Spectral Energy Distributions of Companion Galaxies to z ∼ 6 Quasars

We collected optical and NIR spectroscopic data for the quasars and their respective companions.

We observed the quasars PJ231 and J2100 with the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al. 2010) at the Very Large Telescope (VLT), imaging a total field of view of 1 × 1 arcmin², with a spatial resolution of 02 pixel⁻¹ and a spectral coverage between 4650 Å and 9300 Å. We observed the field of the quasar J2100 using Director's discretionary time (Program ID: 297.A-5054(A), PI: Decarli) during the nights of 2016 August 25 and 26. Sky conditions were good, with seeing varying from 08 to 13. PJ231 was observed on 2017 July 2 as a part of our program 099.A-0682A (PI: Farina) in almost photometric sky conditions and median seeing of 08. We reduced the data using the MUSE Data Reduction Software (Weilbacher et al. 2012, 2014). The final cubes were then post-processed as in Farina et al. (2017). In particular, the pipeline-produced variance cube was rescaled to match the observed variance of the background at each wavelength channel. This allowed us to compute more realistic errors that reflect possible correlations between neighboring voxels. The spectrum of J2100c was extracted with a fixed aperture of 1'' radius centered at the position derived from our ALMA data. In PJ231, the quasar and companion are separated by only 15, requiring careful removal of the quasar contribution. We created a point-spread function (PSF) model directly from the quasar by collapsing the spectral region >2000 km s⁻¹ redward of the Lyα line, at a wavelength not contaminated by strong sky emission. At each wavelength channel, the PSF model was rescaled to match the flux of the quasar within 2 spaxels (04) of the central emission and then subtracted. The spectrum of the companion was then extracted from this PSF-subtracted data cube with an aperture of 1'' radius. A more detailed analysis of this full data set will be presented in E. P. Farina et al. (in preparation).

We also acquired spectra of the quasar J0842 with the Multi-Object Double Spectrograph (MODS; Pogge et al. 2010) at the Large Binocular Telescope (LBT), in binocular mode on 2016 May 8 and 10. The orientation of the slit covered both the quasar and the [C ii] companion galaxy. We used the 12 slit and the GG495 filter. We collected two exposures of 1320 s, for a total of 1^h28^m on target. Data reduction was performed with standard Python and IRAF procedures. In particular, we corrected for bias and flat with the modsCCDRed package¹⁴ and we wavelength- and flux-calibrated the data using IRAF. The wavelength scale was calibrated using bright sky emission lines, delivering an accuracy of ∼0.2 Å at λ > 7000 Å. The standard star GD153 was observed to flux-calibrate the data. We further scale the spectrum of the quasar J0842 to match the observed z_P1 magnitude, as taken from the internal final release, PV3, of the Pan-STARRS1 Survey (z_P1 = 19.92 ± 0.03, Magnier et al. 2016; see also Jiang et al. 2015 for further details on the discovery and the photometry of this quasar). We applied this scaling to the spectrum of the companion, as extracted with a boxcar filter at the position obtained from the ALMA data.

We observed the companions of PJ231 and J0842, and the quasar PJ231, with the Folded-port InfraRed Echelette (FIRE; Simcoe et al. 2008) at the Magellan Baade Telescope. We observed PJ231 and its companion simultaneously, while we performed a blind offset from the quasar to J0842c. The data were reduced following standard techniques, including bias subtraction, flat field, and sky subtraction. The wavelength calibration was obtained using sky emission lines as reference (see also Bañados et al. 2014). We used the standard stars HIP43018 and HIP70419 to flux calibrate and correct for telluric contamination in the spectra of J0842c and PJ231c, respectively; we implemented the absolute flux calibration considering the J magnitude of PJ231 (J AB = 19.66 ± 0.05; Mazzucchelli et al. 2017b).

