THE ALMA SPECTROSCOPIC SURVEY IN THE HUBBLE ULTRA DEEP FIELD: SEARCH FOR [${\rm{C}}\,{\rm{II}}$] LINE AND DUST EMISSION IN 6 < z < 8 GALAXIES

We used ALMA to conduct a spectroscopic survey of a region of the Hubble UDF, scanning essentially all of the 1 mm and 3 mm windows, corresponding to the ALMA bands 6 and 3, respectively. Observations were performed in a single pointing in band 3, and using a seven-point mosaic in band 6, to map the same region in the sky, covering roughly a region of ∼1 arcmin² of the HUDF. For details about our survey and blind line search, see Walter et al. (2016)—Paper I in this series.

Our spectral line survey covers the frequency ranges of 84.0–115.0 GHz and 212.0–272.0 GHz of the ALMA bands 3 and 6, respectively, thus encompassing the redshift range of 0 < z < 6 for the CO line emission (see Paper I). Most importantly for this paper, the 1 mm frequency scan covers the redshift range of 5.99 < z < 7.96 for [C ii] line emission. This redshift range is also covered by the 3 mm scan for the CO J = 6 to 8 emission lines (see Figure 1).

Zoom In Zoom Out Reset image size

The survey setup and data reduction steps are described in detail in Walter et al. (2016; Paper I). Here we repeat the most relevant information for the study presented here.

ALMA band 3 and band 6 observations were obtained during Cycle-2 as part of projects 2013.1.00146.S (PI: F. Walter) and 2013.1.00718.S (PI: M. Aravena). Observations in band-3 were conducted between 2014 July 01 and 2015 January 05, and observations were conducted between 2014 December 12 to 2015 April 21 under good weather conditions following observatory project execution restrictions.

Observations in band 3 were performed in a single pointing in spectral scan mode, using five frequency tunings to cover the frequency range of 84.2–114.9 GHz. With this setup, there were a few ranges where there was overlap between independent spectral windows (SPWs). Over this frequency range, the ALMA half power beam width (HPBW), or primary beam (PB), ranges between 61'' and 45''. Observations in band 6 were performed in a seven-point mosaic, using a hexagonal pattern: the central pointing overlaps the other six pointings by about half the ALMA PB, i.e., close to Nyquist sampling. We scanned the band 6 using eight frequency tunings, covering the frequency range of 212.0–272.0 GHz. With this configuration, there is no frequency overlap between independent SPWs, and there are no gaps in frequency. The frequency coverage of the individual frequency setups is shown in Figure 2. Over this frequency range, the ALMA PB ranges between 30'' and 23''.

Zoom In Zoom Out Reset image size

Observations in bands 3 and 6 were taken with ALMA's compact array configurations, C34-2 and C34-1, respectively. The observations used between 30 and 35 antennas in each bands, resulting in synthesized beam sizes of 35 × 20 and 15 × 10 from the low- to high-frequency ends of bands 3 and 6, respectively.

Flux calibration was performed on planets or Jupiter's moons, with passband and phase calibration determined from nearby quasars. Calibration and imaging was done using the Common Astronomy Software Application package (CASA). The calibrated visibilities were inverted using the CASA task CLEAN using natural weighting to create data cubes at different channel resolutions. In particular, for the line search in the 3 mm and 1 mm bands, we created data cubes at 8.0 MHz channel⁻¹ and 31.25 MHz channel⁻¹, equivalent to 24 and 37 km s⁻¹ per channel, respectively.

The final rms varies mildly as a function of frequency, but such variation is mostly dominated by atmospheric lines across the 1 mm window and by the loss of sensitivity at the SPW edges. We find an average rms of 0.53 mJy beam⁻¹ in the 1 mm cube at 31.25 MHz channel⁻¹ resolution (no PB corrected). This is shown in Figure 2: the increased noise in some parts of the spectrum can be explained by the expected variation of the sky transmission.

