CO and Fine-structure Lines Reveal Low Metallicity in a Stellar-mass-rich Galaxy at z ∼ 1?

Using the ALMA continuum observations centered at 480.5 GHz (rest frame) presented here, together with our previous ALMA continuum measurements at 205 μm (rest frame; Lamarche et al. 2017), we can calculate the slope of the Rayleigh–Jeans power law for the thermal dust continuum of 3C 368. This is particularly interesting in this case, since the core component of 3C 368, the star-forming galaxy, makes up the smallest contribution to the continuum flux at rest frame 480.5 GHz, the flux being dominated instead by the radio lobes. Hence, unresolved continuum measurements at millimeter/submillimeter wavelengths may have overestimated the flux from the core of 3C 368. We obtain a Rayleigh–Jeans power-law index, S_ν ∼ ν^α, of 3.7 ± 0.4, or equivalently a dust-emissivity β value, S_ν ∼ ν^2+β, of 1.7 ± 0.4. This is consistent with the dust-emissivity β value assumed in Podigachoski et al. (2015), who used it to derive an FIR luminosity of 2.0 × 10¹²L_⊙, which we used in our previous work and will adopt throughout this paper.

We can also decompose the radio SED from the core of 3C 368 into thermal and nonthermal components, using our previous ALMA 230 GHz (rest frame) continuum observations (Lamarche et al. 2017), together with radio-continuum observations at 8.21 and 4.71 GHz (observed frame) (Best et al. 1998a), using an equation of the following form (e.g., Condon 1992; Klein et al. 2018):

$$\begin{eqnarray}&&{S}_{\mathrm{total},r}={S}_{\mathrm{th},0,r}{\left(\displaystyle \frac{\nu }{{\nu }_{0,r}}\right)}^{-0.1}+{S}_{\mathrm{nth},0,r}{\left(\displaystyle \frac{\nu }{{\nu }_{0,r}}\right)}^{-{\alpha }_{\mathrm{nth}}},\end{eqnarray} \tag{ 1 }$$

where S_th,0,r and S_nth,0,r are the (rest frame) contributions to the total radio flux from the thermal and nonthermal components, respectively, at ν_0,r (rest frame), and α_nth is the nonthermal power-law index. Adopting a ν_0,r value of 230 GHz and holding α_nth fixed at 0.7 (e.g., Shu 1991), we fit for S_th,0,r and S_nth,0,r. We find best-fit values of S_th,0,r = 45 ± 18 μJy and S_nth,0,r = 4 ± 3 μJy (see Figure 4).

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We do not consider any contribution to this part of the SED from thermal dust emission, which continuing the Rayleigh–Jeans power law found above, would contribute only ∼5% of the flux measured at 230 GHz (rest frame). Indeed, the continuum flux from the core of 3C 368 is observed to be brighter at rest frame 230 GHz than at rest frame 480.5 GHz, indicating that the dominant emission mechanism at 230 GHz is not thermal dust—an inference made possible by the continuum observations presented here.

Beyond the core component of 3C 368, we note that the radio lobes have considerable emission even in the high-frequency observations presented here (rest frame 480.5 GHz). Between the observed frame 8.21 and 4.71 GHz, Best et al. (1998a) find a spectral index, S_ν ∼ ν^α, of ∼−1.5 for both the northern and southern radio lobes. While the flux densities at rest frame 480.5 GHz fall below the extrapolated power-law values, by factors of ∼1.4 and 2.3 for the northern and southern lobes, respectively, the fact that such energetic electrons are present within the radio-emitting lobes is noteworthy. While detailed modeling is beyond the scope of this paper, the observations presented here suggest that the radio-emitting lobes of 3C 368 are quite young (e.g., Murgia et al. 1999).

Having determined that the radio SED of the star-forming core of 3C 368 is dominated by thermal free–free continuum at 230 GHz (rest frame), we can estimate the gas-phase oxygen abundance in 3C 368 using our previous observations of the [O iii] 52 μm line (Lamarche et al. 2017).

