GOODS-ALMA: The slow downfall of star-formation in $z$ = 2-3 massive galaxies

We investigate the properties of a sample of 35 galaxies, detected with ALMA at 1.1 mm in the GOODS-ALMA field (area of 69 arcmin$^2$, resolution = 0.60", RMS $\simeq$ 0.18 mJy beam$^{-1}$). Using the UV-to-radio deep multiwavelength coverage of the GOODS-South field, we fit the spectral energy distributions of these galaxies to derive their key physical properties. The galaxies detected by ALMA are among the most massive at $z$ = 2-4 (M$_{\star,med}$ = 8.5$ \times$ 10$^{10}$ M$_\odot$) and are either starburst or located in the upper part of the galaxy star-forming main sequence. A significant portion of our galaxy population ($\sim$ 40%), located at $z\sim$ 2.5-3, exhibits abnormally low gas fractions. The sizes of these galaxies, measured with ALMA, are compatible with the trend between $H$-band size and stellar mass observed for $z\sim2$ elliptical galaxies suggesting that they are building compact bulges. We show that there is a strong link between star formation surface density (at 1.1 mm) and gas depletion time: the more compact a galaxy's star-forming region is, the shorter its lifetime will be (without gas replenishment). The identified compact sources associated with relatively short depletion timescales ($\sim$100 Myr), are the ideal candidates to be the progenitors of compact elliptical galaxies at $z$ $\sim$ 2.


Introduction
Over the last 8 billion years, the cosmic star formation density has decreased by a factor ∼ 10 (e.g. Madau & Dickinson 2014). One of the major key questions in astrophysics is to understand why the Universe's star-forming activity reaches a peak around z = 2 and why it is now so ineffective at generating stars.
Due to the lack of infrared (IR) surveys able to detect "typical" star-forming galaxies at z > 2, the actual contribution of dust-obscured galaxies to the cosmic star formation history at these redshifts remains largely unknown, especially at high masses where galaxies are known to be metal-rich (e.g. Tremonti et al. 2004) and dust-rich (e.g. Boissier et al. 2004;Reddy et al. 2010). The star-formation rates (SFRs) of these high redshift galaxies are mostly estimated from ultra-violet (UV) measurements emitted by short-lived massive stars (e.g. Kennicutt & Evans 2012). This UV emission is strongly affected by the presence of dust in the interstellar medium (ISM) which absorbs part of this emission to be re-emitted in IR. Therefore, to correctly estimate the SFR, a dust correction needs to be applied. This approach has proved effective for distant galaxies up to epochs close to reionization (e.g. Oesch et al. 2015;Bouwens et al. 2015;McLeod et al. 2015) but suffers from caveats due to uncertainties on the attenuation law and the difficulties to constrain it (e.g. Cowie et al. 1996;Pannella et al. 2009). For this reason, constraining galaxy IR emission is essential to obtain a robust star formation estimate. E-mail: m.franco@herts.ac.uk The rest-frame peak of a galaxy's spectral energy distribution (SED) with a dust temperature between 30 and 50 K can vary between 72 and 125 µm (e.g. Casey et al. 2014), corresponding to an observed peak between ∼280 and 500 µm at z = 3. To constrain the shape of the IR SED, at least one measurement must be done beyond this peak in the FIR part of the spectrum. This is why (sub)millimeter observations are necessary to constrain the IR luminosity of a galaxy. Thanks to the negative K-correction submillimeter observations of galaxies are not affected by the flux decrease with increasing redshift over 2 < z < 10 (Blain et al. 2002). With the Atacama Large Millimeter/Submillimeter Array (ALMA), it is now possible to detect galaxies with continuum emission below 1 mJy and angular resolution lower than 1 , which makes it possible to overcome the limit of confusion.
The study of distant and massive galaxies is essential to understand our models of galaxy formation and evolution, as they are the ideal candidate progenitors of compact quiescent galaxies at z ∼ 2 (Barro et al. 2013;Williams et al. 2014;van der Wel et al. 2014;Kocevski et al. 2017, see also Elbaz et al. 2018) and of present-day elliptical galaxies (Swinbank et al. 2006;Michałowski et al. 2010;Ricciardelli et al. 2010;Fu et al. 2013) that represent 60% of the total stellar mass in the local Universe (e.g., Fukugita et al. 1998;Hogg & Turner 1998;Bell et al. 2003). In particular, one of the most critical questions about the growth of galaxies concerns the evolution of the gas fraction over cosmic time and of the efficiency of galaxies to transform this gas into stars (e.g. Somerville & Davé 2015;Schinnerer et al. 2016;Tacconi et al. 2018). Therefore, the study of massive and distant galaxies is of utmost importance to constrain galaxy evolution models. The Great Observatories Origins Deep Survey-South (GOODS-South) field benefits from deep and ultra-deep surveys over a large range of wavelengths (the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, CANDELS (Koekemoer et al. 2011;Grogin et al. 2011, PIs: S. Faber, H. Ferguson), the Spitzer Extended Deep Survey (Ashby et al. 2013), the GOODS-Herschel Survey , the Chandra Deep Field-South (Luo et al. 2017), ultra-deep radio imaging with the Karl G. Jansky Very Large Array (VLA) (Rujopakarn et al. 2016) and the Hubble Ultra Deep Field, HUDF). This large effort allows us to study the whole SED of massive and distant galaxies by securing the cross-identification of ALMA detected galaxies thanks to its high angular resolution.
The GOODS-ALMA large survey covers 69 arcmin 2 in the deepest region of CANDELS, with a depth of 0.18 mJy, in which 20 sources were blindly detected (Franco et al. 2018, hereafter F18). A detailed description of this survey, detection techniques, first results, and the presentation of optically-dark galaxies revealed by ALMA are presented in F18. Going further in the analysis of these data, we used Spitzer/IRAC and VLA to extend our catalog to 16 additional sources detected down to 3.5σ (see Franco et al. 2020, submitted, hereafter F20a).
Beyond cosmic noon (z 2) most studies on the evolution of star formation density are based on Lyman break galaxy (LBG) samples (e.g. Steidel et al. 1999;Álvarez-Márquez et al. 2016;Bouwens et al. 2016). Already, evidence exists that above a stellar mass of typically 5 × 10 10 M the LBG technique misses the majority of massive dusty galaxies, because of their faintness and the redness of their UV slope (van Dokkum et al. 2006;Bian et al. 2013;Wang et al. 2016;Wang et al. 2019). Furthermore, recent studies with ALMA of a population of galaxies previously undetected by the Hubble Space Telescope (HST) has shed new light on our understanding of the origin and formation of massive galaxies (Wang et al. 2016;Fujimoto et al. 2016;Elbaz et al. 2018;Schreiber et al. 2018b). These optically dark galaxies constitute 20% of the sources detected in GOODS-ALMA (F18), 17% if we include the sources detected down to 3.5σ (see F20a). Despite the fact that they are undetected by the HST (at 5σ limiting depth H = 28.2 AB at 1.6 µm), they are detectable through their thermal dust emission thanks to the depth and capabilities of ALMA. The systematic study of massive galaxies (M > 5 × 10 10 M ) during this period of rapid transition between star-forming and quenched galaxies (Muzzin et al. 2013) is crucial to understand the mechanism by which star formation ceases in these galaxies.
Several surveys of the GOODS-South field have been carried on with ALMA around 1 mm, resulting in a 'wedding cake' distribution of surveys. A deep survey in the Hubble Ultra Deep Field (HUDF, 20 h, 4.5 arcmin 2 , RMS = 35 µJy, λ = 1.3 mm, Dunlop et al. 2017), a wider, shallower survey encompassing the HUDF, the ALMA 26 arcmin 2 survey of GOODS-S at one millimeter (ASAGAO, 45 h, 26 arcmin 2 , RMS = 61 µJy, λ = 1.2 mm, Hatsukade et al. 2018) and finally the GOODS-ALMA survey itself encompassing both fields and covering the full area of GOODS-South with the deepest WFC3/H-band coverage (PI: D. Elbaz, 20 h, 69 arcmin 2 , RMS = 182 µJy, λ = 1.1 mm, F18). In addition, two spectroscopic surveys (the ALMA Spectroscopic Surveys; ASPECS), a pilot ) and large program (González-López et al. 2019), were performed with ALMA over an area of ∼1 arcmin 2 and ∼3 arcmin 2 respectively, inside the HUDF. This 'wedding cake' approach allows us to both to collect information on extreme and rare galaxies in mapping large regions and also to have a precise view of more common and abundant galaxies with deep observations on a small area. Interestingly, extending the survey area allows the detection of more distant galaxies than deep observations of a smaller area. Indeed, while only ∼13% of the galaxies detected with ALMA have a redshift ≥ 3 in the deep ALMA survey of HUDF (Dunlop et al. 2017), ∼40% of the F18 galaxies are at z 3. In addition, ALMA surveys over large areas allow the detection of particularly massive and dusty galaxies that are rare in terms of surface density.
This paper is organized as follows: in §2, we will describe the data used in this paper. In §3, we will describe how we took advantage of our large multiwavelength coverage to fit the spectral energy distributions (SEDs) of the galaxies detected in GOODS-ALMA. In §4 we will explain how we derived the main parameters of the galaxies (M dust , M gas , SFR, depletion time). In §5, we will discuss the results and interpret them as the evidence for a slow downfall of star-formation in z ∼ 2 − 3 massive galaxies.

