ALMA 200 pc Resolution Imaging of Smooth Cold Dusty Disks in Typical z ∼ 3 Star-forming Galaxies

Figure 2 shows the rest-frame 240 μm emission of UDF1. The cold dust emission is spatially resolved into ≃60 resolution elements (the area enclosed within the FWHM extent). It is best modeled in the uv plane by two concentric elliptical Gaussians with integrated fluxes of 1.56 ± 0.16 mJy and 1.84 ± 0.16 mJy (corrected for the primary beam attenuation), and with FWHMs of 0.67 ± 0.04 × 0.63 ± 0.03 kpc and 1.90 ± 0.20 × 1.76 ± 0.18 kpc. A single elliptical Gaussian model can only recover 83% of the integrated flux, leaving an extended halolike residual and necessitating a second, larger component (we will touch on the possibility of the model being a single Sérsic component in Section 4.1). After removing these two components, the background noise is uniform; no residual ≳3σ remains (the local σ = 15.7 μJy beam⁻¹).

The HST H₁₆₀ emission is dominated by a point source (i.e., a point-spread function) and a fainter Sérsic component, likely representing the AGN and disklike emission, respectively. The Sérsic component has an effective radius r_e = 3.16 ± 0.17 kpc and a Sérsic index n = 2.13 ± 0.13. There appears to be an offset of 013 between the Sérsic component and the AGN (Figure 1 and Appendix A), which may be a sign of a recent interaction. The cold dust is cospatial with the AGN/point source, that is, the dust emission is cospatial with the AGN and offset from the stellar mass centroid. There are no off-center star-forming clumps in the HST rest-frame UV images.

The rest-frame 240 μm emission of UDF2 is spatially resolved into ≃70 resolution elements. The source is well modeled with two concentric elliptical Gaussians: one bright, extended component, and a fainter compact one, nicknamed hereafter as the "disk" and "core," respectively. The disk is best modeled by an elliptical Gaussian with an FWHM of 3.63 ± 0.17 × 1.51 ± 0.09 kpc, with an integrated flux of 2.0 ± 0.1 mJy. The core is modeled by an elliptical Gaussian with an FWHM of 0.79 ± 0.05 × 0.36 ± 0.04 kpc and a flux of 0.80 ± 0.05 mJy. These two components were fitted simultaneously, yielding a combined flux of 2.80 ± 0.1 mJy. After subtracting the core and disk from the image, no residual peak ≳3σ remains (local σ = 9.6 μJy beam⁻¹).

The H₁₆₀ morphology is significantly disturbed. Full morphological modeling using GALFIT requires fitting simultaneously six components to yield a uniform residual image (model shown in Appendix A). There are two dominant ones: a Sérsic disk and a compact component indicating a substantial concentration of stellar mass. The dominant Sérsic component has an effective radius r_e = 3.71 ± 0.06 kpc, a Sérsic index n = 0.73 ± 0.04, and a position angle of 56° ± 1°. There is a broad similarity in the orientation of the optical Sérsic component and that of the dust disk, PA = 16° ± 3°. However, the misalignment is significant, undermining the interpretation that they originate from a common physical structure. Subtracting only the dominant Sérsic component reveals multiple stellar mass substructures (Figure 1); the dust emission is not cospatial with any of them. The offset from the dust emission peak to the largest stellar mass concentration is ∼025. The offset between the centroid of the best-fit Sérsic component and dust emission is ≲1/6th of the effective diameter of the Sérsic component. That is, the cold dust emission appears to originate within the geometric centroid of the stellar distribution that could be characterized as the core area of UDF2. However, the region of dust emission is devoid of stellar mass substructures, which could be an effect of strong extinction associated with the dust concentration.

None of the remaining four stellar mass substructures coincide with the dust emission; they have a range of offsets of 03–13 (2–10 kpc) from its center. These substructures have corresponding counterparts in the HST i₇₇₅ and V₆₀₆ images that probe the rest-frame emission at ≃1300–2200 Å, suggesting that they harbor unobscured star formation. The SFR of these substructures is <1 ${M}_{\odot }$ yr⁻¹, less than 0.5% of the total SFR.

The dust emission of UDF7 is well modeled with an elliptical Gaussian and a cospatial point source, with the point source a factor of 4 fainter than the Gaussian component. The Gaussian FWHM is 0.90 ± 0.10 × 0.29 ± 0.07 kpc in size, containing 0.58 ± 0.05 mJy of integrated flux, whereas the point source is 0.13 ± 0.03 mJy (both corrected for the primary beam attenuation). This is an example where the uv-based analysis is necessary to measure the size of the dust-emitting region, as the minor axis of the Gaussian is comparable in size to the native beam. After subtracting the two components, no residual peak ≳3σ remains (local σ = 17.6 μJy beam⁻¹).

