GOODS-ALMA: Using IRAC and VLA to probe fainter millimeter galaxies

In this paper, we extend the source detection in the GOODS-ALMA field (69 arcmin$^2$, rms sensitivity $\sigma$ $\simeq$ 0.18 mJy.beam$^{-1}$), to deeper levels than presented in Franco et al. (2018). Using positional information at 3.6 and 4.5 $\mu$m (from Spitzer-IRAC), we explore the presence of galaxies detected at 1.1 mm with ALMA below our original blind detection limit of 4.8-$\sigma$ at which the number of spurious sources starts to dominate over that of real sources. In this Supplementary Catalog, we find a total of 16 galaxies, including 2 galaxies with no counterpart in HST images (also known as optically-dark galaxies) down to a 5$\sigma$ limiting depth of H = 28.2 AB (HST/WFC3 F160W). This brings the total sample of GOODS-ALMA 1.1 mm sources to 35 galaxies. Galaxies in the new sample cover a wider dynamic range in redshift ($z$ = 0.65 - 4.73), are on average twice as large (1.3 vs 0.65 kpc) and and have lower stellar mass (M$_{\star}^{\rm SC}$ = 7.6$\times$10$^{10}$M$_\odot$ vs M$_{\star}^{\rm MC}$ = 1.2$\times$10$^{11}$M$_\odot$). Although exhibiting larger physical sizes, these galaxies have still far-infrared sizes significantly more compact than inferred from their optical emission. We show that the astrometry of the HST image does not only suffer from a global astrometric shift, as already discussed in previous papers, but also from local shifts. These distortions were artificially introduced in the process of building the mosaic of the GOODS-South HST image. By comparing the positions of almost 400 galaxies detected by HST, Pan-STARRS and ALMA, we create a distortion map which can be used to correct for these astrometric issues.


Introduction
The formation and evolution of the most massive galaxies (M > 5×10 10 M ) at redshifts z > 2 is still largely debated. Their observed number density exceeds theoretical expectations assuming typical dark matter to stellar mass ratios (Steinhardt et al. 2016). The downsizing of galaxy formation challenges theoretical models which match either the low or high mass end but are unable to match both ends (e.g., Fontanot et al. 2009). The presence of a population of massive passive galaxies at z ∼2 with compact stellar surface densities challenges searches for their progenitors (van der Wel et al. 2014).
Because infrared (IR) wavelengths contribute to approximately half of the total Extragalactic Background Light (EBL; e.g., Dole et al. 2006), the study of dust-enshrouded starformation in distant galaxies is an important tool to progress in our understanding of the evolution of massive galaxies. The first submillimeter extragalactic surveys (Smail et al. 1997;Barger et al. 1998;Hughes et al. 1998) performed with the Submillimetre Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope (JCMT) have revealed a population of high-redshift galaxies that are massive, highly obscured and have high star formation rates (SFRs; see Casey et al. 2014 for a review). Recent observations using the Atacama Large Millimetre/submillimetre Array (ALMA), which provides a spatial resolution more than an order of magnitude higher than SCUBA, have since refined our understanding of E-mail: m.franco@herts.ac.uk galaxy evolution by securing the identification of optical counterparts and allowing us to detect not only extreme galaxies (galaxies with particularly high star formation rates, e.g., starburst or lensed galaxies), but also "normal" galaxies that are secularly forming stars. This paper extends our previous analysis (Franco et al. 2018, hereafter F18) of a deep continuum 1.1 mm survey with ALMA over an area of 69 arcmin 2 . This survey is located in the Great Observatories Origins Deep Survey-South (GOODS-South) at a location covered with the deepest integrations in the H-band with the HST-WFC3 camera. In F18, we limited our analysis to the blind detection of ALMA sources without considering other wavelengths. Due to the large number of independent beams in the high-resolution ALMA image, we were limited to sources with a signal-to-noise ratio greater than 4.8. Here we extend the detection limit to 3.5-σ by cross-matching the ALMA detections with catalogs in the near and mid-infrared. The need for a good astrometric calibration led us to introduce an improved correction for the astrometry of the HST image of the GOODS-South field.
This paper is organized as follows: in §2, we present the data used. In §3, we describe the astrometric correction to be applied to HST positions to align them with those of ALMA. We give the astrometric correction to be applied for all galaxies in the GOODS-South field present in the Guo et al. (2013) catalog, provided as an external link. In §4, we present the criteria and methods used to select the sample of galaxies which constitutes a Supplementary Catalog to the Main Catalog presented in F18. In Article number, page 1 of 18 arXiv:2005.03040v1 [astro-ph.GA] 6 May 2020 A&A proofs: manuscript no. main §5, we present the properties of the galaxies of the Supplementary Catalog, including two optically-dark galaxies. Finally, in §6, we perform a comparative analysis of the distribution of stellar masses, redshifts, and sizes between the sample of galaxies presented in this paper and in F18 and discuss the implications on the nature of the ALMA sources. Throughout this paper, we adopt a spatially flat ΛCDM cosmological model with H 0 = 70 kms −1 Mpc −1 , Ω m = 0.3 and Ω Λ = 0.7. We assume a Salpeter (Salpeter 1955) Initial Mass Function (IMF). We use the conversion factor of M (Salpeter 1955 IMF) = 1.7 × M (Chabrier 2003 IMF). All magnitudes are quoted in the AB system (Oke & Gunn 1983).

ALMA data
This paper uses the 1.1 mm photometric survey obtained with the Atacama Large Millimeter/Submillimeter Array (ALMA) between August and September 2016 (Project ID: 2015.1.00543.S; PI: D. Elbaz). The survey performed using band 6 covers an effective area of 69 arcmin 2 matching the deepest HST/WFC3 H-band observation taken as part of the Cosmic Assembly Nearinfrared Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011, Koekemoer et al. 2011, in the GOODS-South field. It is centered at α = 3 h 32 m 30.0 s , δ = -27 • 48 00 (J2000). The original 0 . 2 angular resolution was tapered with a homogeneous and circular synthesized beam of 0 . 60 Full-Width Half Maximum (FWHM; hereafter 0 . 60mosaic). The sensitivity of the 0 . 60-mosaic varies within the six slices of the survey with a median value of 0.18 mJy beam −1 .