ALMA data
This paper uses the ALMA observations obtained between August and September 2016 (Project ID: 2015.1.00543.S; PI: D. Elbaz), extending over an effective area of 69 2 , covering the deepest part of the CANDELS field -in the GOODS-South fieldcentered at α = 3 h 32 m 30.0 s , δ = −27 • 48 00 (J2000). We perform this analysis in a 0.60 -tapered mosaic reaching a RMS 0.18 mJy beam −1 . The complete description of this survey and the data reduction are presented in detail in F18, where the properties of 23 bright ALMA sources discovered as the result of the blind survey in this field are discussed and cataloged. Sources that were most likely false (indicated by an * in Table 2 in F18 and AGS22) as well as the sources for which we have only incomplete information about stellar mass and redshift (AGS15 and AGS17) are not taken into account in the rest of this paper.
In addition, this catalog has been enriched with 16 galaxies, detected with a lower S/N, using the VLA and Spitzer/IRAC counterparts (see F20a for more details). In this work, we will analyze a sample of 35 galaxies with redshifts between 0.6 and 4.7 (z med = 2.7) and stellar masses ranging from 10 10.3 to 10 11.5 M (M ,med = 10 10.93 M ).
As the SPIRE beam is very large (18.1 , 24.9 , and 36.6 at 250 µm, 350 µm, and 500 µm, respectively) and yielding a high confusion limit, we use the catalog of Wang et al. (in prep.), which is built with a state-of-the-art de-blending method, using optimal prior source positions from 24 µm and Herschel/PACS detections.

