VLA AND ALMA IMAGING OF INTENSE GALAXY-WIDE STAR FORMATION IN z ∼ 2 GALAXIES

The far-infrared/radio correlation (Helou et al. 1985) has been demonstrated to hold in statistical (i.e., stacked) samples out to z ∼ 2 (Ivison et al. 2010; Magnelli et al. 2015; Pannella et al. 2015), but this has not been established for individual galaxies in the main sequence of SFGs. Yet the correlation is important as a physically motivated rationale that radio and millimeter observations trace the same extent of star-forming regions. We explore the validity of the correlation for the individual VLA-ALMA-selected SFGs by investigating their S_{5 cm}/S_{1.3 mm} flux ratios as a function of redshift (e.g., Carilli & Yun 1999) in comparison with the ratio predicted by the Rieke et al. (2009) infrared SED library. To ascertain that the 5 cm fluxes for galaxies in this test are not contaminated by AGN emission, we select a star-forming subsample by conservatively excluding all objects with L_X(0.5–8 keV) ≥ 3 × 10⁴² erg s⁻¹ following Xue et al. (2011). That is, AGN candidates are excluded from this test on the basis of X-ray luminosity regardless of whether their radio emission is enhanced over the level of star formation.

We find that for all five galaxies in the star-forming subsample, S_{5 cm}/S_{1.3 mm} at z = 1–3 is well predicted by that of a local SED template for SFG with infrared luminosity of 10^11.5 L_⊙ (Figure 2); the rms scatter of the ratio for these five objects around this template is 0.03 dex, which suggests that the far-infrared/radio correlation does hold for these SFGs. That a single SED is a good descriptor of the flux ratio should not come as a surprise because of the small dispersion of dust temperature found in main-sequence SFGs at z ∼ 2 (Magnelli et al. 2014; Scoville et al. 2016).

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On the other hand, all but one of the X-ray-selected AGN also have enhanced S_{5 cm} over the level of S_{1.3 mm} to varying degrees. X-ray-luminous AGN (UDF1 and 8) tend to have relatively small radio enhancement, having S_{5 cm} similar to the levels predicted by the far-infrared/radio correlation given the S_{1.3 mm}, whereas X-ray-weak AGN candidates are among the most radio-luminous. This may be indicative of an anticorrelation between radiative and mechanical power that is well established in the local universe (Best & Heckman 2012), although analysis of a larger radio and X-ray sample is required to test whether such a dichotomy in the Eddington ratio of AGN exists at high redshift.

We classify as radio AGN those with S_{5 cm} enhancement greater than twice the highest level expected from star-forming SED templates, about 0.5 dex higher than the observed S_{5 cm}/S_{1.3 mm} ratios for the star-forming subsample, which is ∼15× the rms scatter of S_{5 cm}/S_{1.3 mm}. These radio AGN are indicated in Table 1 and in the corresponding VLA images in Figure 1.

In the local universe, e.g., Beck (2007) and Fletcher et al. (2011) have shown that the morphology of SFGs is not strongly dependent on frequency at ≃1.5–10 GHz (20–3 cm). While the rest-frame ≈1.7 cm continuum emission probed by our 5 cm VLA observations at z ∼ 2 is dominated by synchrotron emission from supernovae, the thermal fraction associated with H ii regions that may be present is not well constrained at these redshifts, and could be a source of morphological uncertainties. The agreement between S_{5 cm}/S_{1.3 mm} and the template prediction suggests that this is not a strong effect. Furthermore, the scale length of synchrotron and inverse-Compton losses decreases rapidly with the increasing ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ and are ≪1 kpc at the typical ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ of z ∼ 2 SFGs (Murphy et al. 2006). Hence we expect that for non-AGN, both VLA and ALMA should trace similar extents of star formation, i.e., if both are detected at a comparable S/N, they can be used interchangeably to measure the extinction-free star formation sizes at z ∼ 1–3. Although we are only able to investigate the correlation for five SFGs with SFRs ∼100 M_⊙ yr⁻¹, the success of this test highlights that it would be worth examining a larger sample of individual SFGs with future ultra-deep VLA and ALMA observations.

In Figure 1, a common picture emerges that intense star formation usually occurs at the location of the stellar-mass concentration. The sizes of star-forming regions, as independently traced by the VLA and ALMA images, extend over the dominant buildup of stellar mass. In this section, we discuss the size and location measurements to quantify these observations. None of these star-forming regions are identifiable in the rest-frame ultraviolet images, which show clumps of unobscured star formation that tend to occur in the areas peripheral to the intense obscured star formation and that comprise 0.1%–5% of the galaxy-integrated SFR (D16).

