ALMA OBSERVATION OF 158 μm [C ii] LINE AND DUST CONTINUUM OF A Z = 7 NORMALLY STAR-FORMING GALAXY IN THE EPOCH OF REIONIZATION^*

The study by da Cunha et al. (2013) describes how the CMB affects measurements of FIR continuum emission of high-redshift galaxies. Hence, before we derive and discuss constraints on the dust properties of IOK-1 from the observed 1.26 mm continuum flux limit, we first describe the effects of CMB on FIR continuum and how we actually apply them to our observed continuum flux limit (see also González-López et al. 2014, for details).

CMB affects measurements of FIR continuum in two ways. One is that CMB heats the dust of galaxies to higher temperature as redshift gets higher. According to da Cunha et al. (2013), the dust temperature at a redshift z is

$$\begin{equation} T_{\rm dust}(z) = \left(\left(T_{\rm dust}^{z=0}\right)^{4+\beta }+\left(T_{\rm CMB}^{z=0}\right)^{4+\beta }[(1+z)^{4+\beta }-1]\right)^{\frac{1}{4+\beta }}. \end{equation} \tag{ 1 }$$

Here, $T_{\rm dust}^{z=0}$ is the temperature of dust heated by and in thermal equilibrium with the radiation field produced by stars in a galaxy at z = 0, where the effects of CMB radiation are negligible. Also, $T_{\rm CMB}^{z=0}=2.73$ K and β are temperature of CMB at z = 0 and dust emissivity index of a thermal spectrum. This equation suggests that effect of CMB heating on dust temperature becomes non-negligible at high redshifts (e.g., see Figure 1 in da Cunha et al. 2013, for a case of $T_{\rm dust}^{z=0}=18$ K and β = 2.0). The ratio (hereafter referred to as M_ν) between the dust continuum flux densities at a rest-frame frequency ν and a redshift z when including dust heating by CMB and not including it is

$$\begin{equation} M_{\nu } = \frac{F^*_{\nu /(1+z)}}{F^{\rm int}_{\nu /(1+z)}} = \frac{B_{\nu }(T_{\rm dust}(z))}{B_{\nu }\left(T_{\rm dust}^{z=0}\right)}, \end{equation} \tag{ 2 }$$

where $F^{\rm int}_{\nu /(1+z)}$, $F^*_{\nu /(1+z)}$, and B_ν are the intrinsic dust continuum flux density of a galaxy, the dust continuum flux density after including the effect of CMB heating of dust, and the Planck function. This M_ν is a factor for correcting the effect of CMB heating of dust (for example, see Figure 3 top panel of da Cunha et al. 2013, for the case of $T_{\rm dust}^{z=0}=18$ K and β = 2).

Meanwhile, another effect of CMB on dust continuum measurements is that CMB itself becomes a background against which FIR continuum flux should be measured. da Cunha et al. (2013) have shown that the ratio (hereafter referred to as C_ν) between the flux at a frequency ν that can be measured against CMB at a redshift z and the flux emitted by dust in a galaxy at that frequency and redshift including heating of dust by CMB is

$$\begin{equation} C_{\nu } = 1 - \frac{B_{\nu }(T_{\rm CMB}(z))}{B_{\nu }(T_{\rm dust}(z))}, \end{equation} \tag{ 3 }$$

where $T_{\rm CMB}(z) = T_{\rm CMB}^{z=0} (1+z)$ is a temperature of CMB at a redshift z. This is a factor for correcting the effect of CMB as background (for example, see Figure 3 bottom panel of da Cunha et al. 2013, for the case of $T_{\rm dust}^{z=0}=18$ K and β = 2).

Finally, we can estimate the intrinsic FIR continuum flux $F_{\nu /(1+z)}^{\rm int}$ emitted by a galaxy from the observed continuum flux $F_{\nu /(1+z)}^{\rm obs}$ by using the equation

$$\begin{eqnarray} F_{\nu /(1+z)}^{\rm obs} &=& C_{\nu } \times M_{\nu } \times F_{\nu /(1+z)}^{\rm int} \nonumber \\ &=& \left[ \frac{B_{\nu }(T_{\rm dust}(z)) - B_{\nu }(T_{\rm CMB}(z))}{B_{\nu }\left(T_{\rm dust}^{z=0}\right)} \right] F_{\nu /(1+z)}^{\rm int} \end{eqnarray} \tag{ 4 }$$

and Equation (1) by assuming $T_{\rm dust}^{z=0}$ and β.

Since we have obtained the 3σ upper limit on the observed 1.26 mm continuum flux of IOK-1, $F_{\nu /(1+z)}^{\rm obs} < 63$ μJy, we can infer what type of galaxy this object is from its SED at rest-frame UV to FIR (observer frame optical to millimeter) including our ALMA flux limit. In Figure 2, we compare the SED of IOK-1 with template SEDs of several different types of local galaxies. We reproduce the SED of IOK-1 using the fluxes measured in the optical to FIR images taken with the Subaru Telescope Suprime-Cam BVRi'z'y bands (Ota et al. 2008, 2010b; Jiang et al. 2013); Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) F110W, F125W, and F160W bands (Cai et al. 2011; Jiang et al. 2013); Spitzer Space Telescope Infrared Array Camera (IRAC) 3.6, 4.5, 5.8, and 8.0 μm bands (Ota et al. 2010b); Herschel Space Telescope Spectral and Photometric Imaging Receiver (SPIRE) 250, 350, and 500 μm bands (the images of IOK-1 are cut out from the completed Herschel-ATLAS North Galactic Plane (NGP) project images; Eales et al. 2010; Pascale et al. 2011; R. J. Ivison et al. 2013, private communication); and our ALMA 3σ upper limit on 1.26 mm dust continuum. These images are shown in Figure 3. IOK-1 is not detected in any of the SPIRE bands where the beam-convolved map 1σ point source sensitivities (including both instrumental and confusion noises) are 4.6, 5.3, and 6.0 mJy for 250, 350, and 500 μm bands, respectively. Note that for comparison, in Figure 2, we also plot 3σ upper limits on 1.26 mm continuum from the previous IRAM/Plateau de Bure Interferometer (PdBI) and Combined Array for Research in Millimeter-wave Astronomy (CARMA) observations of IOK-1 conducted by Walter et al. (2012b) and González-López et al. (2014), which are shown by the lower and upper open triangles, respectively. Our ALMA upper limit is about one order of magnitude deeper than these previous limits.

