Early Science with the Large Millimeter Telescope: Detection of Dust Emission in Multiple Images of a Normal Galaxy at z > 4 Lensed by a Frontier Fields Cluster

The FFs program¹⁹ started as a large Hubble Space Telescope (HST) survey of low redshift clusters in order to identify and study high-redshift background galaxies that are gravitationally lensed. In this paper, we use the 13-band HST data, the Spitzer-IRAC imaging from 3.6 to 8 μm, and K-band imaging from Keck-MOSFIRE (program N097M and N135M, PI: Marchesini, Brammer et al. 2016). The HST data include the F435W, F606W, F814W, F105W, F125W, F140W, and F160W images from the FF program; the F475W, F625W, F775W, and F850LP images from CLASH (Postman et al. 2012); and the F275W and F336W images from the program GO-13389 (PI: Siana). The v2.1 UV-to-IRAC multi-wavelength photometric catalog used in this paper was constructed following Skelton et al. (2014). The final catalog construction accounting for the intra-cluster light and contamination from brightest cluster galaxies will be described in H. Shipley et al. (2017, in preparation)

Since our target is a multiply imaged, strongly lensed galaxy, interpretation of its intrinsic properties will depend on the lensing model. STScI has released magnification maps as a function of background galaxy redshift for all FF clusters calculated from several independent lensing models.²⁰ In this paper, we use the updated lensing models from Limousin et al. (2016) and Diego et al. (2015), and we verified that our results are robust with other lensing models from STScI (Johnson et al. 2014; Zitrin et al. 2015). We present our results for two different lensing models to give a sense of how the parameters we are interested in (stellar mass, star formation rate, UV slope) change under different lensing models.

In 2014 November and December, we imaged the FF cluster MACSJ0717.5+3745 with AzTEC during early science with the LMT. During early science operations, we used the inner 32 m of the eventual 50 m aperture.²¹ AzTEC is a 1.1 mm bolometer array camera, with a beam size of 8.5 arcsec (FWHM) on the 32 m LMT. Data were taken in good weather conditions (τ_{225 GHz} = 0.05–0.12). The on-source integration time was 21.1 hr. Our map covers 25 sq. arcmin field reaching a mean rms of 0.24 mJy (central rms is 0.19 mJy).

The calibration and analysis of the AzTEC data follow the procedure described in Wilson et al. (2008) and Scott et al. (2008). The results on the number counts and source properties from the full LMT FF program²² will be presented in future papers. Here we focus on a unique and rare source detected in our AzTEC map (MACS0717_Az9), which is coincident with an optically detected, multiply imaged lensed galaxy (known as 5.1/5.2/5.3, Zitrin et al. 2009). This is the only strongly lensed, multiply imaged system detected in our AzTEC survey. Figure 1 left shows AzTEC contours on the HST F160W image; two optical images (labeled 5.2 and 5.1) of the known multiply imaged system are detected with AzTEC (3.7 and 3.3σ respectively). In Section 3.1, we demonstrate that at least half the millimeter flux detected by AzTEC must be associated with this system. A third >3σ AzTEC detection is visible in the top left corner of the left side of Figure 1, but it is unassociated with the multiply imaged system that is the focus of this paper.

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In order to test the robustness of MACS0717_Az9 both as a millimeter source and as the counterpart to the z > 4 multiply imaged galaxy, we perform several simulations. We stress that since we have prior information on the positions of a known multiply imaged galaxy, we have more confidence in lower signal-to-noise detections.

First we determine the chance that our millimeter detections (3.7 and 3.3σ) of the multiple-images 5.2 and 5.1 are spurious. We perform source extraction on 3000 noise maps. As with our original source list, we limit source extraction to regions of the map with noise <0.4 mJy. We detect an average of 1 and 4 random >3.7σ and >3.3σ sources, respectively, in the noise maps. However, the sources we are interested in are not at random positions and specifically we detect two components of a previously known multiply imaged system. With this prior information, we find the chance of randomly detecting a > 3.7σ source within 1 AzTEC beam of 5.2 and a > 3σ source within 1 AzTEC beam of 5.1 is <0.03%. We find the same answer if we vary the position of 5.2 and 5.1 on the map but conserve their relative separation. Therefore, the probability that our millimeter detection of this multiply imaged system (5.1 and 5.2) is a spurious detection is negligible.