We measure the extinction-independent effective radius of the star formation distribution, r_SF, from the VLA and ALMA images by means of deconvolved source sizes determined from two-dimensional (2D) elliptical Gaussian fitting (the position, major and minor axes, flux, and position angle of the Gaussians are free parameters); multiple Gaussians are permitted, in which case all Gaussian components from the same flux "island" above 3σ are grouped together into a source. This is carried out with PyBDSM.²⁷ We also construct images at multiple u, v tapering scales to accurately measure sizes of extended sources; the scale with the highest S/N for each object is adopted for the size measurement. All VLA sources except UDF11 and all ALMA sources are well described with a single component. In all cases, the typical average residual background rms values (PyBDSM's RESID_ISL_RMS parameter) are 0.2 μJy beam⁻¹ for VLA and 11 μJy beam⁻¹ for ALMA. All VLA detections are spatially resolved, and 9 of 11 of ALMA sources are resolved (all except UDF7 and 16). Comparing the circularized half-light radii, r_1/2, from VLA and ALMA (Table 2) for non-AGN, we find that except for UDF2, all of them agree within the range of uncertainties. While a larger sample is required to provide a robust comparison, this gives an early indication that radio and millimeter observations probe the same regions at z ∼ 2. In light of this agreement, we adopt the average of r_1/2 from VLA and ALMA as the r_SF when both bands are spatially resolved and the object is non-AGN. For AGN, we adopt the ALMA r_1/2 (or the r_1/2 limit when the ALMA image is not spatially resolved) with the exception of UDF8, which harbors an X-ray AGN but does not appear to have enhanced radio emission, which we treat as non-AGN for the purpose of the r_SF measurement. The VLA and ALMA r_1/2 and the band(s) used for the r_SF measurement, along with the criteria for band selection, are tabulated for each object in Table 2.

Table 2.  Size Measurement of VLA-ALMA-selected Star-forming Galaxies

ID	S/N	S/N	VLA Deconvolved FWHM	ALMA Deconvolved FWHM	VLA r1/2	ALMA r1/2	Adopted rSF
	VLA	ALMA	θmajor × θminor	θmajor × θminor	(kpc)	(kpc)	(kpc)
UDF1	15.9	18.4	097 ± 014 × 049 ± 006	039 ± 004 × 033 ± 004	2.7 ± 0.4	1.4 ± 0.2	1.4 ± 0.2c
UDF2	10.8	16.8	042 ± 008 × 025 ± 004	053 ± 006 × 045 ± 005	1.3 ± 0.2	2.0 ± 0.2	1.6 ± 0.2a
UDF3	22.9	14.0	048 ± 004 × 027 ± 002	075 ± 009 × 027 ± 005	1.5 ± 0.1	1.8 ± 0.3	1.8 ± 0.3c
UDF4	5.0	6.6	051 ± 014 × <009	054 ± 012 × 028 ± 009	2.1 ± 0.6	1.6 ± 0.4	1.9 ± 0.5a
UDF5	13.7	6.3	079 ± 018 × 039 ± 006	096 ± 025 × 019 ± 010	2.4 ± 0.5	1.8 ± 0.7	2.1 ± 0.6a
UDF6	16.1	4.9	086 ± 012 × 038 ± 005	106 ± 041 × 020 ± 017	2.4 ± 0.3	2.0 ± 1.2	2.2 ± 0.7a
UDF7	31.4	4.9	027 ± 002 × 022 ± 001	<024 × <013	1.0 ± 0.1	<3.0 (2σ)	<3.0d
UDF8	15.3	4.5	080 ± 015 × 029 ± 006	135 ± 045 × 072 ± 024	2.1 ± 0.4	4.3 ± 1.4	3.2 ± 1.0e
UDF11	12.6	4.0	108 ± 031 × 058 ± 016	143 ± 057 × 069 ± 028	3.4 ± 1.0	4.2 ± 1.7	4.2 ± 1.7c
			039 ± 010 × 006 ± 003
UDF13	8.8	3.9	067 ± 016 × 040 ± 010	086 ± 034 × 047 ± 020	2.1 ± 0.5	2.6 ± 1.1	2.6 ± 1.1c
UDF16	11.9	3.5	107 ± 029 × 060 ± 014	<023 × <015	3.4 ± 0.9	<3.1 (2σ)	3.4 ± 0.9b