The method for determining gas-phase absolute ionic abundances using fine-structure line emission and radio free–free continuum has been applied historically to galactic H ii regions (e.g., Herter et al. 1981; Rudolph et al. 1997) and more recently to high-redshift galaxies (e.g., Lamarche et al. 2018). This technique provides an alternative to optically derived metallicities, which suffer both from uncertainties in the temperature structure of H ii regions, as well as dust extinction of the line flux. Dust obscuration is important in the local universe, especially in the more luminous star-forming galaxies, and becomes an increasingly important effect in the epoch of peak cosmic SFR density, at redshifts ∼1–3. It can be shown that the abundance of ion i, relative to hydrogen, is given by

$$\begin{eqnarray}&&\displaystyle \frac{{n}_{{{\rm{X}}}^{i+}}}{{n}_{{{\rm{H}}}^{+}}}=\displaystyle \frac{{F}_{\lambda }}{{S}_{\nu ,r}}\displaystyle \frac{4.21\times {10}^{-16}{T}_{4}^{-0.35}{\nu }_{9}^{-0.1}}{{\epsilon }_{\lambda }}\left(\displaystyle \frac{{n}_{e}}{{n}_{p}}\right),\end{eqnarray} \tag{ 2 }$$

where F_λ is the fine-structure line flux in units of erg s⁻¹ cm⁻², S_ν,r is the rest-frame radio free–free flux density at rest-frequency ν in units of Jy, T₄ is the electron temperature in units of 10⁴ K, ν₉ is the radio emission rest frequency in units of GHz, n_e/n_p is the electron to proton number density ratio, which accounts for the contribution of electrons from non-hydrogen atoms present in the H ii regions, and _λ is the emissivity per unit volume of the fine-structure line at wavelength λ, given by

$$\begin{eqnarray}&&{\epsilon }_{\lambda }=\displaystyle \frac{{j}_{{ul}}}{{n}_{i}{n}_{e}}=\displaystyle \frac{h{\nu }_{{ul}}{A}_{{ul}}{n}_{u}}{{n}_{e}{n}_{i}},\end{eqnarray} \tag{ 3 }$$

where h is the Planck constant, A_ul is the Einstein A coefficient for the line transition at frequency ν_ul, 9.8 × 10⁻⁵ s⁻¹ and 5785.9 GHz, respectively, for the [O iii] 52 μm line (Carilli & Walter 2013), and the ratio of the level population in the upper state (n_u) to the total (n_i) is determined by detailed balance. Adopting the collisional coefficients of Palay et al. (2012), and an H ii region electron density of 1000 cm⁻³, as has been determined to be the case in 3C 368 (Lamarche et al. 2017), we calculate a value of _λ = 7.6 × 10⁻²² erg s⁻¹ cm³ for the [O iii] 52 μm line. We additionally assume n_e/n_p = 1.05, which accounts for the electrons contributed from helium, and T₄ = 1, a typical value for H ii regions.

Combining the total integrated [O iii] 52 μm line flux (1.34 × 10⁻¹⁷ W m⁻²; Lamarche et al. 2017) with the estimated free–free flux density at 230 GHz (rest frame), and using Equation (2), we calculate [O⁺⁺/H] = 1 × 10⁻⁴. Then, to determine the [O⁺⁺/O] ratio, and hence scale our ionic oxygen abundance to total oxygen abundance, an estimate for the hardness of the ambient radiation field within 3C 368 is required. Using the H ii region models of Rubin (1985), we predicted that ∼84% of the oxygen within the H ii regions of 3C 368 is in the O⁺⁺ state (Lamarche et al. 2017). Using that ionization fraction here, we obtain an estimated [O/H] ratio of 1.2 × 10⁻⁴, or ∼0.3 Z_⊙ (Asplund et al. 2009), within about a factor of 2 uncertainty, where this uncertainty is dominated by both the uncertainty in determining the free–free contribution to the radio SED and the uncertainty in the measured [O iii] 52 μm line flux.

This low-metallicity value is consistent with the results of Croxall et al. (2017), who found empirically that the [C ii] 158 μm/[N ii] 205 μm line ratio is highly elevated in low-metallicity sources. In Lamarche et al. (2017) we found a lower bound of [C ii] 158 μm/[N ii] 205 μm > 60, which would indicate 12 + log(O/H) ∼8.1, or equivalently Z ∼ 0.25 Z_⊙, in the sample from Croxall et al. (2017).