The H₁₆₀ image shows complex morphology, requiring five components to model using GALFIT (Appendix A). The dominant Sérsic component has r_e = 3.95 ± 0.04 kpc and n = 1.17 ± 0.01, with a ≃01 offset from the centroid of the dust emission. Nevertheless, given that the dust emission is very compact, it originates entirely from the central area of the stellar mass concentration. There are five distinct rest-UV-bright clumps identifiable in the i₇₇₅ and V₆₀₆ images, with counterparts in every band out to H₁₆₀, indicating considerable underlying stellar mass. No cold dust feature is observed at the positions of these star-forming clumps. The dominant Sérsic component is marginally detected in the V₆₀₆ image, but it is fainter than the UV star-forming clumps. Again, the unobscured star formation in UDF7 contributes <1 ${M}_{\odot }$ yr⁻¹ to the global star formation.

We will first focus on the recent reports of star-forming substructures at z ≃ 1–3 from optical and near-IR observations. As clump properties depend strongly on the SFR of their host galaxy, we will discuss the results in the following descending order of SFR: Genzel et al. (2011), Wisnioski et al. (2012), Swinbank et al. (2012), Guo et al. (2018), and Soto et al. (2017).

The Genzel et al. (2011) sample of five typical SFGs is the most similar to our HUDF galaxies in terms of redshift, SFR, and stellar mass: z ∼ 2.3, SFR ≃ 70–180 ${M}_{\odot }$ yr⁻¹, and log(M_*/${M}_{\odot }$) ≃ 10.3–11.0. The galaxies are drawn from the spatially resolved spectroscopic sample of Hα emission using VLT/SINFONI (Förster Schreiber et al. 2009); additional AO-assisted SINFONI observations were conducted to achieve a typical resolution of 02. (Genzel et al. 2011). More than 20 kpc-sized star-forming clumps are found in five galaxies with individual clumps the sites of SFRs of 3–40 ${M}_{\odot }$ yr⁻¹ (typically 10–20 ${M}_{\odot }$ yr⁻¹), which are 6%–20% of the total SFR in each galaxy (we will refer to this percentage as the "fractional SFR" hereafter) based on their Hα emission. Such star-forming clumps, especially considering their fractional SFR, would have been very strongly detected if any existed in our HUDF galaxies.

Wisnioski et al. (2012) describe a sample at a slightly more recent cosmic epoch, z ≃ 1.3, and less strong SFRs, 20–50 ${M}_{\odot }$ yr⁻¹, but similar stellar masses, log(M_*/${M}_{\odot }$) ≃ 10.7–11.0, i.e., those assembling their stellar mass at relatively later time compared to the Genzel et al. (2011) sample. They find eight clumps in three galaxies from spatially resolved Hα observations using Keck/OSIRIS. Overall, their clumps contain a median SFR of 4 ${M}_{\odot }$ yr⁻¹, which is 13% in terms of the median fractional SFR. The Swinbank et al. (2012) sample of AO-assisted SINFONI spatially resolved Hα spectroscopy of nine galaxies, drawn from a narrowband Hα imaging survey, is at similar redshifts of z ≈ 0.8 and 1.4 but with a much lower median stellar mass of log(M_*/${M}_{\odot }$) ≈ 10.1. With the total host SFRs of 1–10 ${M}_{\odot }$ yr⁻¹, the SFR of individual clumps is also smaller at 0.5–2.9 ${M}_{\odot }$ yr⁻¹, implying an even larger fractional SFR of ∼25%. Our imaging sensitivity is not sufficient to detect the level of SFRs in the individual Wisnioski et al. (2012) and Swinbank et al. (2012) clumps if they are at z = 3 (possibly detecting two to three clumps from the former). However, if the fractional SFRs in our targets were as large as in these hosts, they would also have been well detected.

For completeness, we also consider the comprehensive selections of rest-frame UV clumps by Soto et al. (2017) and Guo et al. (2018) using the HST rest-frame far-UV and near-UV imaging, respectively. At z = 1.5–3.0, the Guo et al. (2018) catalog contains 1083 clumps in 501 galaxies; the selection bands are the CANDELS imaging at V₆₀₆ for 1.0 ≤ z ≤ 2.0 and i₇₇₅ for 2.0 ≤ z ≤ 3.0 galaxies. These clumps have a median log(M_*/${M}_{\odot }$) of 8.4 (see the stellar mass of gravitationally lensed star-forming clumps in Section 4.2.2) and a median SFR of the clumps and hosts of 1.2 and 22.2 ${M}_{\odot }$ yr⁻¹, respectively (7% fractional SFR). At lower redshifts (z = 0.5–1.5), the Soto et al. (2017) sample contains typical SFGs selected from HST F225W, F275W, and F336W imaging, with median stellar mass and SFR of ≃10⁷ ${M}_{\odot }$ and 0.29 ${M}_{\odot }$ yr⁻¹, respectively, again, with a fractional SFR of 5%. We would not be able to detect these unobscured UV clumps if they are at z = 3, as evident from the optical comparisons in Section 3.1. Two UV clumps in UDF7, the brightest in the optical among our three galaxies, are actually cataloged by Guo et al. (2018), but no dust emission is observed at their locations.