IRAC catalog
We use the Spitzer-Cosmic Assembly Near-Infrared Deep Extragalactic Survey (S-CANDELS; Ashby et al. 2015) catalog of galaxies detected at 3.6 and 4.5 µm with the Infrared Array Camera (IRAC; Fazio et al. 2004) aboard the Spitzer Space Telescope (Werner et al. 2004). The catalog (Ashby et al. 2015) -hereafter S-CANDELS catalog -that reaches a 5-σ depth of 26.5 mag (AB) includes 2627 galaxies in the GOODS-ALMA field, i.e. approximately 38 sources/arcmin 2 .

Near-infrared K s -band catalog
We use the 2.2 µm catalog described in Straatman et al. (2016) that uses an ultradeep image resulting from the combination of multiple observations in the K and K s bands from: (i) the Very Large Telescope (VLT), which combines the images of GOODS-South done with the Infrared Spectrometer and array camera (ISAAC; Moorwood et al. (1999)) in the K s -band (Retzlaff et al. 2010) with the High Acuity Wide-field K-band imager (Hawk-I; Kissler-Patig et al. 2008) image in the K-band (Fontana et al. 2014), (ii) the 6.5m Magellan Baade Telescope combining the K s -band image from the FourStar Galaxy Evolution Survey (ZFOURGE, PI: I. Labbé) using the FourStar near-infrared Camera (Persson et al. 2013) with the K-band image using the Persson's Auxillary Nasmyth infrared camera (PANIC; Martini et al. 2004) in the HUDF (PI: I. Labbé), (iii) the Canada-France-Hawaii Telescope (CFHT), with the K band image done with the wide-field infrared camera (WIRCam; Puget et al. (2004) as part of the Taiwan ECDFS Near Infrared Survey (TENIS; Hsieh et al. 2012).
The 5-σ point-source detection threshold in this ultradeep K s image reaches a magnitude between 26.2 and 26.5, which leads to an average galaxy surface density of approximately 168 sources/arcmin 2 .

Radio catalog
A radio image that encompasses the GOODS-ALMA field was observed with the Karl G. Jansky Very Large Array (VLA) at a frequency of 3 GHz (10 cm) and an angular resolution of ∼0 . 3 for a total of 177 hours (configurations A, B, & C; PI: W. Rujopakarn). Down to the average depth of the radio catalog within the GOODS-ALMA region of RMS = 2.1 µJy.beam −1 , the average surface density of radio sources is approximately 5 sources/arcmin 2 .

HST H-band catalog
The GOODS-ALMA area covers the deepest H-band part of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011) field (central one-third of the field). The point source catalog reaches a 5-σ depth of 28.16 mag (AB) in the H 160 filter (measured within a fixed aperture of 0 . 17; Guo et al. 2013). The surface density of galaxies detected at 1.6 µm with the Wide Field Camera 3 / infrared channel (WFC3/IR) within the GOODS-ALMA field is approximately 233 sources/arcmin 2 .

Astrometric correction of the HST image of GOODS-South
We describe in F18 the presence of a systematic offset of ∆RA = −96 ± 113 mas in right ascension, and ∆Dec = 261 ± 25 mas in declination between the ALMA and HST images. This offset, interpreted as a positional shift of the HST image with respect to all other reference frames, is in good agreement with the offset previously discussed in Dunlop et al. (2017) and Rujopakarn et al. (2016). However, this correction has not been made to the HST v2.0 release for GOODS-South, in part because no external astrometric reference data with both suitable absolute accuracy and faint source density (such as the SDSS) were available 1 . The offset used until now only corrects for the bulk global shift in astrometry but it does not account for the relative error in the astrometric calibration that was introduced in the building of the HST mosaic. In the following, we propose to determine this local correction that behaves like a distortion correction. This correction is important in the present study since we aim at using knowledge of existing sources from other wavelengths in order to push the ALMA detection limit to deeper levels.
We take advantage of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) Data Release 2 (Flewelling et al. 2016). We note that this survey is astrometrically tied to Gaia (Gaia Collaboration et al. 2018). The offset between HST and Pan-STARRS images computed using an ensemble of 375 common detections (see Fig. 1 left panel) is comparable to the one presented in F18: ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas. Left: offset between Pan-STARRS (PS) and the HST; Middle: offset between the VLA and Pan-STARRS; Right: offset between the VLA and ALMA. For each panel, the histogram of the offsets in RA and Dec is shown as well as a fit with a Gaussian function (orange curve). The position of the peak and the standard deviation of the Gaussian is indicated for each curve. The middle and the right panels show that there are no significant astrometric differences between ALMA and the VLA nor between the VLA and Pan-STARRS, while the left panel shows a clear shift in both RA and Dec between the positions of 375 sources in common between the Pan-STARRS and HST images. We measure a systematic offset of ∆RA = −96 ± 83 mas and ∆Dec = 252 ± 107 mas. In addition, a local offset is presented in Fig. 2.  The comparison of the positions of 69 sources in common between our 3 GHz VLA catalog (5σ detections; Rujopakarn et al., in prep.) and Pan-STARRS within a radius of 0 . 6 shows that there is no offset between both images ( Fig. 1 middle panel). To reduce the risk of misidentification, in all the astrometric analysis, we only retained galaxies that had been detected at least twice in the same filter during the Pan-STARRS survey. The average deviations are found to be ∆RA = 0 ± 98 mas and ∆Dec = 12 ± 160 mas.
Similarly, we find no offset between our ALMA sources (both the Main catalog presented in F18 and the supplementary catalog presented in the following) and their VLA counterparts for the 27 galaxies in common between both catalogs ( Fig. 1, right panel). The average offset is ∆RA = 3 ± 113 mas and ∆Dec = 16 ± 93 mas, well within the expected uncertainties for S/N ∼ 4 sources (Ivison et al. 2007;Hatsukade et al. 2018). We note here that we derive this astrometric correction using both the main catalog from F18 and the supplementary catalog discussed in the following sections of this work.
The excellent agreement in the astrometry of the VLA, ALMA, and Pan-STARRS implies that it is most likely the HST coordinate system that needs to be corrected.
After subtracting this systematic and global offset from the HST data, the residuals offsets present spatially coherent patterns (see Fig. 2). Each arrow represents the median offset between Pan-STARRS and HST positions, for a sliding median containing on average 15 sources. This local offset varies with position in the GOODS-South field, and we refer to this as a distortion offset artificially introduced during the mosaicing of the HST data. The absolute value of the distortion offset is lower than the systematic offset, but it is not negligible, and can reach values higher than 0 . 15 at the edge of our GOODS-ALMA survey. These local distortions in the CANDELS astrometry are likely to originate from distortions in the ground-based images that were used for astrometric reference when the HST data were mosaicked.
The combined effect of the global offset and distortion offset between the ALMA and HST positions is illustrated in Fig. 3 and listed in Table 1 both before and after applying the global offset of ∆RA = -96 ± 83 mas and ∆Dec = 252 ± 107 mas and the distortion offset. With the exception of two galaxies for which the offset between the ALMA detected position and that of HST is ∼ 0 . 4 (after correction of both the global offset and the distortion offsets, AGS27 and AGS34), all other galaxies have a difference in the two positions of < 0 . 33. The average deviation after correction is −72 ± 143 mas in RA and −58 ± 143 mas in Dec for the sample of galaxies selected in this study (indicated by a magenta cross in Fig. 3). The updated RA and Dec positions derived for all galaxies in the Guo et al. (2013) catalog after the correction of both systematic and local offset are given at https://github.com/maximilienfranco/astrometry/.