Method
We fit the spectral energy distributions using two different methods, depending on whether or not the galaxy has a Herschel counterpart.
For galaxies that have a far-IR flux density measured by the Herschel space observatory, we employ the SED-fitting code CIGALE 1 (Code Investigating Galaxies Emission; Boquien et al. 2019). We use the stellar population models of Bruzual & Charlot (2003) and the attenuation law of Calzetti et al. (2000). The IR SED fitting was performed using the dust infrared emission model given by Draine et al. (2014). We independently fit the wavelengths from the UV up to 16 µm, and from 24 µm up to the millimeter wavelengths respectively (see Fig. 1 for an example and Fig. A.1 for the full sample). The radio portion has been added after the fitting process, using the FIR/radio correlation, with a constant ratio between FIR and radio luminosity of 2.34 (Yun et al. 2001). The parameters used in CIGALE were given by Ciesla et al. (2018) and are shown in Table 1.
In contrast, if the galaxy has no Herschel infrared counterpart, we fit the data with the dust spectral energy distribution library 2 presented in Schreiber et al. (2018a), and normalized to the ALMA flux density at 1.13 mm in the SED. We proceed iteratively. After fitting the galaxy with a star-formation main sequence (MS; Noeske et al. 2007;Rodighiero et al. 2011;Elbaz et al. 2011) SED, we compute the distance to the main sequence (R S B = SFR/SFR MS ) using the output IR luminosity (8-1000 µm) and the redshift. The R S B and the redshift of the galaxy can be used to calculate the dust temperature (T dust ) and IR8 (L IR /L 8 ) from Eq. 18 and 19 of Schreiber et al. (2018b). IR8 can be used as an indication of the compactness of distant galaxies . T dust and IR8 are therefore set to these newly calculated values in the SED-fitting process, and an updated SED is generated.

AGN subtraction
To fit an SED with an AGN component, we used the code decompIR by Mullaney et al. (2011). This code proposes to fit an AGN according to the spectrum of a sample of host galaxies representative of galaxies with an AGN. The contribution of the AGN to the IR luminosity can lead to an overestimation of the dust infrared emission and therefore an overestimation of the SFR. The AGN SED used in decompIR does not include the wavelengths below 5µm. To better characterize the contribution of AGN to the total infrared luminosity of galaxies, we need to know their behavior at rest-frame wavelengths lower than 5 µm, corresponding to the domain where the contribution of AGN is most important. Since this AGN model is only defined for wavelengths > 5 µm, we therefore used another AGN model for wavelengths shorter than 5 µm. We extrapolate AGN emission to shorter wavelengths, using an AGN model from Kirkpatrick et al. (2015), by fitting the flux of the AGN model from Kirkpatrick et al. (2015) to the one from decompIR at 5 µm. The subtraction of the AGN contribution from the optical part of the galaxy spectrum remains highly uncertain, so we have chosen not to modify the stellar masses of galaxies hosting an AGN, whilst keeping in mind that they could be overestimated.

Dust Temperature
For the sake of simplicity and comparison with previous studies, we measure the dust temperature by fitting a modified black body (MBB) model, following: where k B is Boltzmann's constant, h is the Planck's constant, β is the dust emissivity spectral index, T dust is the dust temperature, and S ν is the flux density. We have assumed a spectral index β = 1.5 (e.g., Kovács et al. 2006;Gordon et al. 2010). We fit the flux densities at λ rest ≥ 0.55λ peak using the MBB model as suggested by Hwang et al. (2010), and exclude the synchrotron contribution. The criteria we have defined to select the points to be modelled with a MBB are as follows: at least one data point between 0.55 × λ peak and λ peak .
at least one data point beyond λ peak , with a wavelength lower than or equal to 3 mm.
Galaxies selected in (sub)millimeter flux density are expected to be biased towards low dust temperatures (e.g. Magdis et al. 2010;McAlpine et al. 2019). Indeed, at fixed redshift and IR brightness, the (sub)millimeter flux of a galaxy with a colder dust temperature will be higher than that of a galaxy with a warmer dust temperature. We investigated where the galaxies detected in the GOODS-ALMA survey are located in the IR Luminosity-Temperature plane (Fig. 2, left panel) and in the Redshift-Temperature plane (Fig. 2, right panel). For comparison, we also plot the dust temperature of all the galaxies located in GOODS-ALMA with an MBB fit, as described above. We find that the galaxies detected by ALMA do not exhibit a systematic offset compared to those undetected by ALMA. For an SMG, the dust temperature is correlated with the IR luminosity (e.g. Wardlow et al. 2011). We have found a median dust temperature of 40 K for our sample. However, we note that the spectral index β has an influence on the temperature. We chose to fix it, at β = 1.5 in order to have fewer free parameters in our fit and to compare all galaxies consistently. If we had taken β = 2, on the other hand, the MBB temperatures would have been slightly lower (1 -4 K lower). Note that we do not use this T dust temperature to determine dust masses (see Sect. 4.1).

Dust mass
Following Draine et al. (2007), we adopt the maximum starlight intensity relative to the local interstellar radiation field U max = 10 6 U , and the power-law index α = 2 in Eq. 2. The dust mass is estimated with the CIGALE code using the formula of Draine et al. (2007): where U min ≤ U max , α 1 is the exponent of the power law describing the intensity distribution of the interstellar radiation field, and γ is the relative fraction of dust heated by each source. Draine et al. (2007) showed that α = 2 and U max = 10 6 provided a good fit to a large sample of nearby galaxies from the Spitzer SINGS program.