Note. Circularized SFG radii, r_SF, are measured from the deconvolved FWHMs of VLA and/or ALMA images with the following criteria, as noted for each object in the r_SF column: (a) non-AGN, both VLA and ALMA are resolved, take average of the two bands; (b) non-AGN, only VLA is resolved, use VLA; (c) AGN, ALMA is resolved, use ALMA; (d) AGN, ALMA is unresolved, adopt 2σ deconvolved size limit as upper limit; and (e) AGN present, but has negligible contribution to radio emission, both VLA and ALMA are resolved, same as (a). Uncertainties in the deconvolved FWHM columns are 1 − σ. UDF11 has two VLA components; its r_SF reflects the total size.

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We tested the robustness of our size measurements by injecting simulated sources into the HUDF maps. We find no bias in extracted sizes down to our S/N limit of 4, although at the lowest values of S/N (4–6) some sources are extracted with only upper limits on size. There are six ALMA sources with S/N < 5 (Table 2). From the simulations, we might expect to fail to measure sizes for 1–2 of them, consistent with the two cases in the ALMA images (UDF7 and 16) where this has occurred. In addition, the relative uncertainties indicated by the simulations are consistent with those in Tables 2 and 3.

To compare the star formation size with the size of stellar-mass buildup, we quantify the effective radius for the stellar-mass distribution by a circularized radius that encircles half of the stellar mass, ${r}_{{\text{}}{M}_{* }}$. This is measured non-parametrically from the stellar-mass map by determining the area of the stellar-mass "island" that contains half of the total stellar mass. In the case of an ideal Gaussian, this size measure yields the same radius as Gaussian fitting, which allows us to compare the ${r}_{{\text{}}{M}_{* }}$ and r_SF. The ${r}_{{\text{}}{M}_{* }}$ uncertainties are estimated from the rms maps from the spatially resolved SED fitting.

The location of star formation concentration in relation to the hosts' stellar-mass concentration is quantified by the separation between their barycenters, measured from stellar-mass and star formation maps. The choice of band(s) used to determine the star formation barycenter follows those of r_SF measurements, i.e., we adopt a geometric mean of the barycenters from VLA and ALMA images for non-AGN, and from the ALMA images otherwise (again, UDF8 is treated as a non-AGN for this purpose). The uncertainties are the sum in quadrature of the resolution of the stellar-mass maps (006) and the uncertainties of Gaussian fitting (θ_beam/(2 S/N), see σ_pos discussion in Section 2).

We find a median SFGs r_SF of 2.1 ± 0.9 kpc. The separations between the star formation and stellar-mass barycenters (Table 3) are smaller than this radius in all cases except UDF7, which appears to be interacting. On average, the star formation and stellar-mass peaks are separated by 0.53 ${r}_{{\text{}}{M}_{* }}$ (the median separation is 0.36 ${r}_{{\text{}}{M}_{* }}$, corresponding to 0.9 kpc), indicating that star formation occurs nearly cospatially with the stellar-mass concentration. Individually, the r_SF broadly follows the ${r}_{{\text{}}{M}_{* }}$ (median ${r}_{{\text{}}{M}_{* }}=2.6\pm 0.7$ kpc) as shown in Figure 3 (left panel), consistent with the picture of star formation extending over a similar area as the stellar mass distribution (see also Tacconi et al. 2013). Our median SFG radius is similar to those of the star formation-dominated subsample of Biggs & Ivison (2008) SMGs, which has a median r_SF of 2.3 kpc (their star-forming subsample is reproduced in Figure 3). On the other hand, the SFG radii from our sample are ≈2–4 times larger than those of submillimeter (submm) galaxies studied with ALMA at high resolution (r_SF = 0.7–1.2 kpc, Ikarashi et al. 2015; Simpson et al. 2015). These submm galaxies have median SFRs 3–8 times those of our sample, hence an explanation is that the more compact star formation could be a characteristic of this higher SFR regime, but not for main-sequence SFGs (Figure 3).

