Dust Attenuation, Bulge Formation, and Inside-out Quenching of Star Formation in Star-forming Main Sequence Galaxies at z ∼ 2^*

The 10 targets of this study (Table 1, Figures 1 and 2) are drawn from our SINS/zC-SINF AO program that has yielded AO-SINFONI IFU spectroscopy of the Hα and [N ii] emission lines spatially resolved on ∼1 kpc scales for 35 massive SFMS galaxies at z ∼ 2 (Förster Schreiber et al. 2014; Genzel et al. 2014a, 2014b; Newman et al. 2014; Tacchella et al. 2015a, 2015b; Förster Schreiber et al. 2018). The sample is virtually unique, given the long integration times of usually >10 hr to obtain Hα spectroscopy at 8 m AO resolution. Our 10 targets were initially taken from various spectroscopic surveys, namely, seven targets are from the zCOSMOS-DEEP survey (Lilly et al. 2007, 2009), two targets are from the "BX/BM" sample of Steidel et al. (2004), and one target is from the "Deep-3a" survey (Kong et al. 2006). The specific selection criteria for the SINFONI AO observations were an uncontaminated Hα emission line and a minimum expected Hα line flux (corresponding roughly to a minimum SFR of $\sim 10\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$; Förster Schreiber et al. 2009; Mancini et al. 2011; Förster Schreiber et al. 2018).

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Table 1.  Sample Galaxies with Hα Redshifts and Main Stellar Population Properties

Source	zHα	M⋆	(U − V)rest	AV,SED	AV,map	SFRSED	SFRUV+IR	Indicator	SFRUV	SFRUV,map
		(1010 M☉)	(mag)	(mag)	(mag)	($\tfrac{{M}_{\odot }}{\mathrm{yr}}$)	($\tfrac{{M}_{\odot }}{\mathrm{yr}}$)		($\tfrac{{M}_{\odot }}{\mathrm{yr}}$)	($\tfrac{{M}_{\odot }}{\mathrm{yr}}$)
ZC400569	2.241	23.3	1.29	1.4	1.5	241.0	239.3	UV+24 μm	168.0	156.6
ZC400528	2.387	16.0	0.84	0.9	0.5	148.0	556.5	UV+100 μm	148.0	46.7
Q2343-BX610	2.211	15.5	0.93	0.8	1.2	60.0	⋯	⋯	60.0	85.5
D3A-15504	2.383	15.0	0.71	1.0	1.0	150.2	145.6	UV+24 μm	150.0	116.1
ZC406690	2.195	5.3	0.56	0.7	1.0	200.0	296.5	UV+24 μm	337.0	201.2
ZC407302	2.182	2.98	0.50	1.3	0.6	340.0	358.1a	UV+24 μm	130.0	67.0
ZC412369	2.028	2.86	0.88	1.0	1.3	94.1	IR-undet	⋯	130.0	140.2
Q2346-BX482	2.257	2.5	0.77	0.8	1.1	79.8	⋯	⋯	80.0	95.8
ZC405226	2.287	1.13	0.56	1.0	0.9	117.0	IR-undet	⋯	87.0	58.3
ZC405501	2.154	1.04	0.33	0.9	0.6	84.9	IR-undet	⋯	68.0	28.1

Note. Listed are the Hα spectroscopic redshifts from the AO-SINFONI data (z_Hα), the stellar masses (M_⋆; defined as the integral of the SFR), the rest-frame U − V colors, the dust attenuation A_V,SED from galaxy-integrated SED modeling, the dust attenuation A_V,map from the (FUV–NUV) color maps, the SFRs from SED (SFR_SED), the UV+IR SFRs (SFR_UV+IR), the SFR indicator of the IR, SFR from the aperture UV photometry (SFR_UV), and the SFR from the UV maps (SFR_UV,map). For the SED modeling we use the Bruzual & Charlot (2003) model and assume a Chabrier (2003) IMF, solar metallicity, the Calzetti et al. (2000) reddening law, and either constant or exponentially declining SFRs. The uncertainties on the stellar properties are dominated by systematics from the model assumption and are up to a factor of ∼2–3 for M_⋆ and ∼3 or more for SFRs. Sources undetected with Spitzer/MIPS and Herschel/PACS are indicated explicitly with "IR-undet," to distinguish them from objects in fields without MIPS and PACS observations.

^aUnreliable IR flux due to blending; see Appendix B.

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In addition to our AO-SINFONI Hα data, these galaxies have a wealth of ancillary ground- and space-based multiwavelength data that give integrated stellar masses, global UV+IR SFRs, and other key galactic properties. Furthermore, our HST WFC3 Cycle 19 no. GO12578 program (eight targets; Tacchella et al. 2015b), together with our NICMOS pilot study (two targets; Förster Schreiber et al. 2011a, 2011b), has provided rest-frame optical F110W (J) and F160W (H) data for all targets of this study. These data have given us their rest-frame optical morphology and their 1 kpc distribution of the oldest stellar populations through mass-to-light ratio estimates from the 4000 Å break (see Tacchella et al. 2015a). Figure 1 presents the data used in this paper. In particular, HST images, dust attenuation maps, UV and Hα SFR maps, stellar mass maps, and Hα velocity maps are shown.

Table 1 lists the Hα redshift and the main stellar properties. The SED modeling has been presented in Förster Schreiber et al. (2009, 2011a, 2011b) and Mancini et al. (2011). Briefly, we adopt the best-fit results obtained with the Bruzual & Charlot (2003) code, a Chabrier (2003) initial mass function (IMF), solar metallicity,¹⁵ the Calzetti et al. (2000) reddening law, and constant SFRs. We define the stellar mass to be the integral of the past SFR. There are two motivations for doing this: (i) this stellar mass remains constant after the galaxy ceases its star formation, which makes the comparison with quiescent galaxies across different epochs simpler; and (ii) the sSFR defined with this stellar mass definition is a good indicator for the inverse of the e-folding timescale (i.e., roughly the mass-doubling timescale). These are about 0.2 dex larger than the commonly used definition, which subtracts the mass returned to the interstellar medium, i.e., the mass of surviving stars plus compact stellar remnants (Carollo et al. 2013). For our sample the stellar masses adopted here (and also in Tacchella et al. 2015a, 2015b) are on average 0.12 ± 0.3 dex higher (with a maximum difference of 0.19 dex) than the ones presented in Förster Schreiber et al. (2009, 2011a, 2011b) and Mancini et al. (2011). Importantly, all estimates from the literature have been converted to this stellar mass definition. The uncertainty on the stellar mass is a factor of ∼2–3, while on the SFRs and stellar ages it is even larger. These uncertainties mainly arise from the basic assumption of the SED modeling, namely, the IMF and the star formation histories (SFHs). Besides the SED-derived quantities and the UV+IR SFRs, Table 1 presents the integrated values of the 2D maps of dust attenuation and UV SFR (see Section 4 for details).