Gas mass
As we will discuss in Sect. 4.3.1, the ALMA detected galaxies are located in the SB region or in the upper part of the MS. To understand if their position is due to an increased star formation efficiency (SFE ≡ SFR/M gas ) or a large gas reservoir compared to normal MS galaxies, we computed their gas mass M gas as well as their gas fraction f gas , defined by: To compute the gas mass, we assume a gas-to-dust ratio (δ GDR ) depending only on metallicity. This method of derivation of the gas mass, its comparison with the CO-to-H 2 factor as well as its limitations have been explained in the literature (e.g., Magdis et al. 2011Magdis et al. , 2012Berta et al. 2016;Magdis et al. 2017). This ratio was directly derived by Leroy et al. (2011) in the local Universe, and can be applied to our sample, assuming that this relation is valid at all redshifts: where M gas = M(H 2 )+ M(H I ). At the redshifts of this study, the atomic hydrogen can be considered negligible compared to the molecular form (e.g. Leroy et al. 2008;Obreschkow & Rawlings 2009;Daddi et al. 2010). We note that recent studies have found evidence for a steep increase in the gas-to-dust ratio of sub-solar metallicity galaxies at z∼2 compared with this local relation (Coogan et al. 2019), but we do not expect this effect to be significant for our more massive, enriched galaxies. As we do not have direct metallicity measurements for our galaxies, we use the equation given by Genzel et al. (2012) to compute the metallicity: − 0.0896 log 10 (M /1.7) 2 (5) In this equation, we include a conversion factor (1/1.7) to transform the original formula from a Chabrier IMF to a Salpeter IMF. However, the metallicity can be underestimated for galaxies above the main sequence (e.g. Silverman et al. 2015), which could artificially increase the proportion of gas and conversely underestimate the gas depletion time . We compared our calculated metallicities to the metallicities obtained using the fundamental metallicity relation (FMR) of Mannucci et al. (2010): with m = log 10 (M /1.7)-10, and s = log 10 (SFR/1.7). We applied an average correction factor of -0.25 ± 0.02 to convert from the FMR derived using the Kewley & Dopita (2002) metallicity calibration to the calibration of Pettini & Pagel (2004), as given in in mind that the uncertainties on the determination of M gas are large, taking into account all of the assumptions used. We also verified that the mass of gas derived by the method described above was in agreement with that derived using the method of Scoville et al. (2016). The Scoville et al. (2016) method is based on the assumption that continuum measurements of the Rayleigh-Jeans tail can be used to estimate the mass of dust and therefore, the mass of gas. Since this method is based on the Rayleigh-Jeans tail, it can only be used at long wavelengths (λ > 250 µm). However, if the dust emission is optically thin, the Scoville et al. (2016) method may underestimate the gas mass (Miettinen et al. 2017). At 1.13 mm, the estimate of the gas mass can be written, according to equations Eq. 6 and Eq. 16 of Scoville et al. (2016), as: with S ν the flux at 1.13 mm in mJy and Γ z RJ the correction for departure in the rest frame of the Planck function from Rayleigh-Jeans (Scoville et al. 2016): where h is the Planck's constant and k b is the Boltzmann constant.
Using a fixed dust temperature (25K), we find a difference between the calculated gas mass (M (gas, this work) ) and that derived following Scoville et al. (2016): The gas mass is directly related to the depletion time (τ dep ) by: 4.3. SFR

SFR IR
The infrared luminosity of each galaxy has been converted to SFR using the Kennicutt relation (Kennicutt 1998) below: with L IR in L , and where d l is the luminosity distance. In Fig. 3, we illustrate the distribution of SFRs as a function of redshift for the ALMA-detected galaxies. We also represent the theoretical detection limit of the galaxies present in the survey at the limit of 4.8σ (solid black line) used to create the main catalog, assuming a constant RMS (RMS = 0.182 mJy) over the whole map, as well as the 3.5σ (dashed black line) limit used to build the supplementary catalog. However, as the RMS is not constant, and therefore may be lower at some points in the map, some galaxies (AGS21, for example) appear below this line.
We note that there is a galaxy (AGS36) that is clearly offset from the detection limit, with a SFR ∼ 20 M yr −1 . This galaxy is atypical, as it has the lowest redshift in our sample (z = 0.66, the same redshift as AGS30) and it also hosts a powerful AGN with an X-ray luminosity = 1.39 ×10 43 erg sec −1 .
The SFR limit has been computed taking into account the main sequence SED from Schreiber et al. (2018a), with the tem-perature and the fraction of polycyclic aromatic hydrocarbon (PAH) emission evolving as a function of redshift. The IR luminosity was calculated by integrating the flux from the SED using Eq. 11, and was then converted into SFR using Eq. 10.
This IR luminosity limit allows us to detect galaxies down to an IR luminosity of 10 12 L at redshift z = 1.5, and down to 3×10 12 L at redshift z = 4. In other words, for a MS galaxy, this allows us to detect galaxies with a minimum stellar mass of 2.5 × 10 11 M , 1.8 × 10 11 M and 1.5 × 10 11 M for redshifts z = 2, z = 3 and z = 4 respectively, using Eq. 9 of Schreiber et al. (2015).
The majority of the galaxies detected in this ALMA survey are starbursts, or in the upper part of the MS (see Fig. 4). Among the galaxies for which we determined the SFR, 54% of them have a R S B (SFR/SFR MS ) > 3 (see Table 2).
Not surprisingly, the most IR luminous galaxies have been listed in the main catalog. However, we note the presence of a portion of galaxies from the supplementary catalog that are also among the most IR luminous galaxies. The size of the galaxies explains this behavior. The galaxies detected in the supplementary catalog generally have larger sizes than those in the main catalog (F20a). Even though the peak flux is fainter on average, the integrated flux can reach values close to those of the main catalog.
The vast majority (86%) of the galaxies analyzed in this study can be classified as ultraluminous infrared galaxies (ULIRGs) with 12 < log 10 (L IR /L ) < 13. Only one galaxy has an infrared luminosity slightly above this threshold. All of the galaxies with log 10 (L IR /L ) < 12 are galaxies less distant than the average of the galaxies detected in this survey, with z < 1.5.

SFR UV
Massive galaxies are known to be heavily dust-obscured at z > 2 (e.g., Magnelli et al. 2009;Murphy et al. 2011). While the SFR IR is derived from the dust emission, we also consider the unobscured contribution to the total SFR, observed through UV emission. For the most massive galaxies (M > 10 10.5 M ), the fraction of obscured to unobscured star formation (SFR IR /SFR IR+UV ) is greater than 90% (Whitaker et al. 2017).
We derive L UV from the observed magnitude as follows: where d L is the luminosity distance and m is the observed magnitude. The SFR UV , uncorrected for dust attenuation, is in turn derived from the L UV , following (Daddi et al. 2004): The total SFR (SFR tot = SFR UV + SFR IR ) is given in Table 2. The median contribution from SFR UV to SFR tot is only 1.3%.

