Detections of [C ii] 158 μm and [O iii] 88 μm in a Local Lyman Continuum Emitter, Mrk 54, and Its Implications to High-redshift ALMA Studies^*

Studying high-redshift (z ≳ 6) galaxies at the epoch of reionization (EoR) is essential to understand cosmic reionization. An important parameter of galaxies necessary to understand cosmic reionization is the Lyman continuum (LyC) escape fraction, f_esc, which indicates the fraction of ionizing photons (λ ≤ 912 Å) in a galaxy that escapes from the galaxy into the intergalactic medium (IGM; e.g., Inoue et al. 2006; Robertson et al. 2013; Robertson 2022).

Numerous efforts have been made to directly observe LyC. Space telescopes such as FUSE and HST identified LyC in more than ∼100 galaxies in the local and nearby universe at z ≲ 0.4, and measured f_esc ranging from a few percent to more than 70% (e.g., Deharveng et al. 2001; Bergvall et al. 2006; Leitet et al. 2011, 2013; Borthakur et al. 2014; Izotov et al. 2016a, 2016b; Leitherer et al. 2016; Puschnig et al. 2017; Izotov et al. 2018; Wang et al. 2019; Flury et al. 2022a). At higher redshift, spectroscopic detections of LyC in individual galaxies are limited so far. An AstroSat spectroscopically identified LyC in a z = 1.42 galaxy, whose f_esc is constrained to be higher than 20% (Saha et al. 2020). Large ground-based telescopes such as Keck, VLT, and GTC spectroscopically identified LyC in ∼20 individual galaxies at z ∼ 3–4 with f_esc ranging from a few percent to 90% (e.g., de Barros et al. 2016; Shapley et al. 2016; Vanzella et al. 2018; Marques-Chaves et al. 2021; Pahl et al. 2021; Marques-Chaves et al. 2022). Complementary to these individual spectroscopic detections, there are spectroscopic and imaging surveys at z ∼ 3–4 that statistically targeted the LyC radiation from galaxies. On the spectroscopy side, the Keck Lyman Continuum Spectroscopic Survey targeted LyC from 124 galaxies at z ∼ 3.1, and obtained a sample average f_esc of 6% ± 1% (Steidel et al. 2018; Pahl et al. 2021). On the imaging side, using narrow-band filters that are free from non-ionizing photons, one can observe LyC from galaxies with large ground-based telescopes such as Subaru, VLT, and Keck (e.g., Inoue et al. 2005; Iwata et al. 2009; Nestor et al. 2011; Micheva et al. 2017; Iwata et al. 2019). Compared to spectroscopic surveys, narrow-band imaging observations can efficiently target LyC owing to large fields of view. However, ground-based imaging data can be affected by chance overlap with foreground interlopers (e.g., Vanzella et al. 2010; Nestor et al. 2013). To mitigate such interlopers, Iwata et al. (2019) combined the narrow-band imaging data of Subaru with the high angular resolution imaging data of the Hubble Space Telescope (HST) data. The authors obtained f_esc < 8% (3σ) in a sample of 103 and eight star-forming galaxies and active galactic nuclei (AGNs) with spectroscopic redshifts at 3.06 < z < 3.5 and 157 photometrically selected z = 3.1 Lyα-emitting galaxies. In addition to the narrow-band imaging surveys, Fletcher et al. (2019) and Begley et al. (2022) used broadband filters to target LyC in samples of 61 and 148 galaxies at z ∼ 3.1 and 3.5, respectively, and obtained an average f_esc of 20% and 7% ± 2% (see also, e.g., Jones et al. 2021; Saxena et al. 2022a; Rivera-Thorsen et al. 2022). At z > 4, it is virtually impossible to directly observe LyC due to absorption by the intervening IGM (Inoue & Iwata 2008). Therefore, it becomes important to establish a link between f_esc and other observables at z = 0–4, which allows us to indirectly estimate how EoR galaxies have contributed to reionization.