ALMA Main Catalog
The main ALMA catalog consists of 20 sources detected above 4.8 σ (F18). This catalog was built without any prior assumptions. It is a blind source extraction down to 4.8 σ, using Blobcat (Hales et al. 2012).
The detection limit was set to S/N ≥ 4.8 due to the large number of independent beams that leads to spurious detections that become rapidly more numerous than the number of robust detections below this threshold, despite the tapering at 0 . 60 (see Fig. 4-left panel in F18). Here the 4.8 σ-limit concerns the central pixel detection threshold (σ p = 4.8) and is associated with a constraint on the adjacent surrounding pixels that are included in the source if they pass a detection threshold of σ f = 2.7. This combination of parameters ensures an 80 % purity where the purity criterion p f is defined as: Before correction After correction  where N p and N n are the number of positive and negative detections across the whole survey. The negative detections refer to the detections in the inverse map (in other words detections in the continuum map multiplied by -1).
The initial catalog coming out of the blind source extraction contains 23 detections including 3 detections that we flagged as spurious in F18 (marked with an asterisk in the  . Distance between the ALMA positions and the closest IRAC galaxies listed in the S-CANDELS catalog for the sources presented in F18 (red-dashed line), for the supplementary catalog (gray) and for all of the 3.5σ detections (blue). We also represented the VLA counterparts (at 3GHz) with a black solid line. All of the ALMA 3.5σ detections with both IRAC and VLA counterparts between 0 . 3 and 0 . 7 from the ALMA detections have been selected.
matches the 4 ± 2 spurious sources expected, based on the difference between positive and negative peaks above 4.8 σ. These three sources are the only ALMA detections without counterparts in the ultra-deep 3.6 and 4.5 µm IRAC images available for this field (26.5 AB mag, Ashby et al. 2015). The possibility that these sources are most likely spurious was later on confirmed by Cowie et al. (2018) using a 100 arcmin 2 survey of the field down to an RMS ∼0.56 mJy at 850 µm with SCUBA-2. None of the three detections listed as spurious were detected by SCUBA-2, while 17 out of our 20 brightest ALMA sources were detected. The remaining 3 sources were either confirmed with ALMA by Cowie et al. (2018) -AGS21 and AGS23 -or lie outside of the SCUBA-2 field of view -AGS22. We note however, that AGS22 is both at the very limit of our detection threshold and that it is the only galaxy in our list that does not show any IRAC counterpart. In view of the very large number of expected spurious detections at the 3.5σ limit that we plan to reach in the present paper, we will adopt the strategy to limit ourselves to the most secure ALMA detections, which exhibit a clear IRAC counterpart. As a result, we will limit the original main sample to the 19 galaxies with IRAC counterparts only, leaving aside AGS22 for consistency.