The noise behavior across the observed frequencies translates into a detection limit on the [C ii] luminosity in the 1 mm scan, as well as luminosity limits for the high-J CO lines covered by our 3 mm scan in the redshift range of 6 < z < 8. Figure 3 shows the luminosity limits obtained in our spectral scans. Assuming a typical line width of 300 km s⁻¹, we find that the 3σ detection limit for the [C ii] luminosity varies between L_{[C ii]} = (1.6–2.5) × 10⁸ L_☉. Over the same redshift range, the 3σ detection limit for the CO(6-5), CO(7-6), and CO(8-7) lines also varies with frequency ranging between L'_CO = (1.2–2.5) × 10⁹ (K km s⁻¹ pc²).

Zoom In Zoom Out Reset image size

The Hubble UDF is the cosmological field with the deepest observations in all important wavebands, with 18,000 cataloged galaxies (Coe et al. 2006). In this study, we use a sample of 58 z > 5.5 optical dropout galaxies that were located within the 1 arcmin² region covered by our 1 mm mosaic in the Hubble UDF. This sample, enabled by the great depth of the UDF in all optical and NIR bands, was compiled from several searches for such objects based on Hubble Space Telescope (HST) imaging over the deepest area, the 4.7 arcmin² eXtremely Deep Field (Illingworth et al. 2013). This includes all available HST Advanced Camera for Surveys optical and Wide Field Camera 3 IR data from the HUDF09, HUDF12 and from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) programs. For more details about these data sets, see Bouwens et al. (2014) and references therein. In particular, we use the most complete catalog of galaxies selected to have photometric redshifts in the range of 5.5–8.5 compiled by Schenker et al. (2013), McLure et al. (2013), and Bouwens et al. (2015). None of these objects have optical or NIR spectroscopy or previously confirmed redshift that could allow us to directly look for the [C ii] line emission in our data cube. The full list of dropout galaxies investigated in this paper is given in Table 1.

The HST observations and dropout catalogs are complemented with recent spectroscopic constraints and redshifts from deep Multi Unit Spectroscopic Explorer (MUSE) integrations taken with the Very Large Telescope (VLT) as part of the Guaranteed Time Observations on the Hubble UDF (R. Bacon et al. 2016, in preparation). These correspond to optical Integral Field Unit spectroscopic observations covering the full region targeted by our ASPECS program, comprising the wavelength range between 4650 and 9200 Å. As such, this provides effective coverage of the Lyα line emission out to redshifts of z < 6.6 down to unprecedented levels. Since our targets are at 6 < z < 8, they can be observed by MUSE in the wavelength range of 8500–9200 Å. Over the area covered by our ASPECS observations, the MUSE spectra reach an emission line limiting flux at 5σ of ∼2 ×  10⁻¹⁹ erg s⁻¹ cm² for a point source within a 1'' aperture and at 8500–9200 Å (measured where no sky emission lines exist).

Photometric redshifts and redshift probability distributions (P(z)) for the sources in this study are computed based using the best-fit chi-square at a given redshift derived from the full set of HST optical and NIR photometry for a source using the EAZY photometric redshift code (Brammer et al. 2008). We use the EAZY_v1.0 template set supplemented by the spectral energy distribution (SED) templates from the Galaxy Evolutionary Synthesis Models (Kotulla et al. 2009). A flat redshift prior is assumed. As such, the full optical and NIR SEDs are taken into account in the computation of the most likely redshifts and distributions.

For the line search, we used a data cube that had been deconvolved using a natural weighting scheme, without PB correction using the CASA task CLEAN. This ensures a similar noise behavior across the image, for all source positions. PB correction is taken into account later on for all subsequent quantitative analyses. In order not to introduce any priors to the inverted cube related to particular sources in the field, we do not apply the clean algorithm and directly work on the dirty images. We do not subtract the continuum because this requires a specific frequency range to subtract on and this could potentially affect the detection of lines in the selected frequency ranges. Instead, after the lines have been searched for, we remove sources coincident with strong continuum or line sources manually.

