ALMA WILL DETERMINE THE SPECTROSCOPIC REDSHIFT z > 8 WITH FIR [O iii] EMISSION LINES

Finding the highest redshift objects is placing constraints on the theory of baryonic physics to form luminous objects in the universe. The latest survey with the Hubble Space Telescope (HST) has provided a number of candidates of z > 7 galaxies by the so-called drop-out technique (e.g., Ellis et al. 2013). However, the redshifts of these Lyman break galaxies (LBGs) are not yet confirmed through spectroscopy. Since the rest-frame ultraviolet (UV) continuum of the LBGs are too faint (>27 AB) to be detected with current spectrograph, it was often assumed that Lyα emission is the best tool to confirm the redshift. Yet, attempts to detect Lyα for z > 8 LBGs failed (Brammer et al. 2013; Bunker et al. 2013; Capak et al. 2013; Treu et al. 2013), indicating that Lyα was substantially weakened by the intergalactic neutral hydrogen before the completion of the cosmic reionization. Otherwise, the LBGs were just interlopers (Pirzkal et al. 2013; Brammer et al. 2013). If Lyα emission at z > 8 is so weakened that we cannot detect it, we should consider other emission lines to confirm their redshift.

Considering the superb ability of the Atacama Large Millimeter/submillimeter Array (ALMA), the rest-frame far-infrared (FIR) emission lines may be attractive. For example, the [C ii] 158 μm line is very luminous and often detected from high-z sources, including z > 6 QSOs (Maiolino et al. 2005). However, the line is not detected from z > 6 Lyα emitters (Walter et al. 2012; Kaneker et al. 2013; Ouchi et al. 2013), suggesting a different situation of the interstellar medium in these high-z, low-metallicity galaxies. In addition, the [C ii] line at 8.0 < z < 10.6, where the highest-z LBGs reside, is redshifted into the ALMA band 5 which is not available soon.

The FIR [O iii] lines at 52 and 88 μm have been known as prominent lines from H ii regions since the 1970s (Ward et al. 1975) but the lines have rarely been discussed in the high-z context so far because of the lack of suitable instruments. The first FIR [O iii] detection from cosmologically distant sources is reported by Ferkinhoff et al. (2010) from two z ≃ 3 and 4 gravitationally lensed dusty active galactic nucleus/starburst galaxies. In the local universe, the Infrared Space Observatory and the Japanese Infrared Satellite AKARI detected the lines from Galactic H ii regions (Mizutani et al. 2002; Matsuo et al. 2009), from a giant H ii region, 30 Doradus, in the Large Magellanic Cloud (LMC) (Kawada et al. 2011), and from many nearby galaxies (Brauher et al. 2008). Interestingly, recent Herschel observations have revealed that the [O iii] 88 μm line is often stronger than the [C ii] line in low-metallicity nearby dwarf galaxies (Figure 5 of Madden et al. 2012; see also Cormier et al. 2012), suggesting the usefulness of the [O iii] line at high-z where most galaxies are low-metallicity. Last but not least, the [O iii] 88 μm line at 8.1 < z < 11.3 falls into the ALMA band 7 in operation.

In Section 2, we construct a FIR nebular emission model in the high-z universe based on our cosmological simulation and the photoionization code cloudy, followed by the expected FIR line fluxes presented in Section 3. Finally, we discuss the feasibility of detecting the lines from z > 8 galaxies with ALMA in Section 4.

Throughout this Letter, we adopt a ΛCDM cosmology with the matter density, Ω_M = 0.27; the cosmological constant, Ω_Λ = 0.73; the Hubble constant, h = 0.7 in the unit of H₀ = 100 km s⁻¹ Mpc⁻¹; and the baryon density, Ω_B = 0.046. The matter density fluctuations are normalized by setting σ₈ = 0.81 (Komatsu et al. 2011). All magnitudes are quoted in the AB system (Oke 1990).