Second, we test the chance that we should detect a multiply imaged source given the known lensing models and a model for a background population of millimeter sources. We develop 500 simulated maps using the empirical galaxy evolution model of Béthermin et al. (2012) for the input background millimeter galaxies and the lensing models of MACSJ0717 from the CATS group (Limousin et al. 2016). Here we report results using the cored mass model, and verified that there are no measurable differences with the non-cored mass model. We randomly populate simulated maps with millimeter sources down to intrinsic (e.g., non-lensed) 1.1 mm fluxes of ≥0.01 mJy. Redshifts are assigned to each millimeter source from the Béthermin et al. (2012) model. Then we run the background population through the cluster using the mass model in LENSTOOL (Kneib et al. 1996; Jullo et al. 2007) to find the observed population of millimeter sources and ask how often the millimeter sources are multiply imaged. With no observed flux limit, multiple-image systems are found in all (99.4%) of our simulated maps, with an average of 6–7 systems per map. When we impose an observed flux limit of 0.7 mJy (i.e., >3.5σ), we find that 30% of these multiple systems have at least one image detectable in our simulated maps. Coupled with our estimated completeness limit of 50% at this low flux level (A. Montaña et al. 2017, in preparation), our simulations predict that we will detect one multiply imaged system in our AzTEC map of MACS0717. Besides MACS0717_Az9, there are no other known multiply imaged sources in MACS0717 (using catalogs of known multiply imaged systems, e.g., Limousin et al. 2016) that are individually detected in our AzTEC maps. We take the full list of multiply imaged sources including their magnification values and we stack the intrinsic millimeter flux for each multiply imaged source. We do not find that any other systems are detected, even when averaging the individual components in this way. Furthermore, none of the other AzTEC detections are in regions of strong magnification. Therefore, our simulations predict that we should detect one multiply imaged system like MACS0717_Az9.

Finally, we can further test the robustness of this millimeter detection by showing that the millimeter fluxes that we measure for 5.1, 5.2, and 5.3 are consistent with each other given their known magnifications (see Section 3.1). The results of all three of these simulations and tests show that we have unambiguously detected dust emission in this multiply imaged system.

Before we can discuss the nature of this millimeter source, we need to demonstrate that the multiply imaged system is the correct optical counterpart. From our simulations (A. Montaña et al. 2017, in preparation), we find a positional accuracy for this system of 3.1 arcsec with 90% confidence. Within the search radius of MACS0717_Az9, we find two multiply imaged systems (Figure 1 right): 5.2 (z > 4) and 12.2 (z = 1.71). But our AzTEC map also covers the other multiple images of these systems: 5.1/5.3 and 12.1/12.3 (Figure 1 left). We detect 5.1 in our AzTEC map at 3.3σ. Source 5.3 has a lower magnification; as a result, the measured AzTEC flux is only 1.4σ (Table 1). Both 12.1 and 12.3 are undetected in our AzTEC map. In this Section, we show that the counterpart to MACS0717_Az9 must be 5.2.

The magnifications (μ) are known for all components of systems 5 and 12 (Diego et al. 2015; Limousin et al. 2016), and so we test if the observed fluxes of each component are consistent with the predicted fluxes. Figure 2 left shows the observed fluxes of all three images of system 5 as the solid circles. If we assign some fraction F of the MACS0717_Az9 flux to 5.2 (S_5.2,obs = S_Az9∗F) and the remainder of the flux to 12.2, then we can predict the flux of 5.1 and 5.3 as follows:

$$\begin{eqnarray}&&{S}_{5.1,\mathrm{pred}}=({S}_{5.2,\mathrm{obs}}/{\mu }_{5.2})\times {\mu }_{5.1},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{S}_{5.3,\mathrm{pred}}=({S}_{5.2,\mathrm{obs}}/{\mu }_{5.2})\times {\mu }_{5.3}\end{eqnarray} \tag{ 2 }$$

where μ_5.2, μ_5.1, and μ_5.3 denote the known magnifications of 5.2, 5.1, and 5.3. The triangles and squares in the left panel of Figure 2 show the predicted fluxes from two different lensing models assuming F = 1, which are remarkably consistent with the observed fluxes of 5.1 and 5.3. If instead we perform this calculation assuming the millimeter emission comes from 12.2 (Figure 2 right), we find that the observed fluxes of 12.1 and 12.3 are inconsistent with the expected fluxes under each of the two lensing models.

