SEARCH FOR [C ii] EMISSION IN z = 6.5–11 STAR-FORMING GALAXIES

The three Lyα emitters targeted in this study were discovered in the Subaru Deep Field (SDF). Two of the LAEs observed belong to the sample of LAEs at z ∼ 6.6 discovered by Taniguchi et al. (2005). The targets are the brightest LAEs (sources 3 and 4 in their catalog) and have a narrow and bright Lyα emission line. The third LAE (IOK-1) was discovered at z ∼ 7 by Iye et al. (2006). It is one of the brightest and most distant LAEs known to date.

The fourth target, MACS0647-JD, is a lensed Lyman-break galaxy (LBG) discovered behind the galaxy cluster MACSJ0647.7+7015 at z = 0.591 (Coe et al. 2013). The galaxy was discovered as a J-dropout galaxy lensed into three magnified images as part of the Cluster Lensing and Supernova survey with Hubble (CLASH; Postman et al. 2012). The three images of the galaxy, MACS0647-JD1, MACS0647-JD2, and MACS0647-JD3, have magnifications of ∼8, ∼7, and ∼2, respectively. The photometric redshift of the galaxy is $10.7^{+0.6}_{-0.4}$ (95% confidence limits). This is one of the highest-redshift galaxy candidates known to date.

Observations of the three z ∼ 6.5–7 LAEs were carried out using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) between 2008 July and 2010 July. The array configurations used were the most compact, D and E, to minimize phase decoherence and maximize point source sensitivity. The [C ii] line has a rest frequency of 1900.54 GHz (157.74 μm). For the redshifts of the targets, the line is shifted to the 1 mm band. The receivers were tuned to a frequency ∼150 km s⁻¹ bluer than the expected frequency from the redshift determined by the peak of the Lyα line. This is to take into account the possible absorption by the IGM in the Lyα line. The setups provide an instantaneous bandwidth of ∼1.5 GHz (∼1800 km s⁻¹) with a spectral resolution of 31.25 MHz (∼37–39 km s⁻¹).

The observations were processed using MIRIAD (Sault et al. 1995). The absolute flux calibrators used are 3C84, MWC349, 3C273, and Mars, the latter being the most used. As passband calibrators the QSOs 3C273, 3C345, and 0854+201 were used. As a gain calibrator the QSO 1310+323 was used. The time on source for IOK-1 was 58.5 hr, for SDF J132415.7+273058 it was 15.9 hr, and for SDF J132408.3+271543 it was 4.6 hr. The final cubes were made using natural weighting to maximize point source sensitivity. The observations resulted in the following beam sizes: for IOK-1, 186 × 133, position angle (P.A.) =−034; for SDF J132415.7+273058, 192 × 156, P.A. =8345; and for SDF J132408.3+271543, 254 × 201, P.A. =8802 (all targets are D and E configurations). For the D configuration the minimum baseline is 11 m, and the maximum is 150 m. For the E configuration the minimum baseline is 8 m, and the maximum is 66 m. Table 1 summarizes the sensitivities reached for the observations of the LAEs.

Table 1. Summary of Observations and Results for the LAEs

Source	R.A.	Decl.	za	νobsb	σcontc	σlined	$L_{\rm [C\,\scriptsize{II}]}$e	$L_{\rm IR, CMB}^{\rm N6946}$f	SFRdust, CMBg	SFRUVh
	J2000.0	J2000.0		(GHz)	(mJy beam−1)	(mJy beam−1)	(108 L☉)	(1011 L☉)	(M☉ yr−1)	(M☉ yr−1)
IOK–1	13:23:59.80	+27:24:56.0	6.965	238.881	0.19	1.17	<2.05	<6.34	<109.1	∼24
SDF J132415.7	13:24:15.70	+27:30:58.0	6.541	252.154	0.37	2.82	<4.52	<10.3	<177.2	∼34
SDF J132408.3	13:24:08.30	+27:15:43.0	6.554	251.594	0.75	5.67	<10.56	<21.0	<360.9	∼15