The sensitivity and resolution of sub/millimeter observations have only started to approach optical observations with the advent of ALMA, and still can only reach the more luminous SFR regimes. A majority of high-resolution (e.g., resolution ≲02) studies of unlensed galaxies with ALMA were carried out on SMGs selected from single-dish surveys (e.g., the JCMT and APEX surveys of COSMOS, ECDFS, and UDS at 850 μm and 1.1 mm by Scott et al. 2008; Weiß et al. 2009; Geach et al. 2017). These surveys pushed their sensitivities to the limit of the confusion noise, typically ∼1 mJy, yielding reliable detections above sub/millimeter fluxes of ∼4 mJy, and hence the parent samples for the following observations are populated by luminous SFGs.

Iono et al. (2016) carried out 350 GHz ALMA observations of three sources from the AzTEC survey in COSMOS (AzTEC-1, 4, and 8; z = 3.12–4.34) with SFR ∼ 1300–2800 ${M}_{\odot }$ yr⁻¹ at angular resolutions of 15–50 mas. They reported spatially resolving the sources into multiple substructures; two of the brightest ones in AzTEC-1 (each with SFR ≃ 50 ${M}_{\odot }$ yr⁻¹) were confirmed with CO (4−3) kinematics by Tadaki et al. (2018). Hodge et al. (2016) observed 16 sources from the ALESS survey (Hodge et al. 2013) at 354 GHz with 016 resolution, revealing them to be extended dust disks with typical diameters of 3.6 ± 0.4 kpc. While a majority of the Hodge et al. (2016) galaxies appear smooth at their resolution and sensitivity, some do show signs of substructures. Hodge et al. (2016) demonstrated with simulations that at moderate S/Ns of 5–10, smooth disks can be broken up into visually convincing spurious clumps. However, with improved ALMA data, Hodge et al. (2019) have shown many of the clumps in these galaxies to be real (Section 4.2.3 is dedicated to discussing this result). Similarly, dust continuum and [C ii] imaging at 30 mas resolution by Gullberg et al. (2018) of four z ≃ 4.4–4.8 SMGs visually show multitudes of substructures. As with Hodge et al., they caution that there is a significant probability that this result may be consistent with a smooth disk. These studies are reminders that high-fidelity observations are required in pushing the resolution and sensitivity of interferometric imaging to search for star-forming substructures.

As a result of the confusion limit, even the comparably faint single-dish-selected SMGs are brighter in the far-IR than typical SFGs: they have typical S_{870 μm} of 5–15 mJy (Weiß et al. 2009; Hodge et al. 2013), whereas massive main-sequence SFGs have S_{870 μm} of about 1–3 mJy at z ∼ 3 (Scoville et al. 2017 and those in this work). As discussed in the following section, observations of gravitationally lensed main-sequence SFGs at z ∼ 2–3 also provide no evidence of substructures. To date, there is no confirmed report of substructures in the bulk of star formation in main-sequence SFGs at z ∼ 2–3.

Strong gravitational lensing by a galaxy or galaxy cluster preserves surface brightness while spatially magnifying background sources by a factor of as much as a few hundreds. With proper lens modeling, this technique allows current-generation observing facilities to capture high-resolution details in distant galaxies not otherwise feasible. Highly magnifying lenses are often selected from optical surveys of galaxy clusters by identifying bright, extended arcs (e.g., Gladders & Yee 2005; Bayliss 2012).

Gravitational lensing provides more tests for clumps at lower redshifts (z ≲ 2) and/or at lower SFRs. Recent observations of these lensed "giant arcs" often achieve physical resolution in the source plane of ≃50–100 pc. For example, Sharon et al. (2012) and Wuyts et al. (2014) observed a giant lensed arc RCSGA 0327 with HST and Keck/OSIRIS, a z = 1.70 galaxy forming stars at 29 ± 8 ${M}_{\odot }$ yr⁻¹. Source reconstruction indicated at least seven star-forming clumps, each 300–600 pc in diameter. In SDSS J1110 + 6459, a z = 2.48 galaxy with a global SFR of 8.5 ${M}_{\odot }$ yr⁻¹, Johnson et al. (2017a, 2017b) reported 27 clumps, each 60–100 pc in diameter and forming stars at a few 10⁻³ ${M}_{\odot }$ yr⁻¹(see also Jones et al. 2010; Menéndez-Delmestre et al. 2013; Livermore et al. 2015; Girard et al. 2018).

Cava et al. (2018) reported 55 star-forming clumps in the "Cosmic Snake," a galaxy at z = 1.04 forming stars at 30 ${M}_{\odot }$ yr⁻¹. The background galaxy is lensed into two images: a highly magnified one with magnifications of tens to more than 200 along the namesake arc and a much less magnified counterimage that has a magnification of 4.5. The physical resolution that can be reconstructed from the Snake is as small as 30 pc, whereas the resolution from the counterimage is limited to 300 pc (comparable to HST's). Notably, the clumps identified from the 30 pc image have an average mass of log(M_*/${M}_{\odot }$) = 8.0, compared with log(M_*/${M}_{\odot }$) = 8.7 from the 300 pc reconstruction; the sizes of the clumps identified in the 300 pc image are also twice as large (after correcting for the lensing effect). The differences highlight the fictitious increase in clump size and mass when measured at lower resolution, due to clusters of smaller clumps blending together into the appearance of larger clumps, even with other systematics mitigated by observing the same background source via a natural lens.