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We compare the UV–FIR fluxes/flux limits of IOK-1 with the local galaxy templates of Arp 220, M82, M51, and NGC 6946 (the left panel in Figure 2) taken from Silva et al. (1998) and other local spiral/barred, dwarf, and irregular galaxies (Mrk 33, NGC 0925, IC 2574, Holmberg II, and DDO 165 in the left panel and all the galaxies in the right panel in Figure 2) from Dale et al. (2007). We shift these galaxy SEDs to the redshift of IOK-1, z = 6.96, normalize them to the rest-frame UV continuum flux density redward of Lyα (the HST/F125W band flux) and plot them by the color coded solid lines in Figure 2. We also show their galaxy morphological types in the figure. These are the SEDs not including the effects of CMB on their FIR continua.

We also plot the SEDs of these template galaxies with their FIR continua (a part of the SED that corresponds to the emission of the cold dust) including the effects of CMB by the color coded dashed lines in Figure 2. We convert the original FIR continua of the template galaxies, $F_{\nu /(1+z)}^{\rm int}$, to those including the effects of CMB, $F_{\nu /(1+z)}^{\rm obs}$, by using their dust temperatures $T_{\rm dust}^{z=0}$ and emissivity indices β obtained from literature and Equations (1)–(4) but following the prescription given by González-López et al. (2014) to calculate the factor M_ν as follows. First, from the literature that conducted single-component modified blackbody (MBB) fittings to the observed FIR continua of the galaxies, we adopt $T_{\rm dust}^{z=0}=66.7$ K and β = 1.83 for Arp 220 (Rangwala et al. 2011), $T_{\rm dust}^{z=0}=48.0$ K and β = 1.0 for M82 (Colbert et al. 1999), $T_{\rm dust}^{z=0}=24.9$ K and β = 2.0 for M51 (Mentuch Cooper et al. 2012), $T_{\rm dust}^{z=0}=40.4$ K and β = 1.3 for Mrk 33 (Dunne et al. 2000), $T_{\rm dust}^{z=0}=26.0$ K and β = 1.5 for NGC 6946, $T_{\rm dust}^{z=0}=23.7$ K and β = 1.5 for NGC 0925, $T_{\rm dust}^{z=0}=25.9$ K and β = 1.5 for IC 2574, $T_{\rm dust}^{z=0}=36.5$ K and β = 1.5 for Holmberg II, and $T_{\rm dust}^{z=0}=23.5$ K and β = 1.5 for DDO 165 (Skibba et al. 2011). These are the galaxies shown in the left panel of Figure 2. We adopted $T_{\rm dust}^{z=0}$s and βs obtained by Skibba et al. (2011) for all the galaxies shown in the right panel of Figure 2. Then, to compute the factor M_ν at each frequency ν for each template galaxy, we scale the MBB with $T_{\rm dust}^{z=0}$ and β to the peak of the FIR emission of the galaxy's SED and calculate the ratio R_ν of emission associated with the cold dust at each frequency ν.

$$\begin{equation} R_{\nu } = \frac{K \nu ^{\beta } B_{\nu }\left(T_{\rm dust}^{z=0}\right)}{F_{\nu }^{\rm int}}, \end{equation} \tag{ 5 }$$

where K is the scaling factor. With this R_ν, the Equation (2) can be now expressed as

$$\begin{equation} M_{\nu } = (1 - R_{\nu }) + R_{\nu } \times \frac{B_{\nu }(T_{\rm dust}(z))}{B_{\nu }\left(T_{\rm dust}^{z=0}\right)}. \end{equation} \tag{ 6 }$$

Using Equations (1) and (3)–(6), we convert the original FIR continuum emission of each template galaxy at each frequency ν to the one including the effects of CMB and show the results in Figure 2.

Comparison of the solid lines (intrinsic dust SEDs) and the dashed lines (observed dust SEDs that include the effects of CMB) in Figure 2 shows two notable differences. First, due to the extra heating of dust by CMB at z = 6.96, the peaks of the SEDs shift toward shorter wavelengths (or higher frequencies). Also, the Rayleigh–Jeans tails of the dust emission observed against the CMB (dashed lines) are steeper than those of the intrinsically emitted SEDs (solid lines). This is because at a higher-redshift, CMB temperature is closer to the dust temperature, making the intrinsic dust emission more difficult to detect against CMB. The effects of CMB are stronger for galaxies with lower dust temperatures $T_{\rm dust}^{z=0}$. As the CMB temperature is ∼21.84 K at z ∼ 7, SEDs of the template galaxies with $T_{\rm dust}^{z=0}$ closer to this (i.e., M51, NGC 6946, NGC 0925, IC 2574, and DDO 165) are more remarkably affected by the CMB effects than those with $T_{\rm dust}^{z=0}$ much higher than 21.84 K. As discussed in da Cunha et al. (2013), considering the effects of the CMB is required for the correct interpretation of dust continuum observations as it would change estimation of a dust continuum flux density and thus subsequent derivations of dust masses, total (F)IR luminosities, and dust-obscured SFRs of galaxies.