Our 10 galaxies have stellar masses between ${10}^{10}\,{M}_{\odot }$ and a few times ${10}^{11}\,{M}_{\odot }$ and SFRs between 60 and $\sim 560\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. In Figure 2 we show our sample of 10 galaxies in the wider context of the general population of SFGs at the same redshifts (converted to the same stellar mass definition as used in this work). Since our analysis is limited to 10 galaxies, we inevitably probe a limited parameter space of the massive galaxy population at z ∼ 2. We use the SFGs at z = 2.0–2.5 from the 3D-HST survey (Brammer et al. 2012; Skelton et al. 2014) as our reference sample. Panels (a) and (b) show that our sample probes the typical SFGs on the SFMS at z ∼ 2.2: it lies slightly above the SFMS ridgeline by ${0.14}_{-0.30}^{+0.32}$ dex. We use the SFMS ridgeline of Whitaker et al. (2014), which is based on the z = 2.0–2.5 star-forming galaxy population from the CANDELS/3D-HST survey (Brammer et al. 2012; Skelton et al. 2014). In panel (c) we compare the (U − V)_rest − (U − J)_rest colors of our sample to the ones of the overall galaxy population drawn from the CANDELS/3D-HST survey at z = 2.0–2.5 and with ${M}_{\star }={10}^{10.0}\mbox{--}{10}^{11.5}\,{M}_{\odot }$. We have color-coded the points according to their stellar mass in order to highlight that more massive galaxies are on average redder and more dusty. Our galaxies overlap with the bulk of the SFGs in terms of (U − V)_rest − (U − J)_rest colors, but we do not probe massive and dusty SFGs in the upper right corner of the UVJ diagram, which may partially be due to small number statistics in addition to our sample selection criteria. Similarly, looking at the ratio of IR and UV SFR (panel (d)), while our sample overlaps with the global population traced by the stacking analysis of Whitaker et al. (2014) of the CANDELS/3D-HST data, our most massive galaxies lie slightly below the ridgeline of SFR_IR/SFR_UV versus M_⋆ of the larger sample. Finally, our sample probes the typical trends in the planes of size (circularized H-band half-light radius) versus M_⋆ and Sérsic index versus M_⋆ for star-forming galaxies at z = 2.0–2.5 (van der Wel et al. 2014b), as shown in panels (e) and (f), respectively. The gray circles indicate our galaxies with unreliable measurements because the light distributions are not centrally concentrated (assumed Sérsic models do not represent the galaxy well). See also Tacchella et al. (2015b) for an extended discussion and detailed description of the structural measurements.

Based on Tacchella et al. (2015b; see also stamps in Figure 1), 9 out of our 10 galaxies are disk galaxies, and only one is a clear merger. D3A-15504, Q2343-BX610, ZC405226, and ZC405501 are classified as regular disks, since at the rest-frame optical wavelengths the galaxies show a relatively symmetric morphology featuring a single, isolated peak light distribution and no evidence for multiple luminous components. The velocity maps show clear rotation, and the dispersion maps are centrally peaked; the kinematic maps are fitted well by a disk model with v_rot/σ₀ ≳ 1.5, where v_rot is the inclination-corrected rotational velocity and σ₀ is the velocity dispersion corrected for instrumental broadening and beam smearing. Furthermore, Q2346-BX482, ZC400528, ZC400569, ZC406690, and ZC407302 are classified as irregular disks, because in the optical light the galaxies have two or more distinct peaked sources of comparable magnitude. Their velocity maps show clear signs of rotation. The dispersion maps show a peak, which is, however, shifted in location relative to the centers of the velocity maps. Finally, ZC412369 is classified as a merger, since in the rest-frame optical light two or more distinct peaked sources of comparable magnitude are detected at a projected distance of ∼5 kpc from each other. The velocity maps are highly irregular with no evidence for ordered rotation (i.e., v_rot/σ₀ ≲ 1.5); the velocity dispersion maps show multiple peaks.

The active galactic nucleus (AGN) activity in our sample has been discussed in Förster Schreiber et al. (2014). None of the sources in our sample are detected in the deepest X-ray observations with Chandra (Civano et al. 2016); their flux upper limits imply $\mathrm{log}({L}_{X}/\mathrm{erg}\,{{\rm{s}}}^{-1})\lt 42.5$. For some galaxies, an AGN contribution can be argued based on the mid-IR colors (Q2343-BX610), emission lines (D3A-15504), or radio data (ZC400528).

In our Cycle 22 HST program no. GO13669, we followed up these galaxies with WFC3/UVIS and ACS/WFC observations between 2014 December and 2015 June using the F438W (B) and F814W (I) filters. Our galaxies lie in a narrow redshift range 2.03 < z < 2.39, which puts the FUV into the B band and the NUV into the I band. Therefore, these two passbands cover the entire rest-frame ∼1200–2700 Å wavelength window. This gives us the possibility of measuring the UV continuum slope β in order to constrain the attenuation distribution, one of the main scientific goals of this paper. The WFC3 F438W filter is perfect for the FUV image: the cutoff wavelength of 4000 Å corresponds to 1230–1270 Å in the rest frame, the long-wavelength cutoff to 1450–1500 Å. Furthermore, the ratio of Hα to rest-frame 1400 Å (probed with F438W) versus F438W–F160W will enable us to best disentangle extinction and evolutionary effects among clumps and between clumps and interclump regions, which will be addressed in a future publication.

Each target was observed for four orbits with F438W and, if necessary,¹⁶ one orbit in F814W, with each orbit split into two exposures with a subpixel dither pattern to ensure good sampling of the PSF and minimize the impact of hot/cold bad pixels and other such artifacts (e.g., cosmic rays, satellite trails). For F438W, the individual exposure time was 1376 s, giving a total on-source integration of 11,008 s, and for F814W, the individual exposure time was 544 s, giving a total on-source integration of 2176 s.

2.3.1. Charge Transfer Efficiency

2.3.2. WFC3/UVIS Dark Calibrations

2.3.3. Astrometric Alignment

In order to derive PSF-matched color maps and PSF-corrected profiles as described below, PSFs of the different bandpasses are required. PSFs for each HST camera are created in slightly different fashions, due to varying constraints of the data.

The creation of the WFC3/NIR data PSFs is described in Tacchella et al. (2015b). Briefly, we have stacked six well-exposed and nonsaturated stars. The stars are registered to their subpixel centers, normalized, and then co-added via a median. The FWHM is 016 and 017 for the J and H band, respectively.

The ACS/WFC data and WFC3/UVIS PSFs are created with a hybrid PSF in a similar manner to the PSFs created by Rafelski et al. (2015). We follow the approach of the hybrid PSF because the wings of the PSFs cannot be recreated from a stack of stars owing to the low number of stars. The PSF model is created with the TinyTim package (Krist 1995), subsampled to align the PSFs, resampled to our pixel scale, distortion corrected, and then combined with the same dither pattern and drizzle parameters as were used for the data reduction. The ACS/WFC and WFC3/UVIS stacks of stars are created from 4 and 10 unsaturated stars, respectively. The stars are registered to their subpixel centers, normalized, and then co-added via a median. The final hybrid PSF is a combination of the two, composed of the stack of stars up to a radius of 20 pixels (0''–10) and of the PSF model from 20 to 75 pixels (10–375). In order to prevent discontinuities in the resultant PSF, the PSF model and the star are added together, weighted by a smooth transition window with a full width of 20 pixels (10). The resulting FWHM is 011 (2.16 pixels) and 011 (2.17 pixels) for the ACS/WFC F814W and WFC3/UVIS F438W, respectively.

3.1.1. SFR from UV

The UV continuum (1250–2800 Å) intensity of a galaxy is sensitive to massive stars (≳5 M_⊙), making it a direct tracer of current SFR. By extrapolating the formation rate of massive stars to lower masses, for an assumed form of the IMF, one can estimate the total SFR.

We adopt the conversions of Kennicutt (1998), who assumed a Salpeter (1955) IMF with mass limits of 0.1 and 100 M_⊙, and stellar population models with solar metal abundance. Furthermore, they also assumed that the SFH is constant for at least the past 100 Myr. We modify their calibration downward by a factor of 0.23 dex to match a Chabrier (2003) IMF (Madau & Dickinson 2014):

$$\begin{eqnarray}&&\displaystyle \frac{{\mathrm{SFR}}_{\mathrm{UV}}}{{M}_{\odot }\,{\mathrm{yr}}^{-1}}=0.82\times {10}^{-28}\,\displaystyle \frac{{L}_{\mathrm{UV},\mathrm{corr}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1}},\end{eqnarray} \tag{ 1 }$$

where L_UV,corr is the UV luminosity at 1500 Å corrected for attenuation, i.e., ${L}_{\mathrm{UV},\mathrm{corr}}={L}_{\mathrm{UV},\mathrm{obs}}\times {10}^{0.4{A}_{\mathrm{UV}}}$. We derive L_UV,obs from the observed magnitude as follows:

$$\begin{eqnarray}&&{L}_{\mathrm{UV},\mathrm{obs}}=\displaystyle \frac{4\pi {D}_{L}^{2}(z){10}^{-0.4(48.6+{m}_{\mathrm{UV}})}}{1+z},\end{eqnarray} \tag{ 2 }$$

where D_L(z) is the luminosity distance at z and m_UV is the observed magnitude in the B band. We estimate the amount of UV attenuation, A_UV, from the UV continuum slope (i.e., if ${f}_{\lambda }\propto {\lambda }^{\beta }$), following Meurer et al. (1999):

$$\begin{eqnarray}&&{A}_{\mathrm{UV}}=4.43+1.99\beta .\end{eqnarray} \tag{ 3 }$$

We estimate the UV continuum slope β from the FUV–NUV color (observed B − I color), as detailed in Section 3.3.