AGN
Of the 1008 sources detected in X-ray during the 7 Ms exposure survey of the Chandra Deep Field-South presented in Luo et al. (2017), 397 lie in the GOODS-ALMA field. We adopted a crossmatching radius of 0.6", after applying the offset corrections presented in F20a. We found that 13/23 (6/20) of our main (supplementary) catalog galaxies had matches with the Luo et al. (2017) catalog. However, the detection in X-rays is not definitive proof The SFR IR of these galaxies have been used. Galaxies with Herschel counterparts are color-coded as a function of the f gas . The other galaxies are represented by gray dots. We have rescaled all of the SFRs by multiplying by SFR MS (z)/SFR MS (z = 2.7), in order to maintain their relative positions with respect to the main sequence. We indicated the MS using Eq. 9 from Schreiber et al. (2015), with a dispersion of 0.3 dex (solid and dashed lines respectively).
that a galaxy hosts an AGN. We corrected the Luo et al. (2017) cataloged X-ray luminosities when redshift deviations were observed, using the following formula: and assuming a fixed Γ = 2. In the following paragraphs, a galaxy will be considered as hosting an AGN if the galaxy has an X-ray luminosity L X,int > 10 43 erg s −1 (luminous X-ray sources).

5.
The slow downfall of star-formation in z = 2-3 massive galaxies

A large fraction of galaxies in our sample with low gas fractions
In this survey, we have detected particularly massive galaxies, the majority of which are beyond cosmic noon at z ∼1-2. The study of the gas mass reservoirs is essential to understand how the galaxies will evolve with redshift and whether these galaxies could be the progenitors of passive galaxies at z ∼ 2. To obtain the most robust results possible, we have considered in the following section only galaxies with a Herschel counterpart. The galaxies without a Herschel counterpart are marked with † in Table 2. In Fig. 5 (left panel), we compare the gas fraction of our galaxies as a function of their deviation from the MS, with the relationship presented in Tacconi et al. (2018): In the same way, we compare the depletion time with the relationship presented in Tacconi et al. (2018): .
We have rescaled this relationship to correspond to the median redshift (z med = 2.7) and the median stellar mass of our sample (M ,med = 8.5 × 10 10 M ). To be able to directly compare the gas fraction of our galaxies to the relationship of Tacconi et al.  40.6 ± 1.7 0.80 ± 0.23 Table 2 (10) Dust temperature derived from a MBB model assuming β=1.5. † indicates galaxies without a Herschel counterpart and whose L IR is determined only by the ALMA contribution. For these galaxies, we show the mass of gas as an indication but we do not use it in the rest of this paper; (11) Flux density at 1.1 mm. indicates changes in the flux density since F18. A summary of the fluxes (peak and integrated) as well as the sizes measured in the Main and Supplementary catalogs are given in Table A.1. (2018), we have also scaled our gas fractions according to the median redshift and stellar mass of our sample. The gas fractions, before rescaling, are presented in Table 2.
The depletion times span a large range, between 30 and 1600 Myr. The galaxies studied here show a dependence between depletion time and distance to the main sequence (R SB ), although very scattered (see Fig. 5).
About half of the GOODS-ALMA galaxies follow the f gas -R S B relation from (Tacconi et al. 2018, Eq. 20). However, we find a surprisingly large fraction (40%) of galaxies lying well below this relation, i.e., with excessively short depletion times (see Fig. 5). Interestingly, this fraction is not correlated with the starburstiness R S B , as defined by the distance to the MS. The galaxies with the shortest depletion times are also those with the lowest gas fraction. This is because despite exhibiting lower gas masses, these galaxies keep forming stars with a high SFR.
We note that the majority of the ALMA galaxies experiencing a strong AGN episode with L X > 10 43 erg sec −1 lie below the τ dep -R S B and f gas -R S B relations (stars in Fig. 5). This suggests that the low gas content and associated short depletion time of the galaxies may be due to the AGN feedback, heating the surrounding extragalactic medium and preventing further infall of gas. In other words, about half of the galaxies at these flux densities and redshifts appear to suffer from starvation and constitute excellent candidate progenitors of z 2 massive and compact elliptical galaxies. To further investigate this possibility, we show in Sect. 5.2.1 that the ALMA sizes, i.e., where the stars are formed, are consistent with the compact cores of z = 2 elliptical galaxies.
However, there is a trend between R S B and the stellar mass of the galaxies, in that the less massive galaxies in our sample have a larger average R S B . We also investigated the evolution of the depletion time as a function of the stellar mass but we found no correlation. This means that the star-formation efficiency (SFE = M gas /SFR = 1/τ dep ) does not change according to the stellar mass of the galaxy.  The gas fractions cover a significant range of values, between f gas = 0.21 and 0.84, with a median of f gas = 0.52 (mean = 0.52). These values are consistent with other studies, such as Wiklind et al. (2014). We do, however remark that for the two common galaxies between this work and Wiklind et al. (2014), there is a significant difference in the calculated gas fractions. These two common galaxies are outliers from the rest of the Wiklind et al. (2014) sample as they have gas fractions close to unity, and in fact, correspond to two HST-dark galaxies that were previously falsely attributed with optical counterparts.
We note that a significant number of the outliers with low gas fractions are classified as AGN. The presence of an AGN can influence the measurement of the stellar mass of the galaxy and artificially lower the calculated gas fraction of the galaxies. This result is consistent with Perna et al. (2018) who found systematically low gas fractions in obscured AGN at z > 1 and suggests that AGN feedback could lead to the expulsion of gas. One of these galaxies has a low gas fraction (21%) and does not show any sign of an AGN. This galaxy is a particularly striking example of interacting galaxies, with strong tidal tails. This galaxy does not have a high star formation rate, it lies on the MS, but it does display a starburst-like behavior since it exhibits a short gas depletion time. This galaxy could, therefore, be a member of the population of galaxies described in Elbaz et al. (2018), a starburst galaxy hidden in the main sequence.
We find a negative correlation between the stellar mass and the gas fraction (see Fig. 6, right panel). The following equation characterizes this relationship: A similar relationship has been found in other studies (e.g. Popping et al. 2012;Magdis et al. 2012;Sargent et al. 2014;Schinnerer et al. 2016). Galaxies hosting an AGN do not seem to occupy a particular position in Fig. 6. We also indicate in the left panel the distance to the main sequence as a function of the stellar mass. We can also see a clear negative correlation between the stellar mass and R S B . On the other hand, it is not possible to say whether selection effects are driving this trend. To be detected, a galaxy of low mass must have a larger R S B than a massive galaxy. On the other hand, we do not find massive galaxies (M > 10 11 M with R S B > 5).
We found no correlation between the depletion time and the stellar mass. This means that the star-formation efficiency (SFE = M gas /SFR = 1/τ dep ) does not change according to the mass of the galaxy. Galaxies transform their gas into stars at a rate independent of the stellar mass of the galaxy.
Galaxies with the lowest gas fractions also appear to be the most massive, suggesting that we are witnessing a slow downfall of the galaxies with the most massive galaxies dying first to become elliptical galaxies, in a similar way to what has been shown in Schreiber et al. (2016), but at higher redshifts.

