1046+4047 has a sufficiently high signal-to-noise ratio to show two high-ionization emission lines [FeV] $\lambda4227$ and He II $\lambda4686$ [inset (2) in Fig. 1 a and Table 2], indicative of the presence of hard ionizing radiation (with energies greater than 54 eV). The [FeV] $\lambda4227$ emission line is frequently seen in spectra with high signal-to-noise ratio of low-metallicity SFGs (e.g. Fricke et al. 2001; Izotov, Chaffee & Schaerer 2001; Thuan & Izotov 2005; Berg et al. 2021; Izotov, Thuan & Guseva 2021b). Its presence is associated with that of the He II $\lambda4686$ emission line. On the other hand, the low-ionization lines [N II] $\lambda6583$ and [S II] $\lambda6717$, 6731 are very weak [inset (3) in Fig. 1(a)], indicative of a very high ionization parameter.

# 3 DIAGNOSTIC DIAGRAMS AND INTEGRATED CHARACTERISTICS OF J1046+4047

## 3.1 Diagnostic diagrams

It is known (e.g. Izotov, Thuan & Guseva 2012; Hirschauer et al. 2016; Izotov et al. 2018a) that XMD SFGs strongly deviate in the diagnostic diagrams from the main-sequence SFGs with higher metallicities. This difference can be used to search for the most metal-deficient galaxies by analysing the relations between the strongest emission lines in the optical spectra.

The most commonly used diagnostic diagram is the one proposed by Baldwin, Phillips & Terlevich (BPT; Baldwin, Phillips & Terlevich 1981). It is shown in Fig. 2(a). The most metal-deficient SFGs with $12 + \log(O/H) < 7.1$ (filled circles) and the SFGs with $12 + \log(O/H) = 7.1–7.3$ (open circles) are located far from the main-sequence SFGs (grey dots). The latter are in general much more enriched with heavy elements, having a characteristic $12 + \log(O/H)$ in the range ~7.9–8.1. The SFGs shown by coloured symbols form two well-separated distinct sequences: SFGs shown by
<table><caption>**Table 3.** Electron temperatures, electron number density, and heavy element abundances in J1046+4047.</caption><thead><tr><th rowspan="2">Property</th><th colspan="2">Value</th></tr><tr><th>C(H β) is derived including H α</th><th>C(H β) is derived excluding H α</th></tr><tr><th></th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>T<sub>e</sub>(O III), K</td><td>28300 ± 2000</td><td>25300 ± 1600</td></tr><tr><td>T<sub>e</sub>(O II), K</td><td>22800 ± 800</td><td>20700 ± 700</td></tr><tr><td>T<sub>e</sub>(S III), K</td><td>25200 ± 1700</td><td>22700 ± 1300</td></tr><tr><td>N<sub>e</sub>(S II), cm<sup>-3</sup></td><td>920 ± 1800</td><td>880 ± 1800</td></tr><tr><td>O<sup>+</sup>/H<sup>+</sup> × 10<sup>6</sup></td><td>0.232 ± 0.034</td><td>0.227 ± 0.033</td></tr><tr><td>O<sup>2+</sup>/H<sup>+</sup> × 10<sup>5</sup></td><td>0.931 ± 0.045</td><td>1.163 ± 0.043</td></tr><tr><td>O<sup>3+</sup>/H<sup>+</sup> × 10<sup>6</sup></td><td>0.224 ± 0.091</td><td>0.212 ± 0.086</td></tr><tr><td>O/H × 10<sup>5</sup></td><td>0.977 ± 0.046</td><td>1.207 ± 0.044</td></tr><tr><td>12+log(O/H)</td><td>6.990 ± 0.021</td><td>7.082 ± 0.016</td></tr><tr><td>N<sup>+</sup>/H<sup>+</sup> × 10<sup>7</sup></td><td>&lt;0.208</td><td>&lt;0.307</td></tr><tr><td>ICF(N)</td><td>36.672</td><td>46.133</td></tr><tr><td>N/H × 10<sup>6</sup></td><td>&lt;0.763</td><td>&lt;1.417</td></tr><tr><td>log(N/O)</td><td>&lt; -1.108</td><td>&lt; -0.931</td></tr><tr><td>Ne<sup>2+</sup>/H<sup>+</sup> × 10<sup>6</sup></td><td>2.220 ± 0.132</td><td>2.184 ± 0.127</td></tr><tr><td>ICF(Ne)</td><td>1.021</td><td>1.017</td></tr><tr><td>Ne/H × 10<sup>6</sup></td><td>2.267 ± 0.135</td><td>2.221 ± 0.130</td></tr><tr><td>log(Ne/O)</td><td>-0.634 ± 0.033</td><td>-0.735 ± 0.030</td></tr><tr><td>Ar<sup>2+</sup>/H<sup>+</sup> × 10<sup>7</sup></td><td>0.120 ± 0.058</td><td>0.185 ± 0.091</td></tr><tr><td>ICF(Ar)</td><td>2.993</td><td>3.557</td></tr><tr><td>Ar/H × 10<sup>7</sup></td><td>0.359 ± 0.504</td><td>0.658 ± 0.748</td></tr><tr><td>log(Ar/O)</td><td>-2.435 ± 0.610</td><td>-2.263 ± 0.494</td></tr></tbody></table>