3.1.2. SFR from Hα

Another widely used diagnostic for measuring the SFR is nebular emission, with Hα being the most common because it is the strongest of the Balmer H recombination lines, and it is least affected by underlying Balmer stellar absorption features and by extinction compared to the higher-order Balmer lines at shorter wavelengths.

The conversion factor between ionizing flux and the SFR is usually computed using an evolutionary synthesis model. Only stars with masses ≳10 M_⊙ and lifetimes <20 Myr contribute significantly to the integrated ionizing flux, so the emission lines provide a nearly instantaneous measure of the SFR, independent of the previous SFH. We again adopt the conversions of Kennicutt (1998) (Salpeter IMF and solar metal abundance), with the assumption that the SFH is constant for at least the past 10 Myr and that Case B recombination at T_e = 10,000 K applies. We modify their calibration downward by a factor of 0.23 dex to match a Chabrier (2003) IMF:

$$\begin{eqnarray}&&\displaystyle \frac{{\mathrm{SFR}}_{{\rm{H}}\alpha }}{{M}_{\odot }\,{\mathrm{yr}}^{-1}}=4.7\times {10}^{-42}\,\displaystyle \frac{{L}_{{\rm{H}}\alpha ,\mathrm{corr}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}.\end{eqnarray} \tag{ 4 }$$

where L_{Hα, corr} is the Hα luminosity corrected for attenuation, i.e., ${L}_{{\rm{H}}\alpha ,\mathrm{corr}}={L}_{{\rm{H}}\alpha ,\mathrm{obs}}\times {10}^{0.4{A}_{{\rm{H}}\alpha }}$.

Since Hα lies at 6563 Å, it suffers much less dust extinction compared to the UV rest frame of a galaxy spectrum. On the other hand, the Lyman continuum ionizing radiation that gives rise to the Hα emission is mainly produced by massive, short-lived stars that are probably deeply embedded in the giant H ii regions, whereas less massive (<10 M_⊙) stars still contribute to the UV rest-frame stellar continuum on the long term, shine over timescales 10 times longer, and have time to clear or migrate out of the dense H ii regions. The net outcome of this process is that Hα emission probably suffers from an extra attenuation, parameterized by the f-factor that relates E(B − V)_star = f × E(B − V)_gas.

However, the Hα luminosity depends also on the actual extinction in the Lyman continuum, as one gets one Hα photon for each Lyman continuum photon that does not get absorbed by a dust grain (see, e.g., Boselli et al. 2009; Puglisi et al. 2016). Since we are unable to constrain the extinction in the Lyman continuum, we absorb this part of physics in the overall uncertainty of the f-factor (see below), which itself is very uncertain since it depends on the actual extinction law (from the optical to the Lyman continuum) and on the geometry of the emitting regions.

The extra amount of attenuation suffered by nebular emission is still debated, especially at high redshifts. In the local universe, the stellar continuum undergoes roughly half of the reddening suffered by the ionized gas, namely, f = 0.44 (Calzetti et al. 2000). Important to note is that Calzetti et al. (2000) used two different extinction curves for the nebular (k(λ)_gas; Cardelli et al. 1989; Fitzpatrick 1999) and continuum (k(λ)_star; Calzetti et al. 2000), which have similar shapes but different normalizations (R_V = 3.1 and 4.05, respectively). If not differently noted, we adopt the same extinction curves here. At higher redshifts, Wuyts et al. (2013) present a polynomial function to derive extra attenuation from the continuum attenuation; hence, the f value may not necessarily be a constant value for all types of galaxies (see also Price et al. 2014). It is also suggested by recent studies that the typical f value may be higher (f = 0.5–1.0) for high-redshift galaxies (see, e.g., Erb et al. 2006; Reddy et al. 2010; Kashino et al. 2013, 2017; Koyama et al. 2015; Valentino et al. 2015).

Because we lack Hβ data for our galaxies, in this paper we constrain the attenuation of the Hα emission line, A_Hα, by converting the dust attenuation in the continuum at V, A_V, using

$$\begin{eqnarray}{A}_{{\rm{H}}\alpha ,\mathrm{gas}} & = & \displaystyle \frac{E{(B-V)}_{\mathrm{gas}}}{E{(B-V)}_{\mathrm{star}}}\cdot \displaystyle \frac{k{({\rm{H}}\alpha )}_{\mathrm{gas}}}{{R}_{{\rm{V}},\mathrm{star}}}\cdot {A}_{{\rm{V}},\mathrm{star}}\\ & = & \displaystyle \frac{1}{f}\cdot \displaystyle \frac{2.36}{4.05}\cdot {A}_{{\rm{V}},\mathrm{star}},\end{eqnarray} \tag{ 5 }$$

with f = E(B − V)_star/E(B − V)_gas (f = 0.44 from Calzetti et al. 2000; f = 0.7 from, e.g., Kashino et al. 2013). We note that the prescription of Wuyts et al. (2013) gives very similar results to this fiducial relation using a value of f = 0.44.

In this section we briefly mention the effect of varying the stellar population properties on the (FUV−NUV) color. A more detailed discussion including figures can be found in Appendix A.

As highlighted in the Introduction, by far the largest potential effect on the UV color of SFGs is the presence of dust. Therefore, reddening of the UV colors provides a good diagnostic of the magnitude of the dust attenuation. However, other stellar population parameters have also some effect on the UV color. Most importantly, variations in the SFH can lead to a significant effect in the (FUV–NUV) color. For example, for a given total stellar mass, reducing the age of a constantly star-forming population by a factor of 10 (i.e., from 1 Gyr to 100 Myr) makes a color by Δ(FUV–NUV) ≈ −0.1 mag bluer. More importantly, increasing the SFR by a factor of 10 from 10 to 100 M_⊙ yr⁻¹ leads to a bluer (FUV–NUV) color by about 0.3 mag, while a reduction of the SFR from 100 to 10 M_⊙ yr⁻¹ leads to a 0.3 redder (FUV–NUV) color (see Appendix A) for a given metallicity and dust attenuation. Furthermore, lowering the metallicity from Z = 0.02 to 0.004 results in Δ(FUV–NUV) ≈ −0.1 mag. Finally, changing the IMF from Chabrier to Salpeter makes the color redder by a negligible amount (Δ(FUV–NUV) = 0.01 mag).

Summarizing, for a given dust attenuation, the (FUV–NUV) can vary owing to variations in the SFH, metallicity, and IMF by at most ∼0.4 mag. This age–dust degeneracy has important consequences for the derived SFRs. For a galaxy with an almost completely quenched bulge, we would infer a high dust attenuation and hence would overcorrect the central SFR. Therefore, the quoted central SFRs should be considered as upper limits.

We derive the (FUV−NUV)−A_V and (FUV−NUV)−β conversions in Appendix A. Briefly, we obtain the conversions by generating a set of model SEDs from Bruzual & Charlot (2003), for six different metallicities (Z = 0.0001, 0.0004, 0.004, 0.008, 0.02, and 0.05) and three different SFHs (constant, exponentially rising, and exponentially decreasing). We find tight correlations between the (FUV−NUV) color and A_V and β, which are given by Equations (7) and (9).