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Next, we calculate the P-value for all values of F from 0 to 1 under the hypothesis that the predicted fluxes equal the observed fluxes:

$$\begin{eqnarray}&&{S}_{5.1,\mathrm{obs}}-{S}_{5.1,\mathrm{pred}}\sim N(0,{\sigma }_{5.1,\mathrm{obs}}^{2}+{\sigma }_{5.1,\mathrm{pred}}^{2}),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{S}_{5.3,\mathrm{obs}}-{S}_{5.3,\mathrm{pred}}\sim N(0,{\sigma }_{5.3,\mathrm{obs}}^{2}+{\sigma }_{5.3,\mathrm{pred}}^{2})\end{eqnarray} \tag{ 4 }$$

where N is a normal distribution. σ_5.1,pred and σ_5.3,pred include the uncertainties from all quantities in Equations (1) and (2): the flux measurement of 5.2, the magnification of 5.2, and the magnification of 5.1 and 5.3, respectively. We perform this hypothesis test for 5.1, 5.3, 12.1, and 12.3, and combine the P-values using Fisher's method (Fisher 1925). The combined P-value as a function of F is plotted in Figure 3. We can reject the null hypothesis that F ≤ 0.45 at a significance level of 0.05; this means that at least half the flux of MACS0717_Az9 must be associated with 5.2. For the analysis in this paper we assume the most likely scenario: that all of the flux of MACS0717_Az9 is associated with 5.2 (i.e., F = 1). In Section 4.3, we discuss how our main results are affected under the conservative assumption that only half the millimeter flux is associated with 5.2.

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The multiple images (5.1, 5.2, 5.3) have independent redshift estimates from blind photometric redshift catalogs (Figure 4 right, see also Postman et al. 2012) and from the lensing models (Diego et al. 2015; Limousin et al. 2016, see also Johnson et al. 2014; Zitrin et al. 2015). Table 2 summarizes the redshift estimates for each multiple image. As described in Section 3.3, fitting the optical spectral energy distribution gives photometric redshifts of ∼4.4–4.6. The lensing models agree on a redshift of z ≳ 4 for this multiply imaged source, and are consistent with the ±3σ limits from the photometric redshift. Treu et al. (2015) suggest a low redshift solution of z = 0.928 for image 5.1 based on HST grism data. However, we do not see any strong features in the spectrum and this redshift is not compatible with the mass models of MACSJ0717.5+3745.

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In this paper, we consider two redshift solutions: (1) z = 4.1 ± 0.2 from the non-cored mass model of Limousin et al. (2016), and (2) z = 4.3 from the lens model of Diego et al. (2015). Table 2 lists the magnifications for each of these solutions. While a spectroscopic redshift for this multiply imaged system will be important for further studies, the uncertainty in the analysis in this paper is less affected because of the negative K-correction, which makes the relation between millimeter flux and luminosity roughly constant between z = 1–6.

Measuring the UV to near-IR photometry for this multiply imaged system is complicated since the images are extended (Figure 1 right) and resolve into separate entries in our multi-wavelength catalog. We take the weighted mean of these entries to estimate the total flux in each band for 5.1, 5.2, and 5.3. Having three lensed images of the same galaxy provides an independent check on the photometry.

We fit the de-magnified UV to the near-IR photometry using FAST (Kriek et al. 2009) adopting Bruzual & Charlot (2003) stellar populations (BC03), a Chabrier (2003) IMF and a delayed exponentially declining SFH in order to determine the stellar mass. Since we find that this galaxy lies closer to the Small Magellanic Cloud (SMC) dust curve (see Section 4.1), we perform the SED fitting using SMC dust attenuation and sub-solar metallicity²³ (Z = 0.2 × Z_⊙). The difference in stellar mass between a Chabrier (2003) and Kroupa (2001) IMF is negligible (e.g., Speagle et al. 2014). The uncertainties in the stellar masses include the photometric error, the uncertainty in the magnification (including an additional 10% for differential lensing, Section 3.5), and the uncertainty in the SED fitting. The stellar masses and their 68% confidence ranges are given in Table 3. The left panel of Figure 4 shows the SED fits for the z = 4.1 lens model; given the large magnification values for each multiple image, the de-magnified SEDs show very good agreement.