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Table 3.  Sizes and Locations of Star Formation

ID	rSF	${r}_{{{\rm{M}}}_{* }}$	Δp(M*, SF)	Average ΣSFR
	(kpc)	(kpc)	(kpc)	(M⊙ yr−1 kpc−2)
UDF1	1.4 ± 0.2	1.4 ± 0.7	0.6 ± 0.5	18.0 ± 6.3
UDF2	1.6 ± 0.2	2.5 ± 0.9	0.7 ± 0.5	11.3 ± 3.7
UDF3	1.8 ± 0.3	2.7 ± 0.5	1.7 ± 0.5	6.4 ± 3.0
UDF4	1.9 ± 0.5	2.4 ± 1.0	0.8 ± 0.6	3.3 ± 1.8
UDF5	2.1 ± 0.6	2.7 ± 0.5	0.9 ± 0.6	2.5 ± 1.4
UDF6	2.2 ± 0.7	3.5 ± 0.7	<0.6	1.9 ± 1.2
UDF7	<3.0	2.7 ± 1.2	5.8 ± 0.6	>2.9
UDF8	3.2 ± 1.0	1.8 ± 0.4	0.8 ± 0.6	1.2 ± 0.9
UDF11	4.2 ± 1.7	4.0 ± 0.7	1.1 ± 0.7	1.0 ± 1.0
UDF13	2.6 ± 1.1	1.9 ± 0.8	0.9 ± 0.7	1.1 ± 0.9
UDF16	3.4 ± 0.9	2.5 ± 0.4	<0.7	0.4 ± 0.2

Note. Δ_p(M_*, SF) is the physical separation between the barycenters of stellar-mass and star formation concentrations (details of sizes and separation measurements are in Section 3.2); upper limits indicate separations smaller than the positional uncertainties. The Σ_SFR is averaged over the entire star formation surface areas indicated by r_SF.

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The increasing compactness of SFGs at SFR ≳ 300 M_⊙ yr⁻¹ is independently indicated by the decreasing ratio of mid-infrared aromatic luminosity to the total infrared luminosity (L_{6.2 μm}/L_IR trend shown in Figure 3; Nordon et al. 2012; Pope et al. 2013; Shipley et al. 2016). Consistent with this trend, the two most intense SFGs in our sample (UDF1 and 2) are also the most compact. While the origin of such a trend is at present unclear, if the SFR in the interstellar medium (ISM) is regulated by some internal process (such as a form of stellar feedback), then this result may be expected. At the centers of massive starbursts, the surface densities rise and the vertical weight on a cloud can hinder the effectiveness of internal feedback processes at dispersing gas (e.g., Ostriker & Shetty 2011; Hopkins et al. 2013). In these environments, the star formation efficiency can rise dramatically, decreasing the effective radius for star formation within the galaxy.

A major result from our observations is that main-sequence SFGs at z ∼ 2 exhibit vigorous star formation in a distributed manner over size scales of a few kiloparsec, which is to be contrasted with the typical sub-kpc size scales of comparably luminous galaxies in the local universe (Condon et al. 1991; Rujopakarn et al. 2011; Lutz et al. 2016). Such a result is expected from numerical simulations of galaxy growth via in situ star formation that is fed by the accretion of gas from the intergalactic medium (e.g., Dekel et al. 2009; Davé et al. 2010). High-resolution cosmological simulations have found that star formation may remain distributed even in the most extreme systems at this epoch in the submillimeter-selected population (Narayanan et al. 2015).

The similarity of the effective radii of star formation and stellar-mass in our field-galaxy sample is to be contrasted with recent ALMA high-resolution studies that target high-SFR galaxies. Barro et al. (2016) found that the 870 μm sizes of main-sequence SFGs (median SFR ∼ 300 M_⊙ yr⁻¹) selected by their compact optical sizes to represent the progenitors of compact galaxies at z ∼ 2 have r_SF ≈ 1 kpc, and do not show the star formation size trend with stellar-mass distribution sizes. Similarly, the Tadaki et al. (2016) 870 μm observations of Hα-selected SFGs at z = 2.2–2.5 (median SFR ∼230 M_⊙ yr⁻¹, also in the main sequence) found their star formation radii to be <1.5 kpc, a factor of two smaller than their average rest-frame optical size (3.2 kpc). These two samples exhibit a similar characteristic of star formation distribution to our sample in that their star formation concentrations also peak at the same locations as the hosts' stellar-mass concentrations, but they appear to lack the extended component of galaxy-wide star formation. A possible explanation is that the extended star formation found in field galaxies could be a distinct evolutionary state from (and possibly preceding) the compact star formation in the Barro et al. (2016) and Tadaki et al. (2016) samples, with the latter representing a state closer to the conclusion of bulge formation and the subsequent cessation of the bulk of star formation (e.g., Barro et al. 2015).