two orders of magnitude lower than the mass-to-light ratios of the majority of compact SFGs in the SDSS shown by grey dots in Fig. 2.

# 4 HEAVY ELEMENT ABUNDANCES

## 4.1 Direct method

We use the extinction-corrected emission-line fluxes derived from the SDSS spectrum and the prescriptions of Izotov et al. (2006) to derive heavy element abundances in J1046+4047. The electron temperature $T_e(O III)$ is calculated from the [O III] $\lambda$4363/(λ4959 + λ5007) emission-line flux ratio. It is used to derive the abundances of O$^3+$, O$^2+$, and Ne$^2$. The abundances of O$^+$, N$^+$, and S$^+$ are derived with the electron temperature $T_e(O II)$ and the abundance of Ar$^2+$ is derived with the electron temperature $T_e(S III)$, using the relations of Garnett (1992) between $T_e(O II)$, $T_e(S III)$, and $T_e(O III)$. The electron number density was derived from the [S II] $\lambda$6717/λ6731 flux ratio. The electron temperatures and electron number densities are shown in Table 3. We note that the [S II] $\lambda$6717, $\lambda$6731 emission lines are very weak [inset (3) in Fig. 1(a)]. Therefore, the electron number density is uncertain.

For comparison, we first consider the case with $C(H \beta) = 0.520$, which is the value derived when the $H \alpha$ emission line is included in the determination of extinction. The emission-line intensities are shown in column (1) of Table 2. The derived electron temperature $T_e(O III)$ of 28300 K is very high (Table 3). It is likely to be overestimated because of the overestimation of $C(H \beta)$. The electron number density is also higher than typical values for SFGs, though it is very uncertain because of the weakness of [S II] $\lambda$6717, $\lambda$6731 emission lines [inset (3) in Fig. 1(a)]. We note that uncertainties in the electron number density play a minor role as long as the low-density limit is satisfied, i.e. when the observed electron number density is less than critical densities of $\ge 10^5$ cm$^{-3}$ for forbidden transitions, including [S II] $\lambda$6717, $\lambda$6731 transitions. That is the case here. The

ionic abundances, ionization correction factors, and total O, N, Ne, and Ar abundances are obtained using relations by Izotov et al. (2006). They are presented in Table 3. We derived the extremely low oxygen abundance 12 + log(O/H) of 6.99, in part due to an overestimated $T_e(O III)$. The logarithm of the Ne/O abundance ratio log(Ne/O) = -0.634 is somewhat higher compared to the values of -0.75 to -0.85 for SFGs with low metallicities (e.g. Izotov et al. 2006). This is because the [Ne III] $\lambda$3868 emission line, used for the Ne abundance determination, has been overcorrected for extinction as compared to the [O III] emission lines.

Adopting the more reasonable value $C(H \beta) = 0.180$, derived by excluding the $H \alpha$ emission line, we obtain $T_e(O III) = 25300$ K [column (2) in Table 3]. Although this temperature is high, it is still similar to that in other most metal-deficient SFGs. The nebular oxygen abundance of 12 + log(O/H) = 7.082 ± 0.016 in J1046+4047 is very close to that in J2229+2725 (Izotov, Thuan & Guseva 2021a). It is among the lowest found for SFGs. The logarithms of the Ne/O and Ar/O abundance ratios (Table 3) for this galaxy are similar to those in other low-metallicity SFGs (e.g. Izotov et al. 2006).

## 4.2 Strong-line method for oxygen abundance determination in XMD galaxies

The extraordinarily high O$_{32}$ ratio of 57 in J1046+4047, together with O$_{32}$ = 53 in J2229+2735, makes both objects excellent targets for testing and improving the calibration of the strong-line method for oxygen abundance determination in rare extremely low-metallicity SFGs, with the highest O$_{32}$ ratios, using the strong oxygen emission lines in the optical range.