Table 3.  Derived Intrinsic Physical Properties

ID	za	log(M*/[M⊙])	L1600 Åb	β	${\mathrm{SFR}}_{\mathrm{UV}}$	${\mathrm{SFR}}_{\mathrm{IR}}$	${\mathrm{SFR}}_{\mathrm{total}}$	${f}_{\mathrm{obscured}}$ c
		[1σ lower, 1σ upper]	(1010 L⊙)		(${M}_{\odot }\,{\mathrm{yr}}^{-1}$)	(${M}_{\odot }\,{\mathrm{yr}}^{-1}$)	(${M}_{\odot }\,{\mathrm{yr}}^{-1}$)
5.1	4.1	9.87 [9.44, 10.13]	2.03 ± 0.24	−0.47 ± 0.39	3.4 ± 0.4	14.4 ± 6.3	17.8 ± 6.3	0.81
5.2 (MACS0717_Az9)	4.1	9.52 [9.37, 9.76]	2.29 ± 0.23	−0.95 ± 0.33	3.8 ± 0.4	14.6 ± 5.8	18.4 ± 5.8	0.79
5.3	4.1	9.87 [9.52, 10.08]	2.95 ± 0.44	−0.67 ± 0.26	4.9 ± 0.7	14.6 ± 10.8	19.5 ± 10.8	0.75
5 (average)		9.84 [9.58, 9.94]	2.43 ± 0.18	−0.70 ± 0.19	4.1 ± 0.3	14.6 ± 4.5	18.7 ± 4.5	0.78
5.1	4.3	10.16 [9.87, 10.47]	3.51 ± 0.29	−0.48 ± 0.26	5.9 ± 0.5	21.6 ± 9.3	27.5 ± 9.3	0.79
5.2 (MACS0717_Az9)	4.3	9.82 [9.54, 9.96]	2.68 ± 0.25	−0.95 ± 0.30	4.5 ± 0.4	15.3 ± 6.3	19.8 ± 6.3	0.77
5.3	4.3	10.11 [9.72, 10.37]	3.76 ± 0.56	−0.59 ± 0.31	6.3 ± 0.9	16.8 ± 12.8	23.1 ± 12.8	0.73
5 (average)		10.12 [9.82, 10.28]	3.31 ± 0.23	−0.67 ± 0.17	5.5 ± 0.4	17.9 ± 5.7	23.4 ± 5.7	0.76

Notes.

^a From the Limousin et al. (2016) non-cored lensing model (z = 4.1) and the Diego et al. (2015) lensing model (z = 4.3). For corresponding magnifications,see Table 2. ^bL_FUV ∼ 0.97 ×  L_{1600 Å} for these galaxies. ^c ${f}_{\mathrm{obscured}}={\mathrm{SFR}}_{\mathrm{IR}}$/${\mathrm{SFR}}_{\mathrm{total}}$.

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We also fit the de-magnified UV to the near-IR photometry using EAZY (Brammer et al. 2008) to independently determine the photometric redshift. In the right panel of Figure 4, we show the redshift probability distribution for each multiple image and the average of the three. While the redshift solutions from the lensing models are lower, they are consistent within the ±3σ limits of the photometric redshifts from the SED fitting. A spectroscopic redshift for this multiply imaged source will help further refine the lensing models.

The rest-frame UV spectral slope (β, where ${f}_{\lambda }\propto {\lambda }^{\beta }$) is calculated by fitting a power law to the rest-frame photometric data between the wavelength range of 1300–3000 Å. Prior to fitting, the lensing magnification is removed from the photometric data and we propagate the magnification uncertainty. The UV luminosity, ${L}_{1600}={\nu }_{1600}{L}_{\nu }(1600$ Å), is determined using the fitted value for β. Table 3 lists these derived UV properties corrected for magnification for each multiple image and the average of all three.

