The Main Sequence at z ∼ 1.3 Contains a Sizable Fraction of Galaxies with Compact Star Formation Sizes: A New Population of Early Post-starbursts?

The stellar mass (M_⋆)–size relation provides important insights on M_⋆ assembly processes. Observational studies in the rest-frame optical/near-infrared (NIR) have shown that the dependence of size on M_⋆ varies with galaxy type: star-forming, late-type galaxies (LTGs) have sizes that are mildly dependent on M_⋆ and are larger than quiescent early-type galaxies (ETGs; van der Wel et al. 2014). Instead, local luminous infrared galaxies (LIRGs), ultraluminous infrared galaxies (ULIRGs) and high-redshift starburst galaxies (SBs) have very compact gas/star formation rate (SFR) sizes, driven by the ongoing merger (Tacconi et al. 2008). Thus, sizes appear to be related to star formation (SF) activity.

To better understand how galaxies are growing, optical/NIR continuum studies, tracing M_⋆, ought to be complemented by structural analyses of the star-forming component. Observations of the Hα emission show that low-to-moderately obscured SF at z ≳ 1 takes place generally within disks similarly or even more extended than M_⋆ (e.g., Nelson et al. 2016a), although dust attenuation might reduce their effective radius (Nelson et al. 2016b).

A different picture is emerging from studies imaging high-z galaxies at long wavelengths. Various works show that obscured SF is hosted in compact regions of massive main-sequence (MS) galaxies (Tadaki et al. 2017; Elbaz et al. 2018), submillimeter galaxies (SMGs; Hodge et al. 2016; Miettinen et al. 2017; Fujimoto et al. 2018), and "blue nuggets" (Barro et al. 2016). On the other hand, stacking Atacama Large Millimeter/submillimeter Array (ALMA) images in the uv plane reveals that "typical" high-z galaxies host extended obscured SF (Lindroos et al. 2016; Zanella et al. 2018).

In this Letter we constrain the ALMA sizes for a statistical sample of 93 far-infrared (FIR)-selected galaxies at 1.1 ≤ z ≤ 1.7 in COSMOS spanning a wide range in M_⋆ and SFR. We use a Chabrier (2003) initial mass function (IMF) and a standard cosmology (H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.3, Ω_Λ = 0.7).

2.1. ALMA Observations and Size Measurements

We use ALMA observations targeting the CO(5–4) transition and λ_obs ∼ 1.3 mm underlying continuum (circularized beam ∼07) in 123 FIR selected galaxies with 1.1 ≤ z_spec ≤1.7 in COSMOS (Program-ID 2015.1.00260.S, PI: E. Daddi). Galaxies were selected requiring a 3σ detection at 100 and/or 160 μm in PACS-Herschel catalogs from the PEP survey (Lutz et al. 2011), implying L_IR ≳ 10¹²L_⊙. We also have CO(2–1) observations for a subset of 75 galaxies (∼15 beam; Program-ID 2016.1.00171.S, PI: E. Daddi) and CO(4–3), [C i] and underlying continuum observations for 29 objects (∼2'' beam; Valentino et al. 2018). We analyze these tracers together to increase the accuracy of the size measurements. Here we focus on the 93 sources detected at ≳5σ in at least one continuum or line tracer, for which we can estimate reliable sizes or robust upper limits. For a full description of the data set, data reduction, and measurements, we refer to future papers.

To analyze the data we use GILDAS-based²¹ scripts. The scripts optimize spectral extraction spatial position (constant over all data sets) and emission line ranges iteratively for each detected emission, based on the recovered signal (see Daddi et al. 2015 and Valentino et al. 2018).