Using IRAC counterparts to identify robust ALMA sources down to 3.5-σ
In the present paper, we propose to use counterparts at other wavelengths to identify robust ALMA detections below the 4.8σ limit of the Main Catalog described in Sect. 4.1. This approach is similar in philosophy to a prior source extraction approach, except that we start from the ALMA blind source extraction at a lower threshold and then only keep sources with counterparts already identified in the near and mid infrared.
We start with the list of sources detected using the same algorithm as the Main Catalog but push it down to the σ p = 3.5 limit. A total of 1077 sources are detected down to this threshold, most of which are spurious simply due to the large number of independent beams (more than one million in the 0 . 60 tapered map). Indeed the inverse map exhibits an even larger number of detections, 1157. This high number of detections clearly includes noise fluctuations, but does not preclude the existence of real positive sources. Hence we cannot rely on Eq. 1 to calculate the probability that a source is real from a purely blind detection approach.
We observed in F18 that all the ALMA robust detections of the Main Catalog present an IRAC counterpart, hence we start by imposing the requirement that all candidate detections exhibit an IRAC counterpart. We note that this criterion may lead us to reject real ALMA sources without any IRAC counterpart with the possible consequence of biasing our sample towards the most massive galaxies, but this is for the sake of the robustness of the sources. ALMA sources without any IRAC counterpart may well exist (see e.g., Williams et al. 2019) and would be particularly interesting to analyse, but this is out of the scope of the present paper. We choose the cross-matching radius between the positions of the ALMA detections and the IRAC (S-CANDELS), VLA and ZFOURGE K-band catalogs to be equal to the value of the largest FWHM. It is equal to 0 . 60, the FWHM of the tapered 1.1 mm ALMA image, for the cross-match with the VLA and ZFOURGE K-band catalogs. For IRAC, although this value would be 1 . 95 for the cross-match with the IRAC channel 1 (3.6 µm) catalog (FWHM IRAC = 1 . 95 at 3.6 µm and FWHM IRAC = 2 . 05 at 4.5 µm), we have only considered sources closer to 0.7" (see explanation below). Before performing this cross-matching, we apply the astrometric correction to the CAN-DELS and ZFOURGE catalogs which use the HST reference frame, as described in Sect. 3.
In the process of cross-matching the ALMA and IRAC images, we identified, thanks to VLA images, 2 IRAC sources (AGS24 and AGS25) that were present in the IRAC image but were not listed in the S-CANDELS catalog (see Sect. 4.2.2). These sources were systematically located close to one or several brighter IRAC sources. We therefore implemented a new source extraction for those sources taking care to model the neighboring sources to obtain a clean de-blending of the IRAC sources (see Fig. 4). The use of the HST catalog in band H did not provide any reliable additional sources (see below).
A total of 67 sources detected with ALMA between 3.5 and 4.8 σ at 1.1 mm have a counterpart in at least one of the three catalogs (see Fig. 5). We have included in this figure the 2 sources (AGS24 and AGS25) missed in the S-CANDELS catalog due to the presence of a bright neighbor. In comparison, in the inverse image, there are 51 detections above 3.5-σ that also fulfill these criteria.
We note that 84 % (16 out of 19 sources) of the ALMA sources in the Main Catalog described in F18 have an IRAC counterpart closer than 0 . 3 (red dashed line in Fig. 6). Since our goal here is not to include all possible ALMA sources but to limit the Supplementary Catalog to the most robust candidates, we decided to impose a more stringent constraint on the association with IRAC counterparts by keeping as robust candidates those within a distance of 0 . 3. In total, 9 ALMA sources detected between 3.5σ and 4.8σ fulfill this criterion.
Looking at the remaining three sources in the Main Catalog (sources with a distance greater than 0 . 3 from their IRAC counterpart), we see another interesting characteristic. They are all closer than 0 . 7 from their IRAC counterpart and nearly all exhibit a radio counterpart as well (2 out of 3). In fact, out of the 19 sources in the Main Catalog, 16 (84 %) exhibit a radio counterpart. We therefore list in the Supplementary Catalog the sources that have both an IRAC and a radio counterpart closer than 0 . 7. This extra condition adds an extra 6 ALMA sources detected between 3.5σ and 4.8σ.
In total, we end up with a list of 16 sources which fulfill the criteria of having an IRAC counterpart either (i) closer than 0 . 3 or (ii) closer than 0 . 7 but associated with a radio counterpart in the 3 GHz catalog.
It is possible that using these criteria does not allow us to detect all "real" ALMA detections with a S/N > 3.5 but these conservative criteria ensure a high purity rate. Applying these criteria to the inverse image, we find only 4 resulting sources. We performed Monte Carlo simulations to estimate the probability that an ALMA detection lies randomly close to a galaxy listed in the S-CANDELS catalog. We randomly define a position within GOODS-South and then measure the distance to its closest IRAC neighbour using the source positions listed in Ashby et al. (2015) for IRAC sources with S/N > 5. We repeat this procedure 100 000 times. This method gives results comparable to those presented in Lilly et al. (1999). The distance from the nearest IRAC galaxies is given Table 1. In our supplementary catalog, for the farthest source to an IRAC counterpart (0 . 64), the percentage of a random IRAC association is 1.38 %.
With the exception of one other source (AGS29), the other detections have a probability of random IRAC association ≤ 1%. The surface density of radio sources is significantly lower than the surface density of IRAC sources (about 8 times lower), so the probability of a false association is also lower. A radio source at a distance from 0 . 6 from the ALMA counterpart has a probability of a random association of ∼ 0.1%.
We checked whether deeper surveys covering parts of the GOODS-South field could be used to validate or invalidate those ALMA Supplementary Catalog sources. The HUDF (Dunlop et al. 2017) and ASAGAO (Hatsukade et al. 2018) surveys reach a depth of RMS 35 µ Jy at 1.3 mm and RMS 61 µ Jy at 1.2 mm respectively. Using the same scaling factors as those presented in F18, these depths correspond to RMS 52 µJy and RMS 79 µJy respectively, at the wavelength of 1.1 mm relevant to this GOODS-ALMA survey. Only three ALMA 1.1 mm sources from the Supplementary Catalog fall in the area covered by these deeper surveys and all of them were detected and listed in the associated catalogs (see Fig. 7), demonstrating the robustness of our approach. AGS29 and AGS35 are listed as sources 18 and 26 respectively in the ASAGAO survey (Hatsukade et al. 2018) while AGS38 is known as UDF16 in the HUDF survey (Dunlop et al. 2017). Our independent identification of sources down to the 3.5-σ level did not therefore introduce any spurious sources without counterparts in deeper ALMA surveys.