Before proceeding, we want to highlight some key assumptions behind our results and discuss systematic uncertainties in turning the (FUV−NUV) color to a dust attenuation. First, it is well known that the chemical and physical properties and the geometrical distribution of dust within external galaxies are a major uncertainty in the evaluation of their dust attenuation properties. In the absence of reliable constraints, we are working here within the traditional framework of the uniform screen approximation. This means that all effects of dust geometry, extinction, and scattering from the interstellar medium and star-forming regions are packaged into an attenuation curve (see, e.g., Penner et al. 2015; Salmon et al. 2016, for a more detailed discussion).

Clearly, galaxies are entities in which stars, gas, and dust are spatially mixed. Indeed, in the local universe, Liu et al. (2013) analyzed the dust distribution of M83 at a resolved spatial scale of ∼6 pc, finding that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground dust screen assumption. However, when averaged over scales of 100–200 pc, the extinction becomes consistent with the dust screen approximation, suggesting that other geometries tend to be restricted to smaller spatial scales. At high z, the dust-star geometry of galaxies is still largely unconstrained. Based on a massive z = 1.53 SFG, Genzel et al. (2013) argued that the resolved molecular gas surface density and the resolved attenuation are well modeled by a mixed model of dust and star-forming regions (consistent with Wuyts et al. 2011).

Since in the screen approximation all effects of dust geometry are hidden in the attenuation curve, it is important to have a good understanding of attenuation curve. Unfortunately, it is uncertain whether the attenuation curve should be universal, given that the conditions that produce the attenuation curve are complex and the nature and properties of dust grains may vary from one galaxy to another. They depend on the covering factor, dust grain size (which is dependent on metallicity), and line-of-sight geometry; these can therefore change when, for example, galaxies are viewed at different orientations (Witt & Gordon 2000; Chevallard et al. 2013) or have different stellar population ages (Charlot & Fall 2000).

In the local universe, we know that the attenuation curve is not universal and varies between the SMC and LMC, the Milky Way, and starburst galaxies. At high z, the attenuation curve is less well constrained (see, e.g., Noll et al. 2009; Kriek & Conroy 2013; Zeimann et al. 2015; Forrest et al. 2016; Salmon et al. 2016). Reddy et al. (2015) suggest that the attenuation curve for z ∼ 2 galaxies is lower by 20% in the UV with respect to the Calzetti law, which leads to SFRs that are ∼20% and stellar masses that are 0.16 dex lower. On the other hand, McLure et al. (2018) present a stacking analysis of ALMA data that at z ∼ 2.5 are fully consistent with the IRX–β relation expected from the Calzetti law (see also Bourne et al. 2017; Koprowski et al. 2018, for consistent results). A detailed analysis of different attenuation curves at different positions within galaxies is beyond the scope of this work and of our data. Therefore, we self-consistently assume the Calzetti et al. (2000) attenuation curve for k(λ)_star and Fitzpatrick (1999) for k(λ)_gas through this paper, but we highlight that this issue is worth investigating in future work. Overall, assuming a 0.5 dex scatter in the IRX–β relation, we infer an uncertainty in A_UV of ∼0.6 mag and hence an SFR uncertainty of 0.3 dex. This is of similar order to the systematic uncertainty of the conversion factor from UV (Hα) luminosity to SFR introduced by the assumed IMF, of order 0.2–0.3 dex, or variations of the SFH that amount to ∼0.1–0.2 dex (see Section 3.1).

Finally, regions of total dust obscurations would not be detected in our UV analysis. Compact obscured star formation has been seen in other samples whose selection criteria, as mentioned in the introduction of this paper, are, however, clearly very different from ours (Tadaki et al. 2015, 2017; Barro et al. 2016). Specifically for our sample, we present below a strong argument against the presence of totally obscured centers, namely, the good agreement between UV and Hα integrated SFRs after dust correction using our dust attenuation maps, and IR-based SFRs obtained from archival Spitzer and Herschel data.

In Figure 3 we compare the dust attenuation A_V obtained from our maps (A_V,map) with the one obtained from SED modeling (A_V,SED), i.e., from the photometry measured in an aperture of 3''. We derive A_V,map by summing up all pixels within a 3'' aperture, masking neighboring galaxies, and weighing each pixel according to the flux in the observed HST H-band image since this band corresponds to the rest-frame V-band image.

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Overall, the attenuation measured by SED fitting and via the integration of the resolved A_V,map is broadly similar but correlates poorly on a galaxy-by-galaxy basis (Pearson correlation coefficient of 0.14). The average difference is −0.01 ± 0.35 mag, i.e., we find good agreement between A_V,map and A_V,SED, especially after taking into account the relatively large systematic uncertainty of 0.3–0.4 mag. Seven of our 10 galaxies lie—within the uncertainty—close to the one-to-one relation. There are three significant outliers (Q2343-BX610, ZC400528, ZC407302). Both ZC400528 and ZC407302 have close neighbors (see Figure 1) that are masked in the A_V maps but not in the aperture photometry, which can explain the difference. Furthermore, the A_V map of Q2343-BX610 shows a large dynamic range, in particular, the center shows a high A_V value of ≳2.5 mag (see Figure 6). A_V from aperture photometry tends to miss these high attenuation values.

The two main SFR indicators used in this paper, the Hα recombination line and the UV emission, must be corrected for dust attenuation to recover the intrinsic SFR. In this subsection we use the SFR from IR in order to constrain the intrinsic SFR—and therefore the effect of dust attenuation—with an independent method. The IR is a good SFR indicator since, in the limit of high obscuration, most of the UV–optical light from young stars is absorbed and re-emitted into the IR. However, as for other SFR indicators, several assumptions must be made to convert the IR luminosity into an SFR (Kennicutt 1998). An important caveat of the IR SFR indicator is that dust can also be heated by older stars and/or AGNs. If such dust heating is non-negligible, converting the IR luminosity into an SFR using a standard calibration will overestimate the true SFR (e.g., Sauvage & Thuan 1992; Smith et al. 1994; Kennicutt et al. 2009; Salim et al. 2009; Kelson & Holden 2010; Leroy et al. 2012; Hayward et al. 2014; Utomo et al. 2014; Leja et al. 2018).

Since we do not have spatially resolved IR data, we have to compare our SFR estimates with the ones from IR measured over the whole galaxy. Figure 4 shows a direct comparison of the integrated dust-corrected UV SFR obtained from our resolved maps (SFR_UVmap,corr) and total UV+IR SFR, including the upper limits. Furthermore, in Figure 5 (left panel), we compare SFR_UVmap,corr both with the UV SFR (SFR_UV) and with the total UV+IR SFR (SFR_UV+IR) obtained from aperture photometry. The SFR_UV is derived from the UV rest-frame luminosity, according to the relation of Daddi et al. (2004), and adjusted to a Chabrier IMF. For the SFR_UV+IR, we follow the approach of Wuyts et al. (2011): we use either UV + PACS for Herschel PACS-detected galaxies (PACS Evolutionary Probe [PEP] program; Lutz et al. 2011)¹⁸ or UV + MIPS 24 μm for Spitzer MIPS-detected galaxies to compute the sum of the obscured and unobscured SFRs. For galaxies lacking an IR detection, the SFR is adopted from the best-fit SED model in Figure 5, while upper limits are plotted in Figure 4. The values SFR_UVmap are obtained by summing up the SFR within the 3'' aperture of the UV SFR map, masking neighboring objects.

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Only 1 of our 10 galaxies (ZC400528) is detected at PACS 100 μm with ${\mathrm{SFR}}_{\mathrm{UV}+100\mu {\rm{m}}}=556\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. This is a factor of ∼3.8 and ∼9 larger than the dust-corrected UV SFR estimate from the aperture photometry and the integrated map, respectively. As shown in Appendix B, ZC400528 has a close but faint neighbor galaxy that is not resolved as an individual source in the Spitzer MIPS 24 μm data. Furthermore, this is the only source that is detected with the VLA (Schinnerer et al. 2010), with a 1.4 GHz flux density of 67 μJy that would imply an SFR $\approx \,790\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. Together with the broad component in Hα, [N ii], and [S ii] emission lines, with a typical velocity FWHM of 1500 km s⁻¹ and an [N ii]/Hα ratio of ∼0.6 measured in this galaxy (Förster Schreiber et al. 2014, 2018), this points to AGN activity. However, it is unclear how much an AGN could contribute to the IR and radio measurements. Hence, this measurement of the UV+IR SFR should be interpreted with caution. Mapping of the dust continuum emission with high spatial resolution will provide further insight in the future.