To measure sizes, the scripts extract the signal amplitude as a function of the uv distance from each tracer, combining their signals scaling the uv-distances to a common frequency and marginalizing over a free normalization constant for each tracer. The galaxy best-fit size (defined as the effective radius r_eff = FWHM/2) and its 1σ uncertainty is determined by comparing the uv distance versus amplitude distribution to circular Gaussian models (see Figure 1). The goodness of the fit is estimated from the χ² minimization as a function of the size. Unresolved sources would show a constant amplitude profile in the uv-plane. To quantify the probability of each galaxy to be unresolved (P_unres) the scripts compare the best-fit χ² to the χ² for a point source. A source is considered to be resolved when P_unres ≤ 10%. We obtain 32 resolved sources (average size/size error ∼5.3) with this threshold, which is determined a posteriori in a way that we statistically expect only 0.5 of these to be spuriously resolved, on average. For 61 sources we cannot derive robust size constraints, and we show these as 1σ upper limits in our plots. Depending on the combined signal-to-noise ratio (S/N) of the emission line/continuum detection, size upper limits vary from being quite stringent (r_eff ∼ 010) to fairly loose. The median upper limit is r_eff = 028. Thirty sources have no significant detection in the ALMA data set. We use Monte Carlo simulations to test this method. We create 1000 mock realizations of our data sets by perturbing the best-fit model within the measured uncertainties in the uv-amplitudes plot, assuming Gaussian noise, and we measure sizes of each synthetic data set. We simulate sources covering a broad range of sizes, from much smaller to comparable to the beam (similarly to what has been found for real galaxies) and over a range of S/Ns as spanned by real galaxies. We find no significant systematics to within 5%, which is much lower than any measurement errors.

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Our procedure combines information from tracers with potentially different spatial distributions, requiring an intrinsic surface brightness distribution consistently extended within the uncertainties. This is confirmed with our data set as sizes from independent tracers are in good agreement (see Figure 1). We do expect consistency among individual sizes as all the tracers considered here are directly sensitive to the star-forming gas. The dust continuum and low-J CO emission are expected to be highly equivalent tracers of the gas (e.g., Magdis et al. 2012). The higher-J CO emission are sensitive to higher density gas, being closer proxies to the SFR (e.g., Daddi et al. 2015). However, given the overall tight correlations between gas and SFR (e.g., Sargent et al. 2014), we expect any intrinsic galaxy-wide size difference to be subtle. Furthermore, Figure 1 shows that the ALMA size is mostly driven by CO(5–4), typically detected with highest S/N and having also the smallest beam. Considering the CO(5–4) size measurements only does not affect our conclusions.

2.2. M_⋆, SFRs, and K_s-band Sizes

We use K_s-band and ALMA sizes to construct the M_⋆–size plane for the sample (see Figure 2). At these redshifts, the K_s-band (rest frame ∼1 μm) roughly traces the M_⋆. Galaxies in our sample have the "typical" extension of star-forming disks in K_s-band as they nearly all locate within the LTG relation of van der Wel et al. (2014). Instead, ALMA measurements are skewed toward smaller sizes.

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We compute the χ² of the data distribution as

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}\displaystyle \frac{{\left({\mathrm{Size}}_{\mathrm{ALMA},{\rm{i}}}-{\mathrm{Size}}_{\mathrm{LTG},{\rm{i}}}\right)}^{2}}{{\sigma }_{\mathrm{ALMA},{\rm{i}}}^{2}+{\sigma }_{\mathrm{LTG},{\rm{i}}}^{2}},\end{eqnarray} \tag{ 1 }$$

where σ_LTG and σ_ALMA are the LTG scatter and the 1σ size error, respectively. We consider here all sources with their size measurements and errors (including those shown on plots as upper limits). Sixty-six galaxies are consistent with the LTG relation, whereas 27 are more compact than expected in an average implementation of the LTG. These 27 are our "compact sample" reported in red in the plots. Of these, 18 are inconsistent with the LTG relation at ≥3σ significance and are highlighted with larger symbols. To verify the robustness of our results, we compute the compact fraction via a survival analysis approach through the nonparametric Kaplan–Meier estimator, using 1σ upper limits. The lower 1σ boundary in the compact fraction derived in this way is in good agreement with our conservative estimate described above. To obtain an improved average constrain on unresolved compact galaxies, we combine their observations in the uv distance versus amplitude plane measuring the size as in Section 2.1. This results in an unresolved average source with a 3σ upper limit r_eff = 013 (downward triangle in Figure 2).

To compare the M_⋆ and molecular gas size on an individual basis, we plot the K_s-band-to-ALMA and the LTG-to-K_s-band size ratios as a function of the compactness (Figure 3). The compactness is defined as the ratio between the LTG size at the galaxy M_⋆ and the ALMA size. Even if compactness measurements are lower limits for most compact galaxies, the y-axes in this figure show that compact galaxies have an ALMA component that is smaller than the K_s-band. By considering the average constraints, the compact population is >3.2× smaller in ALMA than in the K_s-band at 3σ. The lower panel shows that most galaxies have an LTG-to-K_s-band size ratio around one within a factor of two.