An alternative explanation for the radio emission emanating from the core component of 3C 368 is that it originates from the AGN itself. Strong synchrotron self-absorption can lead to AGN with flat radio spectra, such that the radio emission that we attribute to thermal free–free emission from extended star-forming H ii regions may instead come from a compact AGN (e.g., Roellig et al. 1986). As a check on this possibility, we examine the radio/IR correlation, q_IR (e.g., Ivison et al. 2010), where

$$\begin{eqnarray}&&{q}_{\mathrm{IR}}\equiv {\mathrm{log}}_{10}\left(\displaystyle \frac{{S}_{\mathrm{IR}}/(3.75\,\times \,{10}^{12}\,{\rm{W}}\,{{\rm{m}}}^{-2})}{{S}_{1.4\mathrm{GHz}}/({\rm{W}}\,{{\rm{m}}}^{-2}\,{\mathrm{Hz}}^{-1})}\right),\end{eqnarray} \tag{ 4 }$$

S_IR is the total integrated IR flux (rest frame 8–1000 μm) in units of W m⁻², and ${S}_{1.4\mathrm{GHz}}$ is the flux density at 1.4 GHz in units of W m⁻² Hz⁻¹. Extrapolating the SED-decomposed rest-frame thermal contribution to the radio emission at rest frame 230 GHz (45 μJy) to the expected value at 1.4 GHz using a free–free power-law index of −0.1, and using the total FIR luminosity attributed to star formation in 3C 368 (2.0 × ${10}^{12}\,{L}_{\odot }$, Podigachoski et al. 2015) to calculate S_IR, we obtain a value of q_IR = 2.6. This value is within the range seen in star-forming galaxies (e.g., Ivison et al. 2010), suggesting that the attribution of the radio continuum to free–free emission in 3C 368 is appropriate.

Unfortunately, our 230 GHz rest-frame ALMA observations (Lamarche et al. 2017), with a synthesized beam of size 312 × 181, do not resolve the core of 3C 368. We will propose higher resolution continuum imaging with ALMA to test the theory of extended H ii regions versus compact AGN as the source for the high-frequency radio continuum in 3C 368, thereby supporting or disfavoring the low-metallicity hypothesis for the ISM within 3C 368.

The subsolar oxygen abundance that we derive for 3C 368 using the [O iii] 52 μm line and radio free–free continuum can be compared to the same value derived using optical lines. Observations exist for 3C 368 in the [O iii] 5007 Å, [O ii] 3727 Å, and Hδ lines, such that R₂₃ (e.g., Pagel et al. 1979) can be calculated by assuming a scaling from Hδ to Hβ, where

$$\begin{eqnarray}&&{R}_{23}\equiv \displaystyle \frac{[{\rm{O}}\,{\rm{ii}}]\lambda 3727+[{\rm{O}}\,{\rm{iii}}]\lambda \lambda 4959,5007}{{\rm{H}}\beta }.\end{eqnarray} \tag{ 5 }$$

Adopting an [O iii] 5007 Å line flux of 6.8 × 10⁻¹⁸ W m⁻² (Jackson & Rawlings 1997), an [O ii] 3727 Å line flux of 5.9 × 10⁻¹⁸ W m⁻² (Best et al. 2000), an Hδ line flux of 2.8 × 10⁻¹⁹ W m⁻² (Best et al. 2000), and assuming the theoretical scaling of Hδ/Hβ = 0.26 (Case-B recombination, e.g., Osterbrock & Ferland 2006), we obtain an R₂₃ value of ∼12. This R₂₃ value indicates 12 + log(O/H) ∼8.3 (Kewley & Dopita 2002), or ∼0.4 Z_⊙ (Asplund et al. 2009), making it consistent with the FIR/radio-derived estimate.

In Lamarche et al. (2017), we modeled the PDRs within 3C 368, utilizing the PDR Toolbox (Kaufman et al. 2006; Pound & Wolfire 2008), together with detections of the [C ii] 158 μm (Stacey et al. 2010) and [O i] 63 μm (Lamarche et al. 2017) lines, as well as the modeled FIR continuum luminosity (Podigachoski et al. 2015), obtaining best-fit parameters of G₀ ∼280 Habing units and n ∼7500 cm⁻³. Here we update the model to include the two newly detected lines.

Including the CO(4–3) and [C i] 609 μm lines, we obtain new best-fit values of G₀ ∼320 Habing units and n ∼3200 cm⁻³, with a PDR surface temperature of ∼200 K (see Figure 5). These PDR parameters are similar to those that we obtained previously, up to a decrease in the density, due to the detection significance of the CO(4–3) and [C i] 609 μm lines, which tightly constrain that parameter. We again see that the [C ii] emission is high relative to the CO emission, and now also relative to the [C i] emission.

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The penetration of far-UV photons capable of photodissociating CO and ionizing carbon is limited by dust extinction. Therefore, assuming dust content scales with metallicity, the CO-photodissociated surface of a molecular cloud becomes much larger relative to the shielded CO-emitting core in low-metallicity environments. In PDR models (e.g., Kaufman et al. 2006), [C i] line emission arises from a thin transition region of neutral carbon that lies between the C⁺ and CO regions. The [C ii] line flux is therefore enhanced relative to both CO and [C i] in these environments (e.g., Maloney & Black 1988; Stacey et al. 1991).