Size
Several studies have reported the observation of massive starforming galaxies, compact in the H-band (e.g., blue nuggets; Barro et al. 2013;Dekel & Burkert 2014). It has been proposed that these galaxies are the progenitors of massive, compact and passive galaxies at z = 2 (e.g., Barro et al. 2013;Williams et al. 2014;Toft et al. 2014;van der Wel et al. 2014;Barro et al. 2016;Kocevski et al. 2017).
We have, thanks to the GOODS-ALMA survey, selected a sample of massive star-forming galaxies. These galaxies are among the most massive ones within the UVJ active -i.e., starforming -galaxies (Williams et al. 2009, using the same definition as in F18) listed in the ZFOURGE catalog (see Fig. 10 in F20a). For example, with ALMA we have detected the most massive ZFOURGE galaxy in the redshift range 1 < z < 2, the most massive galaxy at 2 < z < 3, the second most massive galaxy at 3 < z < 4. These galaxies cannot continue to form stars for long periods. If this were the case, they would become much more massive than the most massive galaxies we have observed at z ∼ 1, or in the local universe.
The galaxies in the present paper have not been selected to be compact in the H-band. They are flux-selected. Due to the low dispersion of the main sequence, this selection is equivalent to a stellar mass selection. We aim to study here whether galaxies that have not been selected to be compact in the Hband can also be the progenitors of compact galaxies at z 2. To do this, we have compared the H-band sizes of the galaxies de- tected by ALMA with the H-band sizes of the galaxies present in GOODS-ALMA. The majority of the galaxies studied in this paper have a redshift between z = 2 and 4. We report in Fig. 7-left panel, the H-band sizes of all galaxies within 2 < z < 4 located in the area defined by the GOODS-ALMA survey, as a function of stellar mass, in blue. We also show the H-band size of the ALMAdetected galaxies with black open markers. Galaxy sizes and Sérsic indices are obtained from van der Wel et al. (2014). These values have been computed by fitting a single-component Sérsic profile using GALFIT (Peng et al. 2010) at both 1.4 and 1.6 µm. We focus here on the results at 1.6 µm. We also show the trends for the UVJ active and UVJ passive galaxies with blue and red lines respectively. These two relations were parametrized by van der Wel et al.  18) where r e is the effective radius, in other words, the semi-major axis of the ellipse that contains half of the total flux of the best-fitting Sérsic model, in kpc. We use the following parameters: log 10 (A) = -0.06 ± 0.03, α = 0.79 0.07, and the scatter in (r e ) in logarithmic units σlog 10 (r e ) = 0.14 ± 0.03 for earlytype galaxies and log 10 (A) = 0.51 ± 0.01, α = 0.18 ± 0.02, and σlog 10 (r e ) = 0.19 ± 0.01 for late-type galaxies.
We see that there is a significant difference in size between active and quiescent galaxies. The size of star-forming galaxies is on average larger than passive galaxies. Mosleh et al. (2011) noted, for example, that UV-bright galaxies with 10 10 < M /M < 10 11 and 0.5 < z < 3.5 are larger than quiescent galaxies in the same mass and redshift range by 0.45 ± 0.09 dex.
For the vast majority of the ALMA detected galaxies (open black squares), their optical rest-frame sizes are comparable to the sizes of the H-band UVJ active galaxies (blue hexagons) at 2 < z < 2 selected in the same field of view. We also over-plot, in Fig. 7, the compactness criterion given in Barro et al. (2013) and modified by Barro et al. (2016): Only three GOODS-ALMA galaxies are compact following the compactness criterion of Eq. 19. These galaxies lie on the trend for quiescent galaxies. We note that those galaxies that do not follow the trend of star-forming galaxies systematically host an AGN. If these galaxies suddenly stopped forming stars, they would already be located on the right trend in the mass-size diagram to be compact massive galaxies. With the data available to us, it is not possible to distinguish whether the compaction of the galaxy has triggered the AGN or, on the contrary, it is the presence of the AGN that has caused its compaction.
We also show the ALMA 1.1 mm sizes in comparison to the H-band sizes in Fig. 7, right panel. The ALMA sizes for the main and supplementary catalogs are given in F20a and in A.1. The size distribution differs slightly between the two samples. We showed in F18 that we were biased towards compact sources with our detection limit of 4.8σ. By lowering this detection threshold in the supplementary catalog, which was made possible as a result of basing our detections on IRAC and VLA detections, we are now detecting galaxies with larger ALMA sizes. For the 26 galaxies for which we have both HST H-band sizes and could measure a 1.1 mm size with ALMA, we find that ALMA sizes are generally smaller, with a median r e,HST /r e,ALMA = 2.3. This ratio is significantly higher than the ratio of 1.4 found by Fujimoto et al. (2017) at 870 µm, for a sample of 1034 ALMA sources.
Considering that dust emission is a good indicator of dustobscured star formation, this result indicates that compact dustobscured star formation (at least more compact than optical emission) is taking place in the core of the galaxies studied here. This study confirms the comparison of optical and millimeter sizes performed at z 1.3 by Puglisi et al. (2019), and extends it to higher redshifts, at and before the epoch of the peak of cosmic star-formation.
For these galaxies to be the progenitors of compact elliptical galaxies at z 2, they need to become more compact than their H-band size. The observed strong star formation activity concentrated in a small region of the galaxy can morphologically transform a galaxy into a more compact object. Assuming that there is no addition of gas, the majority of these galaxies have gas reservoirs equal to or close to their stellar mass. If this gas is transformed into stars in the compact emission region detected by ALMA, these galaxies will become compact and gradually migrate into the location of the mass-size diagram reserved for passive galaxies.
The ALMA galaxies presented here exhibit a present Sérsic index in the H-band of <n AGS > = 1.63. We have seen that . The density of the UVJ active galaxies (with 2 < z < 4) in the GOODS-ALMA field is represented by the blue hexagons. The blue and red lines represent the trends of active and passive galaxies respectively, while the dashed lines give the scatter on these relations (van der Wel et al. 2014). The ALMA-detected galaxies are shown with black squares. Right panel: ALMA size-mass plane for the ALMA detected galaxies. For comparison, the trends for active and passive galaxies are also shown. We indicate the compactness criterion described in Eq. 19 to visualize which galaxies are compact in H-band. In this Figure, ALMA sizes have been divided by a factor of √ 0.65, which corresponds to the median of the b/a ratio, to reflect size differences with HST. the amount of star formation associated to the compact 1.1 mm emission is large enough to bring the half-light radius of the ALMA galaxies on top of the one expected for passive compact galaxies at z ∼ 2, hence the question that remains to be answered is whether this evolution will also be accompanied with an increase of the Sérsic index that will bring them closer to the one observed for passive compact galaxies, i.e., increasing from n = 1.6 to n = 2.6. To answer this question, we would need to know with enough accuracy what is the actual Sérsic index of the ALMA sources in the 1.1 mm band. Unfortunately our resolution and depth are not sufficient to derive a Sérsic index for the dust emission, hence we cannot answer the question without supplementary information. We note however, that at least some of the ALMA sources may present Sérsic indices similar to those measured by Hodge et al. (2016), Elbaz et al. (2018) and Rujopakarn et al. (2019) who measured Sérsic indices close to n ∼ 1. A simple model of the impact of the newly formed stars following such an index to the final stellar distribution of the galaxies suggests that they would remain below n = 2.6. Hence we conclude that despite the fact that the ALMA galaxies will inevitably have compact final half-light radii, only a fraction of them will end up showing the high Sérsic index of the compact ellipticals observed at z ∼ 2. We note that this index itself presents a distribution, hence we cannot reject the possibility that most of the present ALMA sources represent reliable progenitors of compact ellipticals at z ∼ 2.