Figure 2 also shows that the SED of IOK-1 is neither similar to those of highly dust-obscured galaxies such as Arp 220 and M82 (see also Walter et al. 2012b; González-López et al. 2014) nor less extreme dust-rich nearby spirals such as M51 and NGC 6946. It is rather more likely similar to SEDs of dwarfs/irregulars. More specifically, UV continuum slopes (see the insets in Figure 2) and FIR continuum SEDs of IC 2574 (morphological type SABm), Holmberg II (Im), DDO 053 (Im), Holmberg I (IABm), and NGC 2915 (I0) are consistent with the detection data points of IOK-1 at rest-frame UV and the ALMA FIR continuum upper limit (morphological types were taken from Dale et al. 2007). As local dwarf/irregular galaxies have been observed to have low-IR luminosities and dust masses, IOK-1 could be such a system with low dust obscuration. Meanwhile, conducting SED-fitting to rest-frame UV to optical fluxes, Ota et al. (2010b) estimated the upper limit on the stellar mass of IOK-1 to be either M_* ≲ 2–9 × 10⁸M_☉ for a young age (≲ 10 Myr) and low dust reddening (A_V ∼ 0) or a mass as high as M_* ≲ 1–4 × 10¹⁰ M_☉ for either an old age (>100 Myr) or high dust reddening (A_V ∼ 1.5). Given that LAEs at high redshifts (e.g., z ∼ 5.7–6.6) tend to be very young, low dust systems (e.g., Ono et al. 2010), and considering the non-detection of IOK-1 in dust continuum with ALMA, the former M_* limit would be more likely. For comparison, we have calculated the average stellar mass of 17 local dwarf and irregular galaxies (Sd and later) in Skibba et al. (2011) KINGFISH survey sample and obtained M_* ∼ 9.1 × 10⁸ M_☉ (the stellar mass ranges from 2.2 × 10⁶ M_☉ to 5.8 × 10⁹ M_☉ within the sample). Hence, the stellar mass of IOK-1 is comparable to those of local dwarf/irregular galaxies. This also supports the idea that IOK-1 would be a system similar to local dwarf/irregular galaxies.

Given our 3σ ALMA upper limit on the 1.26 mm continuum flux density F_{ν/(1 + z)}, we can estimate the upper limit on the dust mass M_dust of IOK-1 from the following relation:

$$\begin{eqnarray} M_{\rm dust} &=& \frac{F_{\nu /(1+z)} D_{\rm L}^2}{(1+z)\kappa _{\rm d}(\nu _{\rm rest})B_{\nu }(T_{\rm dust})} \nonumber \\ &=& \frac{F_{\nu /(1+z)}^{\rm int} D_{\rm L}^2}{(1+z)\kappa _{\rm d}(\nu _{\rm rest})B_{\nu }\left(T_{\rm dust}^{z=0}\right)} \nonumber \\ &=& \frac{F_{\nu /(1+z)}^{\rm obs} D_{\rm L}^2}{(1+z)\kappa _{\rm d}(\nu _{\rm rest})C_{\nu }M_{\nu }B_{\nu }\left(T_{\rm dust}^{z=0}\right)} \nonumber \\ &=& \frac{F_{\nu /(1+z)}^{\rm obs} D_{\rm L}^2}{(1+z)\kappa _{\rm d}(\nu _{\rm rest})[B_{\nu }(T_{\rm dust}(z)) - B_{\nu }(T_{\rm CMB}(z))]}. \qquad \end{eqnarray} \tag{ 7 }$$

Here, D_L is a luminosity distance, κ_d(ν_rest) is the rest-frame frequency dust mass absorption coefficient, and B_ν(T_dust) is the Planck function at a rest-frame frequency ν_rest and a dust temperature T_dust. We adopt κ_d(ν_rest) = 0.77 (850 μm/λ_rest)^β cm² g⁻¹ from Dunne et al. (2000) with the rest-frame wavelength of λ_rest = 158 μm. $F_{\nu /(1+z)}^{\rm int}$ is the intrinsic continuum flux that can be obtained after correcting the observed continuum flux $F_{\nu /(1+z)}^{\rm obs} = 63$ μJy for the CMB effects by using Equation (4). Because the SED of IOK-1 is similar to those of local dwarf and irregular galaxies (see Section 3.1.2 and Figure 2), we model the dust continuum SED of IOK-1 as an MBB with $T_{\rm dust}^{z=0}=27.6$ K and β = 1.5, the average values of 17 local dwarf and irregular galaxies (Sd and later) derived by Skibba et al. (2011) from their KINGFISH survey. Then, Equation (7) gives M_dust < 6.4 × 10⁷ M_☉. The upper limit on dust mass estimated here is also listed in Table 1. If we do not correct the effects of CMB (i.e., if we use the observed continuum flux limit $F_{\nu /(1+z)}^{\rm obs} = 63$ μJy with $B_{\nu }(T_{\rm dust}^{z=0})$ instead of $C_{\nu }M_{\nu }B_{\nu }(T_{\rm dust}^{z=0})$ for Equation (7)), this leads to $M_{\rm dust}^{\rm CMB} < 4.9 \times 10^{7}\, M_{\odot }$, a factor of 0.76 (=C_νM_ν) underestimation compared to the intrinsic dust mass limit. Meanwhile, if $T_{\rm dust}^{z=0}$ of IOK-1 was actually lower (higher) than what we assumed here (27.6 K), the upper limit on M_dust would be higher (lower).

Table 1. Summary of the ALMA Observation and Derived Properties of IOK-1

za	νobsb	σcontc	σlined	$S_{\rm cont}^{\rm obs}$e	$S_{\rm line}^{\rm obs}\,$f	$L_{[{\rm C}\,{\scriptsize{II}}]}$g	Mdusth	LFIRh	LIRh	SFRdusth	SFRUVi
	(GHz)	(μJy beam−1)	(μJy beam−1)	(μJy)	(μJy)	(107 L☉)	(107 M☉)	(1010 L☉)	(1010 L☉)	(M☉ yr−1)	(M☉ yr−1)
6.96	238.76	21	240	<63	<720	<3.4	<6.4	<3.7	<5.7	<10.0	23.9

Notes. All the upper limits are 3σ at a resolution of 15 × 12 (see Section 3.1 for details.) ^aThe redshift measured from the Lyα of IOK-1 (Iye et al. 2006; Ota et al. 2008). Ono et al. (2012) also reported z = 6.965. ^bObserving frequency tuned to the redshift measured from the Lyα of IOK-1. ^cContinuum sensitivity at 1.26 mm (rest frame 158 μm) at a resolution of 15 × 12. ^d[C ii] line sensitivity over a channel width of 40 km s⁻¹ at a resolution of 15 × 12. ^e3σ continuum flux density limit. ^f3σ [C ii] line flux density limit over a channel width of 40 km s⁻¹. ^g[C ii] line luminosity limit over a channel width of 40 km s⁻¹. We assumed $L_{\rm line}=1.04 \times 10^{-3} F_{\rm line}\nu _{\rm rest}(1+z)^{-1}D_{\rm L}^2$, where the line luminosity, L_line, is measured in L_☉, the velocity-integrated flux, F_line = S_lineΔv, in Jy km s⁻¹ with a velocity width, Δv = 40 km s⁻¹, the rest frequency, ν_rest = ν_obs(1 + z), in GHz, and the luminosity distance, D_L, in Mpc (Walter et al. 2012b). ^hIntrinsic dust mass, FIR luminosity (42.5–122.5 μm), total IR luminosity (8–1000 μm), and dust-obscured SFR all corrected for the effects of CMB. These quantities including the effects of CMB are a factor of C_νM_ν = 0.76 lower (see Sections 3.1.1 and 3.1.3 for details). ⁱSFR derived from the UV continuum of IOK-1 by Jiang et al. (2013).