Supplementary catalog: optically dark galaxies
As discussed above, thanks to the known position of the VLA detections, we have de-blended the IRAC sources to find two additional sources that satisfy our selection criteria (AGS24 and AGS25). Although AGS25 is listed in the ZFOURGE catalogue, AGS24 is not. More interestingly, neither of these two sources have been detected by the HST even in the 1.6 µm H-band (down to the 5σ limiting depth of H = 28 AB), hence they are opticallydark like 4 sources listed in F18 and as also discussed in Wang et al. 2016;Elbaz et al. 2018;Schreiber et al. 2018;Yamaguchi et al. 2019;Wang et al. 2019. In this section, we will describe these two detections.
The source AGS24 exhibits extended IRAC emission (after de-blending) that is 0 . 28 away from the ALMA position. This source is also detected in the radio at 6 GHz (3.7σ) and 3 GHz (5.7σ). The S/N of this source is higher in the 0 . 29 mosaic than in the 0 . 60 tapered image, which suggests that it is particularly compact at 1.1 mm. This galaxy will be presented in detail in Zhou et al. (submitted), where a stellar mass and redshift are estimated to be z ∼ 3.5 and M = 2.09 +0.10 −0.74 ×10 11 M . The source AGS25 is 0 . 1 away from its K-band counterpart in the ZFOURGE catalog (after applying the astrometric correction to the position of the ZFOURGE source), the source ID ZFOURGE = 11353 with a magnitude K = 25.9 AB shown by a circle in Fig. 4. This source is not listed in the CANDELS catalog (Guo et al. 2013), nor in the S-CANDELS catalog (Ashby et al. 2015). It is marginally detected in radio at 5 and 10 cm with a S/N ratio close to 3.7. AGS25 is close (3 ) to a massive galaxy listed in CANDELS, ID CANDELS = 8067 with a stellar mass of M = 5.6×10 10 M at a redshift of z sp = 1.038). ID CANDELS = 8067 is the bright neighbor that explains the absence of AGS25 in S-CANDELS. We subtracted it from the IRAC image by modeling a Sérsic profile with GALFIT (Peng et al. 2010) and measured an IRAC flux density of 0.81±0.19 mJy (see Fig. 4). The IRAC source is 0 . 43 away from the ALMA position of AGS25.
Since the ALMA source is only 0 . 1 away from the ZFOURGE source ID ZFOURGE = 11353, we use the stellar mass and redshift from the ZFOURGE catalog for this source. The characteristics of this galaxy make it particularly interesting, with z AGS 25 = 4.64 +0.25 −0.26 and M ,AGS 25 = 2.5 × 10 10 M . We note that the 6 optically-dark galaxies discovered with this survey (4 described in F18 and 2 described in this paper) appear to be particularly distant (z ≥ 3.5). Among these galaxies we also see that two are particularly massive (AGS4 and AGS24) with M > 10 11 M .
Ultimately, we end up with a list of 16 sources in the Supplementary Catalog including the two optically-dark sources AGS24 and AGS25. Their properties are listed in Table 1 and  Table 2.

Consistency test of the Supplementary Catalog: stellar mass distribution
If we compare the nature of the counterparts of ALMA detections above 3.5-σ in the image and the inverse image, we can see a difference that strengthens the robustness of the 16 sources of the Supplementary Catalog. There are 62 and 45 detections above 3.5-σ in the ALMA image that have a counterpart in the K-band of the ZFOURGE catalog in the image and inverse image respectively. The stellar mass distributions of both samples are represented by dashed black and green lines for the image and inverse image respectively in Fig. 8. Both histograms show the same behavior at stellar masses below 10 10 M but there are nearly no galaxies (2) above this mass threshold in the inverse image while there is a second bump in the histogram of the sources in the real image. Massive galaxies being rarer than low mass ones, the probability to get an association with such galaxy is lower and the fact that there is a second bump at high stellar masses in the real image supports the conclusion that these may   Fig. 8. Stellar mass distribution for the sources that were cross-matched between the ZFOURGE catalog and the image (black contours) or the inverse image (green contours). The sample galaxies selected in this study are shown in gray. be real sources. The Supplementary Catalog histogram shown in filled gray matches very nicely this second bump of massive galaxies. We recall that we did not impose any criterion of brightness or stellar mass in the selection of the Supplementary Catalog but only distances to IRAC, K-band and radio sources. If we limit ourselves to the galaxies above a stellar mass of 10 10 M , we can see that the number of sources in the Supplementary Catalog is close to the difference in the number of detections between the image and inverse images.
In the sample of cross-matched galaxies from the positive image, 22/63 galaxies (∼ 35 %) have a stellar mass greater than 10 10 M , compared with only 2/45 galaxies (∼4 %) in the inverse image (see Fig. 8). A Kolmogorov-Smirnov (KS) test on these data gives a p-value of 1.2×10 −2 between these two samples, meaning that the likelihood that the two samples were drawn from the same distribution is extremely low. When we remove the sample of 16 galaxies listed in Table 1, the two samples become more similar. The p-value from a KS test then reaches 0.88. This means that once the galaxies in our study have been removed, the detections that remain have as high a probability of originating from the same parent sample as the inverse image detections, so that they are no longer statistically different from noise.
This suggests that not only the Supplementary Catalog is robust but also that there is little margin for an extra population of real sources that we would have missed.

Catalog
The positions of the ALMA sources listed in the Main and Supplementary catalogs are shown in Fig. 7 where they can be compared to the locations of other ALMA surveys. The postagestamp images of the sources are shown in Appendix A.1.