Notes. All luminosity upper limits are 3σ. ^aReferences: IOK-1: Iye et al. (2006); Ono et al. (2012)—SDF J132415.7+273058 and SDF J132408.3+271543: Taniguchi et al. (2005) ^bObserving frequencies; tuned ∼125 MHz blueward of the Lyα redshifts for all targets. ^c1σ continuum sensitivity at a 158 μm rest wavelength. ^d1σ [C ii]  line sensitivity over a channel width of 50 km s⁻¹. ^e3σ [C ii]  luminosity limit over a channel width of 50 km s⁻¹ assuming $L_{\rm line} = 1.04 \times 10^{-3} \, I_{\rm line} \, \nu _{\rm rest} (1+z)^{-1}\, D_{\rm L}^{2}$, where the line luminosity, L_line, is measured in L_☉; the velocity integrated flux, I_line = S_line Δv, in Jy km s⁻¹; the rest frequency, ν_rest = ν_obs(1 + z), in GHz; and the luminosity distance, D_L, in Mpc (e.g., Solomon et al. 1992). ^f3σ limit based on the SED of NGC 6946 and including the effect of the CMB. ^g3σ limit based on $L_{\rm IR}^{\rm N6946}$ including the effect of the CMB. ^hUV-based SFR from Jiang et al. (2013).

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All MACS0647-JD observations were carried out in 2012 November as part of a Director's Discretionary Time program with the Plateau de Bure Interferometer (PdBI). The target was observed with four WideX frequency setups (3.6 GHz bandwidth each), covering 80% of the photometric redshift range (z = 10.1–11.1). Two of the three lensed images (JD1 and JD2) are within 18'' of each other, and they were covered in a common 2 mm pointing. The absolute flux calibrators used are MWC349, 2200+420, 3C279, and 0716+714. As gain calibrator the QSO 0716+714 was used. The total on-source time for all tunings was 7.4 hr (six-antenna equivalent). The observations were processed using GILDAS. The beam size of the observations is the following: for MACS0647-JD, 210 × 176, P.A. =1020 (C configuration). For the C configuration the minimum baseline is 22 m, and the maximum is 184 m. Table 2 summarizes the sensitivity reached for the observations of MACS0647-JD.

Table 2. Summary of Observations and Results for MACS0647JD

Parameter	MACS0647-JD1, JD2
Coordinates (J2000) JD1	06:47:55.731, +70:14:35.76
Coordinates (J2000) JD2	06:47:53.112, +70:14:22.94
μ (JD1+JD2)	∼15
Redshift	$10.7^{+0.6}_{-0.4}$
UV SFR	∼1 (M☉ yr−1)
ν	156.7–171.1 (GHz)
σconta	0.17 mJy beam−1
σline (setup A)b	3.31 mJy beam−1
σline (setup B)b	4.12 mJy beam−1
σline (setup C)b	3.19 mJy beam−1
σline (setup D)b	6.42 mJy beam−1
$L_{{[\rm C\,\scriptsize{II}]}}$ (setup C)c	<6.78 × 107 × (μ/15)−1( L☉)
$L_{{[\rm C\,\scriptsize{II}]}}$ (setup D)c	<1.36 × 108 × (μ/15)−1( L☉)
$L_{\rm IR}^{\rm N6946,}$d (corrected CMB)	<1.65 × 1011 × (μ/15)−1( L☉)
SFR (LIR) (corrected CMB)e	<28 × (μ/15)−1 (M☉ yr−1)
SFR ($L_{{[\rm C\,\scriptsize{II}]}}$) (setup C)f	<5 × (μ/15)−1 (M☉ yr−1)
SFR ($L_{{[\rm C\,\scriptsize{II}]}}$) (setup D)f	<9 × (μ/15)−1 (M☉ yr−1)

Notes. All luminosity upper limits are 3σ. References: coordinates, magnification, redshift, and UV SFR from Coe et al. (2013). All the luminosities and SFR are corrected by magnification. ^a1σ continuum sensitivity at a 158 μm rest wavelength. ^b1σ [C ii]  line sensitivity over a channel width of 50 km s⁻¹. ^c3σ [C ii]  luminosity limit over a channel width of 50 km s⁻¹ as in Table 1. The two results correspond to the most sensitive and the least sensitive setups. ^d3σ limit based on the SED of NGC 6946 and including the effect of the CMB. ^e3σ limit based on $L_{\rm IR}^{\rm N6946}$ including the effect of the CMB. ^fBased on the De Looze et al. (2011) $L_{{[\rm C\,\scriptsize{II}]}}\hbox{--} {\rm SFR}$ relation. The two results correspond to the most sensitive and the lest sensitive setups.