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We also estimate the upper limit on intrinsic FIR luminosity L_FIR of IOK-1 by again modeling its dust continuum SED as an MBB with $T_{\rm dust}^{z=0}=27.6$ K and β = 1.5 (the average values of local dwarfs and irregulars derived by Skibba et al. 2011, see above), scaling it to our CMB-corrected 3σ ALMA upper limit on 1.26 mm continuum (i.e., $F_{\nu /(1+z)}^{\rm obs}/C_{\nu }M_{\nu } = F_{\nu /(1+z)}^{\rm int}$) and integrating it from 42.5 μm to 122.5 μm. We obtain L_FIR < 3.7 × 10¹⁰ L_☉. Moreover, integrating the same scaled MBB from 8 μm to 1 mm, we estimate the intrinsic total IR luminosity to be L_IR < 5.7 × 10¹⁰ L_☉. These intrinsic luminosities correspond to only the contribution from the stars in IOK-1 to dust heating and do not include the contribution from CMB. Hence, especially, L_IR is appropriate for estimating the dust-obscured SFR. If we use the Kennicutt (1998) relation with the Salpeter (1955) initial mass function (IMF), SFR_dust = 1.73 × 10⁻¹⁰L_IR [L_☉], the total IR luminosity converts to the dust-obscured SFR of SFR_dust < 10.0 M_☉ yr⁻¹. Jiang et al. (2013) estimated the SFR of IOK-1 to be SFR_UV ∼ 23.9 M_☉ yr⁻¹ from the HST/WFC3 band magnitudes that cover the rest-frame UV continuum of IOK-1, not including Lyα emission. This is the SFR not obscured by dust. Hence, the upper limit on the total (obscured plus un-obscured) SFR of IOK-1 is SFR_total = SFR_UV + SFR_dust < 33.9 M_☉ yr⁻¹. This implies that f_obscured = SFR_dust/SFR_total < 29% of star formation is obscured by dust in IOK-1. On the other hand, if we scale the MBB to just the observed continuum flux density limit $F_{\nu /(1+z)}^{\rm obs}$ (i.e., the flux not corrected for the CMB effects) and integrate it, this would result in underestimations of L_FIR, L_IR, and SFR_dust by 24% (a factor of C_νM_ν = 0.76) compared to the intrinsic ones we have obtained above due to the extra heating of dust by CMB and the reduction of observed dust continuum flux by the CMB as a background.

The dust mass and FIR/IR luminosity of IOK-1 are ∼1–2 orders of magnitude lower than those of a host galaxy of the quasar ULAS J112001.48+064124.3 at a similar redshift z = 7.08 (Venemans et al. 2012) and the most distant SMG known, HFLS 3, at z = 6.34 (Riechers et al. 2013) as well as those of the quasar host galaxies at z ∼ 1.8–6.4 studied so far (Pety et al. 2004; Maiolino et al. 2005; Beelen et al. 2006; Iono et al. 2006; Maiolino et al. 2009; Wagg et al. 2010; Wang et al. 2013; Willott et al. 2013) and z ∼ 2–5 SMGs (Riechers et al. 2010; Dwek et al. 2011; Cox et al. 2011; De Breuck et al. 2011; Valtchanov et al. 2011; Walter et al. 2012a). Furthermore, though the sensitivities are about one order of magnitude lower than that of ALMA, Walter et al. (2012b) also observed IOK-1 in dust continuum, Kanekar et al. (2013) and González-López et al. (2014) carried out 1.2 mm continuum observations of three other z ∼ 6.6 LAEs, and they all ended up with non-detections. Our and their results together imply that high-redshift LAEs at the epoch of reionization are likely systems with very little dust, quite different in dust content from extreme starbursts or highly dust-obscured galaxies such as quasar hosts and SMGs at similar and lower redshifts.

Moreover, Ouchi et al. (2013) observed dust continuum of a z = 6.595 LAE, Himiko, which has a similar SFR_UV (∼30 M_☉ yr⁻¹) to IOK-1, with ALMA to a similar sensitivity to ours at 082 × 058 resolution but found only a ∼2σ weak signal at the expected position and considered it a non-detection. Thus, Himiko could be similar to typical high-redshift LAEs in dust content. However, Himiko has at least twice as larger size than IOK-1 in Lyα (≳ 3'' in extent) and is considered a Lyα blob (LAB). Also, its UV continuum shows a few knots over about 2'' (Ouchi et al. 2013). Hence, to search for possible extended emission, we have re-calibrated, flagged, and imaged the public Himiko ALMA Cycle 0 data. We made the continuum map that is based on all data, except the SPW in which the [C ii] line is expected, to avoid a possible contamination from that line. As seen in Figure 4, at a nearly full resolution of 08 × 05, we found that there is a 3.4σ possible weak continuum source at the position of Himiko, as pointed out by Ouchi et al. (2013). The source shows a possible extension east–west along the UV continuum direction, although low signal-to-noise ratio does not allow us to confirm if the source is extended. If we consider this 3.4σ signal the upper limit (as it is marginal) and model the dust SED of Himiko as an MBB with $T_{\rm dust}^{z=0}=27.6$ K and β = 1.5 typical of dwarf/irregular galaxies, then integrations of the MBB scaled to 67.5 μJy/C_νM_ν (C_νM_ν ∼ 0.80 for Himiko) give L_FIR < 3.5 × 10¹⁰ L_☉ and L_IR < 5.4 × 10¹⁰ L_☉. The Kennicutt (1998) relation converts the L_IR to SFR_dust < 9.3 M_☉ yr⁻¹ and SFR_total < 39.3 M_☉ yr⁻¹, implying that f_obscured < 24% of star formation is obscured by dust. Also, Equation (7) gives the dust mass of Himiko, M_dust < 6.1 × 10⁷ M_☉.