Four galaxies have been detected in Spitzer MIPS 24 μm, and we estimated SFR_UV+24μm. For three galaxies (D3A-15504, ZC400569, ZC406690), these estimates agree well with the dust-corrected UV SFR estimates. On average, the UV+IR SFR is 0.15 ± 0.04 dex higher than the SFR estimated from the UV maps, which is well within the uncertainty of 0.3 dex. For one galaxy (ZC407302) the SFR estimated from UV+24 μm is a factor of three higher than the UV estimate (see Figure 5). This is explained by source confusion: ZC407302 has a close, low-z neighbor that contributes significantly to the 24 μm flux (see Appendix B). Therefore, we ignore IR measurement for this galaxy and indicate in Figure 4 that this galaxy does not have any reliable IR data. We use the dust-corrected UV SFR estimate as the total SFR instead of the UV+IR SFR for this galaxy throughout this paper.

Moreover, three zCOSMOS galaxies (ZC405226, ZC405501, and ZC412369) have no IR detection and upper limits of $\sim 100\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. For ZC405226 and ZC412369, this indicates within the errors that the SFR hidden in large amounts of dust is negligible. For ZC405501, the IR upper limit is 0.5 dex above the SFR estimated from the UV map, and hence additional star formation cannot be ruled out. Finally, two galaxies (Q2343-BX610 and Q2346-BX482) have no IR coverage. For all galaxies that have not been detected in the IR we can estimate the upper limit on the SFR. The PEP COSMOS field is observed for 200 h to a 3σ depth at 160 μm of 10.2 mJy, reaching at z ∼ 2 IR luminosities of a few times $\sim {10}^{12}\,{L}_{\odot }$ (SFR about $350\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$). A more stringent upper limit can be obtained for the COSMOS MIPS 24 μm data: the flux limit of these data is ∼80 μJy, which corresponds at z ∼ 2 to an SFR of about $150\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$.

Summing up, 6 of our 10 galaxies have only weak or no detection in the IR, 3 galaxies have no or not reliable IR coverage, and 1 galaxy (ZC400528) has a clearly higher UV+IR SFR than dust-corrected UV SFR. ZC400528 has a faint neighbor and also shows features that are consistent with AGN activity, making the IR flux difficult to interpret. Nevertheless, we use UV+IR SFR as a fiducial SFR estimate for this galaxy. Overall, we conclude that, in our sample, there is no evidence for substantially more star formation hidden by dust relative to what we infer from our dust-corrected, resolved UV and Hα SFRs. This is consistent with the overall sample properties shown in Section 2, where we show that our galaxies are not very dusty. This gives us confidence that correcting UV and Hα SFR profiles with the UV-based dust attenuation profiles that we derive in this paper will return reliable estimates of where, spatially resolved within galaxies, most of the star formation activity is localized.

We compare the integrated SFR maps from UV and Hα in Figure 5 (right panel). Since the Hα maps do not extend over the full 3'' aperture (see Figure 1), we have to match the UV and Hα apertures and PSFs. We define the Hα aperture by the pixels with signal-to-noise ratio (S/N) ≥ 3. Clearly, the measured SFR in this aperture is not fully representative of the total SFR, but it is good for the purpose of comparing the UV with the Hα SFR map.

As mentioned in Section 3.3, correcting the Hα SFR estimate for dust attenuation (A_Hα,gas; Equation (5)) depends on the adopted prescription. In Figure 5 we show the SFR_Hα,map assuming f = 0.44 and 0.70. Overall, the SFRs estimated from UV and Hα agree well. The average log-difference between SFR_UV,map and SFR_Hα,map is ${0.21}_{-0.13}^{+0.05}$ dex and $-{0.06}_{-0.14}^{+0.07}$ dex for f = 0.44 and 0.70, respectively. The SFR_Hα,map with f = 0.70 slightly underpredicts the SFR_UV,map values, while the SFR_Hα,map with f = 0.44 slightly overpredicts the SFR_UV,map values. We use f = 0.70 as our fiducial conversion factor for the rest of the paper.

It is actually unclear whether the UV and the Hα SFRs must be the same since they probe different timescales. In particular, as discussed in Section 3.1, Hα probes mainly ∼10⁷ yr old stars, while the UV-derived SFR is somewhat sensitive to the SFH over a ∼10 times longer interval. Overall, considering the uncertainty from the f-factor, together with the possibility of probing the SFRs on different timescales, we find that our Hα SFRs with both f = 0.44 and 0.70 are in the same ballpark as expectations from the UV SFRs.

To study the variation of extinction within galaxies, we used the rest-frame FUV and NUV (observed B- and I-band) images to construct a 2D (FUV−NUV) color map for each galaxy, following a similar procedure to that used in Tacchella et al. (2015b) for estimating the mass surface density distribution from the J − H color map. Since the FUV and NUV observations have different PSFs, we cross-convolved each passband with the PSF of the other passband. To increase the S/N of the color maps in the outer regions of galaxies, where the flux from the sky background is dominant, we performed an adaptive local binning of pixels using a Voronoi tessellation approach, using the publicly available code of Cappellari & Copin (2003). These color maps are then converted to A_V maps using Equation (7), which are shown in Figure 6.

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In order to compute the PSF-corrected A_V profiles, we measure the 1D profiles in elliptical apertures with the same ellipticity and center as obtained by the rest-frame optical (observed H-band) image GALFIT fits (Tacchella et al. 2015b). At each radius, the profile value consists of the median of all A_V at that radius. Taking the mean instead of the median does not change the profiles. Furthermore, using the B- and I-band light profiles to derive the color and then the A_V profiles also produces similar results.

These 1D A_V profiles were then fitted with a Sérsic (1968) profile taking into account each galaxy's PSF. We choose to use a Sérsic function for modeling the A_V profiles simply as a mathematical representation of the data and because the three free parameters in the Sérsic function give a high flexibility. Although the A_V profiles are shallower than the typical galaxy surface brightness profiles (and also the SFR and stellar mass surface density profiles), they are still well described by a Sérsic profile. In order to correct the profiles for deviation from the best-fit single Sérsic model, we derive the residual profile and add this to the best-fit deconvolved Sérsic model, to derive the residual-corrected profiles (Figure 6). Overall, the PSF-convolved model reproduces the data well, with differences ≲0.2 mag.

A center of a galaxy must be chosen for constructing a radial profile. We have extensively discussed the influence on the profiles of choosing different centers in Tacchella et al. (2015b), since it sets the foundation for the physical interpretation. In particular, we have highlighted the differences between dynamical, mass-weighted, and light-weighted (rest-frame optical light) centers. For most galaxies, these centers agree with each other (differences are ≲0.4 kpc, i.e., ≲1 pixel), and we assume the mass-weighted center as our fiducial center. An exception is galaxy ZC406690, which shows a clumpy morphology and for which the center is ambiguous. The kinematic center lies in the center of a ring-like structure, on which the field of view of SINFONI IFU is centered. The center of mass lies about 5 kpc to the east, on the largest clump visible in Figure 1. For this galaxy, we assume the dynamical center determined from the Hα kinematics in order to be consistent with previous studies (e.g., Förster Schreiber et al. 2014, 2018; Genzel et al. 2014a, 2014b; Newman et al. 2014; Tacchella et al. 2015a, 2015b) and to be able to compare the UV and Hα emission on scales out to ∼10 kpc.