We performed a line search using the Astronomical Image Processing System task SERCH. The SERCH task uses a Gaussian kernel to convolve the data cube along the frequency axis with an expected input line width, and reports all channels and pixels having a signal-to-noise ratio (S/N) over the specified limit. For our search, we used a set of different Gaussian kernels, from 180 to 500 km s⁻¹ in order to ensure that all possible line widths were considered. We searched for all line peaks with S/N values above 3.5. Here, the S/N is defined as the maximum significance level achieved after convolving over the various Gaussian kernels. This means that the signal and noise levels are defined after averaging each image plane over several channels. We average over velocity ranges from 180 to 500 km s⁻¹, which corresponds to the typical line widths observed in the ISM of star-forming galaxies (e.g., Goto & Toft 2015; Aravena et al. 2016).

Once all line peaks were identified, we used the IDL routine CLUMPFIND (Williams et al. 2011) to isolate individual line peaks and generate a list of line candidates. A full list of 4200 positive line peaks with S/N = 3.5–10 was thus obtained in the 1 mm data cube using this procedure. We note that the blind line search procedure described here is independent of that described in Walter et al. (2016; Paper I), though the searches use a similar line detection algorithm. Both searches were performed to provide independent checks on the reliability of our algorithms, and they result in a similar list of blindly selected line candidates. This can be quantified by the very similar levels of fidelity and completeness of the 1 mm line candidate samples obtained below compared to that of Walter et al. (2016; see Figure 4 in Paper I): in both independent searches, we find fidelity levels of ∼5%–10%, ∼50%, and ∼90%–100% at S/Ns of 4.0, 5.0, and 6.0, respectively. We also find similar completeness levels in both searches, of ∼50%, ∼80%, and ∼100% at 1 mm line flux densities ∼0.5, 1.0, and 1.5 mJy, respectively. Finally, we note that there is little dependency of the completeness on the line widths, particularly for those between 200–500 km s⁻¹ (this is discussed in more detail in Walter et al. 2016). However, both algorithms appear to recover fewer candidates with line widths below ∼100 km s⁻¹.

To establish the significance level at which we can rely on a given line peak selected by our search, we need to measure the fidelity of our line catalog (also termed as "purity"). We quantify the fidelity level of our sample based on the number of negative peaks in our 1 mm cube, using the same line search procedure. The idea is that negative line emitters are unphysical, i.e., they are a good way to quantify the contamination of the list of positive line candidates. We define the fidelity P as (see also Paper I)

$$\begin{eqnarray}&&P(\gt {\rm{S}}/{\rm{N}})=1-\displaystyle \frac{{N}_{\mathrm{negative}}}{{N}_{\mathrm{positive}}},\end{eqnarray} \tag{ 1 }$$

where N_positive and N_negative are the number of positive and negative line candidates found above a given S/N threshold. The top panel in Figure 4 shows the number of positive and negative line peaks above a certain S/N found by our line search algorithm. We find 2875 positive versus 2771 negative line peaks identified within the HPBW or PB of our data, or an excess of 104 positive line peaks. The bottom panel of Figure 4 also shows the fidelity as a function of the derived S/N. At S/N = 5.8, we reach 100% fidelity in our selection, while at S/N = 4.9 we find 50% fidelity. We note that this fidelity level is almost identical to that found in an independent blind line search of CO line emitters for the full 1 mm data cube presented in Walter et al. (2016; Paper I). An important conclusion is that the sample properties are not statistically affected by the different line searching methods used in both studies. Based on this, we set a threshold at the 70% fidelity level or S/N = 5.3 for considering a blind candidate line detection (without optical counterparts), and at 40% fidelity level or S/N = 4.5 for the line candidates associated with optical dropouts at z > 5.5.

Zoom In Zoom Out Reset image size

We check the completeness level of our sample by inserting 200 fake sources into the 1 mm data cube. We run our line search algorithm on this cube and compare the number of recovered sources with the input catalog. We use the same procedure as in Walter et al. (2016; Paper I) to insert sources, and we refer the reader to this paper for details. In short, fake emission line sources are inserted at random positions and frequencies in the cube, assuming a single three-dimensional Gaussian profile with varying line widths and input fluxes. Since the noise level of our cube is affected by different atmospheric features and SPW edges along the frequency axis, the significances of each line detection will vary. We thus compute the completeness level only for those line peaks that are extracted with an S/N level above 4.5, matching the cut in the significance level we have set. Figure 5 shows the completeness level obtained in this way, as a function of flux density computed at the position of the line peak. For sources with S/N > 4.5, our sample reaches 100% completeness at line peak fluxes above 1.5 mJy, while we reach down to 50% completeness at very faint flux levels of 0.7 mJy.