We show all the spectra extracted at the companion positions in Figure 1. No clear emission from any of the companion's spectra is detected. In all cases, we estimated the 3σ limits on the Lyα emission line as:

$$\begin{eqnarray}&&{F}_{\mathrm{Ly}\alpha ,3\sigma }=3\times \sqrt{\sum _{i=1}^{N}{\mathrm{err}}_{i}^{2}}\times \sum _{i=1}^{N}{\rm{\Delta }}{\lambda }_{i},\end{eqnarray} \tag{ 1 }$$

where err is the error vector, and N is the number of pixels in within a velocity window of (rest frame) 200 km s⁻¹ (i.e., the typical line width measured in LAEs, e.g., Ouchi et al. 2008) around the supposed location of the Lyα emission line (as obtained from the ALMA [C ii] observations). Finally, Δλ = λ_i+1 − λ_i in the considered wavelength interval. Moreover, we calculated the limits on the underlying continuum emission as:

$$\begin{eqnarray}&&{F}_{\mathrm{cont},3\sigma }=3\times \sqrt{\sum _{i=1}^{N}{\mathrm{err}}_{i}^{2}},\end{eqnarray} \tag{ 2 }$$

where we consider here the spectral coverage at hands, excluding noisy regions at the edges. All the estimated values are reported in Table 3.

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We note that the emission from the Lyα line in z ∼ 6–7 LAEs can be redshifted by ∼100–200 km s⁻¹ with respect to the [C ii] line, and/or it can originate from slightly different spatial locations (e.g., Pentericci et al. 2016). Here, the limits we measure by shifting the center of the Lyα emission by ±150 km s⁻¹ are consistent with the fiducial values reported in Table 3, i.e., we do not significantly detect a blue/redshifted line.

We list here the observations and data reduction of the imaging follow-up data, obtained with ground- and space-based instruments.

2.2.1. LUCI/LBT

We imaged the field of J2100 in the J band (λ_c = 1.247 μm and Δλ = 0.305 μm) with the Utility Camera in the Infrared (LUCI1 and LUCI2; Seifert et al. 2003) at the LBT, in binocular mode. We reduced the data following standard techniques, i.e., we subtracted the master dark, divided by the master flat field, and median-combined the frames after subtracting the contribution from the background and after aligning them using field stars. The final astrometric solution used the Gaia Data Release 1 catalog¹⁵ (DR1; Gaia Collaboration et al. 2016a, 2016b) as reference. We flux-calibrated the image with respect to the 2MASS Point Source Catalog. The seeing of the reduced image is 098. We calculated the depth of the image by distributing circular regions with radius equal to half of the seeing over the frame, in areas with no sources. The 1σ error of our image is the standard deviation of the Gaussian distribution of the fluxes calculated in these apertures. We do not detect, at signal-to-noise ratio (S/N) > 3, any emission at the location of the companion, after performing forced photometry in a circular aperture whose diameter is corresponding to the seeing (see Figure 2). The 3σ limit magnitude that we will use in the following analysis is J = 26.24 (F_J = 0.116 μJy; see Table 4).

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Table 4.  Photometric Measurement of the Companion Galaxies to z ∼ 6 Quasars Studied in This Work (See Section 2)

Name	FJ	FF105W	FF140W	F3.6 μm	F4.5 μm	F5.8 μm	F8.0 μm	F1.2 mm
	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(μJy)	(mJy)
SDSS J0842+1218c	⋯	<0.154	<0.061	<0.78	<1.06	<9.54	<12.6	0.36 ± 0.12
PSO J167.6415–13.4960c	⋯	⋯	${0.23}_{0.03}^{0.04}$	<0.78	<1.28	⋯	⋯	0.16 ± 0.03a
PSO J231.6576–20.8335c	⋯	⋯	<0.053	<0.64	<2.79	⋯	⋯	1.73 ± 0.16
CFHQS J2100−1715c	<0.116	⋯	<0.083	<0.53	<1.07	⋯	⋯	2.05 ± 0.27

Note. The limits provided are at 3σ significance.