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The spectra of the three z ∼ 6.5–7 LAEs are presented in Figure 1, and the spectrum of MACS0647-JD is shown in Figure 2. No significant emission is detected at the redshifted line frequencies or close to them. The observations were sampled to a channel resolution of 50 km s⁻¹ similar to the expected FWHM of the [C ii] emission line (see Section 4.1). We use our nondetections to put constraints on the luminosities of the [C ii] lines for all targets. The results for the LAEs can be seen in Table 1, and those for MACS0647-JD are in Table 2. The upper limits were estimated assuming that the sources were unresolved. For MACS0647-JD the spectra of the two images were corrected by the primary beam pattern before combination. The [C ii] luminosities were estimated assuming that the velocity-integrated flux of the line is I_line = S_line Δv, with S_line being three times the rms of the 50 km s⁻¹ channel and $\Delta v=50{{\rm \thinspace km\thinspace s}^{-1}}$ being the range in velocity (details are given in the notes in Table 1). Using 3σ over a 50 km s⁻¹ channel to estimate the upper limit in the luminosities can result in a underestimation. We point out that for a more conservative estimation the luminosities should be multiplied by a factor of two (i.e., 3σ over 200 km s⁻¹ channel). Assuming a channel width of 200 km s⁻¹, our IOK-1 [C ii] limit is ∼10% deeper than the previous PdBI limit (Walter et al. 2012b).

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No continuum emission is detected in our observations of the three LAEs and the z ∼ 11 LBG. The sensitivity reached for the continuum observations is given in the Table 1 for the LAEs, and a continuum map for the three LAEs is shown in Figure 3. The results for the MACS0647-JD are given in Table 2, and the continuum map is shown in Figure 4. In Section 4.2 we discuss how the cosmic microwave background (CMB) affects our continuum observations, and in Section 4.3 we use our continuum measurements to constrain the nature of our targets.

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Previous studies have presented the nondetection of [C ii] (Walter et al. 2012b; Ouchi et al. 2013) with a channel resolution of 200 km s⁻¹, a choice motivated by the width of the Lyα emission line. We argue that recent observations and models of [C ii] in LAEs suggest that the [C ii] line could be narrower than the previously assumed value.

4.1.1. [C ii] Detection on an LAE at z = 4.7

4.1.2. Himiko Simulations

The CMB radiation emits as a blackbody with a temperature of $T_\mathrm{CMB}^{\,z=0}$ =2.7 K. The temperature of the CMB increases linearly with (1 + z), becoming an important factor to take into account for observations of objects at high redshift. da Cunha et al. (2013) showed the effect of the CMB on observations of high-redshift galaxies. Here we will follow the prescription formulated by da Cunha et al. (2013) to take into account the effects of the CMB in the continuum observations of galaxies at high redshift in the millimeter and submillimeter range. We will apply this prescription to the spectral energy distribution (SED) of the local galaxies as if they would be observed at a given redshift z.

The templates that we use are those presented by Silva et al. (1998) for the galaxies Arp 220, M82, M51, and NGC 6946. For the galaxies assume cold dust with temperature $T_\mathrm{dust}^{\,z=0}$ and an emissivity index β. For Arp 220 we used ${T_\mathrm{dust}^{\,z=0}}=66.7$ K and β = 1.86 (Rangwala et al. 2011), for M82 we used ${T_\mathrm{dust}^{\,z=0}}=48$ K and β = 1 (Colbert et al. 1999), for M51 we used ${T_\mathrm{dust}^{\,z=0}}=24.9$ K and β = 2 (Mentuch Cooper et al. 2012), and for NGC 6946 we used ${T_\mathrm{dust}^{\,z=0}}=26$ K and β = 1.5 (Skibba et al. 2011). At a given redshift the CMB contributes to the dust heating such that the equilibrium temperature is