Zoom In Zoom Out Reset image size

We look for possible [C ii] line candidates by directly searching for significant positive line peaks in our 1.2 mm data cube. We restrict this search by setting a limit on the fidelity level down to P = 70%, which is equivalent to a line peak S/N > 5.3. Since the detection of a single line in the 1 mm cube could correspond to CO line emission at lower redshift, we further restrict the sample to those objects that either do not have an obvious optical counterpart in the HUDF catalogs or that have a counterpart with a photometric redshift z > 5.5. The reason to select this fidelity level, compared to the 60% level set in Paper I for detections, is to statistically increase the chances that the identified peak is real as we are explicitly looking for objects that lack or have a faint optical counterpart.

Using this procedure, we found two positive line peaks with S/N = 5.3–5.4 in the 1 mm data cube in which no optical counterpart was identified. Figure 6 shows the millimeter spectra for these line candidates. If we associate these candidate line peaks to the [C ii] emission, they would correspond to redshifts of ∼6.36 and 7.50 for sources IDX25 and IDX34, respectively.

Zoom In Zoom Out Reset image size

For each spectrum, we fit a single Gaussian to the candidate line emission, thereby deriving an integrated intensity (I_{[C ii]}) and line full width at half maximum (FWHM). We checked for extended emission by collapsing each candidate emission line along the frequency axis, and producing an integrated (moment 0) map. This collapsed map was then fitted with a two-dimensional Gaussian. In all cases, the emission was found unresolved and the integrated line intensity obtained in the collapsed map was found to be consistent with the value derived from the fitted spectrum. The integrated intensity as well as the resulting [C ii] luminosities are given in Table 2.

In Figure 6, the location of each frequency setup (SPW) is represented by green bars. Since our frequency setup does not provide frequency overlap between adjacent SPWs, the noise is expected to slightly increase at the SPW edges. This could potentially lead to spurious line peaks along the frequency axis. However, inspection of Figure 6 shows that all of the [C ii] line candidates presented here are located comfortably away (at least ∼100 MHz; or >120 km s⁻¹) from a SPW edge. Furthermore, our line search algorithm, by construction, would discard such line peaks to begin with, as it first convolves the cube along the frequency axis, and thus effectively searches for significant line peaks in the average images centered at a particular channel.

Figure 6 also shows the atmospheric transmission as a function of frequency for PWV = 2.0 (blue curve). Source IDX25 is the only one from these candidates that lies right on top of an atmospheric absorption line, suggesting that this line peak might be produced by this atmospheric feature. However, an atmospheric line should translate into an increase of the overall noise level at a particular frequency and thus not necessarily act to mimic a fake source both in space and frequency. As we will see later on, there is tentative evidence for the parallel detection of CO(6–5) line emission from this source in the 3 mm data cube. For the other two line candidates, there is no further evidence to confirm their emission, and only future spectroscopy with ALMA would be able to confirm their reality.

Figure 7 shows multi-wavelength postage stamps centered at the location of the candidate line emission. In both cases, there is no obvious optical counterpart. IDX25 falls close to a system of nearby galaxies suggesting that the background line emission, if real, could be gravitationally lensed. While there is no quantitative supporting evidence for this scenario, the HST images (see color composite) reveal several blueish sources along the line of sight of the southern bright source. These blue sources do not coincide with the candidate line emission; however, this is expected if the source emission is coming from different regions in the source plane. The only way to verify these blind detections is with deep ALMA follow up.