^aThis flux measurement comes from recent 035, i.e., ∼2 pkpc at z ∼ 6.5, ALMA observations (Neeleman et al. 2019).

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2.2.2. WFC3/HST

We obtained new observations of all the targets studied here with the Wide Field Camera 3 (WFC3), on board the Hubble Space Telescope (HST), using the F140W filter (λ_c = 1.3923 μm and Δλ = 0.384 μm; Program ID:14876, PI:E. Bañados). For the quasar J0842, previous WFC3 observations in the F105W filter (λ_c = 1.0552 nm and Δλ = 0.265 nm) were also retrieved from the Hubble Legacy Archive¹⁶ (Program ID:12184, PI: X. Fan). We refer to Table 2 for further details on this data set. We analyzed both the archival and new observations in a consistent way. We considered the reduced data produced by the HST pipeline, and we took the zero-point photometry from the WFC3 Handbook.¹⁷ We recalibrated the astrometry using the Gaia DR1 catalog (see also Section 2.2.1). We calculated the depth of the images in an analogous way as in Section 2.2.1, considering here circular areas of 04 radius (containing the 84% of the flux from a point source¹⁸ ). We performed aperture photometry using this aperture radius at the positions of the companions. The companion sources of J0842, J2100, and PJ231 were not detected in the F140W filter, and J0842c was also not detected in the F105W image. We report all the 3σ limit fluxes in Table 4. We show the observations of all the fields studied in this work in the F140W filter in Figure 3, and the F105W image of J0842 in Figure 4. In the case of PJ167, the companion is located at a projected distance of only 09, and it is blended with the quasar emission. In order to recover meaningful constraints on the brightness of PJ167c, it is necessary to subtract the quasar contribution by modeling the image PSF. We used the bright star 2MASS J11103221–1330007, in the proximity of PJ167, in order to create an empirical PSF model from the same image. This source is located at a distance of only 30'' from the quasar, limiting the errors due to the changes in the PSF over the field. Its J and H magnitudes from the 2MASS Point Source Catalog are 15.249 and 15.105, respectively. The corresponding J − H color of 0.144 is therefore close to that of the quasar (J − H = 0.216). We shifted, scaled, and subtracted the PSF model from the quasar emission using the software GALFIT (version 3.0.5; Peng et al. 2002, 2010). In Figure 5 we show the native HST image, the PSF star model, and the residual frame, in which the bright quasar emission has been subtracted. The companion galaxy is well isolated, and its F140W PSF magnitude, measured with GALFIT, is equal to 25.48 ± 0.17 (${F}_{{\rm{F}}140{\rm{W}}}\,={0.23}_{-0.03}^{+0.04}\,\mu \mathrm{Jy}$). Diffuse emission extending from the companion to the quasar is also tentatively recovered. Additional, high-resolution imaging and spectroscopy are needed to securely confirm and characterize such emission.

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2.2.3. IRAC/Spitzer

We first compare the SEDs of our companions with those of prototypical galaxies in the local universe. We consider the SEDs of normal star-forming spiral galaxies (M51 and NGC 6946), starbursts (M82), and ultraluminous infrared galaxies (ULIRGs; Arp 220), from Silva et al. (1998). M51 is a nearby (D = 9.6 Mpc) spiral (Sbc) interacting galaxy, which has been studied in detail over a wide range of wavelength and physical scales (e.g., Leroy et al. 2017). NGC 6946, found at a distance of 6.72 Mpc, is an intermediate (Scd) spiral galaxy (Degioia-Eastwood et al. 1984). Its size is approximately a third of that of our Galaxy and it hosts roughly half of the stellar mass (e.g., Engargiola 1991). M82 is a prototypical edge-on starburst (with a galaxy-wide SFR ∼ 10–30 M_⊙ yr⁻¹; Forster Schreiber et al. 2003), whose intense activity has been most probably triggered by a past interaction with the neighboring galaxy M81 (e.g., Yun et al. 1994). Arp 220 is one of the closest (77 Mpc) and best studied ULIRGs, with a total infrared luminosity of L_IR = 1.91 × 10¹² M_⊙ (Armus et al. 2009). It is thought to be the result of a merger that happened ∼3–5 Myr ago (e.g., Joseph & Wright 1985; Baan & Haschick 1995; Scoville et al. 1998; Downes & Eckart 2007), and has extreme conditions in its nucleus (e.g., with an attenuation of A_V = 2 × 10⁵ mag; Scoville et al. 2017)