Our AzTEC detection at 1.1 mm corresponds to a rest wavelength of <220 μm at z > 4, which probes near the peak of the infrared dust emission. At this rest wavelength, we are most sensitive to the IR luminosity and not the dust mass since we are not in the Rayleigh–Jeans tail of the dust distribution (e.g., λ_rest > 250 μm, Scoville et al. 2016). Given the observed faintness of MACS0717_Az9 at 1.1 mm, we do not expect to detected it with Herschel (Rawle et al. 2016). In order to determine the total IR (8–1000 μm) luminosity, L_IR, we must extrapolate using the expected SED for this galaxy. Kirkpatrick et al. (2015) derived representative SED templates from a sample of 343 high-redshift galaxies with extensive IR data including mid-IR spectroscopy. We fit the intrinsic 1.1 mm flux, after correcting for magnification, to the SED template for a typical high-redshift star-forming galaxy (Kirkpatrick et al. 2015). The L_IR of each component of system 5 for the two lensing models are listed in Table 1.

We use the formulas from Murphy et al. (2011b) to calculate the SFRs (assuming a Kroupa IMF). From L_IR and L_FUV, we calculate the obscured SFR_IR and unobscured SFR_UV, respectively. The total SFR is then calculated by summing the IR and UV SFRs. All star formation rate values are listed in Table 3. We find that even though this galaxy has an intrinsically low SFR, at least 75% of the star formation is obscured. We tested our analysis with different SFR calibrations (e.g., Calzetti 2013); the obscured fraction is only slightly lower (65%) and our conclusions are unchanged.

We are assuming that the magnifications derived from the optical lensing maps also apply to the longer wavelength millimeter data. For highly magnified sources, differential lensing becomes important, where extended and compact regions of a galaxy can be magnified by different factors. Hezaveh et al. (2012) model the effects of differential lensing for strongly lensed, dusty galaxies. They find that for moderate magnifications similar to MACS0717_Az9 (μ ∼ 7), the distribution of flux ratios between the extended and compact regions of a galaxy peaks at 1 with a FWHM of ∼0.25 (i.e., ∼10% uncertainty), suggesting that differential lensing does not have a large effect.

In this paper, our main comparison is between the unobscured (UV) and obscured (IR/submm) SFRs. Dusty galaxies have been found to have similar radii of ∼2 kpc as measured in UV and (sub)mm images, while the optical sizes that trace the stellar light are more extended (Swinbank et al. 2010; Hodge et al. 2016). However, the UV and (sub)mm emission is not always co-spatial and can be offset by up to 1 arcsec (e.g., Iono et al. 2006). In order to quantify the range of magnifications that might be applicable to the millimeter emission, we explore a wider area in the non-cored magnification map at z = 4.1. For a lensing magnification of 7.5, 1 arcsecond offset in the source plane corresponds to 2.7 in the image plane. Within a 2.7 arcsec diameter circle around the location of the optical lensed galaxy 5.2 (where μ = 7.5), we find the magnification ranges from 6.0–9.2 with a standard deviation of 0.76. Therefore, if the UV and millimeter emission are not co-spatial and are magnified by different amounts, this would result in an additional uncertainty of ∼10% in the magnification and intrinsic flux that we derive.

Given these two tests of the effects of differential lensing, we conservatively propagate an additional uncertainty of 10% in the lensing magnification factors, which is the best we can do until we are able to spatially resolve the dust emission with ALMA.

UV surveys rely on the UV slope, β, and its dependence on ${L}_{\mathrm{UV}}$ to estimate the dust extinction since IR observations are typically not deep enough. The measured value of β for MACS0717_Az9 is high relative to the distribution of β found for UV-selected galaxies of similar luminosity at z ∼ 4 (Bouwens et al. 2012: β_mean = −2.01, σ = 0.27, see also Bouwens et al. 2016); this means that ${L}_{\mathrm{UV}}$ alone would underestimate the IR luminosity by an order of magnitude.

In Figure 5, we plot the IRX–β relation, which compares the ratio of ${L}_{\mathrm{IR}}$/${L}_{\mathrm{UV}}$ to the UV slope β. The solid curve is the established relationship for local starburst galaxies (Meurer et al. 1999) where z ∼ 2 massive UV-selected galaxies are also found (Reddy et al. 2012). The dotted curve shows the milder dust extinction found in the SMC (Pettini et al. 1998). Capak et al. (2015) found UV-selected galaxies at z ∼ 5 to be closer to this SMC dust curve (see also Murphy et al. 2011a; Lee et al. 2012). Recently, Bouwens et al. (2016) found that sub-L* galaxies also show lower values of IRX, even below the SMC. MACS0717_Az9 is shown as the red and orange stars, which are closer to the SMC dust curve than the Meurer relation, even though the dust-obscured emission dominates the SFR.