Zoom In Zoom Out Reset image size

We searched for additional fainter [C ii] candidates, by cross-matching our catalog of line peaks at S/N > 4.5 with the sample of optical dropout galaxies at z_phot = 5.5–8.5 discussed in Section 2.3. In this case, we select all line peaks at S/N > 4.5 that lie within 1'' of the optical position, i.e., less than one synthesized ALMA beam in the 1 mm band. In the redshift range of z = 5.5–8.5, 1'' corresponds to 4.7–8.1 kpc. The targeted significance level translates into a fidelity of 40% for line detection. Statistically, this implies that roughly 60% of our sample of line candidates correspond to spurious detections. Conversely, the positional prior implies that even if the fidelity level is relatively low at the chosen S/N threshold, the coincidence of a line candidate with an optical dropout galaxy will increase the chances that it corresponds to a real [C ii] detection.

In Figure 8, we present the spectra of the 12 identified [C ii] line candidates matched to optical dropout positions. As in the previous section, for each spectrum, we fit Gaussian profiles to the candidate line emission. In all cases, the collapsed line map source emission was found to be unresolved and the integrated line intensity obtained in the collapsed map was found to be consistent with the value derived from the fitted spectrum. The integrated intensity as well as the resulting [C ii] luminosities are given in Table 2.

Zoom In Zoom Out Reset image size

Figure 8 also shows the location of each frequency setup (SPW) and the atmospheric transmission as a function of frequency. In two cases, ID30 and ID41, the candidate line peak is located at the same frequency as a SPW edge. For ID41, this also coincides with the location of an atmospheric line, strongly suggesting that this line peak is produced by a noise artifact.

In Figure 9, we present the ALMA 1.2 mm continuum and line maps of our optically selected [C ii] line candidates centered at the location of the identified line emission. All of the line candidates are recovered in the collapsed line maps, indicating that the features seen in the spectra are not caused by increased noise at a particular frequency. This is expected since our line search algorithm does average over frequency to isolate individual peaks. By selection, the candidate [C ii] line emission is located within 1'' from the optical high-redshift counterpart; however, in the cases of ID02, ID04, ID09, ID31, and ID44, the coincidence is remarkably closer (within 05).

Zoom In Zoom Out Reset image size

It is difficult to argue that closer associations are more likely. While, in a statistical sense, this is correct, it is always possible that the offset is physical, as it has been argued in previous studies (Capak et al. 2015; Maiolino et al. 2015). None of the sources are detected in continuum emission, yet a few cases show a positive, low-significance continuum signal at the location of the candidate [C ii] emission (ID04, ID27, ID31).

An important piece of information comes from the comparison between the optical/NIR photometric redshift and their probability distributions with the candidate [C ii] redshifts. As mentioned above, the optical galaxies in our study have been selected to have photometric redshifts in the range of 5.5–8.5. Although these sources are faint, even for the deep HST images, the photometric redshifts can still be constrained to within Δz = 0.5 based on the redshifted Lyman break.

Figure 10 shows the redshift probability distributions for the optical associations to the [C ii] line candidates. The red line represents the [C ii]-based redshift estimate. In all cases, the peak in the probability distribution is produced at z > 5. In four cases, there is a non-negligible chance that it could correspond to a lower redshift galaxy at z ∼ 2 (sources ID02, ID38, ID41, and ID49). In most cases, there is a large disagreement between the redshift implied by the identified millimeter line and the bulk of the redshift probability distributions. For sources ID02, ID04, ID27, ID30, ID31, ID44, and ID52 this disagreement is above the 95% confidence level (2σ). For the cases of ID14, ID38, ID41, and ID49, there is better agreement; however, in the latter three cases, this is likely driven by the poorer constraints on the photometric redshift estimate (i.e., broader probability distributions).

Zoom In Zoom Out Reset image size

Even though we have selected millimeter spectra from locations that are consistent with high-redshift galaxies—i.e., undetected in the optical or with an optical dropout counterpart—it is likely that the majority of our candidate [C ii] lines are either spurious (based on fidelity) or have a different identification than [C ii]. The latter case could have two reasons: there could be a dust-obscured galaxy along the line of sight that is not visible by HST (e.g., the case of HDF 850.1, Walter et al. 2012), or the high-redshift identification is not correct; e.g., an optical dropout candidate, selected based on the identification of the redshifted 1216 Å Lyman break, could also correspond to a lower redshift passive galaxy in which instead the redshifted 4000 Å Balmer break has been identified. We have thus used two important sources of information to reject other redshift possibilities and assess the reality of our [C ii] line candidates, as described below.