Redshifts and stellar masses
Except for the two optically-dark galaxies, AGS24 and AGS25 (discussed in Sect. 4.2.2), all sources listed in the ALMA Supplementary Catalog have a photometric redshift reported in the CANDELS (Guo et al. 2013) and ZFOURGE (Straatman et al. 2016) catalogs. Photometric redshifts inferred by these different teams are listed in Col. (5) and Col.(6) of Table 2. They are in excellent agreement (see Fig. 9, left) with < |z CANDELSz ZFOURGE | /(1 + (z CANDELS +z ZFOURGE )/2) > = 0.05, after the exclusion of AGS35, whose redshift in the ZFOURGE catalog (z = 9.48) is much higher than that given in the CANDELS catalog, z = 2.99.
Six galaxies in the Supplementary catalog have a spectroscopic redshift measurement: -AGS26: z sp = 1.619 from VLT/FORS2 (Vanzella et al. 2008). We note that three additional spectroscopic redshifts have been reported for galaxies in the Main Catalog since the publication of F18 . In the following, we will adopt for each source (i) the spectroscopic redshift when available, otherwise (ii) the photometric redshift from the ZFOURGE catalog (except for AGS35 for which we use the CANDELS redshift). These redshifts are given in Table 2.
The stellar masses of the Main and Supplementary catalogs have been taken from the ZFOURGE catalog (except AGS35, for the reasons given above and for the large z discrepancy). They were multiplied by a factor 1.7 to scale them from the Chabrier IMF to a Salpeter IMF. Both catalogs provide gobally consistent stellar masses with no systematic offset, the median of the ratio M ,CANDELS /M ,ZFOURGE is 1.06 (see Fig. 9-right).
For galaxies for which new redshift information has been obtained compared to the redshifts given in Straatman et al. (2016), we have derived new stellar masses to replace those given in the ZFOURGE catalog. For the sake of coherence and homogeneity, we used a similar technique to the one used for the ZFOURGE catalog. We used the code FAST++ 2 based on FAST (Kriek et al. 2009). Stellar masses have been derived from models assuming exponentially declining star formation histories and a dust attenuation law as described by Calzetti et al. (2000).  Table 1. Details of the positional differences between ALMA and HST-WFC3 for our catalog of galaxies identified in the 1.1 mm-continuum map. Columns: (1) Source ID; (2), (3) Coordinates of the detections in the ALMA image (J2000); (4), (5) Positions of HST-WFC3 H-band counterparts when applicable from Guo et al. (2013), (6), (7) Distances between the ALMA and HST source positions before (∆ HS T 1 ) and after (∆ HS T 2 ) applying both the systematic and local offset correction presented in Sect. 3; (8), (9) Offset to be applied to the HST source positions, which includes both the global systematic offset and the local offset; (10) Distance from the closest IRAC galaxy; (11) IRAC random association (RaA) between the ALMA detection and the closest IRAC galaxy.  Table 2. Columns: (1) Source ID; (2), (3), (4) IDs of the HST-WFC3 (from the CANDELS catalog), ZFOURGE and IRAC (SEDS catalog) counterparts of these detections; (5), (6) Photometric redshifts from the CANDELS catalog (Guo et al. 2013), z CLS , and ZFOURGE catalog (Straatman et al. 2016), z ZF (note that AGS24 has a redshift of z 3.472 determined by Zhou et al. (submitted), see Sect. 4.2.2) ; (7) Spectroscopic redshift when available (see Sect. 5.1), flagged with a "sp" exponent to avoid confusion; (8) S/N of the detections in the 0 . 60 mosaic. This S/N is given for the peak flux; (9) Flux and error on the flux as explained in Sect. 5.2. p f indicates that the flux used is the peak flux, as the size measured by uvmodelfit is below the size limit given by Eq. 2. If there is no indication, the flux used is the flux given by uvmodelfit; (10) Stellar mass as described in Sect. 5.1; (11) 3GHz flux density from VLA (PI W. Rujopakarn, private communication Table 3. IDs, redshifts and stellar masses for the optically dark galaxies that have been presented in F18, for which new measurements have now made it possible to refine the results (see Zhou et al., submitted). Spectroscopic redshifts have been flagged with an "sp" superscript.
To ensure homogeneity of our results, we compared the stellar masses obtained using this technique with the ZFOURGE stellar masses (before modification of the redshift) for our sample of galaxies. We find a median difference of ∼8%.
In addition, the masses and redshifts of the four optically dark galaxies presented in F18 have recently been refined and will be presented in Zhou et al. (submitted), and are also summarized in Table 3. The distributions of stellar mass and redshift of all the ALMA detections in GOODS-ALMA (Main Catalog and Supplementary Catalog) can be seen in Fig. 10 and are listed in Table 2 in Franco et al. 2020 (submitted). The galaxies presented in F18 (Main Catalog) are shown in red, while the galaxies presented in this paper are shown in gray. The stellar mass has been scaled from a Chabrier IMF to a Salpeter IMF by applying a factor of 1.7 in the ZFOURGE catalog. In this paper, we will take, with the exception of AGS35 which has an inconsistent redshift (z AGS 35,ZFOURGE = 9.47 and for which we will take the data from the CANDELS catalog), the redshifts and stellar masses from the ZFOURGE catalog. The CANDELS stellar masses come from Santini et al. (2015).