Morphology
We here aim to look at the mechanisms that may have driven the gas in the center of the ALMA galaxies. This may be violent disc instabilities (Dekel & Burkert 2014), or other dissipative processes, including mergers (Wellons et al. 2015). To investigate the role of mergers in the compaction process, we now investigate the morphology of the ALMA-detected galaxies.
Increasing numbers of observations have demonstrated that elliptical galaxies at z = 2 are particularly compact (e.g. Trujillo et al. 2006;van Dokkum et al. 2008;Conselice 2014;van der Wel et al. 2014). Major merger events can give rise to elliptical galaxies (e.g. Dekel & Cox 2006;Hopkins et al. 2006), but can also influence the compactness of the star-formation in galaxies (e.g. Wuyts et al. 2010;Ceverino et al. 2015). Due to their large stellar masses, which has generated and retained a large amount of metals, and hence dust, against outflows (e.g. Dekel & Silk 1986;Dekel & Woo 2003;Tremonti et al. 2004), the galaxies detected in this study are extremely dust-obscured. In addition to this, their redshift makes them particularly faint in UV and optical filters. Some of them are Y-dropout (e.g., AGS5, AGS18), V-dropouts (e.g., AGS9, AGS10) or visible only in the K-band (AGS4, AGS11, etc.). The morphology of these galaxies is therefore difficult to obtain. We cross-matched our sample with the catalog of Huertas-Company et al. (2015a) that estimates the probability of being a spheroid, disk or irregular using the Convolutional Neural Network technique. In addition to the 6 HST-dark galaxies, which, by definition, cannot be categorized, nine other galaxies have H-band fluxes too faint to be classified (F160W > 24. 5 AB mag). This leaves only 20 of our galaxies that are present in this catalog. We use the simplified classification proposed in Huertas-Company et al. (2015b): pure bulges: f sph > 2/3 AND f disk < 2/3 AND f irr < 1/10; pure disks: f sph < 2/3 AND f disk > 2/3 AND f irr < 1/10; -disk+sph: f sph > 2/3 AND f disk > 2/3 AND f irr < 1/10; irregular disks: f disk > 2/3 AND f sph < 2/3 AND f irr > 1/10; irregulars/mergers: f disk < 2/3 AND f sph < 2/3 AND f irr > 1/10.
As a result, 61% (11/18) of our galaxies are classified as irregulars/mergers (two galaxies do not fit into any of the categories presented above). If we also take into account irregular disks, 78% (14/18) have an irregular morphology. Several galaxies show clear morphological characteristics of mergers, for example with large tidal tails. The galaxy AGS31, which exhibits large tidal tails, is an excellent illustration of this (see Appendix A in F20a). For other galaxies, the interaction with another galaxy is more discrete or uncertain.
We compared these proportions against a control sample. We have for each of the 18 galaxies with estimated morphologies from the Huertas-Company et al. (2015a) catalog, a galaxy closest to it in terms of redshift and stellar mass. This control sample exhibits significantly different morphological proportions. Only 6% (1/18) of these galaxies can be classified as irregulars/mergers, 22% (4/18) if we take into account irregular disks. The galaxy population detected by ALMA, therefore, tends to be on average biased towards irregular galaxies. By more precisely considering the morphological classification, we obtain for the sample galaxies detected by ALMA an average f sph = 0.16, f disk = 0.50, f irr = 0.34, while for the control sample, an average of f sph = 0.40, f disk = 0.53, f irr = 0.07. While the disc fraction is relatively constant between these two samples, we are witnessing an inversion of the fraction between the irregulars and the spheroids.
We are therefore in the presence of a heterogeneous population of both secularly evolving disk and merger-type galaxies. The number of galaxies classified as irregulars/mergers is slightly higher with that found by models (Hayward et al. 2011(Hayward et al. , 2013, which predict that for a population of SMGs with S 1.1mm > 0.5 mJy, star-forming galaxy-pairs account for ∼30-50 percent of the galaxies.