We estimate the dust masses from the 1.3 mm fluxes using the Li & Draine (2001) dust mass absorption coefficients. The dominant source of uncertainty in dust mass estimates is the dust temperature T_dust, which is not known precisely for our sample, but Herschel studies have shown that T_dust of main-sequence SFGs at z ∼ 2 is in the range of 20–30 K (Dunne et al. 2011; Auld et al. 2013), prompting us to adopt T_dust = 25 K (Magnelli et al. 2014; Kirkpatrick et al. 2015; Scoville et al. 2016) and estimate the uncertainties using T_dust = 20 and 30 K for upper and lower limits, respectively. Since the ALMA measurements are in the Rayleigh–Jeans regime, the dust masses have only a moderate dependence on the assumed temperature (Hildebrand 1983; Casey 2012; Elia & Pezzuto 2016). Dust masses are in the range of log(M_dust/${M}_{\odot }$) = 8.4–9.1 with a typical uncertainty of 0.2 dex (tabulated in Table 1). The dust mass estimates are in agreement with the Magdis et al. (2012) results of stacking analysis for z ∼ 2 main-sequence SFGs, suggesting that the dust masses of our HUDF sample are representative of main-sequence populations at z ∼ 2.

If we assume a gas-to-dust ratio of 100 (Leroy et al. 2011; Magdis et al. 2012), the gas fraction, ${f}_{\mathrm{gas}}={M}_{\mathrm{gas}}/({M}_{\mathrm{star}}+{M}_{\mathrm{gas}})$, of our sample is on average 0.5 ± 0.2, indicating the gas-rich nature of these systems similar to the normal SFGs at z ∼ 2 studied by Tacconi et al. (2013), although significantly more gas rich than typical submm galaxies (e.g., Narayanan et al. 2012). The average gas depletion time, τ_dep = M_gas/SFR, of our sample is 0.4 ± 0.2 Gyr, comparable to their average mass-doubling time of 0.4 Gyr, assuming that star formation-driven outflows do not result in irreversible mass losses. These τ_dep are similar to the main-sequence samples of Sargent et al. (2014) and Silverman et al. (2015), further ensuring the main-sequence nature of our sample independent of the presence of AGN. We note that if the T_dust is warmer than the assumed 25 K, the gas fraction could be lower (e.g., T_dust = 30 K implies average f_gas and τ_dep of 0.4 ± 0.2 and 0.3 ± 0.1 Gyr) and hence requires a significant amount of cold gas accretion to sustain the current level of star formation for a significant period of time. However, the metallicities of our SFGs are expected to be lower than for local analogs (e.g., Zahid et al. 2013). The rapid reduction in dust mass with decreasing metallicity (Draine et al. 2007) would then argue for larger gas fractions in these galaxies.

The cospatiality and the similar effective radii of radio and millimeter emissions imply that in most cases, the cold gas associated with star formation resides in the star-forming regions, which we have shown occur near the stellar-mass concentrations. Hence, if this level of SFR is sustained through a mass-doubling time, we expect that the newly formed stellar masses will occur near the existing stellar-mass concentrations, i.e., enhancing the stellar mass surface density near the central region, consistent with a picture of in situ bulge formation (see also Barro et al. 2016; Tadaki et al. 2016).

The spatially resolved ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ for 9 of 11 galaxies peaks within ≤1.1 kpc of the stellar-mass distribution (with the exception of UDF3 and 7; Table 3), and all have ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ in the range of 0.4–18 M_⊙ yr⁻¹ kpc⁻² (median ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ = 2.5 M_⊙ yr⁻¹ kpc⁻²), the higher end of which is comparable to local starbursts (Kennicutt 1998). The level of ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ found in our main-sequence sample is significantly below those found in luminous submm galaxies of 90–100 M_⊙ yr⁻¹ kpc⁻² (Ikarashi et al. 2015; Simpson et al. 2015), suggesting very different conditions for star formation between them.