Recently Izotov et al. (2019b) and Izotov, Thuan & Guseva (2021a), have developed a strong-line method for XMD galaxies, calibrated by using high-quality observations of the most metal-poor galaxies with a well-detected [O III] $\lambda$4363 emission line. A common problem of the strong-line methods is that they depend on several parameters. In particular, the method based on oxygen line intensities depends not only on the sum $R_{32} = I([O II] \lambda3727 + [O III] \lambda4959 + [O III] \lambda5007]/I(H \beta)$, but also on the ionization parameter. A good indicator of the ionization parameter is the O$_{32}$ ratio. Izotov, Thuan & Guseva (2021a) have proposed a method which takes into account the correction for ionization parameter in a wide range of O$_{32}$, up to the value of 53. The dependence found by Izotov, Thuan & Guseva (2021a) is shown in Fig. 3(a). It is derived by the maximum likelihood estimation technique (Press et al. 2007),

$$12 + \log \frac{\text{O}}{\text{H}} = 0.950 \log(R_{23} - a_1 O_{32}) + 6.805, \quad (1)$$

where $a_1 = 0.080 - 0.00078O_{32}$. In Fig. 3(a), we also show the position of J1046+4047 by a filled star, for $C(H \beta) = 0.180$, and by an open star, for $C(H \beta) = 0.520$. For comparison, the position of J2229+2725 is shown by an encircled filled circle. For $C(H \beta) = 0.180$, J1046+4047 closely follows the relation for SFGs with 12 + log(O/H) < 7.3, represented by a straight line, whereas a higher offset is present for the case with $C(H \beta) = 0.520$ (open star).

However, a slight offset is present even for the case with $C(H \beta) = 0.180$ (filled star). This can be due to the fact that, at the high O$_{32}$ value for J1046+4047, some improvement of equation (1) is needed. We can achieve this by adding one more term in the polynomial expansion of the dependence of the oxygen abundance on the O$_{32}$ ratio, and by minimizing the position deviations of all galaxies in Fig. 3, including both J2229+2725 (encircled filled circle) and J1046+4047 (filled star), from the linear maximum likelihood fit.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** The (a) log(R<sub>23</sub> - a<sub>1</sub>O<sub>32</sub>) - (12 + log(O/H)), and (b) log(R<sub>23</sub> - a<sub>2</sub>O<sub>32</sub>) - (12 + log(O/H)) relations, where a<sub>1</sub> = 0.080 - 0.00078O<sub>32</sub> (Izotov, Thuan & Guseva 2021a) and a<sub>2</sub> = a<sub>1</sub> + 0.00000095O<sub>32</sub><sup>2</sup>. In both relations 12 + log(O/H) is derived by the direct method, R<sub>23</sub> = I([O III] λ4959+λ5007 + [O II] λ3727)/I(H β) and O<sub>32</sub> = I([O III] λ5007)/I([O II] λ3727). The galaxy J1046+4047 (this paper) is represented by a filled star for the extinction coefficient C(H β) = 0.180 and by a open star for the extinction coefficient C(H β) = 0.520 (Table 2). Other lowest-metallicity SFGs from Izotov et al. (2019b) and Izotov, Thuan & Guseva (2021a) are shown by filled circles (12 + log(O/H) < 7.1) and open circles (12 + log(O/H) = 7.1-7.3). The galaxy J2229+2725 (Izotov, Thuan & Guseva 2021a) with O<sub>32</sub> = 53 is encircled. SFGs from the SDSS with 12 + log(O/H) ≤ 7.65 and an [O III] λ4363 emission line measured with a signal-to-noise ratio ≥10 are represented by dots. The solid lines in (a) and (b) are linear maximum-likelihood fits (Press et al. 2007) obtained by Izotov, Thuan & Guseva (2021a) and in this paper, respectively.</figcaption></figure>

We then iteratively vary the coefficient in the new polynomial term and calculate a new fit in each step with a new value of the polynomial a₂. We obtain

$$12 + \log \frac{O}{H} = 0.917 \log(R_{23} - a_2 O_{32}) + 6.804, \quad (2)$$

where a₂ = 0.080 - 0.00078O₃₂ + 0.00000095O₃₂². This relation is shown in Fig. 3(b). Adding a new term only changes slightly the positions of J2229+2725 and J1046+4047, making them in better agreement with the relation shown by the solid line.