Here, we shift the observed SEDs of these local galaxies to the redshifts of the companions, and we scale them to match the 1.2 mm flux retrieved in the ALMA observations. We plot the SEDs, together with the photometry of the companions presented here, in Figure 6.

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The limits on rest-frame UV/optical brightness of PJ231c, J2100c, and J0842c rule out all the galaxy templates considered here, with the exception of Arp 220. These companions have infrared luminosities in the range of (ultra-)luminous galaxies (e.g., (0.9–5) × 10¹² L_⊙; Decarli et al. 2017). On the other hand, the rest-frame UV emission of PJ167c is detected in our HST/WFC3 observations (see Section 2). Its UV-to-submillimeter ratio is comparable to that of the star-forming galaxy NGC 6946, while the limits from our Spitzer/IRAC data suggest that it has lower stellar content.

We compute the star formation rates for PJ231c, J2100c, and J0842c assuming that their SEDs are equivalent to that of Arp 220, shifted in redshift and scaled as in Figure 6. We derive their star formation rates from the dust emission in the rest-frame infrared region (SFR_IR), assuming that the nonobscured SFR is negligible (see Section 3.2). We calculate the total IR luminosity by integrating the emission from 3 to 1100 μm, and we measure the SFR as SFR = 1.49 × 10⁻¹⁰ L_IR (Kennicutt & Evans 2012). The obtained values range between 120 and 700 M_⊙ yr⁻¹. We note that, if we had instead assumed a modified blackbody model, ${f}_{\nu }\propto {B}_{\nu }({T}_{d}{\nu }^{\beta })$, and adopted typical parameters for high-redshift galaxies (T_d = 47 K and β = 1.6; e.g., Beelen et al. 2006; Venemans et al. 2016), we would have derived comparable star formation rate values (∼140–800 M_⊙ yr⁻¹; see also Decarli et al. 2017).

We can obtain conservative upper limits on the companion stellar masses by subtracting their gas mass (M_gas) from their dynamical mass (M_dyn). The latter can be obtained from the widths of the [C ii] emission line observed with ALMA (see Decarli et al. 2017). We note, however, that these estimates are based on a number of important assumptions on the companions geometry and dynamics (i.e., they are virialized systems), and that they are obtained from data with a relatively modest resolution of ∼1''. We list all dynamical masses in Table 5. On the other hand, we can estimate M_gas from the dust content (M_dust). We take these values from Decarli et al. (2017): M_dust are measured following the prescription by Downes et al. (1992), while M_gas are obtained assuming a typical gas-to-dust ratio of ∼100 (e.g., Berta et al. 2016). We obtain upper limits on the stellar content ranging between ∼16 and 21 × 10¹⁰ M_⊙. In the following analysis, we utilize the latter values as upper limits on the stellar masses of the companions (see Table 5 and Figures 7 and 8).