Recent studies show that ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ is a strong predictor of star formation-driven outflows at z = 1–2. An increased broad-fraction of Hα line flux at z ∼ 2 associated with star formation-driven outflows is found to strongly depend on ${{\rm{\Sigma }}}_{\mathrm{SFR}}$, with a ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ of 1 M_⊙ yr⁻¹ kpc⁻² being the threshold above which the large broad-line fractions are observed (Newman et al. 2012). At a similar ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ threshold of ≈0.3 M_⊙ yr⁻¹ kpc⁻², Bordoloi et al. (2014) also found a significant increase in the equivalent width of the Mg ii absorption line at z ∼ 1, which indicates cool outflowing gas. If ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ is indeed a predictor of star formation-driven outflows at these redshifts, we expect that main-sequence SFGs like those in our sample, whose galaxy-average ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ are higher than these threshold levels (Table 3), will harbor outflows across a significant extent comparable to the areas of stellar-mass buildup (i.e., galaxy-wide). While the presence of outflows appears to depend on ${{\rm{\Sigma }}}_{\mathrm{SFR}}$, how the outflow rate depends on ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ is not well established, especially for molecular gas in a turbulent galactic environment at z ∼ 2. If a strong relationship also exists between them, we expect that the areas exhibiting high ${{\rm{\Sigma }}}_{\mathrm{SFR}}$ near galaxy centers will also be the areas with the largest outflows. Future spatially resolved observations of cold gas dynamics could provide definitive evidence whether this intense galaxy-wide star formation also drives galaxy-wide outflows.

In Section 3.1 we have shown that the 4 Ms Chandra observations in the HUDF allows us to detect X-ray AGN candidates residing in main-sequence SFGs with varying degrees of radio emission enhancement over the level corresponding to their SFRs. Six of 11 galaxies in our SFG sample are detected in X-rays, with the most luminous reaching L_{0.5–8 keV} ≃ 5 × 10⁴³ ergs s⁻¹. Two of the X-ray detected SFGs (UDF3 and 11) are only detected in the soft X-ray band (0.5–2 keV), suggesting that their X-ray emission could originate solely from star formation. However, UDF11 also has radio emission enhanced by more than twice the level associated with star formation (Figure 2 Left; this level of radio enhancement is 15× the scatter around the emission level implied by the far-IR/radio correlation, Section 3.1), which suggests the presence of radio AGN.

Omitting the only ambiguous case of UDF3 from the AGN subsample, the AGN fraction (5 of 11 galaxies) is still higher than typically reported (e.g., Xue et al. 2010) at these redshifts, but not unexpected since AGN activity is known to depend on both stellar mass and gas mass, as evident by its clear dependence on star formation of its host even on a galaxy-wide scale (e.g., Silverman et al. 2009; Brusa et al. 2009). With the ALMA continuum detections at 1.3 mm preferential to the most massive galaxies with high SFRs at z ∼ 1–3 (D16), such a selection is also effective at probing rapidly growing supermassive black holes at z ∼ 2 including those with mild obscuration. Further support of such a high detection rate of AGN using ALMA comes from Umehata et al. (2015). who report a high X-ray AGN fraction in the SSA22 field.

Despite the high sensitivity of the Chandra observations in the HUDF, the X-ray counts in the full 0.5–8 keV band for four of six AGN candidates are still low (16–26 counts), highlighting the necessity of sensitive X-ray observations to characterize AGN populations in main-sequence SFGs at z ∼ 2. In the remaining two sources with sufficient count statistics, UDF1 and UDF8, which have 434 and 878 full-band counts, respectively, the column densities are 1.5 × 10²¹ and 7 × 10²² cm⁻² respectively, based on Web-PIMMS,²⁸ provided by HEASARC, assuming an intrinsic photon index of 2 and the redshift of the source, indicating mild obscuration.

Regardless of the AGN selection method, ALMA imaging shows that all AGN candidates in the sample contain large amounts of cold dust and gas (Table 1) associated with star formation. The trend of the star formation size with SFR shown in Figure 3 is consistent with the ALMA 870 μm sizes of star formation in the hosts of six X-ray detected AGN that have SFRs of ≈130–400 M_⊙ yr⁻¹ (Harrison et al. 2016).

For UDF7, 11, and 13 where the radio flux enhancement allows pinpointing the AGN location using the VLA images, we find that the AGN are within 0.5 kpc of the barycenter of star formation of their host galaxies as measured from the ALMA images (an upper limit given by our ability to pinpoint AGN and star formation given their S/N). For UDF11 and 13, the star formation concentrations are ≈1 kpc from the stellar-mass barycenters, whereas UDF7 is notable for these activities being ≈6 kpc away from the dominant stellar-mass concentration, a possible consequence of galaxy interactions.