On the other hand, the large offset of J1046+4047 when adopting C(H β) = 0.520 (open star), indicates that the oxygen abundance derived by the direct method with this high C(H β) is underestimated by ~0.1 dex. As for the position of J2229+2725 (encircled filled blue circle), it is changed to a lesser extent. The positions of other extremely low-metallicity galaxies with 12+log(O/H) ≤ 7.3 and lower O₃₂ are not changed. We also note that the extrapolation of the relations equations (1) and (2) to higher 12+log(O/H), up to 7.65, fits well the position of SDSS SFGs (grey dots in Fig. 3). There is an improvement of 12 + log(O/H) by ~0.04 dex in J1046+4047 if equation (2) is used instead of equation (1). On the other hand, the calibration by Izotov et al. (2019b) is not applicable to both J1046+4047 and J2229+2725 despite their very similar high O₃₂, as illustrated in fig. 8 of Izotov, Thuan & Guseva (2021a) for J2229+2725.

In summary, both equations (1) and (2) can be used for the determination of oxygen abundances in extremely low-metallicity galaxies with 12 + log(O/H) smaller than 7.65, with an uncertainty of ≤0.05 dex (Fig. 3), when the direct method cannot be applied because of the weakness of the [O III] λ4363 emission line. Particularly, the modified relation (equation 2) should be used for the rare galaxies with extremely high O₃₂ ratios above ~40, whereas the simpler relation derived by Izotov et al. (2019b) can be applied to the vast majority of SFGs with lower O₃₂.

## 5 CONCLUSIONS

We present SDSS and 3.5 m APO telescope/KOSMOS spectrophotometric observations of the compact SFG J1046+4047, selected from the SDSS DR16. This local SFG possesses a very low metallicity and an extremely high O₃₂ ratio. Our main results are as follows.

(1) The emission-line spectrum of J1046+4047, with a stellar mass of 1.8 × 10⁶ M<sub>☉</sub> and an absolute SDSS g-band magnitude of -16.51 mag, originates from a hot [T<sub>e</sub>(O III) = 25 300 K] ionized gas. The detection of the [Fe v] λ4227 and He II λ4686 emission lines indicates the presence of hard ionizing radiation. The oxygen abundance in J1046+4047 is 12 + log(O/H) = 7.082 ± 0.016, one of the lowest for nearby SFGs.

(2) The rest-frame equivalent width EW(H β) of the H β emission line of 411 Å in the J1046+4047 spectrum is one of the highest measured so far in SFGs. Both the very high EW(H β) and very low M<sub>☉</sub>/L<sub>g</sub> indicate that the J1046+4047 emission is strongly dominated by a very young stellar population with an age ≤2 Myr. These properties are similar to those of another very metal-deficient SFG known, J2229+2725 (Izotov, Thuan & Guseva 2021a).

(3) The O₃₂ = I([O III] λ5007)/I([O II] λ3727) flux ratio of ~57 in J1046+4047 is extremely high and is similar to the O₃₂ = 53 of J2229+2725 with nearly the same oxygen abundance. These properties together with the very high rest-frame equivalent width EW(H β) of the H β emission line imply that both galaxies are at a very young stage of their formation. The unique properties of J2229+2725 and J1046+4047 likely make them the best local counterparts of young high-redshift dwarf SFGs with stellar masses and metallicities similar to those of the galaxies, recently discovered at z ~ 6-8 by Atek et al. (2023).

(4) The extremely high O₃₂ ratio in J1046+4047 allows us to verify and slightly improve the strong-line method by Izotov, Thuan & Guseva (2021a), based on the intensities of strong nebular [O II] λ3727 and [O III] λ4959+λ5007 emission lines. We can use it for the determination of the oxygen abundance in extremely low-metallicity SFGs, in the range 12 + log(O/H) ≤ 7.65 and O₃₂ ≤ 60.
(5) We find that the Hα emission line in J1046+4047 is enhanced by some non-recombination processes such as, for example, collisional excitation of Hα in the circumstellar envelopes of luminous massive stars or in dense supernova remnants. Therefore, this line cannot be used for interstellar extinction determination in J1046+4047.

## ACKNOWLEDGEMENTS

YII and NGG acknowledge support from the National Academy of Sciences of Ukraine (Project No. 0123U102248) and from the Simons Foundation. This study is based on observations with the 3.5 m Apache Point Observatory (APO). The APO 3.5 m telescope is owned and operated by the Astrophysical Research Consortium. IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. Funding for the Sloan Digital Sky Survey IV (SDSS-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. Based on observations made with the National Aeronautics and Space Administration (NASA) Galaxy Evolution Explorer (GALEX). GALEX is operated for NASA by the California Institute of Technology under NASA contract NAS5-98034. This research has made use of the NASA/Infrared Processing and Analysis Center (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.

## DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding author.

## REFERENCES

* Ahumada R. et al., 2020, ApJS, 249, 3

* Annibali F. et al., 2019, MNRAS, 482, 3892

* Atek H. et al., 2023, preprint (arXiv:2308.08540)

* Baldwin J. A., Phillips M. M., Terlevich R., 1981, PASP, 93, 5

* Berg D. A., Chisholm J., Erb D. K., Skillman E. D., Pogge R. W., Olivier G. M., 2021, ApJ, 922, 170

* Bouwens R. J., Illingworth G. D., Oesch P. A., Caruana J., Holwerda B., Smit R., Wilkins S., 2015, ApJ, 811, 140

* Filippenko A. V., 1982, PASP, 94, 715

* Fricke K. J., Izotov Y. I., Papaderos P., Guseva N. G., Thuan T. X., 2001, AJ, 121, 169

* Garnett D. R., 1992, AJ, 103, 1330

* Girardi L., Bressan A., Bertelli G., Chiosi C., 2000, A&AS, 141, 371

* Guseva N. G., Izotov Y. I., Fricke K. J., Henkel C., 2012, A&A, 541, A115

* Heintz K. E. et al., 2022, preprint (arXiv:2212.02890)

* Hirschauer A. S. et al., 2016, ApJ, 822, 108

* Izotov Y. I., Thuan T. X., 2009, ApJ, 707, 1560

* Izotov Y. I., Thuan T. X., Lipovetsky V. A., 1994, ApJ, 435, 647

* Izotov Y. I., Chaffee F. H., Schaerer D., 2001, A&A, 378, L45

* Izotov Y. I., Stasińska G., Meynet G., Guseva N. G., Thuan T. X., 2006, A&A, 448, 955

* Izotov Y. I., Guseva N. G., Fricke K. J., Papaderos P., 2009, A&A, 503, 61

* Izotov Y. I., Thuan T. X., Guseva N. G., 2012, A&A, 546, 122

* Izotov Y. I., Thuan T. X., Guseva N. G., Liss S. E., 2018a, MNRAS, 473, 1956

* Izotov Y. I., Schaerer D., Worseck G., Guseva N. G., Thuan T. X., Verhamme A., Orlitová I., Fricke K. J., 2018b, MNRAS, 474, 4514

* Izotov Y. I., Worseck G., Schaerer D., Guseva N. G., Thuan T. X., Fricke K. J., Verhamme A., Orlitová I., 2018c, MNRAS, 478, 4851

* Izotov Y. I., Thuan T. X., Guseva N. G., 2019a, MNRAS, 483, 5491

* Izotov Y. I., Guseva N. G., Fricke K. J., Henkel C., 2019b, A&A, 623, 40

* Izotov Y. I., Thuan T. X., Guseva N. G., 2021a, MNRAS, 504, 3996

* Izotov Y. I., Thuan T. X., Guseva N. G., 2021b, MNRAS, 508, 2556

* Jaskot A. E., Oey M. S., 2013, ApJ, 766, 91

* Kennicutt R. C., Jr, 1998, ARA&A, 36, 189

* Kojima T. et al., 2020, ApJ, 898, 142

* Leitherer C. et al., 1999, ApJS, 123, 3

* Lejeune T., Buser R., Cuisinier F., 1997, A&AS, 125, 229

* Mitra S., Ferrara A., Choudhury T. R., 2013, MNRAS, 428, L1

* Ouchi M. et al., 2009, ApJ, 706, 1136

* Planck Collaboration XVI, 2014, A&A, 571, 16

* Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., 2007, Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge Univ. Press, New York, p. 1235

* Salpeter E. E., 1955, ApJ, 121, 161

* Saxena A. et al., 2023, preprint (arXiv:2306.04536)

* Storey P. J., Hummer D. G., 1995, MNRAS, 272, 41

* Thuan T. X., Guseva N. G., Izotov Y. I., 2022, MNRAS, 516, L81

* Thuan T. X., Izotov Y. I., 2005, ApJS, 161, 240

* Wise J. H., Cen R., 2009, ApJ, 693, 984

* Yajima H., Choi J.-H., Nagamine K., 2011, MNRAS, 412, 411

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