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Table 5.  Physical Properties of the Companion Galaxies to z ∼ 6 Quasars Studied in This Work

Name	SFRUV	SFRIR	SFR[C ii]	fobscured =	Mdyn	M*
	(M⊙ yr−1)	(M⊙ yr−1)	(M⊙ yr−1)	SFRIR/SFRUV+IR	(×1010 M⊙)	(×1010 M⊙)
SDSS J0842+1218c	<2	124 ± 54	260 ± 40	>0.98	12 ± 5	<11
PSO J167.6415–13.4960c	11 ± 3	32 ± 4	182 ± 16	0.74 ± 0.20	⋯	${0.84}_{-0.40}^{+0.64}$
PSO J231.6576–20.8335c	<3	709 ± 157	730 ± 100	>0.99	22 ± 8	<16.8
CFHQS J2100−1715c	<3	573 ± 73	360 ± 70	>0.99	27 ± 13	<21.5

Note. We report the unobscured (rest-frame UV) SFRs calculated from our HST/WFC3 observations (Section 3.2), and the obscured (rest-frame IR) contribution from our ALMA data (Sections 3.1 and 3.2). Finally, the dynamical mass estimates and upper limits on the stellar masses are also listed. In the case of PJ167c, the reported stellar mass is that derived from MAGPHYS-high-z (see Section 3.1). We note that the SFR_{[C ii]} values have an additional uncertainty of 0.5 dex due to the scatter around the relationship from De Looze et al. (2014).

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Alternatively, we can compare our photometric measurements with synthetic galaxy templates. We use the SED fitting code MAGPHYS (Da Cunha et al. 2008), which uses an energy balance argument to combine simultaneously the radiation from the stellar component, the dust attenuation, and the re-emission in the rest-frame IR wavelength range. We consider here the MAPGPHYS-high-z extension (Da Cunha et al. 2015), which was specifically designed to characterize a sample of SMGs at 3 < z < 6 (see also Section 3.3). In particular, this version included younger galaxy templates, with higher dust extinction and a wider choice of star formation histories. Nevertheless, fitting the photometry of the companion galaxies presented here with any code is hard, due to the few (and most of the time only one) broadband detections for each source. This is reflected in strong parameter degeneracies in the fit. Another issue is represented by the potentially inappropriate coverage of the parameter space considered in the fitting machine, which might not be modeling the properties of the peculiar galaxies considered here. Therefore we choose to fit only the companion of PJ167, whose emission is retrieved in more than one broad band. In Figure 6, we show the best-fit template from MAGPHYS-high-z for this galaxy. We take the 50th and 16th/84th percentiles of the marginalized probability distributions as the best-fit values and uncertainties of its SFR and stellar mass. The SED of PJ167c is consistent with that of a star-forming galaxy, $\mathrm{SFR}\,={53}_{-19}^{+27}$ M_⊙ yr⁻¹, with a stellar mass of ${M}_{* }={0.84}_{-0.40}^{+0.64}\,\times {10}^{10}$ M_⊙, a moderate dust extinction (${A}_{V}={0.66}_{-0.25}^{+0.35}$ mag) and a dust content of ${M}_{{\rm{d}}}={4.7}_{-1.7}^{+3.7}\times \,{10}^{7}$ M_⊙.

Finally, we note that, given the close spatial/velocity separation of the companions and the quasar hosts, they are very likely found in physical connection. In particular, PJ167c is located at only 5 pkpc/140 km s⁻¹ away from PJ167, and emission linking these systems is observed both in the dust continuum and the [C ii] line (with a smooth velocity gradient; Decarli et al. 2017; Neeleman et al. 2019) and, tentatively, in the rest-frame UV (see Figure 5). This evidence, together with a measured high velocity dispersion of the cool gas (∼150 km s⁻¹; Neeleman et al. 2019) may suggest that these galaxies have already entered an advanced merging stage.

The rest-frame UV emission of galaxies directly traces young stars, i.e., 10–200 Myr old. It is thus an excellent probe of recent star formation, but it is also heavily affected by dust attenuation. The energy of the UV photons is absorbed by the dust, and re-emitted in the IR. Therefore, there also exists a natural correlation between star formation rate and IR emission (see Kennicutt & Evans 2012 for a review).