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Meanwhile, imaging at 201 × 185 resolution (comparable to the Lyα size of Himiko) resulted in a higher noise and a non-detection with an rms of 42 μJy beam⁻¹. Integrations of the same MBB scaled to the 3σ limit give the conservative upper limits, L_FIR < 6.5 × 10¹⁰L_☉, L_IR < 1.0 × 10¹¹ L_☉, SFR_dust < 17.4 M_☉ yr⁻¹, SFR_total < 47.4 M_☉ yr⁻¹, and f_obscured < 37%. Also, Equation (7) gives the conservative dust mass upper limit, M_dust < 1.1 × 10⁸ M_☉. Hence, although it is not clear that Himiko is extended in the dust continuum, it could be similar to other common LAEs at high redshifts such as IOK-1 in dust content or possibly slightly dustier if the 3.4σ signal is a real detection. It should be noted that comparison of these continuum flux limits at 08 × 05 and 201 × 185 resolutions with dust SEDs of different types of local galaxies in Figure 5 in Ouchi et al. (2013) implies that Himiko could be a system similar to local dwarf/irregular galaxies, not changing the same implication obtained by Ouchi et al. (2013) by using their derived Himiko continuum limit. Thus, our assumption of the MBB with $T_{\rm dust}^{z=0}$ and β typical of local dwarf/irregular galaxies for Himiko to derive its dust-related properties is reasonable.

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The [C ii] line has been considered a tracer of SFR as it is produced by the UV field in star-forming regions. Figure 7 shows the [C ii] luminosity as a function of SFR for several different types of objects. Objects with higher SFRs have higher [C ii] luminosities and different types of objects reside in different locations in the SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ plane in such a way that local late-type and star-forming galaxies are located at the low to intermediate SFR and $L_{[{\rm C}\,{\scriptsize{II}}]}$ regime, low-redshift LIRGs at the intermediate to high SFR and $L_{[{\rm C}\,{\scriptsize{II}}]}$ region, and quasar host galaxies and SMGs at the very high SFR and $L_{[{\rm C}\,{\scriptsize{II}}]}$ domain. For the local late-type and star-forming galaxies, clear correlations have been observed to hold between SFR and $L_{[{\rm C}\,{\scriptsize{II}}]}$ (Boselli et al. 2002; De Looze et al. 2011). In Figure 7, we compare these calibrated relations for local galaxies and locations of all types of objects in the SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ plane with total SFRs and [C ii] luminosities of IOK-1 as well as other LAEs at z ∼ 4.7–6.6 previously observed to see whether they are similar or different systems in gas enrichment or in metallicity as [C ii] luminosity would be proportional to metallicity (e.g., Vallini et al. 2013).

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In Section 3.1.3, we have estimated an upper limit on the total SFR of IOK-1 to be SFR_total < 33.8 M_☉ yr⁻¹ by adding the SFR estimated from its UV continuum (SFR_UV) and the upper limit on the dust-obscured SFR estimated from 1.26 mm continuum (SFR_dust). If IOK-1 had no dust, the lowest possible total SFR would be the one estimated from its UV continuum, i.e., SFR_total ⩾ SFR_UV = 23.9 M_☉ yr⁻¹ (Jiang et al. 2013). In Figure 7, we also plot the possible total SFR range of IOK-1 and the upper limit on [C ii] luminosity. We notice that IOK-1 neither seems to follow the SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ correlations for local star-forming galaxies (though the correlation has some scatters) nor to be within the regions occupied by any other type of objects except for high-redshift LAEs (i.e., Himiko and HCM 6A, which we will mention below). Its [C ii] luminosity is significantly fainter than that expected for a local star-forming galaxy having the same SFR as IOK-1. By using the local star-forming galaxy correlation derived by De Looze et al. (2011), the [C ii] luminosity limit of IOK-1 converts to an SFR of ∼2.5 M_☉ yr⁻¹ (or log  SFR ∼0.51), which is much lower than the possible SFR range of IOK-1, 23.9–33.8 M_☉ yr⁻¹. Hence, the local star-forming galaxy correlation does not seem to apply to IOK-1. IOK-1 could be a system having either lower enriched gas or different photodissociation region (PDR) structure/physical state of ISM than local star-forming galaxies.

A similar result has been reported for a z = 6.595 LAE, Himiko, by Ouchi et al. (2013) who did not detect its [C ii] line by using ALMA at 082 × 058 resolution and 200 km s⁻¹ channel⁻¹. As Himiko is extended over ≳ 3'' in Lyα, we generated the spectrum at 25 resolution and 30 MHz channel⁻¹ (36 km s⁻¹) using the public Himiko ALMA Cycle 0 data to see if we detect any extended source. As with the higher-resolution analysis of Ouchi et al. (2013), no line is detected. The 3σ flux density upper limit at 25 resolution is 2.0 mJy beam⁻¹ channel⁻¹ at 36 km s⁻¹ channel⁻¹ or $L_{[{\rm C}\,{\scriptsize{II}}]} < 7.9 \times 10^7\, L_{\odot }$ (assuming a velocity width of Δv = 36 km s⁻¹), and a factor of 1.7 lower at 100 km s⁻¹ channel⁻¹. However, we have found that the rms noise is about a factor of two higher than this between 249.7 GHz to 250.2 GHz due to atmospheric absorption, so if the line happened to fall in this frequency range, the limits are a factor of two worse. In Section 3.1.3, we also derived the conservative upper limit on SFR_total of Himiko at 201 × 185 resolution (comparable to the Lyα size of Himiko). In Figure 7, we plot the $L_{[{\rm C}\,{\scriptsize{II}}]}$ upper limit and the possible SFR range of Himiko (SFR_UV ∼ 30 M_☉ yr⁻¹ ⩽ SFR_total < SFR_UV + SFR_dust ∼ 47.4 M_☉ yr⁻¹). Himiko is off the local galaxy SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ correlation and close to IOK-1. For comparison, in Figure 7, we also plot the $L_{[{\rm C}\,{\scriptsize{II}}]}$ upper limit of Himiko we derived with SFR_total = 100 M_☉ yr⁻¹, which Ouchi et al. (2013) estimated from SED-fitting at rest-frame UV to optical wavelengths. In this case, Himiko is also off the local galaxy SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ correlation but apart from IOK-1 due to the difference in SFR_total.