Possible signatures of LyC leakage include (i) a small separation of a double-peaked Lyα profile (e.g., Verhamme et al. 2015; Dijkstra et al. 2016; Kakiichi & Gronke 2021), (ii) intense far-ultraviolet (FUV) emission lines such as Lyα (e.g., Steidel et al. 2018; Flury et al. 2022b; Naidu et al. 2022), C iv 1550 Å (e.g., Saxena et al. 2022b; Schaerer et al. 2022), and Mg ii doublet lines at λ λ2796, 2803 (e.g., Henry et al. 2018; Chisholm et al. 2020), (iii) a high ionization parameter traced by the optical line ratio [O iii] 5007 Å/[O ii] 3727 Å (O₃₂, e.g., Jaskot & Oey 2013; Nakajima & Ouchi 2014), (iv) a high star formation rate (SFR) surface density (Flury et al. 2022b), (v) a blue UV continuum slope (e.g., Yamanaka et al. 2020; Chisholm et al. 2022), (vi) and a weak equivalent width of low-ionization metal absorption lines (e.g., Jones et al. 2013; Chisholm et al. 2018) as well as a weak low-ionization optical metal emission lines such as [S ii] at λ λ6717, 6731 (Wang et al. 2019). On the whole, the LyC escape appears to depend on H i column density, ionization parameter, and stellar feedback (Flury et al. 2022b), as also predicted by theoretical studies (see, e.g., Yajima et al. 2011; Zackrisson et al. 2013; Yajima et al. 2014; Ma et al. 2015; Paardekooper et al. 2015; Arata et al. 2019; Barrow et al. 2020; Rosdahl et al. 2022; Yeh et al. 2023).

In addition to these techniques, Katz et al. (2020, 2022) propose the far-infrared (FIR) line luminosity ratios of [O iii] 88 μm and [C ii] 158 μm (hereafter, [O iii]/[C ii]) as a new diagnostic signature of LyC escape. This is motivated by spectroscopic observations of z = 6–9 galaxies with the Atacama Large Millimeter/submillimeter Array (ALMA; Inoue et al. 2016; Laporte et al. 2017; Hashimoto et al. 2018; Tamura et al. 2019). Inoue et al. (2016) observed a z = 7.2 Lyα-emitting galaxy in [O iii] 88 μm and [C ii] 158 μm, and obtained a high line luminosity ratio [O iii]/[C ii] ≳12 (3σ). With a simple one-dimensional photoionization model, the authors for the first time proposed that the high line ratio may indicate a high f_esc because a weak [C ii] emission could be linked to a low amount of H i gas in the interstellar medium (ISM). Hashimoto et al. (2019) compiled a sample of galaxies with [O iii]/[C ii] at z > 6, and found that UV-selected galaxies in the EoR typically show [O iii]/[C ii] ∼ 3–10 or higher (see also Laporte et al. 2019; Bakx et al. 2020; Carniani et al. 2020; Harikane et al. 2020; Witstok et al. 2022). These values are higher than the typical values of local spirals (∼0.5; Brauher et al. 2008) and low-metallicity dwarf galaxies (∼2; Madden et al. 2013; Cormier et al. 2015) observed by ISO and Herschel, respectively, suggesting unusual conditions of the ISM in high-z galaxies (e.g., Sugahara et al. 2022).

Using the photoionization models of CLOUDY constructed by Ferland et al. (2013); Harikane et al. (2020) showed that these high [O iii]/[C ii] ratios can be explained by combinations of various parameters such as a high ionization parameter, low neutral gas covering fraction in the ISM, low gas density, and high O/C abundance ratio, where the scenarios of high ionization parameter and low neutral gas covering fraction would facilitate the LyC escape. In addition, Vallini et al. (2021) theoretically parameterized the [O iii]/[C ii] ratio as a function of the burstiness of star formation activity, gas density, and metallicity. The authors found that the parameter mostly affecting the line ratio is the burstiness. More recently, Ramambason et al. (2022) examined ISM properties of a local sample of the Herschel Dwarf Galaxy Survey (HDGS; Madden et al. 2013; Cormier et al. 2015) using a grid of models of H ii regions and photodissociated regions. The authors also found a positive correlation between [O iii]/[C ii]and predicted f_esc. Although many parameters are degenerate, the fact that the EoR UV-selected galaxies show on average high [O iii]/[C ii] luminosity ratios is interesting because it may suggest high f_esc values. It is crucial to observationally link the luminosity ratios to f_esc, as done with other techniques, as well as to understand the characteristics of galaxies with high [O iii]/[C ii] ratios. If such correlations are established in the local universe, we can apply them to the EoR galaxies observed with ALMA to indirectly infer their properties, including f_esc. Unfortunately, only for one known local Lyman continuum emitter (LCE), Haro 11 (e.g., Hayes et al. 2007; Leitet et al. 2011), the [O iii]/[C ii] ratio has been observed (∼2.0 in Cormier et al. 2015). The reason for the paucity of local LCEs with FIR line observations is that most LCEs were discovered after 2013, when Herschel ended its operations.