Similar results have been reported by others. Dessauges-Zavadsky et al. (2017) compared luminosities and stellar masses of star-forming clumps identified from unlensed and lensed galaxies from the literature and found a systematic difference. Clump stellar masses from lensed galaxies have median log(M_*/${M}_{\odot }$) ≃ 7.0 while the median of those from field galaxies is log(M_*/${M}_{\odot }$) ≃ 8.9. This is also reflected in their median luminosity, M_V, with distributions peaking at M_V ≃ −19 and ≃−17 for the field and lensed galaxies, respectively. The field identification of clumps primarily relies on HST imaging with spatial resolution of 01, corresponding to ≃1 kpc at z ∼ 1–3. Dessauges-Zavadsky et al. (2017) suggest that the limited spatial resolution and the propensity of the intrinsically ∼100pc star-forming clumps with log(M_*/${M}_{\odot }$) ∼ 7–8 to cluster may be responsible for the appearance of giant kiloparsec clumps with log(M_*/${M}_{\odot }$) ≃ 9. Similarly, Rigby et al. (2017) smoothed the model image of the aforementioned SDSS J1110+6459 to simulate the resolution of HST and found that the intrinsic 27 clumps were blended together into a single disk with Sérsic index n = 1.0 ± 0.4 and r_e = 2.7 ± 0.3 (see also a similar result from smoothing low-z galaxy images to simulate z ∼ 2 galaxies by Fisher et al. 2017). It remains an open question whether giant, massive kiloparsec-scale star-forming clumps really do exist and whether clump–clump mergers are capable of producing such massive clumps in the course of their evolution. We will revisit the topic of intrinsic clump sizes from the theoretical perspective in Section 4.2.5.

While the selection of optically bright giant arcs in galaxy clusters affords extraordinary magnification to characterize the intrinsic clumps, it also selects hosts with relatively low SFR that are, by necessity, unobscured. The clumps identified are therefore more similar to rest-frame UV clumps such as those described by Soto et al. (2017) and Guo et al. (2018). Again, highly magnified galaxies in the far-IR are needed to probe the substructures in the bulk of star formation in massive main-sequence SFGs such as those of our HUDF targets.

A notable far-IR search for clumps in main-sequence SFGs at z > 2 was conducted on the strongly lensed "Eyelash." Swinbank et al. (2010) reported four clumps of 100–300 pc diameter in this gravitationally lensed typical SFG with a total unlensed SFR of 210 ± 50 ${M}_{\odot }$ yr⁻¹ at z = 2.33. The reported star-forming substructures are clearly visible at 4σ–7σ in their 870 μm image from the Submillimeter Array (SMA; Swinbank et al. 2010). However, recent ALMA observations at multiple bands with higher sensitivity than those from the SMA indicate that the Eyelash is morphologically smooth (Falgarone et al. 2017; R. J. Ivison et al. 2019, in preparation). While this is a gravitationally lensed system, the disagreement is unrelated to the lens, but rather to the challenges of interferometric imaging.

The most prolific approach to identify far-IR lenses is to conduct large-area shallow surveys for far-IR-bright sources. This is because the bright end of the far-IR number counts plummets rapidly above, e.g., an S_{500 μm} of 100 mJy, such that the fraction of lensed galaxies above this range is near unity (Negrello et al. 2017). The largest samples of far-IR lenses were identified from surveys such as the South Pole Telescope (SPT) 87 deg² surveys at 1.4 and 2.0 mm (Vieira et al. 2010) and the Herschel-ATLAS 570 deg² survey at 100–500 μm (Eales et al. 2010). Far-IR lenses selected from this approach tend to be luminous SFGs at higher redshifts, due to the combination of the aforementioned efficient lens selection at bright far-IR flux and the larger effect of the negative K-correction at z ≳ 2. For example, the Spilker et al. (2016) sample of SPT lenses has a median redshift z = 4.3 and median SFR of 1100 ${M}_{\odot }$ yr⁻¹.

The highest resolution and fidelity observations of a lensed system to date are those of SDP.81 at z = 3.0, identified from Herschel-ATLAS, as part of the ALMA long baseline campaign (ALMA Partnership et al. 2015), which revealed multiple substructures. Given a Toomre parameter Q of ≃0.3, SDP.81 is likely a merger system that drives an intense SFR of ≃500 ${M}_{\odot }$ yr⁻¹ at high star formation efficiency (Dye et al. 2015; Swinbank et al. 2015). Swinbank et al. (2015) and Tamura et al. (2015) reported 5 and 35 star-forming clumps, respectively, from the same data; this apparent disagreement illustrates the challenge in clump identification even with high-fidelity data. As with interferometric imaging of star-forming substructures in field galaxies (Section 4.2.1), low S/N clumps in lensed sources are subject to the same pitfalls of a smooth disk being broken into clumps, because gravitational lensing preserves surface brightness. The ≥5σ clumps reported by Swinbank et al. (2015) are 200–300 pc in diameter after correcting for lensing effects. Such clumps should be well detected in our ALMA data, given their large fractional SFR (Figure 1 of Swinbank et al. 2015) and the comparable sensitivity between our observations and those of SDP.81 (10 versus 11 μJy beam⁻¹ rms at Band 7, respectively) to the rest-frame 240–250 μm dust continuum. However, SDP.81 is ≃5 mJy at 880 μm after correcting for the lensing magnification (Dye et al. 2015; continuum magnification assumed), i.e., more similar in the far-IR flux to SMGs (Section 4.2.3) and two to three times brighter than our HUDF galaxies. While challenging, future high-fidelity observations similar to those of SDP.81, but on lensed sources identified to be representative of main-sequence SFGs, are needed to study intrinsic clumps in the typical SFG population.