3.6.1. MUSE Complementary Information

3.6.2. ALMA 3 mm Scan Constraints

The large frequency coverage of our ALMA observations in the 1 mm band resulted in a very deep collapsed continuum image reaching down to 12.7 μJy in the central regions of the mosaic (see Aravena et al. 2016a, Paper II). Despite the great depth of the continuum map, none of our sources show obvious continuum emission at the 3σ level, even though three sources are associated with ∼2–3σ blobs in the 1.2 mm map (ID04, ID27, and ID31; see Table 2). Our 1.2 mm continuum map reaches a noise level of ∼13–35 μJy over the area where our [C ii] candidates are located (within PB = 0.5). This implies an upper limit of ∼40–100 μJy (3σ) for the 1.2 mm continuum emission of individual objects (see Table 2).

To reach deeper continuum levels, we measure the average emission by stacking the 1 mm continuum map at the location of all the optical dropouts covered by our 1.2 mm mosaic and also at the location of our [C ii] line candidates. In the first case, we use the optical positions to guide the stacking, while in the second case we stack at the location of the [C ii] peaks. Using the positions of the optical associations in the second case, when available, do not alter the results. For the stacking, we extract image cutouts centered at the location of our sources. From this, we compute a weighted average of the individual cutout images, using the sensitivity pattern of the mosaic as weight. In order to avoid contamination from bright sources, we explicitly avoid sources that are within 5'' from the brightest 6 continuum sources detected in our 1.2 mm mosaic.

Zoom In Zoom Out Reset image size

The outcome of the stacking is shown in Figure 12. The stack of the [C ii] line candidates yields a tentative detection at the ∼3σ level with a measured peak flux density of 14 ± 5 μJy. The uncertainty here merely represents the noise in the stacked image. No detection is found in the stack of the optical dropout galaxies yielding a 3σ upper limit of 6 μJy at 1.2 mm. This might not be too surprising given that we expect about 40% of the sample to be composed of real sources based on our purity estimates. However, the detection in the continuum does not provide information of the redshift of these sources or the reality of the [C ii] line emission, since their continuum emission could be produced by sources at lower redshifts.

Zoom In Zoom Out Reset image size

We use these continuum measurements to place a constraint on the far-IR luminosity and SFR of our sources. We adopt a modified blackbody dust model of the form ${S}_{\nu }\ \propto (1+z){D}_{L}^{-2}{M}_{{\rm{d}}}{\kappa }_{\nu }[{B}_{\nu }({T}_{{\rm{d}}})-{B}_{\nu }({T}_{\mathrm{BG}})]$ that becomes optically thick at a wavelength of 100 μm. Here, S_ν represents the observed flux density, z is the source redshift, D_L is the luminosity distance, B_ν is the Planck function, and T_BG is the CMB temperature at the source redshift. M_d and T_d are the dust mass and temperature, respectively. We consider a dust absorption coefficient of the form ${\kappa }_{\nu }={\kappa }_{0}{(\nu /{\nu }_{0})}^{\beta }$, where we adopt a dust emissivity index of β = 1.8 (Kovács et al. 2006; Magdis et al. 2011) and κ₀ = 0.4 cm² gr⁻¹ at 250 GHz (Kruegel & Siebenmorgen 1994). We assume a typical dust temperature of T_d = 50 K at z ∼ 6–8, motivated by recent predictions for the evolution of the dust temperature as T_d = 35 × ((1 + z)/2.5)^0.32 K (see Bouwens et al. 2016; Paper VI but also Bethermin et al. 2015).