The Stratospheric Observatory for Infrared Astronomy (SOFIA) offered a unique opportunity to perform FIR line spectroscopy of local galaxies. Here, we report observations of the FIR lines in Mrk 54 using FIFI-LS (Field-Imaging Far-Infrared Line Spectrometer, Fischer et al. 2018) on board SOFIA; Mrk 54 is the second nearest galaxy after Haro 11 with a direct LyC detection at a luminosity distance of ∼191 Mpc. The galaxy is a blue compact galaxy with 12+log(O/H) = 8.6, SFR =12 M_⊙ yr⁻¹, f_esc = 2.5% (Leitherer et al. 2016) and O₃₂ = 0.4 (Chisholm et al. 2018). These two well-characterized LCEs with FIR line spectroscopy, Haro 11 and Mrk 54, are invaluable to calibrating an observational relationship between [O iii]/[C ii] and f_esc. Because [O iii]/[C ii] depends on various parameters, we also make use of local analogs of high-z galaxies with FIR line spectroscopy (e.g., low stellar mass or gas-phase metallicity), the HDGS and the LITTLE THINGS Survey (LT; Hunter et al. 2012; Cigan et al. 2016, 2021), to statistically examine the correlations between [O iii]/[C ii] and other physical quantities such as ionization parameter, ionized-to-neutral gas volume filling factor, gas-phase metallicity, and burstiness. In light of recent combined observations of high-z galaxies with ALMA and JWST in the rest-frame optical and FIR (e.g., Bakx et al. 2023), respectively, the presented study will be a reference study that is useful (1) to infer f_esc of galaxies in the EoR and (2) to plan and interpret the ALMA+JWST observations (e.g., Kohandel et al. 2023; Nakazato et al. 2023).

This paper is structured as follows. In Section 2, we present the SOFIA observations and data reduction of Mrk 54. In Section 3, we summarize the physical properties of the two literature samples of HDGS and LT. In Section 3, we present analyses of statistical correlations between [O iii]/[C ii] and other physical quantities. In Section 5, we establish a relation between [O iii]/[C ii] and f_esc, and apply it to high-z ALMA galaxies. We summarize our conclusions in Section 6. Throughout this paper, we assume a Lambda cold dark matter cosmology with Ω_m = 0.272, Ω_b = 0.045, Ω_Λ = 0.728, and H₀ = 70.4 km s⁻¹ Mpc⁻¹ (Komatsu et al. 2011). We use L_⊙ = 3.839 × 10³³ erg s⁻¹ as solar luminosity and 12+log(O/H) = 8.7 as solar metallicity (Asplund et al. 2009).

Mrk 54 was observed by the SOFIA FIFI-LS (Fischer et al. 2018) during cycles 7 and 8 (PIDs: 07_0108 and 08_0063, PI: T. Hashimoto). FIFI-LS has two parallel spectral channels that cover $1^{\prime} \times 1^{\prime}$ in the wavelength ranges of 115–203 μm (red channel) and $0\buildrel{\,\prime}\over{.} 5\times 0\buildrel{\,\prime}\over{.} 5$ in the ranges of 51–125 μm (blue channel), split into 5 × 5 spatial pixels. The red and blue channels were used to target the [C ii] 158 μm and [O iii] 88 μm lines. The two observations were executed on 2020 February and 2021 May for a total on-source exposure time of 2426 s. The target galaxy Mrk 54 was entirely covered by a single field of view. The observations were performed in symmetric chopping mode with a 120'' chop amplitude. A spatial dithering pattern was used to cover regions with bad pixels and to better recover the spatial resolution of the instrument. Eight grating positions were used to slightly extend the spectral coverage and to oversample the wavelength range in order to compensate for bad pixels and to better define the line profiles. ¹⁷

At the wavelengths of [C ii] 158 μm and [O iii] 88 μm lines, the spatial resolution is approximately 156 and 88, the instantaneous spectral coverage is 1560 and 2340 km s⁻¹, and the spectral resolution is 260 and 490 km s⁻¹. Further details on FIFI-LS can be found in Fischer et al. (2018) and Colditz et al. (2020).