We here first consider the contribution from the obscured star formation activity, as observed in the rest-frame IR range (SFR_IR). For J2100c, J0842c, and PJ231c, we use the values obtained from the Arp 220 SED (see Section 3.1 and Table 5). In the case of PJ167c, we follow the method described in Section 3.1 to derive its SFR_IR, but, instead of Arp 220, we use the best SED from the MAGPHYS-high-z fit (see Figure 6 and Table 5). An alternative way of computing the star formation rate is through the luminosity of the [C ii] emission line (L_{[C ii]}; e.g., De Looze et al. 2011, 2014; Sargsyan et al. 2012; Herrera-Camus et al. 2015). Here, we take the values of SFR_{[C ii]} reported in Decarli et al. (2017), ranging from ∼260 to ∼730 M_⊙ yr⁻¹, i.e., of the same order of magnitude as those measured from the dust continuum. For PJ167c, we consider the measurement of the [C ii] line from recent high-resolution ALMA observations, i.e., F_{[C ii]} = 1.24 ± 0.09 Jy km s⁻¹ (Neeleman et al. 2019). We measured the corresponding [C ii] luminosity and star formation rate following Carilli & Walter (2013) and De Looze et al. (2014), respectively. In Table 5 we report all the SFR_{[C ii]} values.

On the other hand, we can obtain measurements of (or limits on) the unobscured contribution to the SFR in the companions, using our HST/WFC3 sensitive observations in the F140W filter. We consider the conversion between far-UV (0.155 μm) luminosity (L_FUV) and SFR_UV provided by Kennicutt & Evans (2012):

$$\begin{eqnarray}&&\mathrm{log}\left[\displaystyle \frac{{\mathrm{SFR}}_{\mathrm{UV}}}{{M}_{\odot }\ {\mathrm{yr}}^{-1}}\right]=\mathrm{log}\left[\displaystyle \frac{{L}_{\mathrm{FUV}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right]-{C}_{\mathrm{FUV}}\end{eqnarray} \tag{ 3 }$$

with C_FUV = 43.35. We report in Table 5 the estimated SFR_UV values. The limits achieved by our data are very sensitive, down to a few M_⊙ yr⁻¹. PJ167c, the only companion detected in the rest-frame UV, has an inferred unobscured star formation rate of ∼11 M_⊙ yr⁻¹. We note that the central wavelength of the broadband filter used here (F140W) corresponds to λ_rest ∼ 0.18–0.2 μm for z ∼ 6–6.6, i.e., in between the classically defined FUV and near-UV (NUV; 0.230 μm). In order to check how this impacts our results, we repeat our star formation rate estimates considering the calibration for the NUV (C_NUV = 43.17; Kennicutt & Evans 2012). In this case, we measure SFR values only ∼1.5× larger. We also consider the best SED fit from MAGPHYS-high-z for PJ167c, and we calculate the star formation rate in the exact FUV range. We obtain SFR_UV ∼ 8 M_⊙ yr⁻¹, consistent, within the errors, with the one measured directly from our HST data.

With the exception of PJ167c, the SFRs measured in the IR in the companions studied here are ∼two orders of magnitude larger than the limits we set for the companions rest-frame UV emission. The contribution of SFR_UV to the total star formation budget is therefore negligible. In the case of PJ167c, the unobscured star formation rate is instead only ∼6× lower than the obscured one. Another way of performing this comparison is by looking at the fraction of obscured star formation, defined as ${f}_{\mathrm{obscured}}={\mathrm{SFR}}_{\mathrm{IR}}/{\mathrm{SFR}}_{\mathrm{IR}+\mathrm{UV}}$. Whitaker et al. (2017) reported a tight correlation between this quantity and the stellar mass, irrespective of redshift (up to z < 2.5), in a large sample of star-forming galaxies from CANDELS and SDSS. We calculate (limits on) f_obscured for the galaxies presented here. We report these values in Table 5, and we show them in the context of previous observations in Figure 7. Again, the star formation rate of the companions is highly dominated by SFR_IR, with obscured fractions ranging between 0.74 and 0.99. In particular, taking into account the large uncertainties on M_* and f_obscured, PJ167c is consistent with the expectations from lower-redshift studies. The remaining sources seem to also follow the z < 2.5 trend (with the caution that we are here only able to set upper limits on their stellar masses).