Flux and size measurements
Flux densities of the Supplementary Catalog sources were measured by fitting the light profiles with a circular Gaussian in the uv-plane, using uvmodelfit in CASA (McMullin et al. 2007). Due to the relatively low S/N (3.5 < S/N < 4.8), we chose to fit a circular Gaussian rather than an asymmetric Gaussian, in order to limit the number of free parameters. We use the formula given by Martí-Vidal et al. (2012) (as in F18) to determine the minimum size that can be reliably measured in the uv-plane by an interferometer, as a function of S/N of the source: To calculate θ min , we use the S/N of the sources in the tapered map at 0 . 60, and therefore θ beam = 0 . 60. For galaxies where the circular Gaussian fit in the uv-plane gave a size (FWHM) smaller than θ min (the size limit given by Eq. 2), we take the galaxy to be unresolved, and therefore set the size upper limit of this galaxy to θ beam (see Table 4), and use the peak flux density measured on the direct image. Assuming these sources are pointlike is expected to lead to slightly underestimated flux densities, as the typical size measured for distant ALMA galaxies is on average close to 0 . 3 (Simpson et al. 2015a;Ikarashi et al. 2017;Elbaz et al. 2018). Assuming a point-like source for a real size extension of 0 . 3 FWHM would lead to an underestimation of the real flux density by a factor F ν,real /F ν,peak = 1.2 (see Fig. 11). In the absence of a robust size measurement, we decided to keep the peak flux values having in mind that they may be lower by about 20 %. Using the measurements coming out of uvmodelfit would lead to larger uncertainties for those sources with no reliable size measurement. For galaxies whose sizes measured using uvmodelfit are larger than the size limit given by Eq. 2, the peak flux approximation is no longer valid and we use the integrated flux given by uvmodelfit (see Fig. 12).
In order to check whether our flux density measurements were underestimated by a large factor, we computed the expected ALMA flux density that those sources would have if they had been located on the star-formation main sequence (MS; Noeske  Martí-Vidal et al. (2012). The last column gives the adopted size. If θ uvmodelfit > θ lim , we take θ uvmodelfit as the final size. If θ uvmodelfit < θ lim , we use the upper limit θ lim . The absence of size indicates a non-convergence of uvmodelfit. Rodighiero et al. 2011;Elbaz et al. 2011). Since a large fraction of the ALMA sources are actually starbursting and above the MS, this assumption only provides a rough estimate of a lower-limit to the ALMA flux densities. We used the infrared spectral energy distributions (IR SEDs) from the library presented in Schreiber et al. (2018), with the stellar masses and redshifts listed in Table 1 as input parameters. The measured, F ν,ALMA , and predicted, F ν,S ED , flux densities exhibit a ratio F ν,ALMA /F ν,S ED ranging from 0.73 to 5.2 with a median (average) of 2. 4 (2.7) suggesting that about 50 % of the galaxies of the Supplementary Catalog fall within the factor 2 dispersion of the MS, the remaining half being in a starburst phase. None of the measured flux densities fall more than 25 % below the predicted MS ALMA flux density, which suggests that our flux density measurements are most likely not largely underestimated.   10. Stellar mass as a function of redshift for the galaxies detected in F18 (red points) and in this work (gray points). For comparison, the distribution of all the galaxies, listed in the ZFOURGE catalog, in the same field of view is given in blue. Only UVJ active galaxies are shown. For each bin of redshift (z = 0.5) and stellar mass (log 10 (M /M ) = 0.5), the fraction of sources detected by ALMA compared to the UVJ active galaxies in GOODS-ALMA is indicated with a yellow shading. The optically dark galaxies for which redshifts and masses have been derived are represented by open circles. The upper panel shows the compared distribution of redshift between all the UVJ active galaxies in GOODS-ALMA and the ALMA-detected galaxies while the right panel shows the stellar mass distribution. The median redshift and stellar mass are shown in these two panels. The median redshift is 2.40 for the galaxies presented in this paper, compared to 2.73 in F18 , while the median stellar mass is 7.6×10 10   Flux uvmodelfit / Flux peak Fig. 12. Ratio between the flux extracted using uvmodelfit in CASA and the peak flux as a function of the size of the galaxy for the supplementary catalog. When the measured size is below the reliable size measurement limit (see Eq. 2), we consider the size given by Eq. 2 as an upper limit (see Table 4). The horizontal solid line indicates flux uvmodelfit = peak flux. The dotted lines show a 15 percent deviation from this equality. For galaxies larger than 0 . 25, the approximation of a point source is no longer valid, and we assume the flux value derived from uvmodelfit for these galaxies.

Stellar Masses
All galaxies detected in GOODS-ALMA have stellar masses greater than M = 2×10 10 M . The median stellar mass of galaxies from the Supplementary Catalog, M Supp = 7.6×10 10 M , is 1.6 times smaller than that of galaxies in the Main Catalog, M Main = 1.2 ×10 11 M . Hence by pushing down the ALMA detection limit using the IRAC catalog, we have reached more normal galaxies, with less extreme stellar masses.
We can now compare the galaxies detected by GOODS-ALMA, combining the Main and Supplementary catalogs, to their parent sample of distant star-forming galaxies taken from the ZFOURGE catalog after selecting only the UVJ active (starforming) galaxies (Williams et al. 2009, using the same definition as in F18, see Fig. 10).
In total, GOODS-ALMA detects approximately 38% (12/32) of the most massive star-forming galaxies with redshifts 2 < z < 4 (log 10 (M /M ) = 11 -12), this by taking into account the two optically dark present in this interval.