Data reduction was carried out using the FIFI-LS data reduction pipeline (Vacca et al. 2020) combining the two sets of data taken in cycles 7 and 8. The flux calibration, which is performed using sky calibrators, has an absolute uncertainty of less than 20%. Hereafter, we only consider the measurement uncertainties. The data were corrected for the atmospheric absorption with a transmission curve modeled with ATRAN (Lord 1992), using precipitable water vapor values measured during the flight. The final cubes were sampled on a grid with spatial pixels of 3'' and 15 (a fourth of the original pixels) and spectral pixels of 32.5 and 61.25 km s⁻¹ (oversample of a factor of 8 in spectral resolution) for the red and blue array, respectively.

The data were analyzed with the SOFIA SPectral EXplorer (sospex, Fadda & Chambers 2018). We first obtained a pure line cube by subtracting the dust continuum level from the spectral cube at each spatial pixel. We then defined an elliptical aperture by co-adding the cube along the wavelength dimension and considering ellipses centered on the flux centroid of this image. Major and minor axes were optimized by selecting the smallest ellipse containing the asymptotic value of total flux. Finally, we extracted the spectrum within this elliptical aperture and fit a Gaussian function to the line to estimate total flux, central wavelength, and FWHM.

The top left (right) panel of Figure 1 shows the [C ii] ([O iii]) intensity map with contours of the Pan-STARRS i-band image, whereas the bottom left (right) panel depicts the corresponding [C ii] ([O iii]) spectrum extracted from the aperture. The [C ii] ([O iii]) line is detected at a significance level of 24σ (4σ) integrated over the line profile, where 1σ corresponds to the typical uncertainty per spectral bin measured in the spectrum as indicated by the horizontal dashed lines. ¹⁸

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Motivated by recent observations of high-z galaxies that demonstrated that [C ii] is spatially extended compared with [O iii] (e.g., Carniani et al. 2017; Fujimoto et al. 2019; Vallini et al. 2021; Witstok et al. 2022), we examined the spatial sizes of these emission lines in Mrk 54 with the surface brightness profiles. We found that [O iii] is barely resolved with an upper limit of the intrinsic size of 88, whereas [C ii] is only marginally resolved with an intrinsic size of 79. Thus, we do not find clear evidence of spatially extended [C ii] emission in Mrk 54 at the FIFI-LS's spatial resolution.

With sospex, we found that [C ii] and [O iii] have the line fluxes of (4.68 ± 0.16) and (1.01 ± 0.27) × 10⁻¹⁶ W m⁻², FWHMs of 329 ± 13 and 292 ± 90 km s⁻¹, and redshifts of 0.04497 ± 0.00002 and 0.0443 ± 0.0001, respectively. The [C ii] and [O iii] redshift is consistent with that of the optical redshift, 0.0447 ± 0.0002 (Deharveng et al. 2001), within 1σ and 2σ uncertainties, respectively. The corresponding [C ii] and [O iii] luminosities are (5.90 ± 0.21) and (1.27 ± 0.34) × 10⁸ L_⊙, respectively.

2.1. Comparisons of Line Luminosities to the Literature Samples

The left (right) panel of Figure 2 compares the FIR and [C ii] ([O iii]) luminosity of Mrk 54 with a compiled sample of the literature, where the FIR luminosity of Mrk 54 is obtained from photometry with IRAS 60 and 100 μm as in Helou et al. (1985). The literature sample first includes the data points of Herrera-Camus et al. (2018), a compilation of local H ii galaxies, LINER, Seyfert, and high-z galaxies. The literature data also include a subsample of the Lyman Alpha Reference Sample (LARS; Hayes et al. 2013), z ∼ 0.03–0.18 galaxies characterized by its ongoing starburst and Lyα emission. Seven and two of the LARS galaxies were observed in [C ii] and [O iii], respectively (Puschnig et al. 2020). Finally, we also include the literature data points of Smirnova-Pinchukova et al. (2019), a subsample of five nearby luminous Seyfert 1 AGN host galaxies observed in [C ii]. Interestingly, Mrk 54 has strong [C ii] emission that accounts for as high as ∼1% of the FIR luminosity, whereas it has only moderate [O iii] emission. Based on the two line luminosities, we obtain [O iii]/[C ii] = 0.22 ± 0.06, much lower than those obtained in another LCE, Haro 11 (∼2) and high-z ALMA galaxies (∼3–10).