Hodge et al. (2019), hereafter H19, found multiple clumplike star-forming substructures in six SMGs based on high-fidelity ALMA observations (we use the terms "clump" and "substructure" interchangeably in the following discussion). Observationally, the difference between their and our samples is primarily the far-IR flux densities, due to the selection from single-dish versus ALMA deep-field observations. As all six H19 SMGs are clumpy, whereas all three SFGs in our sample are clumpless, H19 provides a direct comparison sample to investigate the difference between the two.

The six SMGs are at z = 1.53–4.86 in the ECDFS. As with ours, their observations were at 870 μm. They were first identified from a single-dish survey (LESS, Weiß et al. 2009) and followed up with ALMA during Cycle 0 at 1''–3'' resolution (ALESS; Hodge et al. 2013), from which 16 SMGs were selected for 016 resolution observations by Hodge et al. (2016). From these 16 SMGs, six among the brightest (to minimize the observing time) were selected for 70 mas observations with rms sensitivities of 22–26 μJy beam⁻¹, i.e., the same band, approximately a factor of 2 larger synthesized beam diameter, and a factor of 2 less sensitive than our work.

For a rigorous comparison, we took the pipeline product of the H19 archival data (ALMA#2016.1.00048.S) and analyzed the calibrated visibilities in the uv plane with GILDAS using an identical procedure to that for our data (Section 2.3). We fitted all components of the SMGs simultaneously with all parameters of every component being free. Components were added to the model one by one in increasing order of free parameters (e.g., point, circular Gaussian, elliptical Gaussian); the simultaneous fit was rerun each time as necessary to achieve a uniform residual after subtraction, shown in Figure 3. These components and their parameters are listed in Table 4 in Appendix B. The differences between the two data sets are evident: while the HUDF galaxies are well modeled by two cospatial Gaussians, the H19 SMGs require multiple additional small components, confirming the presence of dust substructures reported by H19.

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After modeling all components of each source in the uv plane, we identify their far-IR substructures by subtracting the dominant components, defined by those positions coinciding with the peak emission. As shown in Table 4, there is little ambiguity as to which components are the dominant ones in all cases except that of ALESS 112.1, where there are two dominant components with integrated fluxes of 2.0 ± 0.1 and 2.3 ± 0.2 mJy; we subtract the former because it is at the location of the peak flux of the source. The substructure maps are shown in Figure 3 along with their source models and the ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ maps. Our images are similar to those in H19 from modeling in the image plane; the general agreement shows that the differences between the HUDF and H19 samples are not an artifact of the reductions.

Assuming a constant dust temperature and IMF, i.e., that the SFR varies linearly with the rest-frame 150–350 μm dust emission, the typical fractional SFRs in substructures in the H19 SMGs range from 4% to 10%, with two substructures being as large as 30%–36%. Clearly, this is higher than the 1%–7% (3σ) upper limits in our HUDF galaxies. The average integrated flux of the H19 galaxies from our measurement is 8.0 mJy, whereas the average for HUDF galaxies is 2.3 mJy (see Tables 2 and 4). The presence of dust substructures and the brighter far-IR fluxes are the two concrete observational differences between the HUDF and H19 samples.

While our analysis agreed with H19 in the presence of substructures in H19 SMGs, there are some differences in the identity, size, and flux of the substructures between our morphological decomposition and those of H19. The fraction of total flux contained in individual substructures reported by H19 is smaller (2%–8%) than we have found (2%–36%). These differences could be attributable to, e.g., the choice of model for the main component (single exponential versus nested Gaussians) or the differences in the residual noise characteristics between our substructure maps in Figure 3 and those of H19 (their Figure 3, rightmost column), which serves to highlight the range of possible answers that can arise from the methodological differences.

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The fact that the H19 substructures are found to be as bright (or in some cases brighter than) as the entire HUDF galaxy, illustrated in Figure 4, has an important observational implication. Specifically, some of the H19 substructures have S_{870 μm} and physical sizes comparable to our faintest HUDF galaxy, UDF7, e.g., structure# 3 in ALESS 3.1 and structure# 3 in ALESS 17.1, among others (Table 4). Because UDF7 is significantly detected (≳17σ), even near the edge of our primary beam, substructures such as those in the H19 SMGs would also be well detected if they are present in the HUDF galaxies. This negates the concern that the twice higher resolution of our observations (i.e., four times smaller beam area) may lack the surface brightness sensitivity to detect substructures such as those of H19.