In this Letter, we consider only lines from H ii regions, and then, we assume the line luminosity, L_line, to be proportional to the instantaneous star formation rate (SFR) of a galaxy, $\dot{M_*}$;

$$\begin{equation} L_{\rm line} = C_{\rm line}(Z,U,n_{\rm H}) \dot{M_*}\,, \end{equation} \tag{ 1 }$$

where C_line is the line emissivity per unit SFR and depends on the metallicity, Z, the ionization parameter, U, and the hydrogen number density, n_H, in H ii regions of the galaxy. This assumption is usual for hydrogen recombination lines because the Lyman continuum (LyC) making H ii regions are emitted only by massive stars whose lifetime (∼1 Myr) is short enough to represent the instantaneous SFR of galaxies (e.g., Kennicutt 1998). Given that the same LyC also ionizes the metal atoms, the similar assumption for metal forbidden lines as Equation (1) would be reasonable. However, the proportional factor, C_line, depends on the nebular parameters of U and n_H as well as the metallicity Z for the case of forbidden lines. On the other hand, we avoid modeling photodissociation regions and molecular clouds surrounding H ii regions because it requires more complex physical and chemical processes (e.g., Abel et al. 2005; Nagao et al. 2011) and may cause a large uncertainty, although it enables us to predict some strong FIR lines such as [C ii] 158 μm and [O i] 63 μm. It would be an interesting future work.

Using the photoionization code cloudy version c13.01 (Ferland et al. 2013), we make a model of C_line. The cloudy calculations are similar to Inoue (2011). We assume six metallicities as log₁₀(Z/Z_☉) = −5.3, −3.3, −1.7, −0.7, −0.4, and 0.0; three ionization parameters as log₁₀U = −3.0, −2.0, and −1.0; and four hydrogen number densities as log₁₀(n_H/cm⁻³) = 0.0, 1.0, 2.0, and 3.0. The "H ii region" set of the gas elemental abundance based on the observations of the Orion Nebula is used and the "Orion type" dust grains are included. The nebular and stellar metallicities are assumed to be equal. The shape of the stellar spectra are taken from Starburst99 (Leitherer et al. 1999) and Schaerer (2002), depending on the metallicity. The initial mass function (IMF) is assumed to be a Salpeter one with 0.1–100 M_☉. We consider the scenario of a constant star formation of 10 Myr but the age of the star formation has a negligible impact on C_line. We also note that negligible differences are found when we adopt another population synthesis code, pégase version 2 (Fioc & Rocca-Volmerange 1997). We also assume a constant density throughout the H ii regions and the plain-parallel geometry. The calculations are stopped if the electron temperature becomes less than 10^3.5 K or the electron fraction becomes less than 1%. No escape of the LyC from H ii regions (and galaxies) is considered. The line emissivities are reduced by a factor of approximately 1 − f_esc when the escape fraction is f_esc.

From the cloudy calculations, we find that the [O iii] 88 μm line is the strongest line for the nebular parameters examined in this Letter. Figure 1 shows the [O iii] line luminosities per unit SFR as a function of metallicity for nine combinations of nebular parameters as indicated in the panel. The luminosities with log₁₀(n_H/cm⁻³) = 3.0 are much smaller than those shown in Figure 1 as a trend found in the figure: a smaller emissivity for a higher density. The model line emissivities are roughly proportional to the metallicity when Z < 0.1 Z_☉ as the oxygen abundance increases. When Z > 0.1 Z_☉, the dependence becomes weaker because of lower LyC emissivity for higher metallicity.

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For a comparison, we plot observational estimates in Figure 1. Kawada et al. (2011) reported the flux ratio of $F_{\rm [{\rm O\,\scriptsize{III}}]\,88}/F_{\rm H\alpha }\simeq 0.5$ to 1.0 in 30 Doradus of the LMC. Adopting the conversion formula from Hα luminosity to SFR by Hirashita et al. (2003), we obtain the emissivity shown by the diamond.⁸ The vertical error-bar indicates the uncertainty of the conversion and the sample variance of the flux ratio. The metallicity is taken from van den Bergh (2000). Madden et al. (2012, 2013) reported $\log _{10}(F_{\rm [{\rm O\,\scriptsize{III}}]\,88}/F_{\rm FIR})=-2.04\,{\pm}\, 0.29$ for nearby low-metallicity dwarf galaxies. Converting the FIR luminosity to SFR by using the formula of Hirashita et al. (2003), we obtain the cross point with error-bars.⁹ The vertical error-bar includes the uncertainty of the conversion and the observed sample variance. The horizontal error-bar indicates the sample metallicity distribution taken from Madden et al. (2013). Brauher et al. (2008) presented a compilation of [O iii] 88 μm observations of nearby galaxies. If we select only spiral galaxies from their sample, we obtain $\log _{10}(F_{\rm [{\rm O\,\scriptsize{III}}]\,88}/F_{\rm FIR})=-2.61\pm 0.20$. Again, adopting the formula by Hirashita et al. (2003), we obtain the inverse triangle with error-bars.¹⁰ The vertical error-bar includes the uncertainty of the conversion and the sample variance. The metallicity is estimated from the mean absolute magnitude of the sample galaxies via the correlation between the magnitude and the metallicity presented by Tremonti et al. (2004).