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A lower value in IRX–β relative to the starburst relation is usually interpreted to suggest a lower metallicity. It may seem unusual for such a dust-obscured galaxy (75%–80% of star formation is obscured) to have a lower metallicity. Schneider et al. (2016) recently found significant dust emission in a local, metal-poor dwarf galaxy. By comparing to models of chemical evolution, they conclude that dust content may depend more on the density of the interstellar medium (ISM) than the metallicity, and that in situ grain growth should be especially important in the early universe. Future observations of lines sensitive to the ISM density and metallicity such as CO, [C ii], and HCN in MACS0717_Az9 can be used to test this idea.

At a given epoch, the tight relationship between the star formation rate and stellar mass implies that most normal star-forming galaxies are undergoing steady growth (e.g., Daddi et al. 2007; Noeske et al. 2007). The stellar mass of MACS0717_Az9 is well below the estimated knee in the stellar mass function at z ∼ 4 (Muzzin et al. 2013). In order to determine if MACS0717_Az9 is a normal galaxy for this epoch, we compare the position of this galaxy to the estimated extrapolation of the star formation sequence. In Figure 6, we plot the star formation sequence at z = 3–4 from Tomczak et al. (2016). The z ∼ 5 star-forming galaxies detected in submm continuum with ALMA by Capak et al. (2015) and the extreme submillimeter galaxy, GN20 (Pope et al. 2006; Riechers et al. 2014; Tan et al. 2014), are shown for comparison.

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First, we find that MACS0717_Az9 (red and orange stars for two redshift solutions) is consistent with the estimated star formation sequence for this epoch, and that this galaxy resides in a region that is relatively unexplored in the infrared. Given the error bars on MACS0717_Az9 and the uncertainty in the star formation sequence at these low masses, we do not claim that MACS0717_Az9 is below the star formation sequence but we can confidently say that the source is not an extreme starburst galaxy like GN20.

Second, we show that even though this is a normal star-forming galaxy, its SFR is dominated by the obscured component (${\mathrm{SFR}}_{\mathrm{IR}}$ is at least 75% of the total SFR). This underscores the importance of accurately including this obscured component when accounting for the global SFRD, even at these high redshifts and lower stellar masses, and stresses the need for deep and wide IR/submm surveys.

Two recent papers that surveyed the Hubble Ultra Deep Field with ALMA seem to suggest a smaller number of high-redshift galaxies detected in dust emission than expected (Bouwens et al. 2016; Dunlop et al. 2017). Without lensing, a galaxy like MACS0717_Az9 would not have been detected at the depth of the Dunlop et al. (2017) ALMA map. The one z > 3.5 galaxy detected in the Dunlop et al. (2017) observations has a slightly lower stellar mass ($4\times {10}^{9}\,{M}_{\odot }$) and higher ${\mathrm{SFR}}_{\mathrm{IR}}=37\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ than MACS0717_Az9, but is similarly dominated by the dust-obscured star formation (${f}_{\mathrm{obscured}}=0.94$). The high levels of dust obscuration observed in a handful of normal galaxies at z > 4 suggests that we cannot easily rule out the importance of dust emission in galaxies at z > 4.

In the previous sections, we assumed that all of the millimeter flux from MACS0717_Az9 is associated with 5.2 since that is the most likely result from our statistical analysis (Figure 3). Here we explore how our results are affected if only half the flux of MACS0717_Az9 is associated with 5.2. If the millimeter flux is half what we assumed in Table 1, then ${L}_{\mathrm{IR}}=4.9\times {10}^{10}\,{L}_{\odot }$, ${\mathrm{SFR}}_{\mathrm{IR}}=7.3\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, ${\mathrm{SFR}}_{\mathrm{total}}\ =11.4\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ and ${f}_{\mathrm{obscured}}=0.64$, assuming the z = 4.1 lens model. Under this assumption, the obscured SFR is slightly lower, but the total SFR is still dominated by the dust-obscured contribution. This places MACS0717_Az9 even lower on both the star formation sequence (Figure 6) and the IRX–β plot (Figure 5). Therefore, the results and implications discussed in this paper are unchanged. Future observations with ALMA will confirm how much millimeter flux is associated with this multiply imaged source.