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Strong [C ii] emission in Mrk 54 could be due to the presence of outflow as discussed in, e.g., Smirnova-Pinchukova et al. (2019) and Puschnig et al. (2020). Alternatively, previous theoretical works have shown that FIR line luminosity ratios can be affected by the presence of X-ray-dominated regions in AGNs (e.g., Meijerink et al. 2007; Wolfire et al. 2022). Nevertheless, observational studies of Decarli et al. (2022) and Walter et al. (2018) demonstrated that the FIR line ratios can be reasonably reproduced by the photodissociated region models, indicating that the presence of hidden AGN activity in Mrk 54, if any, may not be the primary cause of the strong [C ii] emission.

2.2. Spatial and Velocity Offsets of [C ii] and [O iii] in Mrk 54

Figure 3 shows a direct comparison of the spatial distributions of [O iii], [C ii], and the i-band position of Mrk 54 in the field of view of [O iii], where the contours are drawn to show the flux centroids. We find that the [C ii] flux centroid matches the i-band position of Mrk 54, whereas the [O iii] flux centroid is spatially offset by ∼5'' (∼4 kpc). In the case of weak detections, the centroid of a point source is not well defined since almost no flux is detected in the adjacent pixels. Nevertheless, the position of the center of the emission can be reconstructed using spatial dithering as done in our observations. Another possible cause of mismatch is a misalignment of the blue and red arrays since the two spectra are acquired simultaneously. This is possible only if the rotation of the K-mirror of FIFI-LS (see Colditz et al. 2020), the beam rotator that rotates the instrument's field of view counteracting the sky rotation experienced by the SOFIA telescope, is not accurately taken into account during the observation. The K-mirror parameters are measured before each FIFI-LS series since the cooling of the instrument slightly modifies its optical path. Since there are no similar issues with other observations in the two series when Mrk 54 was observed we can also exclude this possibility. Finally, we notice that the peak of the [O iii] emission is detected in the same position in the two independent observations obtained in the two different FIFI-LS series. This strongly suggests that the detection is real as well as the difference in position with respect to the peak of the [C ii] emission.

Interestingly, similar spatial offsets among the [C ii], [O iii], and rest-frame UV continuum emitting regions were observed in galaxies in the EoR; Carniani et al. (2017) showed a spatial offset in each of [C ii], [O iii], and the rest-frame UV stellar continuum in a z = 7.11 galaxy, BDF-3229 (see also Laporte et al. 2019). More specifically, the galaxy shows a 4 kpc offset between the UV stellar continuum and [C ii] regions, and 1–30 kpc offset between the [C ii] and [O iii] emitting regions. ¹⁹ Furthermore, in the local universe, Cigan et al. (2016) have shown a spatial offset of [O iii] and [C ii] in local metal-poor dwarf galaxies, DDO 69 and DDO 70, although the offsets are as small as 0.1–0.2 kpc. From the theoretical viewpoint, based on cosmological hydrodynamic simulations combined with radiative transfer calculations, Katz et al. (2019) have shown that the spatial offsets of [C ii] and [O iii] can be caused by a clumpy structure due to, e.g., merger events, presence of small satellites, or a fragmented disk (see also Vallini et al. 2017 for another explanation of the spatial offset due to the stellar photoevaporation feedback effect). Similarly, based on cosmological hydrodynamic simulations implementing the photoionization models of CLOUDY, Moriwaki et al. (2018) have shown that there can be a spatial offset between [O iii] 88 μm and the rest-frame optical continuum that traces the distribution of the bulk stellar population (see their Figure 3). The spatial offset could be due to the fact that the rest-frame optical continuum traces the older stellar population, whereas the [O iii] 88 μm traces the outer region of the actively star-forming regions (K. Moriwaki, private communication). These studies support the claim that the [O iii] emission in Mrk 54 could be real. Hereafter, we treat the [O iii] detection as real. We stress that the [O iii]/[C ii] ratio in Mrk 54 remains low even if [O iii] is considered undetected.