While the uncertainties are still large, we may find a trend that the [O iii] emissivity slowly decreases as the metallicity increases from ≈0.2 Z_☉. We also find that no single combination of the nebular parameters of log₁₀U and log₁₀n_H reproduces this trend. Then, we consider a model with a constant log₁₀n_H but a higher log₁₀U at lower metallicities. Such a trend may be realized by a higher LyC production rate and a harder spectrum of lower metallicity stars. Therefore, we adopt the models indicated by the large five-pointed stars in this Letter. However, we should note that this may not be a unique combination of the parameters compatible with the observations. Table 1 is a summary of C_line for 11 H ii region lines calculated in the adopted models.

In order to predict the FIR line fluxes from high-z galaxies, we need their SFRs in Equation (1). We adopt a cosmological simulation by Shimizu et al. (2013) which was developed to examine physical properties of LBGs at z ∼ 7–10. The simulation code is based on a Tree-PM smoothed particle hydrodynamics code gadget-3 updated from gadget-2 (Springel 2005). We have implemented star formation, supernova (SN) feedback and chemical enrichment following Okamoto et al. (2008), Okamoto & Frenk (2009), and Okamoto et al. (2010). We employ N = 2 × 640³ particles for dark matter and gas in a comoving volume of 50 h⁻¹ Mpc cube. The mass of a dark matter particle is 3.01 × 10⁷ h⁻¹ M_☉ and that of a gas particle is initially 6.09 × 10⁶ h⁻¹ M_☉. Gas particles can spawn star particles when they satisfy a set of criteria for star formation. In each snapshot of the simulation, we run the subfind algorithm (Springel et al. 2001) to identify groups of dark matter, gas, and star particles as galaxies. Parameters in the code, such as SN feedback and dust attenuation, are calibrated so as to reproduce the stellar mass functions and UV luminosity functions observed at z ⩾ 7. We have constructed a light-cone output from a number of snapshots of the simulation, calculated the apparent magnitudes in a number of broadband filters, and then, applied the exact same color selection criteria as real observations to select LBGs at z ∼ 7, 8, 9, and 10. See Shimizu et al. (2013) for more details.

The FIR line fluxes, F_lines, for individual galaxies extracted from the cosmological simulation are estimated by the following procedure. First, we assign C_line(Z_neb)s to each simulated LBG, where Z_neb is the "nebular" metallicity¹¹ of the LBG, by interpolating the values in Table 1. Then, we obtain the line luminosities by Equation (1) with the SFR of the simulated LBG. Finally, the luminosities are converted to the fluxes by the luminosity distance in the light-cone. In addition, the peak intensities of the lines, $F_{\nu _0}^{\rm peak}$, are calculated by the following formula: $F_{\nu _0}^{\rm peak}=F_{\rm line}(1+z)c/\nu _0/v_{\rm 1D}/\sqrt{\pi }$, where c is the light speed, z is the redshift, ν₀ is the rest-frame line center frequency, and v_1D is the standard deviation of the one-dimensional gas velocity which is assumed to be equal to that of the dark matter.

Figure 2 shows the expected flux of the [O iii] 88 μm line, which is the strongest among the lines examined in this Letter, from the simulated LBGs at z ∼ 7 to 10 as a function of the apparent magnitudes. We find that a good correlation between the line flux and the apparent rest-frame UV magnitude does not change along the redshift very much. The dispersion is larger for fainter galaxies because the dispersions of metallicity, SFR, and dust attenuation are also larger for fainter galaxies in our simulation, since the SN feedback significantly affects them and their star formation histories fluctuate more (Shimizu et al. 2013).