To take a closer look at the physical differences (and commonalities) between our HUDF galaxies and the H19 SMGs, we estimate the L_IR, SFR, and stellar masses of the ALESS sample consistently using the same method as described in Section 2.5 using the most recent photometry and redshift. The most significant revisions in the available data from the previously published estimates are the HST H₁₆₀ photometry from Chen et al. (2015) and the 2 mm photometry from ALMA program# 2015.1.00948.S (PI: da Cunha). The optical-to-8 μm and 24–870 μm photometry were taken from Simpson et al. (2014) and Swinbank et al. (2014), respectively, with the addition of the VIDEO and HSC observations (Jarvis et al. 2013; Ni et al. 2019); the z_spec were from H19.

While the M_dust and L_IR are relatively well constrained with the far-IR photometry, estimating the stellar mass is challenging for the H19 SMGs. They are undetected or not significantly detected at any optical/IR bands except at 3.6–8.0 μm. As a result, the SFH, age, metallicity, and extinction, on which stellar mass estimates strongly depend, cannot be firmly constrained. To quantify the extent of these systematics, we experimented with two independent methods, deriving the ALESS stellar masses using the HYPERZ (Bolzonella et al. 2000) and the Pérez-González et al. (2008) codes (i.e., the same as with the HUDF galaxies in Section 2.5), and compared them with the H19 estimates based on MAGPHYS. For the HYPERZ fit, we adopt a constant SFH, the BC03 models with stellar population age priors ranging from 0.05 to 0.4 Gyr, Chabrier IMF, and the Calzetti attenuation law. For the estimates with the Pérez-González et al. (2008) code, we adopt exponentially declining BC03 models with Chabrier IMF, the Calzetti attenuation law and no assumptions about metallicity. Additionally, we explore a range of τ from a single stellar population to constant star formation models; A_V up to 5 mag is allowed. We find a broad agreement of stellar mass estimates from the two methods, but they are significantly lower (in two cases an order of magnitude lower) than the estimates from MAGPHYS. While some of these differences can be attributed to the assumptions of stellar population properties, both MAGPHYS' and our approaches could be affected by different pitfalls: ours from not having a firm constraint on dust extinction (whereby A_V is underestimated), and MAGPHYS from assuming the energy-balancing argument despite the dislocations between the stellar mass buildup and intensely star-forming regions (illustrated by the optical/submillimeter comparisons in Figure 2 of H19). As a result, MAGPHYS could systematically overestimate the A_V of any stellar mass buildup that is not cospatial with the dusty star-forming regions. It is possible that our stellar mass estimates are too low and H19's too high. The conundrums facing both the conventional and energy-balancing approaches will be required to be definitively resolved by JWST and next-generation extremely large telescopes (see also a comprehensive analysis of various stellar mass estimators of SMGs based on simulations by Michałowski et al. 2014). For the purpose of comparing the H19 and HUDF samples, we adopt the average of the estimates from our two methods as the H19 stellar masses, tabulated in Table 3, along with the H19 values for comparison.¹⁷ At the broadest level, this exercise cautions that care is needed in interpreting results pertaining to stellar masses for these extremely dust-obscured SMGs.

Table 3.  Submillimeter-selected Galaxies in the Hodge et al. (2019) ALESS Sample

ID	R.A.	Decl.	z	M*	M*,H19	LIR	SFR	Mdust	Mgas	fgas
	(deg)	(deg)		(log ${M}_{\odot }$)	(log ${M}_{\odot }$)	(log L⊙)	(log ${M}_{\odot }$)	(log ${M}_{\odot }$)	(log ${M}_{\odot }$)
ALESS 3.1	53.33964	−27.9224	3.374	10.2 ± 0.2	${11.30}_{-0.24}^{+0.19}$	12.89 ± 0.03	880 ± 30	9.45 ± 0.04	10.9 ± 0.2	0.8 ± 0.1
ALESS 9.1	53.04722	−27.8700	4.867	10.8 ± 0.3	...	13.33 ± 0.06	2430 ± 160	9.21 ± 0.02	10.7 ± 0.2	0.4 ± 0.2
ALESS 15.1	53.38905	−27.9916	2.67	10.6 ± 0.2	${11.76}_{-0.26}^{+0.21}$	12.62 ± 0.02	470 ± 10	9.65 ± 0.03	11.1 ± 0.2	0.8 ± 0.1
ALESS 17.1	53.03035	−27.8558	1.539	10.8 ± 0.2	${11.01}_{-0.07}^{+0.08}$	12.26 ± 0.05	210 ± 10	9.95 ± 0.03	11.4 ± 0.2	0.8 ± 0.1
ALESS 76.1	53.38479	−27.9988	3.389	10.5 ± 0.3	${11.08}_{-0.34}^{+0.29}$	12.23 ± 0.40	190 ± 90	9.63 ± 0.24	11.1 ± 0.4	0.8 ± 0.2
ALESS 112.1	53.20357	−27.5203	2.315	11.2 ± 0.2	${11.36}_{-0.12}^{+0.09}$	12.57 ± 0.04	420 ± 20	9.57 ± 0.04	11.0 ± 0.2	0.4 ± 0.1

Note. Source IDs are from Hodge et al. (2019). M_* are from our estimate using conventional SED fittings and those from H19 are based on the energy-balancing MAGPHYS tabulated (except ALESS 9.1, which is affected by blending with a nearby object); details in Section 4.2.4. We assume a starburst M_gas/M_dust of 30 here. ${f}_{\mathrm{gas}}={M}_{\mathrm{gas}}/({M}_{\mathrm{gas}}+{M}_{* })$, adopting our M_* estimates.