Finally, we note that the [C ii] line is redshifted with respect to the [O iii] line by 192 ± 30 km s⁻¹ in Mrk 54 (Figure 1). At high-z, Carniani et al. (2017) reported that [C ii] is blueshifted with respect to [O iii] by ∼500 km s⁻¹ in the BDF-3299 galaxy at z = 7.2 (see also, e.g., Algera et al. 2023 for other high-z examples). The authors ascribed the velocity offset to different kinematics of [C ii]- and [O iii]-emitting gas, i.e., predominantly neutral and the ionized-gas phase, respectively. Because Mrk 54 is an LCE, such different kinematics of gas might indicate a hint of LyC photon leakage from galaxies into the surrounding IGM. However, we leave further discussion to future papers because another local LCE, Haro 11, does not show any velocity offset between the [C ii] and [O iii] lines (Cormier et al. 2015).

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For our analysis, we make use of data from HDGS and LT. The HDGS sample consists of 50 local metal-poor dwarf galaxies, including the LCE Haro 11 (Cormier et al. 2012), and it is characterized by low gas-phase metallicity ranging from near solar metallicity down to 12+log(O/H) = 7.14. In most cases, these galaxies have PACS spectroscopic observations for both [C ii] 158 μm and [O iii] 88 μm, followed by [O i] 63 μm and weaker lines of [O i] 145 μm and [N ii] 122/205 μm, in addition to PACS imaging. The sample also includes measurements of various ancillary multiwavelength photometric (UV to radio) and spectroscopic data, best suitable for examining the correlation between the [O iii]/[C ii] line luminosity ratios and other observables or physical quantities. Specifically, we examine the correlations against (i) the ionization parameter, U_ion, traced by O₃₂ ≡ [O iii] 5007 Å/[O ii] 3727 Å, (ii) specific SFR defined as the SFR per unit stellar mass, sSFR, (iii) dust temperature, T_dust, (iv) ionized-to-neutral gas fraction traced by the [O iii] 88 μm-to-[O i] 63 μm line ratio, and (v) the gas-phase metallicity in units of 12+log(O/H). The choice of these parameters is motivated by the theoretical predictions of Vallini et al. (2021) and Katz et al. (2022) except for T_d. The correlation against T_d is considered because Walter et al. (2018) have shown a positive correlation between [O iii]/[C ii] and T_d (see Figure 4 in their paper).

From the parent sample of 50 galaxies, we first narrow down the sample to 41 galaxies with both [C ii] 158 μm and [O iii] 88 μm data across the entire galaxy scale. Among these, the numbers of galaxies with O₃₂, sSFR, T_dust, FIR [O iii]/[O i], and 12+log(O/H) are 18, 36, 33, 35, and 41, respectively. The stellar masses and SFRs are adopted from Madden et al. (2013) and De Looze et al. (2014), respectively. ²⁰ The gas-phase metallicities of the sample are adopted from Madden et al. (2013) and references therein, which are estimated from optical lines. We compute O₃₂ in the sample using these literature data. ²¹ Finally, we adopt T_d of the sample in Rémy-Ruyer et al. (2013) estimated from multiple dust photometry using modified blackbody models. ²² The subsample used in this study has median values of O₃₂ = 5.5, sSFR = 0.5 Gyr⁻¹, T_d = 32 K, FIR [O iii]/[O i] = 2.7, and 12+log(O/H) = 8.0.

The galaxies in the LT survey share similar properties to the HDGS galaxies such as low gas-phase metallicity, but they are characterized by lower surface brightness and moderate star formation activity. Four LT galaxies in Cigan et al. (2016) were observed in both [C ii] and [O iii], and have lower [O iii]/[C ii] luminosity ratios than the HDGS galaxies (Cigan et al. 2016). Thus, the sample is useful to accurately examine the correlation between [O iii]/[C ii] and 12+log(O/H). The numbers of galaxies with O₃₂, sSFR, T_dust, FIR [O iii]/[O i], and 12+log(O/H) are 0, 2, 1, 2, and 4, respectively, and the values are adopted from Cigan et al. (2016) and Cigan et al. (2021).

We examined the correlation of the [O iii]/[C ii] line luminosity ratios with other observable quantities using our combined sample, which consists of Mrk 54, HDGS galaxies, including Haro 11 and LT galaxies. We use the Kendall rank correlation test to statistically examine the correlations, where a p-value of 0.05 is used to reject the null hypothesis that the two quantities do not correlate. The correlations and relative Kendall's correlation coefficients are plotted in Figure 4.