A large number of studies has found a correlation between the SFR and the stellar mass of star-forming galaxies ("main sequence," MS) over a wide redshift range (0 ≲ z ≲ 6; e.g., Brinchmann et al. 2004; Noeske et al. 2007; Rodighiero et al. 2011; Whitaker et al. 2011; for an in-depth analysis of the literature, see Speagle et al. 2014). The tightness (∼0.3−0.2 dex scatter) of this relation has been interpreted as evidence that "regular" star-forming galaxies have smooth star formation histories, in which the majority of the mass is assembled via steady accretion of cool gas from the intergalactic medium on long timescales (e.g., Daddi et al. 2007; Steinhardt et al. 2014). On the other hand, highly starbursting galaxies, which lie above the MS, are also observed, and are thought to grow mainly via efficient, merger-triggered star formation events (e.g., Santini et al. 2014). The MS normalization is observed to evolve with redshift, and this trend suggests that higher specific star formation rates are common at early cosmic times (e.g., Whitaker et al. 2014).

We compare the properties of the companion galaxies considered here with those of typical star-forming galaxies and SMGs at similar redshifts (see Figure 8). We consider the observed MS relation at z ∼ 6 provided by Salmon et al. (2015) and Speagle et al. (2014), together with predictions from semianalytical models by Somerville et al. (2008, 2012). Salmon et al. (2015) examine 3.5 ≤ z ≤ 6.5 galaxies in the GOODS-S field: we take here SFR and M_* values of their ∼200 z ∼ 6 galaxies. Speagle et al. (2014) assemble a comprehensive compilation of 25 studies of the MS at 0 ≲ z ≲ 6. After a careful recalibration of the various data sets, they obtain a robust SFR–M_* relation as a function of the age of the universe (t, here in Gyr):

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{logSFR}[{M}_{* },t]=(0.84-0.026\times t)\mathrm{log}{M}_{* }\\ \ \ -(6.51-0.11\times t).\end{array}\end{eqnarray} \tag{ 4 }$$

They also find a scatter around the MS of ∼0.2 dex, irrespective of redshift. We show this relation, calculated at z = 6 with the representative 0.2 dex scatter, in Figure 8. We consider the semianalytical model by Somerville et al. (2012), who use N-body simulations and several feedback/accretion recipes to specifically reproduce the GOODS-S field. In particular, we consider the MS relation for this model at z ∼ 6, as provided by Salmon et al. (2015; see their Table 4). In addition, we report observed SMGs at 4.5 < z < 6.1 from Da Cunha et al. (2015), whose redshifts and physical parameters were obtained with MAGPHYS-high-z, and at z ∼ 4.5 from Gomez-Guijarro et al. (2018), for which recent ALMA millimeter observations and secure spectroscopic redshifts are available. Finally, we show the massive, extremely starbursting galaxies at z > 6 discovered by Riechers et al. (2013) and Marrone et al. (2018; see Section 1), and z ∼ 5.5 LBGs (Capak et al. 2015).

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We show in Figure 8 the SFR and M_* values obtained with MAGPHYS-high-z for PJ167c. This galaxy lies on the MS at z ∼ 6. For the remaining galaxies, i.e., J2100c, J0842c, and PJ231c, we only consider the obscured star formation rates and the upper limits on the stellar masses (see Section 3.1). These highly conservative constraints place the companions on or above the MS relation.

Future, deeper observations in the IR regime, together with further development of current fitting machines ,will be needed to constrain these galaxies' SEDs and stellar masses.