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

${T_\mathrm{dust}^{\,z=0}}$ is a measurement of the mean dust temperature as determined by a modified blackbody (MBB) fit to an observed galaxy IR SED at z = 0, representing the total IR luminosity of the galaxy. As a representative fit, this is equally applicable to both optically thin galaxies and optically thick galaxies as in the case of Arp 220. As long as the galaxy is transparent to the CMB radiation (true for even Arp 220), Equation (1) holds. The additional heating by the CMB affects the SEDs such that the peak of the emission is shifted to a shorter wavelength and the total luminosity associated with the cold dust is higher by $[{T_\mathrm{dust}}(z)/{T_\mathrm{dust}^{\,z=0}}]^{(4+\beta)}$. We need to modify the intrinsic SED of the galaxies to include this new T_dust(z). The flux density depends on the blackbody radiation for the given temperature,

$$\begin{equation} F_{\nu /(1+z)}\propto B_{\nu }(T_{{\rm dust}}(z)). \end{equation} \tag{ 2 }$$

To include T_dust(z) we have to apply the following factor to convert the intrinsic SED flux density to the emission associated with the new temperature $F^{*}_{\nu /(1+z)}$:

$$\begin{equation} F^{*}_{\nu /(1+z)}=F^{\rm int}_{\nu /(1+z)}\times \frac{B_{\nu }({T_\mathrm{dust}}(z))}{B_{\nu } \left({T_\mathrm{dust}^{\,z=0}} \right)}. \end{equation} \tag{ 3 }$$

This factor will only apply to the part of the SED that corresponds to the emission of the cold dust. To accomplish this, we scale an MBB to the peak of the FIR emission of the SED at ${T_\mathrm{dust}^{\,z=0}}$ and then use this MBB emission to estimate the ratio (R_ν) of emission associated with the cold dust at a given frequency,

$$\begin{equation} R_{\nu } = \frac{K\nu ^{\beta }B_{\nu } \left({T_\mathrm{dust}^{\,z=0}} \right)}{F^{\rm int}_{\nu }}, \end{equation} \tag{ 4 }$$

where K is just the scaling factor. The flux density associated with the new temperature of the cold dust will be

$$\begin{equation} F^{*}_{\nu /(1+z)}=M_{\nu }\times F^{\rm int}_{\nu /(1+z)} \end{equation} \tag{ 5 }$$

with

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

Finally, following da Cunha et al. (2013), we have to take into account the effect of the CMB as an observing background. For this we have to multiply the flux associated with T_dust(z) by C_ν,

$$\begin{equation} C_{\nu }=\left[1-\frac{B_{\nu }({T_\mathrm{CMB}}(z))}{B_{\nu }({T_\mathrm{dust}}(z))}\right], \end{equation} \tag{ 7 }$$

resulting in the observed flux of the galaxies being

$$\begin{equation} F^{\rm obs}_{\nu /(1+z)}=C_{\nu }\times M_{\nu }\times F^{\rm int}_{\nu /(1+z)}, \end{equation} \tag{ 8 }$$

with C_ν × M_ν representing the effect of the CMB in the observations at a given frequency. The same corrections are derived when an optically thick emission is assumed, as in the case of Arp 220.

As we can see in Figure 5, the effect of the CMB decreases the observable flux density at 2 mm by up to a factor of five (in the case of M51) for the galaxy at z ∼ 11 when the temperature of the CMB is higher, as expected. Also, the effect is higher for galaxies with a lower temperature of the cold dust. Galaxies with a temperature of the order of 25–30 K are more affected than those with a temperature of 40–50 K. The CMB effects will be important for estimations of the flux densities of these types of galaxies in the continuum and for correct interpretation of the observations.

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The CMB effects on the [C ii] line observations are similar to those on the continuum. The flux of an emission line observed against the CMB is

$$\begin{equation} \frac{S^{\rm obs}_{\nu /(1+z)}}{S^{\rm int}_{\nu /(1+z)}}=\left[1-\frac{B_{\nu } ({T_\mathrm{CMB}}(z))}{B_{\nu }(T_{\rm exc})}\right], \end{equation} \tag{ 9 }$$