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Even with a rudimentary constraint on stellar masses, it emerges that four in six H19 SMGs have comparable stellar masses to our HUDF galaxies. These four SMGs are within the scatter of the main sequence (Figure 5), rendering them "typical SFGs" by our definition. They also have similar L_IR, which could imply similar SFRs barring the probability of top-heavy IMFs at higher ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ (discussed in Section 3.3). The H19 SMGs appear to have larger dust masses, as evident in the 3×–5× brighter far-IR fluxes (Figure 6). However, this might not be representative of typical submillimeter-selected galaxies because H19 galaxies are among the brightest at the far-IR from the Hodge et al. (2016) sample, which in turn are among the brightest from the Hodge et al. (2013) sample. Also, their larger dust masses do not necessarily imply a larger gas mass, because a lower GDR might be more appropriate if they are merger-driven starbursts. This is because strong starbursting systems typically have a CO-to-M_gas α_CO conversion factor of 0.8 M_⊙/(K km s⁻¹ pc²), which corresponds to GDR ≈ 30 (e.g., Leroy et al. 2011; Genzel et al. 2012; Magdis et al. 2012; Silverman et al. 2018). It is, therefore, possible that both the ALESS and HUDF samples have comparable gas masses.

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Given the comparable L_IR, M_*, and perhaps even M_gas among the four out of six H19 SMGs and our HUDF galaxies, why are H19 SMGs much more dust rich and clumpy? In other words, four of the H19 SMGs and our HUDF galaxies are physically similar, so why do they appear differently? An explanation for the H19 substructures being comparably bright to our HUDF galaxies might be that these substructures originated from a class of disruptive events involving multiple systems with dust/gas reservoirs at the scale of our HUDF galaxies, e.g., major mergers of typical SFGs. The scale of the disruptive event found in our HUDF galaxies, characterized by the lack of star-forming substructures at our resolution and sensitivity, could be less violent, e.g., gas-rich disk instability or minor mergers. We note that at higher redshifts, minor mergers have been proposed as disruptive events triggering intense star formation in submillimeter-bright galaxies (e.g., Gómez-Guijarro et al. 2018, at z ∼ 4.5). Our interpretation of the H19 substructures diverges from that put forward by Hodge et al., that the SMG substructures are potentially signatures of the spiral, ring, and bar structures induced by interactions. Because such structures were not observed in the less violent interactions in our HUDF galaxies, we feel that it is unlikely that the more disruptive interactions characteristic of SMGs will lead to the formation of galactic structures akin to those found in the local universe. Rest-frame optical images could help resolve the question of the degree of disturbance of the galaxies and whether they are possible merger products. The HST H₁₆₀ imaging of the HUDF galaxies reaches a sensitivity of 29.8 mag AB (Illingworth et al. 2013), but that of the ALESS galaxies has a median sensitivity of only 27.8 mag AB (Chen et al. 2015). More sensitive near-IR images are needed to systematically characterize the morphologies of H19 SMGs.

The picture of H19 SMGs representing a more extreme class of disruptive events that induces exceptionally intense starbursts (even though not all of them are presently starbursting) might also explain their larger dust mass. A merger-driven starburst in a gas-rich environment could proceed very rapidly compared to its gas reaccretion timescale (e.g., 0.05–0.1 Gyr). As such, dust and metal contents build up quickly in the observed star-forming regions with rapid consumption of gas, leading to a lower GDR even before an appreciable stellar mass increase occurs (see, e.g., the enhanced M_dust/M_* in starburst galaxies reported by Béthermin et al. 2015). We stress that the proposed scenario is based on a very small number of galaxies. A larger sample of spatially resolved molecular gas distributions as well as ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ maps from multiple bands to accurately constrain the T_dust for a large diversity of SFGs will be vital to testing these possible explanations and is already feasible with ALMA.

Our observations of three typical SFGs at z ∼ 3, selected largely on the basis of stellar mass, shows their star formation to be smoothly distributed without significant clumps. This contrasts with the H19 SMGs, selected on the basis of brightness at 870 μm, which finds significant clumpiness in galaxies of similar stellar mass and far-IR luminosity. However, even in these cases, the clumps account for a minority of the far-IR luminosity and hence most of the star formation is not clumpy in both samples. Likewise, the Genzel et al. (2011) images of z ≃ 2.3 galaxies in Hα, whose stellar masses and SFRs are similar to our HUDF SFGs, indicate some clumps (Section 4.2.1) but, again, accounting for only a small fraction of the total SFR. Studies of lensed galaxies (Section 4.2.2) also show no convincing cases where the star formation is largely due to clumps.