Figure 7 shows the individual and stacked A_V profiles and A_Hα profiles. The top panels of Figure 7 show substantial galaxy-to-galaxy variations in the attenuation profiles. The variation in attenuation at a given radius (physical or scaled) amounts to about 1.5 mag for different galaxies. Most galaxies show increasing attenuation profiles within the inner 5 kpc toward the centers, while a few show the opposite trend. These differences reflect different SFR profiles, as most of the star formation can happen in star-forming clumps in, near, or far away from the galaxy centers.

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The stacked profile shows that galaxies have on average an attenuation profile that rises toward the center to ∼1.8 mag, with a significant amount of dust attenuation (∼0.6 mag) out to 10 kpc. Wuyts et al. (2012) found a similar decline in star-forming galaxies with ${M}_{\star }\gt {10}^{10}\,{M}_{\odot }$ at 0.5 < z < 1.5, but no explicit radial profiles were presented. Furthermore, these rather weak radial trends agree with local SFGs, where continuum extinction was found from ∼1.3 to ∼0.8 mag from the center to the optical radius R₂₅ (Muñoz-Mateos et al. 2009).

Splitting our sample into two mass bins (10.0 <log M_⋆/M_⊙ < 11.0 and 11.0 < log M_⋆/M_⊙ < 11.5), we find that there is not a large difference between the two mass bins. As a way of quantifying the slopes and normalizations of the attenuation profiles, we parameterize them with a two-component Sérsic fit (without implying that this specific profile shape bears any physical meaning for the diagnostic in question). The outer (or "disk") component has an n ≈ 0.3–0.4 and R_e ≈ 8 kpc for both mass bins; the inner (or "bulge") components differ instead for the high- and low-mass bins, yielding n ≈ 0.5, R_e ≈ 1.0 kpc and n ≈ 0.8, R_e ≈ 1.7 kpc, respectively.

The bottom panels of Figure 7 show the median dust attenuation of the ionized gas at Hα, A_Hα. For converting the A_V profiles to A_Hα profiles, we use the procedure described in Section 3.3 and in particular Equation (5). Note that, by construction, using f = 0.44 (or, similarly, the prescription of Wuyts et al. 2013) increases by ∼0.5 mag the attenuation for nebular line regions at Hα relative to the stellar continuum at V; for f = 0.70 the difference amounts instead to about −0.2 mag.

We compare our profiles with the results of Nelson et al. (2016b) at z ∼ 1.4, which are based on a Balmer decrement analysis of the stack of several hundred 3D-HST galaxies with masses in the range of ${10}^{9.8}\mbox{--}{10}^{11.0}\,{M}_{\odot }$, a sample that is much more representative than our sample of 10 galaxies, albeit at lower redshift (see also Nelson et al. 2016a, for a discussion on the SFR profiles in these galaxies). The key finding of 3D-HST analysis is that ${M}_{\star }={10}^{9.8}\mbox{--}{10}^{11}\,{M}_{\odot }$ galaxies have high central dust attenuation. In more detail, their average A_Hα profile exhibits a sharp peak in the galaxy center, but it is nearly transparent beyond 2 kpc. In the central ∼1 kpc region, the A_Hα estimates roughly agree, while the radial trend from the Balmer decrement analysis is much steeper than our slowly declining profiles. The Balmer decrement is measured at longer wavelengths than our estimate that comes from the UV, and thus it probes higher optical depths. We measure similar attenuation values in the central kiloparsec region. The differences of the profiles at 2–3 kpc are difficult to interpret, also because the uncertainties are larger. One could argue for a gradient in the additional dust attenuation toward the star-forming region (i.e., f = 0.44 in the central part, while f = 1.0 in the outskirts). Following the discussion by Wang et al. (2017), this difference in inferred A_Hα profile could reflect blending the [N ii] and Hα in the HST grism data, in appropriate SFH assumptions, and different stacking methods (i.e., Nelson et al. [2016b] is normalizing by F140W flux; hence, high equivalent width regions are more highly weighted, leading to a decrease in the inferred attenuation). Nelson et al. (2016b) considered [N ii] contamination but concluded that it does not affect their results even if there was an [N ii]/Hα gradient as steep as in local SFGs. Overall, it is unlikely that the full difference can be explained by such tweaks. Spatially resolved maps of the Balmer decrement and the UV color in combination with submillimeter dust maps of individual galaxies will shed more light on this in the future.

With the dust attenuation maps and profiles in hand, we are now able to correct the radial SFR density profiles, improving on the analysis of Tacchella et al. (2015a), where a uniform dust attenuation correction throughout the galaxy was applied to the Hα flux. In this section, we present the SFR profiles and how they are affected by different dust attenuation corrections.

In Figure 8 we present the radial Hα and UV SFR surface density profiles. We derive the radial SFR surface density profiles in the same way as the aforementioned dust attenuation profiles (see Section 4.4).

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Overall, there is a large diversity in the SFR profile shapes. Although on average SFR surface density profiles are well represented by an exponential star-forming disk of different sizes, there is richness of behavior in the individual profiles. Some galaxies have steeper profiles (ZC400528 and ZC412369) or flatter profiles due to bumpy features in the outskirts. The bumpy features can be explained by star-forming clumps in the galaxies' outskirts. Two exceptional galaxies are Q2346-BX482 and ZC406690, which show nearly flat or even increasing SFR density profiles toward the outskirts. Galaxy Q2346-BX482 has several star-forming clumps at similar galactocentric distances that together surpass the SFR density in the center (see Figure 1). Galaxy ZC406690 shows a reduction in the SFR density in the center. The SFR density peaks at ∼5 kpc. As mentioned before, this signature must be interpreted with care. We adopted as our fiducial center the kinematic center. Using instead the mass-weighted center (which also coincides with the peak of SFR) would make the profile centrally peaked, i.e., there would be no reduction in SFR toward the center.

We measure a typical inner (<1 kpc) SFR density of ${{\rm{\Sigma }}}_{\mathrm{SFR},1\mathrm{kpc}}\approx 2\mbox{--}12\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\,{\mathrm{kpc}}^{-2}$ for the more massive galaxies in our sample (11.0 < log M_⋆/M_⊙ < 11.5; namely, ZC400569, ZC400528, Q2343-BX610, and D3A-15504), while the lower-mass galaxies (10.0 < log M_⋆/M_⊙ < 11.0) have ${{\rm{\Sigma }}}_{\mathrm{SFR},1\mathrm{kpc}}\,\approx 0.3\mbox{--}3\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\,{\mathrm{kpc}}^{-2}$. In the lower-mass bin, we have excluded ZC412369 with ${M}_{\star }\approx 3\times {10}^{10}\,{M}_{\odot }$, which is a merger, causing probably the enhanced SFR in the center of ${{\rm{\Sigma }}}_{\mathrm{SFR},1\mathrm{kpc}}\,\approx 20\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\,{\mathrm{kpc}}^{-2}$. These quoted Σ_{SFR, 1kpc} can be considered as upper limits (in particular of the most massive galaxies in our sample) because of the age–dust degeneracy that would lead us to infer high attenuation values for galaxies with prominent, nearly quiescent bulges.

Focusing now on the difference between Hα and UV SFR density profiles, we find overall good agreement between the estimators. As highlighted in Section 4.3, the difference in the overall normalization between Hα and UV SFRs depends on the f-factor. The Hα and UV SFRs agree more with f = 0.70 than with f = 0.44.

Since the overall normalization difference between Hα and UV is mainly determined by the dust prescription, it may be more compelling to analyze the difference in the profile shapes. For most galaxies, there are small differences in the profile shape. Some galaxies show steeper SFR profiles in Hα than in UV (D3A-15504, ZC400569, ZC405226), while others show the contrary (Q2343-BX610, ZC400528, ZC405501, ZC407302). More concentrated UV profiles may indicate the progression of the star formation toward the outskirts.