Both IOK-1 and Himiko have several things in common except that Himiko displays more extended Lyα emission and is considered a LAB and that Himiko might be detected in dust continuum. They both consist of two to three merging components (Cai et al. 2011; Ouchi et al. 2013), have similar total UV continuum luminosities (or SFR_UV) of the whole system, and have not been detected in [C ii] line to the similar flux limits (if we assume that the sizes of these LAEs in [C ii] are similar). Hence, if SFR_UV+SFR_dust more likely reflects the actual total SFR of Himiko than the SFR estimated from the SED-fitting, both IOK-1 and Himiko may be normally star-forming galaxies at high redshifts with lower enriched gas/metallicity content than local normal star-forming galaxies.

On the other hand, Kanekar et al. (2013) observed a gravitationally lensed z = 6.56 faint LAE, HCM 6A, in [C ii] emission with the IRAM/PdBI to a deep flux limit but somewhat shallower than ours and Ouchi et al.'s, taking advantage of the lensing magnification. They could not detect the [C ii] line, either. Given SFR_UV ∼ 9 M_☉ yr⁻¹ (Hu et al. 2002a, 2002b), SFR_dust < 19.6 M_☉ yr⁻¹ (we derived this SFR in the same way as we did for IOK-1 and Himiko for a fair comparison), and the $L_{[{\rm C}\,{\scriptsize{II}}]}$ upper limit (Kanekar et al. 2013, they adopted 100 km s⁻¹ width), we also plot HCM 6A in Figure 7. It is close to the local SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ relation, although it could be off the relation as the [C ii] luminosity is an upper limit. This is possibly due to their slightly shallower [C ii] flux limit. Since this LAE is a factor of two to three lower than IOK-1 and Himiko in SFR_UV, its [C ii] luminosity could also potentially be lower than those of IOK-1 and Himiko.

In Figure 7, we also plot the z = 6.554 and z = 6.541 LAEs, SDF J132408.3+271543 and SDF J132415.7+273058 (Taniguchi et al. 2005). González-López et al. (2014) observed them in [C ii] lines and 1.2 mm continuum with CARMA, but they did not detect them. We plot the SFR ranges estimated from SFR_UVs and the SFR_dust upper limits (corrected for the CMB effects on their 1.2 mm continua) derived by Jiang et al. (2013) and González-López et al. (2014), respectively. They are within the local SFR-$L_{[{\rm C}\,{\scriptsize{II}}]}$ relation and the low-redshift LIRG region, but the $L_{[{\rm C}\,{\scriptsize{II}}]}$ upper limits (50 km s⁻¹ channel width) obtained by González-López et al. (2014) are an order of magnitude shallower than those for IOK-1, Himiko, and HCM 6A. Therefore, at this moment, we can neither tell whether these two LAEs follow the local relation nor whether these results are consistent with those of IOK-1, Himiko, and HCM 6A. Deeper observations are required to reveal this.

On the contrary, a z ∼ 4.7 LAE, Lyα-1, observed with ALMA, is detected in the [C ii] line (Carilli et al. 2013) and located in the local SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ relation as well as close to the lower SFR and lower $L_{[{\rm C}\,{\scriptsize{II}}]}$ side of the low-z LIRGs region and the border between data points of the LIRGs and the local star-forming galaxies, as seen in Figure 7. We plot the SFR range estimated from the SFR_UV and the SFR_dust upper limit derived by Ohyama et al. (2004) and Carilli et al. (2013), respectively. Lyα-1 would be a system different from z ∼ 6.6–7 LAEs and possibly similar to low-z LIRGs. Actually, it is in the vicinity of a system BR 1202-0725 comprising a quasar, an SMG, and another LAE, Lyα-2, all at z ∼ 4.7 (e.g., Hu et al. 1996; Ohta et al. 2000; Iono et al. 2006; Wagg et al. 2012; Carniani et al. 2013; Carilli et al. 2013; Williams et al. 2014). Note that we do not plot Lyα-2 in Figure 7 because though detected by ALMA, its $L_{[{\rm C}\,{\scriptsize{II}}]}$ cannot be measured accurately due to the partial truncation at the edge of the ALMA band (Carilli et al. 2013; Decarli et al. 2014). Though an upper limit, Lyα-1 has a FIR luminosity of L_FIR < 3.6 × 10¹¹ L_☉ (Carilli et al. 2013), comparable to those of LIRGs (L_FIR > 10¹¹ L_☉). In addition, Lyα-2 has L_FIR ∼ 1.7 × 10¹² L_☉ (Carilli et al. 2013), even as luminous as ULIRGs (L_FIR > 10¹² L_☉). Moreover, both LAEs have Lyα emission broader (∼1300 km s⁻¹) than most LAEs at similar redshifts (Williams et al. 2014), and Lyα-1 is also spatially extended in the Lyα narrowband image (Hu et al. 1996). Several studies have reported that LAEs at z ∼ 2–4.5 detected in FIR continua and having L_FIR as luminous as ULIRGs also exhibit extended Lyα emission, and some of them are even classified as LABs showing evidence of interaction within the Lyα cloud. They also tend to be found in dense environments such as protoclusters (Steidel et al. 2000; Chapman et al. 2004; Colbert et al. 2006; Matsuda et al. 2011; Bridge et al. 2012; Yang et al. 2012, 2014). Detecting new faint sources, possibly additional LAEs also associated with the quasar and the SMG, Carniani et al. (2013) argue that the BR 1202-0725 system might be a massive protocluster in which the high star formation activity is probably triggered by minor mergers or interactions. Hence, Lyα-1 is probably a system not like usual LAEs such as IOK-1 but rather possibly a fainter and less extended analog of LIRGs/LABs seen in dense environments. Also, at z ∼ 4.7, the universe is a factor ∼1.5–1.7 older than the one at z ∼ 6.6–7. Hence, the difference between Lyα-1 and the z ∼ 6.6–7 LAEs may partly originate from galaxy evolution over cosmic time as well.