When observers started to identify giant clumps at z ∼ 2 using HST images and found them to be ∼1 kpc in size and ∼10⁹ ${M}_{\odot }$ in stellar mass, theorists invoked gas fragmentation driven by gravitational instability in gas-rich turbulent disks fed by intense inflows of gas fuel to reproduce such clumps in simulations of both isolated galaxies (Noguchi 1999; Immeli et al. 2004; Bournaud et al. 2007) and in cosmological simulations (Agertz et al. 2009; Ceverino et al. 2010; Genel et al. 2012). As observational evidence is mounting that the apparent giant clumps are likely caused by the limited angular resolution of observing facilities and the modest S/N of the observations, and any clumps are intrinsically an order of magnitude smaller (Section 4.2.2), the spatial and/or temporal resolution of models have also improved by an order of magnitude along with the more realistic subgrid physics, affording vast improvement in simulation of disk substructures. With the improved models, a new consensus emerged among modelers that typical clumps formed by disk fragmentation should be an order of magnitude smaller than previously thought, with clump mass in the range of 10⁷–10⁸ ${M}_{\odot }$ and clump radii of 100–200 pc (Mandelker et al. 2014, 2017; Moody et al. 2014; Mayer et al. 2016; Oklopčić et al. 2017), and that clumps more massive than 10⁹ ${M}_{\odot }$ are rare, likely the result of clump–clump mergers or further gas accretion (Tamburello et al. 2015, 2017).

To reconcile this prediction of smaller clumps with the observations of kiloparsec-sized clumps, Behrendt et al. (2016) showed that clusters of ∼10 small clumps, each of ∼10⁷ ${M}_{\odot }$ and ∼70 pc in diameter, can appear as a single giant clump when observed at the resolution of HST and AO-assisted ground-based facilities. Perhaps more importantly, these clump clusters can explain the large velocity dispersions observed in the giant clumps (50–100 km s⁻¹; Genzel et al. 2011) as due to the internal motion within the clump cluster, i.e., without having to invoke stellar feedback. Tamburello et al. (2017) constructed mock Hα maps from the simulations of Tamburello et al. (2015) and "observed" them at 0.1 and 1 kpc resolutions. They found that the inferred physical properties of clumps depend sensitively on the observing resolution, e.g., the clump masses differ by a factor of 2 and the typical clump radii by an order of magnitude between the 0.1 and 1 kpc observations.

More recently, B. Faure et al. (2019, in preparation) used hydrodynamic simulations with a subparsec resolution to produce mock observations at "HST-like" and "ALMA-like" resolutions, 800 and 200 pc, respectively. At the HST-like resolution, the gas disk morphologies are dominated by giant clumps each containing a few percent (up to 5%–10%) of the galaxy's gas mass; simulations suggest that these giant gas clumps are the counterparts of optical giant clumps. When observed at the 200 pc resolution of our ALMA observations, these giant clumps break into several smaller clouds. These clouds, resolved in ALMA images, typically contain 0.2%–0.5% of the total gas mass of their host galaxy, with an upper limit of 1.5%. This picture can be tested with ALMA observations slightly more sensitive than those of our HUDF galaxies on a larger sample. These simulations agree with Dessauges-Zavadsky et al. (2017), Fisher et al. (2017), and Rigby et al. (2017) that the blending of multiple small star-forming clumps can explain the apparent clumpiness at the kiloparsec scale. B. Faure et al. (2019, in preparation) also show that these apparent giant kiloparsec-scale clumps, containing multiple smaller clouds, are not transient chance superpositions but gravitationally bound structures that can be gradually dispersed by stellar feedback and/or migrate toward the galactic bulge.

In addition to ruling out the presence of kiloparsec-scale giant star-forming clumps, our observations are in tension with some recent models. Because the intrinsic radii of clumps from simulations and observations of gravitational lens systems are now known to be 50–200 pc, our 200 pc observations are well suited for detecting them. For example, the typical in situ clumps predicted by Mandelker et al. (2017) are 10^7.5–10^8.5 ${M}_{\odot }$ in mass, 300–800 pc in diameter, and harbor SFR ∼ 0.1%–10% of that in the disk. The brighter populations of these predicted clumps should be well detected in our galaxies, contrary to our results. Models predicting lower mass clumps are still consistent with the smooth appearance of our HUDF galaxies. However, the finding that the Eyelash is clumpless (Section 4.2.2) will pose an even stronger tension on clumps, down to a physical scale of 50–100 pc. That is, while some of these simulations are in agreement with the rest-frame UV clumps revealed by gravitational lenses, the situation remains unconstrained in typical massive main-sequence SFGs at z ≃ 3.

We note that the clumps in the formative era of the Milky Way that Clarke et al. (2019) proposed to explain the present-day α-abundance bimodality measured by the SDSS/APOGEE survey (Nidever et al. 2014) are 10^7.5–10^9.5 ${M}_{\odot }$ in mass; the predicted distribution peaks at 10^8.1 ${M}_{\odot }$. The low-mass side of this range is still consistent with our HUDF galaxies being smooth.