Sizes
The sizes of the sources of the Main and Supplementary catalogs were derived by fitting a circular Gaussian in the uv-plane using uvmodelfit in CASA. We find that by pushing down the detection limit to 3.5-σ using IRAC and VLA, we have been able to identify galaxies with nearly twice larger ALMA sizes than those in the Main catalog. The median ALMA 1.1 mm FWHM of the galaxies in the Supplementary Catalog is indeed 0 . 32 as compared to 0 . 18 for the galaxies in the Main Catalog. When accounting for the redshift of the sources, we find that the physical  Fig. 13. Cumulative fraction of sources with a FWHM below a given size for the main (red) and the supplementary catalog (gray). These sizes are computed by fitting the ALMA detections with a circular Gaussian in the uv-plane using uvmodelfit in CASA. The dotted lines refer to the sizes given by uvmodelfit, while the solid lines take into account take into account the upper limits given by Eq. 2. The shaded areas correspond to the integration of the individual uncertainties of the sizes of each detection. circularized half-light radius of the new sources in the present Supplementary Catalog (R 1/2 = FWHM/2) is 1.3 kpc as compared to only 0.65 kpc for the Main Catalog. If we take into account the fact that the Supplementary sources exhibit stellar masses that are half of those of source in the Main catalog, this implies that by pushing down the ALMA detection limit using IRAC and VLA catalogs, we were able to identify lower stellar mass galaxies in which dust-enshrouded star-formation extends over twice larger sizes.
In Fig. 13, we show the cumulative fraction of sources with a major axis below a given size for the Main (red) and Supplementary (gray) catalogs. This figure clearly shows that the galaxies detected in the Main catalog are generally more compact than those in the Supplementary catalog: 90% of galaxies in the Main Catalog have a FWHM below 0 . 25, whereas 90 % of the galaxies found in the Supplementary Catalog have a FWHM of less than 0 . 50. Moreover, 40% of sources in the Supplementary Catalog have a FWHM size above 0 . 30 arcsec.
This shows that while the projected sizes of dust-enshrouded star-formation probed by ALMA are globally small for massive and distant galaxies, the new sources that we present here in the Supplementary Catalog do not extend the sample to much lower flux densities but to sources with a wider extension of the dust emission. This explains in part why these sources were not detected in the Main Catalog. Although their integrated flux densities may be equal (and sometimes higher) than sources in the Main Catalog, this flux is diluted into several beams and therefore drops below the detection limit for the central beam.
We recall that this increase in the ALMA sizes measured in the Supplementary Catalog remains such that globally the ALMA emission extends over much smaller sizes than their Hband sizes, confirming that the ALMA sources are particularly compact at 1.1 mm (e.g., Chen et al. 2015;Simpson et al. 2015b;Rujopakarn et al. 2016;Elbaz et al. 2018;Calistro Rivera et al. 2018;Franco et al. 2020, submitted).

How complete is the Main plus Supplementary catalog?
The average noise in the GOODS-ALMA image is RMS = 0.182 mJy, hence the 3.5-σ limit of the Supplementary Catalog converts into a detection limit of about 0.64 mJy. We note that since the RMS of the noise varies across the image, because it is subdivided in 6 slices taken at different epochs, sources may be detected below 0.64 mJy (e.g., a source was detected at 0.55 mJy).
The various studies that have carried out millimetric source counts (e.g., Hatsukade et al. 2013;Oteo et al. 2016;Aravena et al. 2016;Umehata et al. 2017;Fujimoto et al. 2017;Dunlop et al. 2017;Franco et al. 2018;Hatsukade et al. 2018) allow us to estimate an expected galaxy surface density that varies between ∼2000 and ∼3500 galaxies/deg 2 above 0.65 mJy at 1.1 mm. Over the size of 69.5 arcmin 2 of the GOODS-ALMA survey, this amounts to an estimated number of sources ranging between 39 and 48. By comparison, we have now extended the number of detections in GOODS-ALMA to 35 galaxies. This number is not far from the expected value, especially when one accounts for cosmic variance, and suggests that the present sample may be more than 70 % complete above 0.65 mJy.

Conclusion
Using IRAC and VLA (combined with deep K s images), we are able to explore the presence of galaxies detected at 1.1 mm with ALMA down to the 3.5-σ limit. This was done despite the extremely large number of independent beams in the ALMA image, even after tapering from 0 . 29 to 0 . 6.
In order to avoid introducing spurious associations, we restricted the new sample to ALMA detections with either an IRAC counterpart closer than 0 . 3 or closer than 0 . 7 but with a radio counterpart as well. In two cases, we used the K-band image to deconvolve IRAC sources that were missed by previous studies because of their close proximity to bright IRAC neighbors. These two galaxies do not exhibit any counterpart in the HST images, hence they are optically-dark, but both present a radio counterpart. In total we find 16 galaxies in the Supplementary Catalog that bring the total sample of GOODS-ALMA 1.1 mm sources to 35 galaxies. This number is between 70 and 90 % of the predicted number of galaxies expected to be detected at 1.1 mm above 0.65 mJy as derived from existing millimeter number counts. We now detect in GOODS-ALMA between a third and half of the most massive star-forming galaxies (log 10 (M /M ) = 11 -12), depending on the redshift range within 2 < z < 4.
The redshift range of the Supplementary Catalog covers a wider range (z = 0.65 -4.73) than the sources of the Main Catalog (z = 1.95 -3.85). The median redshift of the Supplementary Catalog z med,S C = 2.40 is slightly lower than that of the Main Catalog z med,MC = 2.73 due to the presence of low redshift galaxies. The typical physical size of the new sources in the present Supplementary Catalog (1.3 kpc) is twice larger than that of the Main Catalog sources (0.65 kpc). The lower surface brightness of these sources explains partly why they were not detected in the Main Catalog. Hence, pushing down the ALMA detection limit using IRAC and VLA allowed us to reach galaxies with lower stellar masses than in the Main Catalog (median stellar mass M = 7.6×10 10 M ) in which dust-enshrouded starformation extends over twice larger sizes. However, this increase in the ALMA sizes is not large enough to question the fact that the ALMA emission globally extends over much smaller sizes than the H-band light, confirming that the ALMA sources are particularly compact at 1.1 mm.
Moreover, we used a comparison of nearly 400 galaxies in common between HST and Pan-STARRS in the GOODS-ALMA field to show that the astrometry of the HST image does not only suffer from a global astrometric shift, as already discussed in previous papers, but also from local shifts that draw the equivalent of a distortion map that was artificially introduced in the process of building the mosaic of the GOODS-South HST image. We present a solution to correct for this distortion and use this correction in our identification of counterparts. We note that in some cases, the absence of this correction led previous studies to attribute the wrong counterpart to ALMA detections. This will be discussed in more detail in a following paper (Franco et al. 2020, submitted).