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The results show that objects with high [O iii]/[C ii] line luminosity ratios are characterized by high O₃₂ (i.e., high U_ion), high sSFR (i.e., undergoing a bursty event or a young stellar age), high FIR [O iii]/[O i] (i.e., large volume fraction of ionized gas to neutral gas), and low metallicity. The result that high [O iii]/[C ii] shows high ionization parameters and burstiness is consistent with Harikane et al. (2020), Sugahara et al. (2022), and Algera et al. (2023), respectively. We do not observe a strong correlation between [O iii]/[C ii] and T_d (but see Walter et al. 2018; Algera et al. 2023). The strongest correlations are found in O₃₂ (i.e., U_ion) and high FIR [O iii]/[O i] (i.e., the ionized-to-neutral gas volume filling factor), which are in qualitative agreement with the claims of Harikane et al. (2020) and Katz et al. (2022). Although we found a correlation between [O iii]/[C ii] and metallicity, it should be noted that all four LT galaxies have low [O iii]/[C ii] ratios despite their low metallicity, supporting the claims of Vallini et al. (2021) who showed that the metallicity is not a main factor that changes [O iii]/[C ii]. The correlations with metallicity and T_d have also been investigated in Cigan et al. (2016), but to our knowledge, this is the first observational study that examines the correlations with O₃₂.

5.1. [O iii]/[C ii]–f_esc Relation

As mentioned in Section 1, a quantitative description of the cosmic reionization process requires estimates of f_esc in galaxies in the EoR. We discuss the possibility to use the FIR [O iii]/[C ii] luminosity ratios to infer f_esc.

Based on observations of LCEs and non-LCEs among the local galaxies, Chisholm et al. (2018) derived an equation that links O₃₂ to f_esc as follows:

$$\begin{eqnarray}&&{f}_{\mathrm{esc},{{\rm{O}}}_{32}}^{\mathrm{pre}}=(0.0017\pm 0.0004){{{\rm{O}}}_{32}}^{2}+(0.005\pm 0.007),\end{eqnarray} \tag{ 1 }$$

where ${f}_{\mathrm{esc},{{\rm{O}}}_{32}}^{\mathrm{pre}}$ is a predicted value of the LyC escape fraction from O₃₂ (see also Izotov et al. 2016b). Note that the correlation between f_esc and O₃₂ has been statistically confirmed in a recent study by Flury et al. 2022b, who significantly increases the sample of LCEs and non-LCEs. Because an equation relating the two quantities is not provided in Flury et al. (2022b), in this study, we use the relation of Chisholm et al. (2018) for simplicity. As shown in Figure 4, we obtained a positive correlation between optical O₃₂ and FIR [O iii]/[C ii]. If we fit the correlation with a linear function, it can be written as

$$\begin{eqnarray}&&{{\rm{O}}}_{32}=(1.311\pm 0.010)[{\rm{O}}\,{\rm\small{III}}]/[{\rm{C}}\,{\rm\small{II}}]+(-0.384\pm 0.016),\end{eqnarray} \tag{ 2 }$$

using a package of scipy.optimize.curve_fit. Combining these two equations, we obtain the following equation that relates [O iii]/[C ii] to f_esc,

$$\begin{eqnarray}\begin{array}{rcl}{f}_{\mathrm{esc}}^{\mathrm{pre}} & = & (0.0029\pm 0.0007){\left([{\rm{O}}\,{\rm\small{III}}]/[{\rm{C}}\,{\rm\small{II}}]\right)}^{2}+\\ & & (-0.0017\pm 0.0004)[{\rm{O}}\,{\rm\small{III}}]/[{\rm{C}}\,{\rm\small{II}}]+(-0.005\pm 0.007).\end{array}\end{eqnarray} \tag{ 3 }$$

The positive correlation between the two quantities is in qualitative agreement with the predictions of Inoue et al. (2016), Katz et al. (2022), and Ramambason et al. (2022).

In the left panel of Figure 5, we plot the predicted relation of LyC escape fraction along with the data points of Mrk 54, Haro 11, and POX 186. Mrk 54 and Haro 11 have direct measurements of the LyC escape fraction. Mrk 54 and Haro 11 measured escape fractions of 0.025 ± 0.007 (Leitherer et al. 2016) and 0.033 ± 0.007 (Leitet et al. 2011), whereas the predicted values are ${f}_{\mathrm{esc}}^{\mathrm{pre}}=$ ${0.005}_{-0.005}^{+0.007}$ and 0.021 ± 0.013, respectively. The measured and predicted values in Mrk 54 and Haro 11 are consistent with each other within 2σ and 1σ uncertainties.