with T_exc being the excitation temperature of the transition. For the case of local thermal equilibrium, when collisions dominate the excitation of the [C ii] line, the excitation temperature of the transition is equal to the kinetic temperature of the gas (T_kin). The kinetic temperature varies for the different [C ii] emission regions. Gas temperatures within PDRs are typically T ∼ 100–500 K (Stacey et al. 2010), for the CNM T ≈ 250 K, for the warm neutral medium (WNM) T ≈ 5000 K, and for the ionized medium T ≈ 8000 K (Vallini et al. 2013). Since the CMB temperature at z = 6.5–11 is much lower than the gas temperature of the [C ii]  emitting region, it will not contribute significantly to the [C ii] excitation but must be taken into account as the background against which the line flux is measured. In most of the [C ii] emission regions, the temperatures are so high that the observed flux of the line against the CMB is similar to the intrinsic flux ($S^{\rm obs}_{\nu /(1+z)}/S^{\rm int}_{\nu /(1+z)}\approx 1$). For the extreme case where the entire [C ii] emission is being produced in PDRs with a temperature of 100 K in a galaxy at z = 11, the observed flux (using Equation (9)) would be 90% of the intrinsic flux. We found this case very unlikely since in low-redshift galaxies the [C ii] emission produced in PDRs is 50%–70% of the total [C ii] luminosity and the gas temperatures associated with the PDRs are higher (Crawford et al. 1985; Carral et al. 1994; Lord et al. 1996; Colbert et al. 1999). We conclude that the CMB effects on the [C ii] line observations are negligible for our observations.

Using the upper limits on the continuum, we compare the targets with the SED templates of local galaxies. For the LAEs, the SEDs of the local galaxies are scaled to the flux of a near-IR filter that is not contaminated by the Lyα emission line. For MACS0647-JD, the filter used for the scaling is the one next to the Lyman break. The photometry of IOK-1 and MACS0647-JD together with the SED of local galaxies is shown in Figure 5. For SDF J132415.7+273058 and SDF J132408.3+271543 (not shown) the situation is very similar: the sources have a similar redshift, the continuum upper limits are comparable and the CMB effects are of the same order. Our upper limit for IOK-1 is comparable to the upper limit found by Walter et al. (2012b) using PdBI observations.

Using the SED of NGC 6946 as a template, we estimate the IR luminosity given the upper limit flux densities, similar to the approach shown by Walter et al. (2012b). We scale the SED of NGC 6946 to the 3σ upper limits of the millimeter observations and integrate from 8 μm to 1 mm (rest frame) to compute the IR luminosity.

The IR luminosity corresponding to this intrinsic SED and the associated star formation rate (SFR; Kennicutt 1998) are given in Table 1 for the LAEs and in Table 2 for MACS0647-JD. We note that estimating the IR luminosity using NGC 6946 without taking into account the CMB results in a significant underestimation of the luminosity upper limits. The IR luminosity limit corrected by the CMB of the LAEs at z ∼ 6.6 is 35% higher than without correcting by the CMB. For IOK-1 at z ∼ 7, the IR luminosity limit is 50% higher than the estimation without correcting by the CMB. For MACS0647-JD at z ∼ 10.7, the IR luminosity limit corrected for the CMB is ∼3.5 times the IR luminosity limit not corrected by the CMB. For galaxies with a cold dust temperature of ∼25 K, the effect of the CMB on the observations is very important at high redshift, and it will significantly limit the feasibility of detecting galaxies that are not extremely starbursting in the IR continuum; it will not greatly affect the detectability of [C ii] emission.

Figure 6 presents our upper limits to $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ and L_FIR together with detections of [C ii] in other galaxies. The arrows represent the region of possible values for $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ and L_FIR (integrated from a 42.5 to 122.5 μm rest frame). If we used UV-based SFR estimates to infer L_FIR, our data points would move across the diagonal arrows toward the region where local galaxies are, putting our $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ upper limits close to the average value found for the local galaxies. The ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ is a measure of how efficient the [C ii] emission is in cooling the gas. The values presented for our targets, $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim -2.9$, do not necessarily imply that [C ii] is not efficient in cooling the gas in these galaxies; it is most likely a consequence of the galaxies having much lower FIR luminosities than our conservative upper limits. Different processes can affect the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$. In galaxies with low extinction and low metallicity, like in Haro 11, about 50% of the [C ii] emission arises from the diffuse ionized medium (Cormier et al. 2012). Variations on the fraction of [C ii] emission associated with the ionized medium will also affect the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$. In some galaxies, the internal dust extinction can affect the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$. In Arp 220, the dust is optically thick at 158 μm and can absorb part of the [C ii] emission, decreasing the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ (Rangwala et al. 2011).