Using the calculated n, G₀, and PDR surface temperature values in 3C 368, we can estimate the PDR mass following Hailey-Dunsheath et al. (2010):

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{{M}_{\mathrm{PDR}}}{{M}_{\odot }} & = & 0.77\left(\displaystyle \frac{0.93{L}_{[{\rm{C}}{\rm{ii}}]}}{{L}_{\odot }}\right)\left(\displaystyle \frac{1.4\times {10}^{-4}}{{X}_{{{\rm{C}}}^{+}}}\right)\\ & & \times \,\displaystyle \frac{1+2\exp \left(\tfrac{-91\,{\rm{K}}}{T}\right)+\tfrac{{n}_{\mathrm{crit}}}{n}}{2\exp \left(\tfrac{-91\,{\rm{K}}}{T}\right)},\end{array}\end{eqnarray} \tag{ 6 }$$

where ${X}_{{{\rm{C}}}^{+}}$ is the abundance of C⁺ per hydrogen atom, taken here to be $1.4\times {10}^{-4}$ (Savage & Sembach 1996), n_crit is the critical density of the [C ii] 158 μm transition (2800 cm⁻³, Stacey 2011), and assuming that ∼93% of the [C ii] emission originates within the PDRs of 3C 368 as we estimated in Lamarche et al. (2017). We calculate a PDR gas mass of ∼1.7 × 10¹⁰ M_⊙ in this source (see Table 2).

With detections of both the CO(4–3) and [C i] 609 μm lines, the molecular gas mass within 3C 368 can be estimated in three ways:

First, using the detection of the CO(4–3) line, we can estimate the molecular gas mass by assuming a conversion factor back to CO(1–0) and then adopting an α_CO value. The measured CO(4–3) line flux of 1.08 ± 0.14 Jy km s⁻¹ equates to a value of L${}_{\mathrm{CO}(4-3)}^{{\prime} }$ = (4.6 ± 0.6) × 10⁹ K km s⁻¹ pc². Our previous non-detection of the CO(2–1) line with ALMA yields a 3σ upper limit of L${}_{\mathrm{CO}(2-1)}^{{\prime} }$ < 3.45 × 10⁹ K km s⁻¹ pc² (Lamarche et al. 2017). This implies that r_43/21 > 1.3, so we use this excitation ratio to scale L${}_{\mathrm{CO}(4-3)}^{{\prime} }$ back to L${}_{\mathrm{CO}(1-0)}^{{\prime} }$. Taking an ultraluminous infrared galaxy (ULIRG) value of α_CO = 0.8 M_⊙(K km s⁻¹ pc²)⁻¹ (e.g., Bolatto et al. 2013), we obtain a molecular gas mass of 2.9 × 10⁹ M_⊙.

If, instead, we calculate a value of α_CO based on the metallicity estimates from Section 3.2, adopting the scaling of Glover & Mac Low (2011) (and see also Bolatto et al. 2013), we obtain α_CO ∼ 18 M_⊙(K km s⁻¹ pc²)⁻¹. Adopting this larger value of α_CO, and assuming the same super-thermal CO excitation as above, we obtain a molecular mass of 6.4 × 10¹⁰ M_⊙ (see Table 2). This metallicity-adjusted α_CO-based molecular gas mass is ∼4× larger than the PDR gas mass estimated above, making the mass ratio consistent with that observed in other starburst galaxies (e.g., Stacey et al. 1991), lending further credibility to the low-metallicity explanation for the small CO luminosity in 3C 368.

The second method is based on a scaling of molecular gas mass with [C I]-line luminosity—which does not assume that the [C I] line arises from a thin transition in the PDRs—as indicated by the work of Papadopoulos et al. (2004). Following Bothwell et al. (2017),

$$\begin{eqnarray}\begin{array}{rcl}M{\left({{\rm{H}}}_{2}\right)}^{[{\rm{C}}{\rm{I}}]} & = & 1375.8{D}_{L}^{2}{\left(1+z\right)}^{-1}{\left(\displaystyle \frac{{X}_{[{\rm{C}}{\rm{I}}]}}{{10}^{-5}}\right)}^{-1}\\ & & \times {\left(\displaystyle \frac{{A}_{10}}{{10}^{-7}{{\rm{s}}}^{-1}}\right)}^{-1}{Q}_{10}^{-1}{S}_{[{\rm{C}}{\rm{I}}]}{\rm{\Delta }}v,\end{array}\end{eqnarray} \tag{ 7 }$$