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The ALMA size is measured on images combining star-forming gas tracers and tightly correlates with the CO(5–4) emission (see Figure 1) being sensitive to the star-forming molecular gas (Daddi et al. 2015; Liu et al. 2015). This implies that compact galaxies in our sample have most of the SF activity occurring in a nuclear, compact region.²³ In the following, we will consider this feature as arising from mergers and interactions (Barnes & Hernquist 1992). Alternative mechanisms such as violent disk instabilities (Bournaud 2016) cannot dramatically reduce the global SF size of galaxies to factors of several below that of normal disks. Anomalous streams of gas may also drive large gas concentrations in the nucleus (Dekel & Burkert 2014). However, the occurrence of those events has never been proven observationally. Moreover, mergers or flybys are often required to trigger those streams in simulations, making this scenario effectively coincident with our proposed interpretation.

Mergers are expected to enhance the galaxy SFR, as suggested in the local universe (Sanders & Mirabel 1996) and at high redshift (Rodighiero et al. 2011). As such, we might expect to find compact galaxies preferentially above the MS. In Figure 4 (left panel) we plot the SFR_FIR as a function of M_⋆ for our sample, including information on the molecular gas size. Surprisingly, we find no clear correlation between the molecular gas size and the MS position. This is in contrast with the regularity seen from Hα (e.g., Nelson et al. 2016a) and possibly in the dust-obscured SF component. For example, Rujopakarn et al. (2016) show that SFR and M_⋆ are similarly extended in dusty MS galaxies, supporting the existence of wide-spread obscured SF within the MS. Similarly, Miettinen et al. (2017) show that SMGs within the MS are extended and disk-like.

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In our study, several MS-outliers are consistent with the LTG relation, at odds with the idea that off-MS galaxies are compact merger-driven starbursts (Silverman et al. 2015, 2018a, 2018b; Calabrò et al. 2018). This is consistent with the idea that these galaxies are gas-rich objects with disk-wide starbursts (e.g., Scoville et al. 2016). We suggest, however, that at least some of these objects might be merging pairs in a precoalescence phase, individually unresolved with our ∼07–15 beam, as HST imaging supports in some cases. This would be consistent with results from hydrodinamical simulations (Perret et al. 2014) and radio sizes of precoalescence MS-outliers (Calabrò et al. 2019). This is also suggested by the case study of an MS-outlier with a ∼10 kpc CO disk at ∼2'' resolution splitting into two ∼1 kpc disks at higher resolution (Silverman et al. 2018a). Follow-up at higher spatial resolution will allow us to distinguish these scenarios.

More puzzling is the presence of compact galaxies within the MS. A quantification of the prevalence of these sources is essential, as, e.g., the bimodal population model of Sargent et al. (2012) predicts the existence of some SBs within the MS. We thus compute the fraction of compact galaxies in three sSFR bins on the MS (light gray lines in Figure 4—left) and we compare this quantity with the expectation from the Sargent et al. (2012) model. We plot the fractions of compact galaxies as a function of the MS position in the right panel of Figure 4. Compact galaxies are the ∼50% of the MS population at M_⋆ > 10¹¹M_⊙, with a negligible uncertainty in this bin coming from size measurement uncertainties (but still limited by statistics). As we consider compact galaxies to be most likely mergers, this result is not consistent with the canonical MS paradigm whereby MS galaxies are disks experiencing steady-state growth.

We note that we observed the ∼1% of all COSMOS galaxies above >10¹²L_⊙, notably requiring a spectroscopic redshift to enable the CO follow-up. However, the biasing effect of the spectroscopic sample on sizes should be small. Nevertheless, we account for selection effects that might bias our observations against the most extended galaxies, which would result systematically in lower S/N for a fixed luminosity. Conservatively, we consider undetected sources in our sample (gray dots in Figure 4—left) as consistent with the LTG relation, together with size upper limits within the LTG relation. We emphasize that ALMA size measurements include low-J CO observations and dust continuum tracing lower density, possibly more extended, molecular gas. Although significant size variations across tracers are not detected in our data set (see Section 2), the presence of such a bias would further strengthen our conclusions. We explore in the following possible causes for the excess of compact galaxies within the MS.