In Figure 7, we also plot a z = 5.295 triple LBG system, LBG-1, detected in [C ii] but undetected in the dust continuum with ALMA and associated with a z ∼ 5.3 protocluster including a z = 5.2988 SMG, AzTEC-3 (Capak et al. 2011; Riechers et al. 2014). LBG-1 has an SFR comparable to those of z ∼ 4.7–7 LAEs in Figure 7, but its $L_{[{\rm C}\,{\scriptsize{II}}]}$ is about an order of magnitude higher than the LAEs (except for SDF J132408.3+271543 and SDF J132415.7+273058 due to their shallow $L_{[{\rm C}\,{\scriptsize{II}}]}$ limits). Moreover, LBG-1 is on the two local galaxy SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ correlations and at the high SFR and high $L_{[{\rm C}\,{\scriptsize{II}}]}$ edge of the local star-forming galaxy data distribution. According to the analysis of Riechers et al. (2014), though LBG-1 comprises three LBG components and is associated with a protocluster, it does not seem to be a galaxy of extreme type but rather "typical" ${\sim } L_{\rm UV}^*$ star-forming system with relatively low dust content. Furthermore, Riechers et al. (2014) compared the SED of LBG-1, including their ALMA dust continuum upper limit, with those of local galaxies (mostly the same local galaxy templates we and Ouchi et al. (2013) used for the same purpose for IOK-1 and Himiko) and found that LBG-1 is similar to local dwarf/irregular galaxies. Hence, all the information taken together implies that both typical LAEs and LBGs would share SEDs similar to those of local dwarf/irregular galaxies, but LBGs would be more enriched in gas (or higher metallicity) or have different PDR structure/ISM physical state than LAEs. However, to securely confirm this, more observations and sample statistics of typical high-redshift LBGs and LAEs are required. Also, note that LBG-1 is not detected in the dust continuum, but the ALMA observation of this object by Riechers et al. (2014) is a factor of three to seven shallower than those of IOK-1, Himiko, and HCM 6A. Thus, observations of LBGs and LAEs to comparable depth are necessary to fairly compare these two galaxy populations in the context of dust content.

Figure 8 shows the luminosity ratio $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ as a function of FIR luminosity L_FIR plotted for different types of objects: z < 0.1 LIRGs (Maiolino et al. 2009), local normal galaxies (Malhotra et al. 2001),¹⁸ z = 1–2 galaxies including starburst-dominated, AGN-dominated, and mixed systems (Stacey et al. 2010), z = 4.1–7.1 quasar host galaxies (Pety et al. 2004; Maiolino et al. 2005; 2009; Iono et al. 2006; Wagg et al. 2010; Venemans et al. 2012; Wang et al. 2013; Willott et al. 2013), z = 3–6.34 submm galaxies (Iono et al. 2006; Cox et al. 2011; De Breuck et al. 2011; Valtchanov et al. 2011; Walter et al. 2012a; Riechers et al. 2013; Rawle et al. 2014), and a well-known dwarf irregular galaxy, the Large Magellanic Cloud (LMC; Rubin et al. 2009), as well as z ∼ 4.7–7 LAEs, IOK-1 (this study), Himiko (Ouchi et al. 2013), HCM 6A (Kanekar et al. 2013), SDF J132408.3+271543, SDF J132415.7+273058 (González-López et al. 2014), Lyα-1 in the quasar+SMG system BRI 1202-0725 (Carilli et al. 2013), and a z = 5.295 triple LBG system LBG-1 associated with a z ∼ 5.3 protocluster (Capak et al. 2011; Riechers et al. 2014). The [C ii] line is the ²P_3/2 → ²P_1/2 fine-structure line that could be emitted by the gas exposed to far-UV radiation in the PDRs, X-ray dominated regions (XDRs) related to an AGN activity, and/or H ii regions (e.g., Kaufman et al. 1999; Meijerink & Spaans 2005; Stacey et al. 2010). Hence, the fraction of [C ii] line luminosity compared to the total FIR luminosity varies with type of object, reflecting its structure of PDR, XDR, and/or H ii region and physical state of ISM. For example, normal star-forming galaxies in the local universe tend to show very strong [C ii] emission, typically nearly up to an order of magnitude stronger luminosity ratio ($\log L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR} \sim -2.5$ on average) than AGN-powered systems such as quasar host galaxies, (U)LIRGs, and SMGs. Hence, an $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ versus L_FIR diagram can distinguish between different types of objects.

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In Figure 8, we compare the z ∼ 4.7–7 LAEs with other objects. The color coded filled and open circles with arrows indicate their data with L_FIR corrected and uncorrected for the CMB effects, respectively. For IOK-1, Himiko, and HCM 6A, we calculated their L_FIR limits with and without the CMB effects corrected by integrating from 42.5 μm to 122.5 μm the MBBs with $T_{\rm dust}^{z=0}=27.6$ K and β = 1.5 (average of dwarf/irregular galaxies; Skibba et al. 2011) scaled to the upper limits on the FIR continuum flux density, which we corrected and did not correct for the CMB effects. For Himiko, we plot the data based on L_FIR upper limits at 201 × 185 resolution (comparable to the size of Himiko in Lyα), where we assume that Himiko is not detected in dust continuum at any resolution, as well as the data based on the L_FIR's at 08 × 05 resolution, where we assume that Himiko is detected in dust continuum at 3.4 σ significance at this resolution (see the text in Section 3.1.3 for details). For HCM 6A, we used its FIR continuum flux density limit taken from Kanekar et al. (2013). For SDF J132408.3+271543 and SDF J132415.7+273058, we calculated their L_FIR limits with and without the CMB effects corrected by integrating from 42.5 μm to 122.5 μm the template SED of NGC 6946 (Silva et al. 1998) scaled to their upper limits on the FIR continuum flux density provided in González-López et al. (2014), as they have done. For each of z ≃ 6.6–7 LAEs, we used its $L_{[{\rm C}\,{\scriptsize{II}}]}$ limit over a channel width we and each author adopted: 40, 36, 100, 50, and 50 km s⁻¹ for IOK-1, Himiko, HCM 6A, SDF J132408.3+271543, and SDF J132415.7+273058, respectively (Kanekar et al. 2013; González-López et al. 2014). We also plot the data of Lyα-1 derived by Carilli et al. (2013) with the asterisks. The arrows of each LAE data indicate the upper limits on the luminosity ratio $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ at a given L_FIR lower than the upper limit on the L_FIR of that LAE. Comparing the filled and open circles in Figure 8, we notice that omitting to correct for the CMB effects results in underestimation of L_FIR and thus overestimation of the ratio $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ as discussed in Section 3.1.3.