For the redshift range of z = 6–8, the average 1.2 mm flux measurement on the [C ii] candidate sample translates into an FIR luminosity (40–500 μm) L_FIR = (2.7 ± 0.9) × 10¹⁰ L_☉. This luminosity value is almost insensitive to small variations on the emissivity index, with β ∼ 1.5–1.8, or variations in redshift as it varies little in the range of z = 6–8. For a Chabrier (2003) initial mass function, this translates into an average IR-derived SFR of 3 ± 1 M_☉ yr⁻¹. However, according to da Cunha et al. (2015), the detectability of the dust continuum against the CMB would decrease drastically at lower dust temperatures. Assuming lower dust temperatures in our calculations, T_d = 25 K, yields FIR luminosity and SFR_IR estimates of a factor of (2.5–3.0) lower. This suggests that the non-detection of most of the [C ii] line candidates could be due to low intrinsic dust temperatures, as well as low SFR_IR.

This tentative detection thus raises the question about the sources that should have been detected in 1.2 mm continuum emission based on their UV-based SFRs. This is the case for ID27 and ID31, which have SFR_UV ∼ 10 and 12 M_☉ yr⁻¹. In both cases, however, there is positive continuum peak within 1'' from the [C ii] candidate position. At the location of the 1.2 mm continuum peak position, we measure S_1.2mm = 34 ± 12 μJy (2.8σ) and 30 ± 13 μJy (2.3σ) for ID27 and ID31, respectively. Using the models presented above (T_d = 50 K), these fluxes yield IR-derived SFRs of ∼8 and 7 M_☉ yr⁻¹, respectively, comparable to the UV-derived SFR values.

The average IR-derived SFR estimate obtained for the [C ii] candidate sample is comparable to its average UV-derived SFR of 2.5 M_☉ yr⁻¹. On average for this sample, we find an IR excess of IRX = SFR_IR/SFR_UV ∼ 1, suggesting that ∼50% of the emission related to star formation in these sources is obscured. For the two individual sources with marginal 1.2 mm continuum detections, ID27 and ID31, this ratio ranges between ∼0.6 and 0.8. Our measurements for the [C ii] candidate sample are consistent with the results reported in Bouwens et al. (2016; Paper VI) using larger samples of star-forming galaxies at z = 4–10 (see also Capak et al. 2015). Note that this also implies SFR_tot = SFR_UV+IR ∼ 2 × SFR_UV, and thus to recover the total SFR value for our galaxies, we need to apply an average correction of ∼2 to the UV-derived SFR (see Section 4.1).

Based on observations of local galaxies, it has recently been suggested that a scaling relation between the SFR and the [C ii] luminosity of galaxies of different types exists (De Looze et al. 2011, 2014; Sargsyan et al. 2012; Cormier et al. 2015; Herrera-Camus et al. 2015; Olsen et al. 2015; Vallini et al. 2015). De Looze et al. (2014) argued that galaxies with lower metallicities and higher dust temperatures, as expected for high-redshift galaxies, would tend to have larger scatter in this relationship, with possibly increasing [C ii] luminosities for a given SFR value. However, recent [C ii] line observations of a sample of dwarf galaxies show that low metallicity galaxies do not have systematically higher [C ii] to IR luminosity ratios (Cormier et al. 2015). It is thus interesting to examine the location of our [C ii] line candidates in the SFR versus [C ii] luminosity plot (SFR–L_{[C ii]}).

Figure 13 presents the [C ii] luminosity and SFR for our [C ii] line candidates in the UDF, compared to previous [C ii] line detections of non-quasar galaxies at z > 5 (González-López et al. 2014; Ota et al. 2014; Capak et al. 2015; Maiolino et al. 2015; Willott et al. 2015; Knudsen et al. 2016). In this plot, we also compare our observations with the relationships found for local galaxies with different environments and metallicities (e.g., De Looze et al. 2014) and simulations of high-redshift galaxies (Vallini et al. 2015). Most of these studies, including the recent [C ii] detections at z > 5 quote total SFRs, including both obscured and unobscured star-formation components. Since the IR-derived SFR appears to be comparable to the UV-derived SFR in our [C ii] line candidate sample, SFR_IR/SFR_UV ∼ 1 or SFR_tot ∼ 2 × SFR_UV (see Section 3.7), we simply apply a factor of two correction to each individual UV-derived SFR value in our sample. This effectively translates into a shift of 0.3 dex to higher SFRs in Figure 13.