where D_L is the luminosity distance in Mpc (7735 in the case of 3C 368), X_{[C i]} is the [C i]/H₂ abundance ratio, taken here to be 3 × 10⁻⁵ (e.g., Weiß et al. 2003; Papadopoulos & Greve 2004), A₁₀ is the Einstein A coefficient, 7.93 × 10⁻⁸ s⁻¹ (Wiese et al. 1966), Q₁₀ is the excitation parameter, which depends on gas density, kinetic temperature, and radiation field (e.g., Papadopoulos et al. 2004), which we take to be 0.6 (Bothwell et al. 2017), and S_{[C i]}Δv is the flux of the [C i] 609 μm line in units of Jy km s⁻¹. We obtain a molecular gas mass of 2.3 × 10¹⁰ M_⊙. We note that this molecular gas mass is ∼3× smaller than that derived using the metallicity-corrected α_CO method above. If we scale the [C i]/H₂ abundance ratio, X_{[C i]}, by the subsolar gas-phase metallicity estimated in Section 3.2, Z ∼ 0.3 Z_⊙, we calculate an H₂ mass of 7.7 × 10¹⁰ M_⊙. Boosting this mass by ∼20% to account for the contribution from helium, which is already accounted for in the α_CO-based method above, increases the mass estimate to 9.2 × 10¹⁰ M_⊙, such that the two methods produce masses that differ by ∼30%.

Finally, we can use the dust mass calculated by multicomponent SED modeling, along with a gas-to-dust conversion factor, δ_GDR, to estimate the molecular gas mass within 3C 368. Adopting an SED-modeled dust mass of 1.4 × 10⁸ M_⊙ (Podigachoski et al. 2015) and a gas-to-dust conversion factor of 540, appropriate for Z ∼ 0.3 Z_⊙ (Rémy-Ruyer et al. 2014), we obtain a molecular gas mass of 7.6 × 10¹⁰ M_⊙. Or, equivalently, if we use the CO-derived gas mass together with the SED-modeled dust mass, we obtain a value of δ_GDR = 464 (see Table 2). Since α_CO and δ_GDR scale differently with metallicity, the CO- and dust-derived gas masses are incompatible at solar metallicity, giving us more confidence that 3C 368 does indeed have subsolar metallicity, and that our derived gas masses are robust.

The calculated molecular gas mass implies that, at its current SFR, ∼350 M_⊙ yr⁻¹ (Podigachoski et al. 2015), 3C 368 will deplete its supply of molecular gas in ∼170 Myr. We can additionally calculate the gas fraction, ${f}_{\mathrm{gas}}\equiv \tfrac{{M}_{\mathrm{gas}}}{{M}_{\mathrm{gas}}+{M}_{\mathrm{stars}}}$, and the specific SFR, $\mathrm{sSFR}\equiv \,\tfrac{\mathrm{SFR}}{{M}_{\mathrm{stars}}}$, in 3C 368, finding values of ∼0.15 and ∼1 Gyr⁻¹, respectively (see Table 2). The calculated sSFR puts 3C 368 on the upper end of the galaxy main sequence as defined by Genzel et al. (2015), SFR/SFR_MS = 2.8, and the gas fraction lies exactly on the scaling with sSFR/sSFR_MS, stellar mass, and redshift found in Scoville et al. (2017). Moreover, 3C 368 lies along the L'_{[C i]} to L_IR correlation found in other high-redshift main-sequence galaxies, however it is elevated in its ${L}_{[{\rm{C}}\,{\rm{I}}]}^{{\prime} }$/${L}_{\mathrm{CO}(2-1)}^{{\prime} }$ ratio, with a lower limit of 0.9, by a factor of ∼4.4 (Valentino et al. 2018). The models of Papadopoulos et al. (2018) find the [C i](1–0)/CO(1–0) brightness ratio to be much larger than unity in low-metallicity or cosmic-ray-dominated regions, however, since we have only a modest lower limit on this ratio, we cannot draw any strong conclusions from it. When compared to a sample of low-metallicity high-redshift sources (Coogan et al. 2019), 3C 368 is observed to be similarly deficient in CO emission, and when compared to a sample of local luminous infrared galaxies and spirals (Liu et al. 2015), it has a CO(4–3) flux that falls below that expected from the scaling with FIR luminosity, by a factor of ∼3.7.