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Diaz-Santos et al. (2013) present the results of a survey of [C ii] in luminous infrared galaxies (LIRGs) observed with the Photodetector Array Camera and Spectrometer (PACS) instrument on board the Herschel Space Observatory. They found a tight correlation between the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ and the far-IR S_ν(63 μm)/S_ν(158 μm) continuum color, independent of their L_IR. They found that the ratio decreases as the average temperature of dust increases, suggesting that the main observable linked to the variation of $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ is the average dust temperature. For galaxies with dust temperatures ∼20 K the average ratio is $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim 10^{-2}$, suggesting that for galaxies like NGC 6946 with a dust temperature of ≈26 K, the ratio $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ should be on the same order of magnitude. Diaz-Santos et al. (2013) also found a correlation between $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ and the luminosity surface density of the mid-IR emitting region ($\Sigma _{\rm IR}=L_{\rm IR}/\pi r^{2}_{\rm mid-IR}$). LIRGs with lower $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ ratios are warmer and more compact. We can use this relation to find a rough estimation of $L_{[\rm C\,\scriptsize{II}]}/L_{\rm FIR}$ for our targets. For r_mid-IR we use the size found in the UV observations of the targets. The half-light radius of IOK-1 is ≈0.62 kpc (Cai et al. 2011). The FWHM size of SDF J132415.7+273058 and SDF J132408.3+271543 is ≈4.0 and 3.2 kpc, respectively (Taniguchi et al. 2005). For MACS0647-JD the delensed half-light radius is ≲0.1 kpc (Coe et al. 2013). Using our L_IR upper limits as an approach to L_IR, we can estimate Σ_IR. For IOK-1 the estimated ratio is $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim -2.9$, for SDF J132415.7+273058 it is $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim -2.5$, and for SDF J132408.3+271543 it is $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim -2.6$. For the LAEs the average of $L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR}$ is similar to the average value for the local galaxies (Figure 6). For MACS0647-JD the estimated ratio is $\log (L_{{[\rm C\,\scriptsize{II}]}}/L_{\rm FIR})\sim -3.2$.

In Figure 7 we present our $L_{{[\rm C\,\scriptsize{II}]}}$ upper limits with the UV SFR estimated for the targets together with upper limit detections for published LAEs (Carilli et al. 2013; Kanekar et al. 2013; Ouchi et al. 2013). The black solid lines corresponds to the relation found by de Looze et al. (2011), with the gray area corresponding to 2σ scatter in the relation. Our upper limits for the [C ii] luminosity fall within the scatter of the SFR $L_{{[\rm C\,\scriptsize{II}]}}$, with the exception of SDF J132408.3+271543, where the upper limit falls above the relation due to the moderate depth of its observations. The detection of the LAE at z = 4.7 (Lyα -1) agrees very well with the relation found by de Looze et al. (2011) using the UV SFR estimated by Ohyama et al. (2004). The upper limits for the lensed LAE at z = 6.56 HCM-6A and Himiko suggest that LAEs at z > 6 could fall below the relation found at low redshift. More observations are needed to clarify if there is an intrinsic difference between the LAEs at z ∼ 4.5 with the higher-redshift population. The high magnification of MACS0647-JD allows us to explore an UV SFR one order of magnitude lower than the ones of the LAEs, showing the advantage of observing lensed galaxies to cover the intrinsically faint population at high redshift.

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Using the same procedure as presented in Vallini et al. (2013) for the [C ii] emission of Himiko, we estimate the emission of [C ii] for IOK-1 at z ∼ 7. For this simulation, the SFR was set to 20 M_☉ yr⁻¹ with a stellar population age of 10 Myr. The metallicity was set to solar to have a conservative estimation of the [C ii] emission. The simulation does not include the emission from PDRs and should be seen as a lower limit. In Figure 8, we show the [C ii] emission produced by the three modeled phases: CNM, WNM, and the ionized medium. Most of the [C ii] emission comes from the CNM (∼50%); the rest comes from the WNM (∼20%) and from the ionized medium (∼30%). For comparison, in Himiko, 95% of the emission is produced in the CNM, and the rest in the WNM. No emission from the ionized medium was modeled in the simulation of Himiko (Vallini et al. 2013). We can also see in the emission that the FWHM of the main peak is ∼50 km s⁻¹, just as expected.