Zoom In Zoom Out Reset image size

Two important things can be extracted from Figure 13. First, most of the high-redshift galaxies with previous [C ii] detections seem to agree, at least to first order, with the local calibrations for SFR–L_{[C ii]}. Second, only three of our candidates are located in this region of the plot, with the rest have SFRs that are too low. These sources would need to have obscured SFRs a factor >10 larger than their SFR_UV to be placed in the local SFR–[C ii] relationship. However, if these sources had SFR_IR ∼ 5–10 M_☉ yr⁻¹—implying that they are highly obscured as most of their emission would be produced in the IR—they would still be at the limit of what can be individually detected in our 1.2 mm continuum map, assuming T_d ∼ 50 K, similar to what is observed in ID27 and ID31 discussed in Section 3.7.

It would therefore be tempting to simply discard the [C ii] line candidates that have SFR_UV < 5–10 M_☉ yr⁻¹. However, the possibility that low SFR galaxies could indeed have significant [C ii] line emission has recently been suggested by the ALMA detection of [C ii] line emission in the vicinity of the normal star-forming galaxy BDF-3299 at z = 7.1, shown as an SFR upper limit in Figure 13 (Maiolino et al. 2015).

Furthermore, and along the same line, most of the galaxies so far detected in [C ii] emission at z > 5 have been pre-selected based on their SFR, a strong Lyα line or high-equivalent width, with typical SFR values above 25 M_☉ yr⁻¹. However, our sample is mostly composed of galaxies with SFR <10 M_☉ yr⁻¹ selected only based on the existence of a Lyman break (Section 2.3). Thus, it is possible that the physical properties of the different samples could differ significantly (e.g., metallicities). In any case, we do not claim that all of the lower–SFR [C ii] candidates are real. In fact, based on statistical grounds, we expect ∼60% of them not to be real lines, as discussed in Section 3.2.

The number of [C ii] line candidates in our ALMA survey of the UDF allow us to investigate the [C ii] luminosity function in the redshift range of 6 < z < 8. Since all of our sources are just candidates, all of the numbers derived here in the following effectively correspond to upper limits until we are able to confirm at least one of of these objects. In the future, this can be done by either deeper integrations to confirm the candidate lines and/or by securing their redshift by detecting a second emission line.

We compute the number counts in two ways. The first assumes that only the brightest [C ii] line candidate (IDX04) is real, and the second uses all the line candidates correcting for purity and completeness at the significance level of the sample at S/N = 4.5, using the values computed in Section 3.2. We thus measure the [C ii] luminosity function by counting the number of [C ii] line candidates within the cosmic comoving volume spanned between z = 6 to z = 8. For the ∼1 arcmin² area of the sky covered by our survey, this volume corresponds to 4678 Mpc³.

Figure 14 shows the observed [C ii] luminosity function at 6 < z < 8 in the UDF. We compare our measurements with the recent constraints obtained by Swinbank et al. (2014) based on the serendipitous detection of two [C ii] line emitters at z = 4.4. We also compare our measurements with the expected [C ii] luminosity function for local galaxies (Swinbank et al. 2014). The latter uses the local IR luminosity function (Sanders et al. 2003) and extrapolates it using either the apparent variation of the [C ii]/IR luminosity ratio with IR luminosity (Brauher et al. 2008), or a fixed ratio of [C ii]/IR = 0.002. We also compare to recent predictions for the [C ii] luminosity function at z = 6–8 by Popping et al. (2016).

Zoom In Zoom Out Reset image size

Our observations show a disagreement of more than an order of magnitude on the number counts with respect to recent models (e.g., Popping et al. 2016). They tend to agree with the IR-derived local [C ii] luminosity function for a fixed [C ii]/IR ratio as well as a rough agreement with Swinbank et al. (2014) measurements based on the two bright submillimeter galaxies (lower limit). If at least one of our [C ii] line candidates is confirmed, this would point to a less abrupt fall on the [C ii] number counts at high redshift than predicted by current models.