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In the left panel of Figure 5, a galaxy called POX 186 shows the highest [O iii]/[C ii] luminosity ratio ∼10 among the local galaxies, which corresponds to a high ${f}_{\mathrm{esc}}^{\mathrm{pre}}\sim (0.32\pm 0.15)$. Although direct LyC observations are not performed in the galaxy, its intense star formation activity (sSFR ∼12 Gyr⁻¹) also supports that the galaxy is a candidate for strong LCE. Recently, Eggen et al. (2021) performed integral field unit observations of optical emission lines, and found evidence of strong ionized gas outflow that can facilitate the LyC escape. The indirect signature of strong LyC escape in POX 186 supports that the FIR [O iii]/[C ii] ratios can be used at least to search for promising LCE candidates.

5.2. Implications for High-redshift ALMA Studies

5.3. Limitations of this Study and Future Prospects

We presented SOFIA [C ii] 158 μm and [O iii] 88 μm observations of the local LCE, Mrk 54, at the luminosity distance of ∼191 Mpc. This is only the second LCE, after Haro 11, observed in the FIR lines, offering the opportunity to test if the [O iii]/[C ii] line luminosity ratio can be used as a tracer of f_esc, as proposed by Inoue et al. (2016) and Katz et al. (2020). Interestingly, we find that Mrk 54 has strong [C ii] emission, whereas it has only moderate [O iii] emission, resulting in the low [O iii]/[C ii] luminosity ratio of 0.22 ± 0.06. Combining Mrk 54 with the literature samples of the HDGS and LT surveys, we find that the [O iii]/[C ii] luminosity ratio correlates with O₃₂, sSFR, and FIR [O iii]/[O i], and anticorrelates with the gas-phase metallicity in units of 12+log(O/H). The strongest correlations are found with O₃₂ and FIR [O iii]/[O i]. By combining the analytical form of f_esc and O₃₂ in Chisholm et al. (2018) and the correlation between [O iii]/[C ii] and O₃₂ found in this study, we obtain a relation between f_esc and [O iii]/[C ii]. The two confirmed LCEs, Haro 11 and Mrk 54, roughly follow the [O iii]/[C ii]–f_esc relation within uncertainties of 1σ and 2σ, respectively. If we assume that the same [O iii]/[C ii]–f_esc relation holds at high-z, galaxies with [O iii]/[C ii] ≳ 7 could have f_esc ≳ 10%, significantly contributing to the reionization process. The presented multi-wavelength study will serve as an invaluable reference for ongoing and planned JWST observations of ALMA [O iii] 88 μm emitters at high-z.

We thank an anonymous referee for valuable comments that have greatly improved the paper. We are grateful to Rodrigo Herrera-Camus, Harley Katz, and Ren W. Yi for providing us with their data. We appreciate Christian Fischer, Irina Smirnova-Pinchukova, Harley Katz, and Kana Moriwaki for useful discussions. This research is based on data from the SOFIA Observatory, jointly operated by USRA (under NASA contract NNA17BF53C) and DSI (under DLR contract 50 OK 0901 to Stuttgart University). T.H. was supported by Leading Initiative for Excellent Young Researchers, MEXT, Japan (HJH02007) and by JSPS KAKENHI grant Nos. (20K22358 and 22H01258). A.K.I., Y.S., and Y.F. are supported by NAOJ ALMA Scientific Research grant No. 2020-16B. E.Z. acknowledges funding from the Swedish National Space Agency. Y.T. was supported by JSPS KAKENHI grant No. (22H04939) and by NAOJ ALMA Scientific Research grant No. 2018-18B. MH is a fellow of the Knut & Alice Wallenberg Foundation. Y.H. was supported by JSPS KAKENHI grant No. (21H04489) and JST FOREST Program, grant No. (JP-MJFR202Z).

Facilities: SOFIA (FIFI-LS) - , IRAS. -

Software: Astropy (Astropy Collaboration et al. 2013, 2018), SciPy (Virtanen et al. 2020) and sospex (https://github.com/darioflute/sospex, Fadda & Chambers 2018).