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In Figure 9, we present the integrated flux of [C ii] for a different combination of metallicities and stellar population ages. This shows a strong dependency on the metallicity, which is expected since it is treated linearly with the abundance of [C ii] in the gas. The second main feature of this result is the dependency on the stellar population age. Here we assumed a continuum SFR of 20 M_☉ yr⁻¹; for the older stellar populations a higher number of heating photons come from the UV part of the spectrum. This is a result of using a continuum star formation mode; for a given SFR, older populations have more time to generate young UV-emitting stars. These extra heating photons avoid the cooling of the gas, which decreases the amount of gas in the CNM, where most of the [C ii] emission is produced.

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For a Gaussian emission line, with an FWHM of 50 km s⁻¹ observed at a channel resolution of 200 km s⁻¹, emission lines will be significantly diluted. In the best case scenario of the line falling completely in one channel, we will recover 38% of the peak flux density of the line. This suggests we should carry out observations of a sufficiently high spectral resolution. For example, with a line of FWHM of 50 km s⁻¹ and a channel resolution of 10 km s⁻¹, we expect to recover 97% of the peak flux density of the line.

We use Equation (1) from Hailey-Dunsheath et al. (2010) to give rough upper limits to to the atomic mass associated with PDRs in our targets (assuming all [C ii] would arise from PDRs). For the PDRs conditions we use the result of Vallini et al. (2013) for the temperature and density in the CNM of Himiko, n = 5 × 10⁴ cm⁻³ and T = 250 K. Using our upper limits for [C ii], we obtain the following upper limits to the atomic mass: for IOK-1 $M_{{\rm H\,\scriptsize{I}}}\lesssim 2\times 10^{8}\ {{M}_{\odot }}$, for SDF J132415.7+273058 $M_{{\rm H\,\scriptsize{I}}}\lesssim 4\times 10^{8}\ {{M}_{\odot }}$, for SDF J132408.3+271543 $M_{{\rm H\,\scriptsize{I}}}\lesssim 1\times 10^{9}\ {{M}_{\odot }}$, and for MACS0647-JD $M_{{\rm H\,\scriptsize{I}}}\lesssim 6\times 10^{7}\ {{M}_{\odot }}$. Assuming that the mass of atomic gas is similar to the mass of molecular gas, we can compare our upper limits with the measurements of similar galaxies at lower redshift.

The only molecular gas masses measured in high-redshift UV-selected star-forming galaxies come from the detection of CO transition lines in lensed LBGs. The measured values are ∼4 × 10⁸ M_☉, ∼9 × 10⁸ M_☉, and ∼1 × 10⁹ M_☉ for MS 1512-cB58 (z = 2.73), the cosmic eye (z = 3.07), and MS1358-arc (z = 4.9), respectively (Coppin et al. 2007; Riechers et al. 2010; Livermore et al. 2012). Our upper limits for the LAEs are similar to the values estimated for the observed LBGs. For MACS0647-JD our upper limit for the molecular mass is at least eight times lower than in the observed LBGs.

Using the UV–SFR relation, we can estimate the gas depletion timescales for our targets, assuming $\tau _{\rm dep}=M_{\rm gas}/{\rm SFR_{\rm UV}}$. We estimate upper limits for the depletion time of ≲8, ≲11, and ≲66 Myr for IOK-1, SDF J132415.7+273058, and SDF J132408.3+271543, respectively. For MACS0647-JD the depletion time is ≲60 Myr. The estimated depletion times for the observed lower-redshift lensed LBGs are within the range of ∼7–24 Myr, similar to our upper limits. The depletion times for the LAEs are consistent with the ages of <15 Myr estimated for the young population of LAEs at z ∼ 4.5 found by Finkelstein et al. (2009) and to the simulated LAEs at ∼3.1 with ages <100 Myr (Shimizu et al. 2011). The depletion times of the LBGs are consistent with the LBG phase predicted duration of 20–60 Myr (González et al. 2012).

Saintonge et al. (2013) presented molecular gas masses and depletion timescales for a sample of lensed star-forming galaxies at z = 1.4–3.1. The range of measured molecular gas masses is 5.6 × 10⁹–4 × 10¹¹ M_☉, and that of depletion timescales is 127–1089 Myr. The longer depletion timescales measured for the lower-z sources could indicate that they experience less "extreme" bursts of star formation in comparison to our z > 6.5 sample. However, assuming a higher molecular-to-atomic gas ratio (of at least 5) would put our upper limits within the values measured by Saintonge et al. (2013).