As seen in Figure 8, IOK-1, Himiko, and HCM 6A are in the region occupied by local normal star-forming galaxies. However, these LAEs are apart from the average point of local normal star-forming galaxies, where log L_FIR ∼ 10.6 and $\log L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR} \sim -2.5$, and IOK-1 and HCM 6A are even at the lower $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ edge of the local normal star-forming galaxy region. Meanwhile, SDF J132408.3+271543 and SDF J132415.7+273058 are in the low-redshift LIRG region, probably because their upper limits on $L_{[{\rm C}\,{\scriptsize{II}}]}$ and L_FIR are an order of magnitude shallower than those of other LAEs. Unless we observe them to much deeper limits, we cannot tell if they are also located in the similar positions as the other z ∼ 6.6–7 LAEs in Figure 8.

We also notice that the possible location of IOK-1 and HCM 6A in Figure 8 includes the data point of the LMC, the most nearby dwarf irregular galaxy. This might be consistent with a picture that high-redshift LAEs could be similar to local dwarf/irregular galaxies as inferred from the comparison of the SED of IOK-1 with those of local dwarfs/irregulars in Figure 2. However, this does not necessarily mean that the similarity in dust continuum SEDs guarantees the similarity in $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratios, as we have not detected [C ii] lines and dust continua of IOK-1 and HCM 6A and uncertainties in their $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ are large. In fact, while the possible location of Himiko in Figure 8 in the case that we assume a non-detection in dust continuum as an extended source (the magenta filled circle) includes the data point of the LMC, the $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ upper limit of Himiko in the case that we assume a detection in dust continuum (the black filled circle) is not consistent with the LMC, although both cases (i.e., the L_FIR upper limit and "detected" L_FIR value) are consistent with the dust continuum SEDs of the dwarf/irregular galaxies in Figure 5 of Ouchi et al. (2013). Thus, it seems that the similarity in dust continuum SED does not necessarily mean similar $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratios. Also, we neither have the dust continuum SED data of the LMC that can be compared with those of IOK-1 and Himiko nor $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratio data of dwarf/irregular galaxies whose dust continuum SEDs were compared with those of IOK-1 and Himiko in Figure 2 in this paper and Figure 5 in Ouchi et al. (2013). Thus, at this moment, we cannot tell if high-redshift LAEs are similar to local dwarf/galaxies in dust continuum SED and $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratio simultaneously. To reveal this, we need a statistically large number of dwarf/irregular galaxy data whose dust continuum SEDs and $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratios are available at the same time.

On the other hand, Lyα-1 is in the low-redshift LIRG region or at the border between the regions of local normal star-forming galaxies and low-redshift LIRGs in Figure 8. This could be because it is associated with the special dense environment consisting of a quasar, an SMG, and other LAE and likely a system different from common LAEs but more similar to LIRGs as discussed in Section 3.2.1.

As for LBG-1 in Figure 8, it has a lower L_FIR and/or a higher $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratio than quasar host galaxies, submillimeter galaxies, and z = 1–2 galaxies and is clearly separate from them. LBG-1 is rather close to the locations of low-redshift LIRGs and the high L_FIR edge of local normal galaxies but far apart from the z ∼ 4.7–7 LAEs. It should be noted that as we mentioned earlier, the ALMA observation of LBG-1 by Riechers et al. (2014) is a factor of three to seven shallower than those of IOK-1, Himiko, and HCM 6A. Thus, we cannot tell how different the z ∼ 4.7–7 LAEs and LBG-1 are in L_FIR and $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratio from the current data alone. However, Figure 8 implies that z ∼ 4.7–7 LAEs and LBG-1 cannot have similar L_FIR's and similar $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratios at the same time because the [C ii] line is detected from LBG-1 at the $L_{[{\rm C}\,{\scriptsize{II}}]}$ about an order of magnitude higher than the $L_{[{\rm C}\,{\scriptsize{II}}]}$ or $L_{[{\rm C}\,{\scriptsize{II}}]}$ limits of z ∼ 4.7–7 LAEs (see Figure 7). In any case, observations of more LBGs and LAEs to comparable depth are necessary to fairly compare LAEs and LBGs in the context of L_FIR and $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratio.

The locations of the z ∼ 4.7–7 LAEs in the $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$–L_FIR diagram in Figure 8 are consistent with what is expected from the locations of these LAEs in the SFR–$L_{[{\rm C}\,{\scriptsize{II}}]}$ diagram in Figure 7. These two diagrams together suggest that the z ∼ 6.6–7 LAEs, IOK-1, Himiko, and HCM 6A are similar to but more likely lower than local normal star-forming galaxies in $L_{[{\rm C}\,{\scriptsize{II}}]}$, L_FIR, and $L_{[{\rm C}\,{\scriptsize{II}}]}/L_{\rm FIR}$ ratios. This implies that these LAEs have either lower enriched gas (or metallicity) and dust contents or different PDR structures/physical states of ISM than local star-forming galaxies. Also, the two diagrams imply that the z ∼ 4.7 LAE, Lyα-1, could be a system similar to low-redshift LIRGs.