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Relating the SFR in Equation (1) to the UV magnitude, we can derive an analytic relation between the line flux and the apparent UV magnitude:

$$\begin{eqnarray} \log _{10} F_{\rm line} &=& {-}0.4 (m_{\rm UV} - A_{\rm UV} + AB_0) + \log _{10}C_{\rm line}\nonumber\\ &&- \log _{10}C_{\rm UV}+ \log _{10}(1-f_{\rm esc}) - \log _{10}(1+z),\nonumber \\ \end{eqnarray} \tag{ 2 }$$

where F_line is the line flux in cgs units, m_UV is the apparent UV magnitude in the AB system, A_UV is the UV dust attenuation, AB₀ = 48.6 is the zero point of the AB system in cgs units, f_esc is the LyC escape fraction, z is the redshift, C_line is the line emissivity in Table 1, and C_UV is the ratio of the UV luminosity-to-the SFR. For >100 Myr constant SFR and the Salpeter IMF in Section 2, we obtain an almost constant value of log₁₀(C_UV(erg s⁻¹/(M_☉ yr⁻¹))) = 27.84 at the rest-frame 2000 Å for Z/Z_☉ = 0.02 to 1.0. In Figure 2, we show three cases of the analytic relations. The metallicity and attenuation values are taken from the results of Shimizu et al. (2013). From this comparison, the readers may confirm that the galaxies are already enriched to Z_neb = 0.01–0.5 Z_☉ and typically ∼0.2 Z_☉ at these high-z.

In Figure 3, we show the expected peak flux density of the [O iii] 88 μm line as a function of the apparent magnitude. The one-dimensional velocity dispersion of the dark matter particles composing the simulated LBGs is 42 ± 4 (or 26 ± 3) km s⁻¹ for H₁₆₀ = 27 (28.5). This is somewhat smaller than those of optical [O iii] lines measured in z ∼ 3 LBGs (e.g., Pettini et al. 1998). However it is reasonable given a lower mass of the z ⩾ 7 LBGs as Shimizu et al. (2013) expect <10¹¹ M_☉ for H₁₆₀ > 27. We expect the [O iii] 88 μm line peak flux density to be 1.3 ± 0.5 (or 0.2 ± 0.1) mJy for H₁₆₀ = 27 (28.5) objects.¹² If the readers require an estimate of the strengths of other emission lines, they can do by a scaling with the numbers in Table 1.

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Let us consider observing the [O iii] 88 μm line with ALMA. In the band 7 (275–373 GHz), we can capture the line from 8.1 ⩽ z ⩽ 11.3 where the current highest-z LBGs reside. Using the ALMA Sensitivity Calculator for the Cycle 2, in which we have assumed 50 antennas (full operation), dual polarization, 30 km s⁻¹ velocity resolution, declination of +22^d25' (the z = 9.6 object by Zheng et al. 2012), and "Automatic Choice" for weather conditions,¹³ we obtain the expected sensitivities in Figure 4. We find that the 1.3 mJy [O iii] line from a H₁₆₀ = 27 object at 8.3 < z < 9.3 or 9.6 < z < 11.5 can be detectable at a >4σ significance with about 1 hr integration. Since there is a rather strong atmospheric water absorption, we cannot easily detect the line from 9.3 < z < 9.6. In fact, H₁₆₀ = 27 is very bright for LBGs at z > 8 but there are some objects found in the recent survey (e.g., Trenti et al. 2011; Oesch et al. 2013). Gravitationally lensed objects are also good targets. Zheng et al. (2012) reported an object with the photometric redshift z = 9.6. This object is apparently as bright as H₁₆₀ = 25.7 but should be 28.6 without magnification. According to Figure 3, we find the intrinsic and lensed line flux densities of this object are about 0.2 and 3 mJy, respectively. Therefore, we can detect the [O iii] line at >5σ from this object with only 15 minutes integration.

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It is a caveat that we do not know exact redshift prior to the detection. So, we have to scan a range of frequency where a possible line exists. After ALMA Cycle 2, we can use the "Spectral Scan" mode which enables us to cover about 30 GHz by five tunings. This corresponds to about Δz ≃ 1 for the [O iii] line at z ≃ 9. This is wide enough to probe the redshift range expected by photometry. Another caveat is that we have only a single line even if we detect a line. Thus, we have to rely on a photometric redshift method to conclude the detected line to be the [O iii] 88 μm line. Fortunately, we can detect other weaker lines such as [O iii] 52 μm and [N iii] 57 μm as well as [O i] 63 μm and [C ii] 158 μm because we already know the exact redshift and can invest more time for one integration. The ratios of these FIR lines are very useful for the diagnostics of the chemical evolution and ionizing sources in the highest-z galaxies.

We would like to thank Tohru Nagao for useful comments on cloudy calculations and Erik Zackrisson for discussions. We acknowledge the financial support of Grant-in-Aid for Young Scientists (A: 23684010; S: 20674003; B: 24740112) by MEXT, Japan. This work is also supported by the FIRST program SuMIRe by the Council for Science and Technology Policy.