Finally, we can also quantify the difference between using the radially varying A_V profiles and using a uniform A_V value (fiducial assumption in the work of Tacchella et al. 2015a) for correcting the SFR density for dust attenuation. In Figure 8 these two different dust corrections are shown with solid and dashed lines, respectively. Since the A_V profiles are increasing toward the centers, it is understandable that correcting the SFR density by those profiles leads to more centrally concentrated SFR density profiles than when using a uniform A_V value. In two cases (Q2343-BX610 and ZC405501), the A_V profiles are so steep that the SFR density profiles reverse, i.e., they are increasing toward the center with the radially varying A_V profiles, while they are decreasing with the uniform A_V value.

The SFR profiles presented in Section 4.5 inform us on the location where z ∼ 2 SFMS galaxies sustain their high SFRs. However, the newly formed stars might be, in principle, a negligible contribution to the local stellar mass density relative to the stellar density already in place. To understand whether these galaxies are caught in the act of changing their structural classification properties (i.e., by increasing their central mass concentration, thereby forming their bulge components, or increasing their stellar mass density at large radii, thereby growing the sizes of their disk components) we switch to a diagnostic that is able to trace the change in shape of the stellar mass profiles, i.e., the sSFR profile defined as

$$\begin{eqnarray}&&\mathrm{sSFR}(r)={{\rm{\Sigma }}}_{\mathrm{SFR}}(r)/{{\rm{\Sigma }}}_{{\rm{M}}}(r),\end{eqnarray} \tag{ 6 }$$

where Σ_SFR is the SFR surface density profile and Σ_M is the stellar mass surface density profile. With our definition of stellar mass as the integral of the past SFR, sSFR gives directly the inverse of the mass e-folding (i.e., roughly the mass-doubling) timescale.

These sSFR profiles are shown in Figure 9. The top and bottom panels show the sSFR based on the UV and Hα SFR, respectively. We show the individual profiles and the stacked profiles in mass bins given by 10.0 < log M_⋆/M_⊙ < 11.0 and 11.0 < log M_⋆/M_⊙ < 11.5. There is a wide range of shapes in the individual profiles, especially in the innermost and outermost regions, but the overall trend is that lower-mass galaxies have on average flat sSFR profiles, and high-mass galaxies have centrally suppressed sSFR profiles. The Hα and the UV SFR tracers agree well with each other and reproduce this same result.

Most importantly, these results stand true not only when adopting the radially constant attenuation profiles but also with the newly derived radially varying dust attenuation corrections. Quantitatively, there are of course differences. Most evident is the difference in the lower-mass bin for the UV-based profiles: the radially constant dust correction gives an outward-increasing sSFR profile; introducing the measured radial dependence for the dust correction leads to a flat sSFR profile. A flat sSFR profile is also what is observed in Hα, which emphasizes the importance of implementing the radial-dependent dust correction to the UV indicators in order to bring the two to agreement. Furthermore, the error bar in the lower right panel of Figure 9 indicates the systematic uncertainty on the measured sSFR: the largest contribution comes from the UV (Hα) to SFR conversion coefficient (variations from the IMF and stellar library), but it also incorporates the uncertainty from the dust attenuation estimation. Even in the light of this large and generously estimated uncertainty, the decline of the sSFR toward the central region is evident. Furthermore, the central sSFR values can be considered as upper limits (in particular of the most massive galaxies in our sample) because of the age–dust degeneracy that would lead us to infer high attenuation values for galaxies with prominent, nearly quiescent bulges.

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The fact that lower-mass galaxies have flat sSFR profiles and high-mass galaxies have centrally suppressed sSFR profiles, even when radial variations of dust attenuation are accounted for, is a result of significance: it confirms that, below the mass scale of $\sim {10}^{11}\,{M}_{\odot }$, SFGs on the SFMS at z ∼ 2 are vigorously doubling their stellar mass at a similar pace in their inner ("bulge") and outer ("disk") regions. In contrast, (at least some of) the most massive of them sustain their high SFRs in their outer disks and host almost-quenched inner "bulges," as already pointed out in Tacchella et al. (2015a). This agrees well with the observations that, at all epochs, SFGs grow on an almost time-independent correlation between stellar density within the central kiloparsec and total stellar mass (dubbed "structural main sequence" by Barro et al. 2017), until they reach a mass of order $\sim {10}^{11}\,{M}_{\odot }$ when quenching intervenes (Peng et al. 2010; Tacchella et al. 2015a).

More in detail, at log M_⋆/M_⊙ < 11.0 we measure on average an sSFR value of $\langle \mathrm{sSFR}\rangle$ ≈ 3 Gyr⁻¹, which is consistent with the sSFR value of the SFMS at z ∼ 2.2 (a mass-doubling time of 0.3 Gyr) at this mass scale (e.g., Rodighiero et al. 2014; Whitaker et al. 2014; Schreiber et al. 2015). In contrast, the higher-mass galaxies log M_⋆/M_⊙ > 11.0 have on average sSFR values that range from $\langle {\mathrm{sSFR}}_{\mathrm{out}}\rangle \approx 2\,{\mathrm{Gyr}}^{-1}$ at large radii (≳4 kpc or ≳1 R_M), again consistent with the SFMS estimates quoted above, to nearly one order of magnitude lower, $\langle {\mathrm{sSFR}}_{\mathrm{in}}\rangle \,\approx 0.1\mbox{--}0.4\,{\mathrm{Gyr}}^{-1}$, in the inner bulge regions. So even though the SFR profiles are centrally peaked, the sSFR profiles drop at the centers. This low inner sSFR value implies a mass-doubling time of ∼2.5–10.0 Gyr, which is comparable to or larger than the Hubble time at z ∼ 2. The star formation activity that is taking place in the centers of these galaxies will therefore not significantly increase the central stellar mass density in these systems: their dense bulge components are already in place, as also argued in Tacchella et al. (2015a). Similarly, Jung et al. (2017) find evidence for reduced sSFRs in the centers of massive galaxies at z ∼ 4. The direct comparison of the UV- and Hα-based sSFR profiles shows not only a qualitative but also a quantitative agreement for the values above.

Our findings for the sSFR profiles also have implications for the evolution of the size–mass relation of galaxies and for identifying the main physical drivers behind this evolution. The fact that at masses below and above log M_⋆/M_⊙ ∼ 11.0 the radial sSFR profiles are, respectively, flat and outward increasing is overall consistent with studies of the average size growth of the SFG population. In the log M_⋆/M_⊙ < 11.0 mass regime, find a slower evolution with cosmic time, and a shallower slope for the mass–size relation at any epoch, relative to the higher-mass population (e.g., Shen et al. 2003; Franx et al. 2008; van Dokkum et al. 2008; Mosleh et al. 2011; Newman et al. 2012; Carollo et al. 2013; Cassata et al. 2013; Cibinel et al. 2013; Belli et al. 2014; van der Wel et al. 2014b).

As shown in Tacchella et al. (2015a), these galaxies have saturated their stellar mass densities within several kiloparsecs to the values that are observed in the z = 0 spheroid population of similar mass. The key result that we report in this paper is that obscuration by dust is not responsible for the low sSFR in their cores and thus the quantification of their inner sSFR, which demonstrates that only a negligible amount of mass will be added to their inner regions in their subsequent evolution. This, together with the fact that they are massive and cannot keep forming stars for long in order to avoid dramatically overshooting the highest observed masses of lower-redshift galaxies (Renzini 2009), implies that these galaxies, which will soon leave the SFMS to reach their final resting place on the quenched sequence, will do so bringing with them, already in place, the high inner stellar densities that we identify with the $\sim {10}^{11}\,{M}_{\odot }$ spheroid population in the local universe. Direct quenching from the SFMS to the red and dead cloud should be no surprise at the mass scales that we are discussing. Indeed, the bulk of the spheroid population around ${M}_{\star }\sim {10}^{11}\,{M}_{\odot }$ shows all signs of a highly dissipative formation history, i.e., disky isophotes (Bender et al. 1988), cuspy nuclei (Faber et al. 1997), outer disks (Rix et al. 1999), generally a high degree of rotational support (Cappellari 2016), and steep metallicity gradients (Carollo et al. 1993). Also at z ∼ 1–2, there is growing evidence that quiescent galaxies are disk-like and rotating (Chang et al. 2013; van de Sande et al. 2013; van der Wel et al. 2014a; Newman et al. 2015; Toft et al. 2017). We note that this is in contrast with the ultramassive spheroid population at ${M}_{\star }\gg {10}^{11}\,{M}_{\odot }$: such ultramassive spheroids are very rare and, as already commented in the Introduction (see references there and also Faisst et al. 2017), bear the clear signs that dissipationless processes such as dry mergers must characterize their assembly (see Carollo et al. 2013; Fagioli et al. 2016, for extensive discussions on the ${M}_{\star }\sim {10}^{11}\,{M}_{\odot }$ mass threshold separating quenched spheroids with dissipative properties from more massive counterparts with dissipationless properties).