A possibility is that we are observing galaxies in which the merger has not been capable of triggering intense SB activity due to the enhanced gas fractions, as suggested by simulations (Fensch et al. 2017). While this might happen in practice, these mergers with failed bursts would likely be classified as such by morphological methods, but our compact fraction significantly exceeds the merger fraction measured on M_⋆ maps (Cibinel et al. 2019, see also Figure 4). Also, we expect that mergers not triggering strong starbursts would also fail at producing very compact SF cores (Bournaud et al. 2015).

We notice though that the different M_⋆ and SFR extensions in compact galaxies (see Figure 3) implies strong specific SFR (sSFR) gradients. Accounting for only the M_⋆ within the star-forming cores by scaling the total M_⋆ by ${r}_{{K}_{{\rm{s}}}}^{2}/{r}_{\mathrm{ALMA}}^{2}$, compact galaxies actually host starbursts in their nuclei, with sSFRs that would place them off the MS (see Figure 5). These nuclear starbursts are not intense enough for the whole galaxy to classify it as an MS outlier. We thus suggest compact MS galaxies to be post-starburst systems in which the burst has subsided their peak levels. We are likely sampling different phases of the merger. In fact, the typical duration of merger-triggered bursts is ∼50–100 Myr (e.g., Di Matteo et al. 2008), and as soon as the activity diminishes after consuming a large fraction of the gas reservoir, the SFR is likely to remain centrally peaked for longer times. The typical timescales for gas reaccretion are in fact much longer (∼0.5–1 Gyr) at these redshifts (Sargent et al. 2012) and similar to galaxies doubling time (Lilly et al. 2013). It is also possible that, following the merger, these galaxies will evolve to become quiescent. Hence, we would expect these post-SB galaxies to be more numerous than SBs, and located inside the MS. Galaxies in this post-SB phase would not be selectable by the Cibinel et al. (2019) method, which is sensitive to mergers up to the coalescence, i.e., until the system retains M_⋆ map asymmetries (see also Cibinel et al. 2015).

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All in all, we find no clear correlation between the molecular gas size and the MS position and ≥50% of MS galaxies above M_⋆ ∼ 10¹¹M_⊙ are compact in the molecular gas. Such a high percentage of compact galaxies within the MS is in line with previous literature results, showing that up to the ∼60% of MS galaxies above 10¹¹M_⊙ host compact molecular gas cores (Tadaki et al. 2017; Elbaz et al. 2018). We suggest that compact galaxies at the massive end of the MS might represent post-SB mergers that have ended the starburst phase in the off-MS region but are still mainly forming stars in a compact nucleus or a post-merger compact disk (see, e.g., Figure 2 in Fensch et al. 2017). This suggests that the contribution of bursty (merger-driven) SF to the cosmic SFR density is larger than previously anticipated (∼15%–20%, e.g., Rodighiero et al. 2011), and might reach up to ∼50% at the high-mass end where SF disks become rarer (as is also expected because we are sampling beyond the characteristic M_⋆ of their mass functions). The ALMA compactness might provide a tool to select MS galaxies in an early post-SB phase, complementary to absorption lines or color selection criteria selecting objects already below the MS (Wild et al. 2009). Further studies on the stellar population properties of the compact population will allow us to confirm this hypothesis. If confirmed, this "early post-SB" population might open scenarios for understanding the role of merger-driven starbursts in the galaxy life-cycle and may possibly provide insights on the passivization mechanisms at high redshift.

We acknowledge funding from INAF PRIN-SKA 2017 1.05.01.88.04, the Chinese Academy of Sciences President's International Fellowship Initiative 2018VMA0014, the Villum Fonden grant 13160, the Cosmic Dawn Center of Excellence by the Danish National Research Foundation, ERC Consolidator 648179, National Science Foundation AST-1614213, the Spanish Ministry of Economy and Competitiveness 2014 Ramon y Cajal MINECO RYC-2014-15686, the National Key R&D Program of China (2017YFA0402704), the CAS Key Research Program of Frontier Sciences, and NSFC 11420101002. J.D.S. was supported by the ALMA Japan Research Grant of NAOJ Chile Observatory, NAOJ-ALMA-0127, JSPS KAKENHI grant No. JP18H04346, and the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. A.P. acknowledges funding from Region Île-de-France and Incoming CEA fellowship from the CEA-Enhanced Eurotalents program, co-funded by FP7 Marie-Skłodowska-Curie COFUND program (grant Agreement 600382). I.D. is supported by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 788679.