IR surface brightness as a prior for the remaining lifetime of a galaxy
The role of compact star-formation in enhancing the efficiency of star-formation is illustrated in Fig. 8. Galaxies forming stars with the largest star-formation surface density, Σ S FR , experience the strongest star-formation episodes with the shortest depletion times (see Table 3). The SFR surface density (Σ S FR ) can be defined as: where R 1.1mm is the half light radius (see Sect. 5.2.1 for a description of the determination of the millimeter size). We have found a strong negative correlation between Σ S FR and depletion time (see Fig. 8). A similar trend was found in Elbaz et al. (2018). This correlation can be characterized by the following equation: (21)

Conclusions
We have taken advantage of the excellent multiwavelength supporting data in the GOODS-South field and the largest contiguous ALMA survey to derive the physical properties of 35 ALMA flux-selected galaxies. This sample of galaxies comes both from a purely blind search (galaxies with a peak flux > 4.8 σ, see F18) and from an extension of this catalog that we have built down to the 3.5 σ limit using IRAC and VLA to probe fainter millimeter galaxies (F20a). The comparison of the number of galaxies detected at 3.5 σ with the number counts indicates that our sample of galaxies is almost complete. These galaxies are massive (M ,med = 8.5 × 10 10 M ) and therefore rare, so in order to be able to detect and analyze them, a sufficiently large survey, such as GOODS-ALMA was needed. It is possible now, for the first time with this survey, covering ∼69 arcmin 2 . The analysis of the SEDs of these galaxies has made it possible to derive some of the physical properties of these galaxies. We are confronted with a heterogeneous population of galaxies. However, we highlight that about 40% of our galaxy sample exhibits a particularly small gas fraction. We remark that the most massive galaxies in   Fig. 8. Depletion time as a function of the Σ S FR , color-coded according to the distance to the main sequence. The solid and dashed lines are the fit to the sliding median and its 68% scatter respectively. The stars represent galaxies with L X,int > 10 43 erg s −1 . For comparison, the results of Elbaz et al. (2018) are shown by gray dots. our sample are also the galaxies with the lowest gas fractions. With their high star formation rates (the galaxies are mostly starbursts, or on the upper part of the main sequence) and without a gas refill mechanism, they will consume their gas reservoirs in a typical time of 100 Myr.
We also studied the sizes of these galaxies. The advantage of conducting a survey is that it does not impose a priori criteria for selecting the galaxies studied. The ALMA detected galaxies have observed H-band sizes comparable to the majority of galaxies with the same stellar masses and redshifts, whereas their dust emission regions, i.e., the regions tracing the obscured part of the star formation, are relatively compact and have sizes comparable to passive galaxies at z ∼ 2.
We have investigated the link between depletion time and star formation surface density. We confirm the result showing a tight correlation between these two quantities. The denser the galaxy star-forming region is, the shorter the gas depletion time is. Mechanisms leading to a compaction of the obscured starforming regions are to be confirmed, but a compact region massively forming stars at the center of a galaxy can lead to a rapid morphological transition from a spiral to a compact elliptical galaxy such as those observed at z ∼ 2, despite the fact that the ALMA selected galaxies are not yet compact in the H-band (they are not yet blue nuggets).
All of these different pieces of evidence indicate that our ALMA-detected galaxies are the ideal progenitors of passive galaxies at z ∼ 2 and natural exhaustion of their gas reservoirs (slow downfall) is sufficient for this transition to happen quickly without needing to invoke a quenching mechanism. The large fraction of AGN among galaxies with the shortest depletion times and gas fractions suggest however that they may act by a starvation mechanism in preventing any further growth.   Optical to radio Spectral Energy Distributions for the 35 galaxies detected in the GOODS-ALMA survey. If the studied galaxy has also been detected with Hershel, we fit the SED using the CIGALE code, otherwise we use the dust spectral energy distribution library presented in Schreiber et al. (2018a). The solid black line represents the best fit, which can be decomposed into the IR dust contribution (brown line), a stellar component uncorrected for dust attenuation (dark blue line), synchrotron emission (purple line) and the AGN contribution (orange line). In addition, we show the best fit of a modified black body, with β = 1.