The evidence for a direct quenching channel of $\sim {10}^{11}\,{M}_{\odot }$ galaxies from the SFMS to the quenched population supports the picture in which, at any epoch, the universe keeps adding, to the red and dead population, quenched galaxies that inherit the properties—including the sizes—of their progenitors on the SFMS (Carollo et al. 2013; Fagioli et al. 2016). Since SFG sizes are seen to roughly scale similarly to the host halos with (1 + z)⁻¹ (Oesch et al. 2010; Mosleh et al. 2011; Newman et al. 2012; Somerville et al. 2018), this "progenitor bias" effect (van Dokkum & Franx 1996), i.e., the addition of larger and larger quenched galaxies to the overall population, becomes therefore a major contribution to the observed size growth of the quenched population with cosmic time. The smaller sizes at any given epoch of quenched galaxies relative to SFGs have been shown to be well explained precisely by the cumulative effects of progenitor bias that piles on the quenched population earlier generations of SFGs (Lilly & Carollo 2016), coupled with the fading of the stellar populations in the disks, once also these outer galactic components exhaust their star formation activity (Carollo et al. 2016).

With dust-corrected sSFR profiles in hand, we can turn to asking whether these show any difference depending on where the galaxies lie on the SFMS, not simply "along" the sequence, i.e., as a function of stellar mass (discussed before), but "across" the sequence, i.e., above and below the SFMS ridgeline. Numerical simulations make predictions on what happens to a galaxy as it grows its mass along the SFMS, with observational consequences, which we can test with our data. In particular, Tacchella et al. (2016a) find that, in cosmological zoom-in hydrodynamical simulations (i.e., the VELA suite of Ceverino et al. 2014), SFGs oscillate up and down the average SFMS, reaching the upper envelope when gas vigorously flows toward the galaxy centers, where it reaches very high densities. This phase, dubbed "compaction" in Zolotov et al. (2015; see also Tacchella et al. 2016a, 2016b), leads to a strong central starburst; it is this starburst that pushes galaxies toward the upper SFMS envelope. The starburst adds substantial stellar mass in the galaxy centers, i.e., to the bulge component. Following the compaction phase, SFGs deplete of gas in the centers owing to the combination of gas consumption into stars and strong outflows from stellar feedback. This indeed halts the compaction phase and pushes galaxies down toward the lower envelope of the SFMS.

In particular, we are now going to interpret our results in the framework discussed by Zolotov et al. (2015) and Tacchella et al. (2016a, 2016b). The testable prediction of this scenario is that the spatial distribution of the sSFR within galaxies should correlate with their position on the SFMS: galaxies above (below) the SFMS ridge should have a higher (lower) sSFR in their centers than in their outskirts.

In Figure 10 we plot the ratio of the sSFR in the centers and in the outskirts (sSFR_in/sSFR_out) as a function of the distance from the SFMS (Δ_MS). The distance from the SFMS is defined as the log-difference of the sSFR of the galaxy to the one of the average SFMS, for which we use a simple linear fit to our sample. The latter agrees well with the SFMS estimates of, e.g., Whitaker et al. (2014) and Schreiber et al. (2015). For the SFR of the SFMS we adopt the total UV+IR SFR that we discuss in Section 4.2. To separate the "center" and "outskirts" of the galaxies, we use two different definitions, one in terms of an absolute physical threshold in radius, and the other in terms of radius normalized by the half-mass radius R_M. We plot in the top panel the inner versus outer sSFR ratio as a function of radius in physical units in kpc, specifically adopting a 3 kpc threshold to separate inner and outer regions. In the bottom panel we plot instead the same ratio as a function of normalized radius, specifically adopting 1R_M as the separating threshold.

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Overall, we observe that galaxies in our sample that lie above the average SFMS (Δ_MS > 0.0) have a higher or at least comparable sSFR in their centers than in their outskirts (sSFR_in ≳ sSFR_out); in contrast, we observe the opposite for galaxies below the average SFMS. This result is robust, and our conclusions do not change when using both physical and normalized units, or when varying the boundaries of the definition of "center" and "outskirts."

Of course, we must exercise care in commenting on this trend, since our galaxy sample is small, and even smaller are thus the below- and above-SFMS subsamples that we are studying. Our (small) sub-SFMS galaxy sample is furthermore dominated by the most massive galaxies (${M}_{\star }\,\gtrsim \,{10}^{11}\,{M}_{\odot }$), which are most probably on the way to being quenched. The sSFR ratio versus Δ_MS relation is, however, not solely driven by stellar mass. The trend of higher sSFR in the center versus outskirts depends more strongly on the distance from the main-sequence ridgeline than on stellar mass: the Pearson correlation coefficient is R = 0.44 (0.56) for UV (Hα) sSFR ratio versus distance from the main sequence and R = −0.09 (−0.27) for UV (Hα) sSFR ratio versus stellar mass.

We have highlighted in Section 2.1 that our sample traces the SFMS, but we do not probe the massive and dusty SFGs in the upper right corner of the UVJ diagram, which may partially be due to small number statistics in addition to our sample selection criteria. Massive, dusty SFGs and therefore IR-bright galaxies have been recently studied with ALMA by Barro et al. (2016) and Tadaki et al. (2017). Tadaki et al. (2017) show that their galaxies lie on extrapolation of the Whitaker et al. (2014) low-mass SFMS; however, we note that they are actually located on the upper envelope of the SFMS when the bending at high masses of the SFMS—as observed by Whitaker et al. (2014)—is taken into account. Furthermore, these galaxies appear to be actively star-forming in their central regions, i.e., the sSFR profiles are rising toward the center. The region in Figure 10 occupied by the corresponding profiles of Barro et al. (2016) is shown as the red hatched area. This is consistent with the framework presented here, where galaxies at the upper envelope of the SFMS are experiencing a dusty nuclear starburst and are doubling their mass quicker in their centers than in their outskirts.

Although our SINS/zC-SINF and the ALMA samples are selected very differently, are small, and are not representative of the whole SFG population at z ∼ 2, a coherent picture emerges when combining the results presented here and in Barro et al. (2016) and Tadaki et al. (2017). These observations are consistent with galaxies growing their inner bulge and outer disk regions as found in the simulations, where they appear to oscillate about the average SFMS in cycles of central gas compaction, which leads to bulge growth, and subsequent central depletion due to feedback from the starburst resulting from the compaction (Zolotov et al. 2015; Tacchella et al. 2016a, 2016b).

We derive the (FUV−NUV)−A_V and (FUV−NUV)−β conversions in Figure 11 by generating a set of model SEDs from Bruzual & Charlot (2003), for six different metallicities (Z = 0.0001, 0.0004, 0.004, 0.008, 0.02, and 0.05) and three different SFHs (constant, exponentially rising, and exponentially decreasing). The timescales used for the rising and declining SFHs are τ = [−5000, −1000, −500, −50, 50, 250, 500, 1000, 5000, 10,000] Myr, respectively. Note that the negative sign indicates rising SFHs. The stellar age is defined as the age since the onset of star formation. We consider a minimum age of 10 Myr and a maximum age of 3.5 Gyr (age of the universe at z ∼ 2). We assume that the dust attenuation is described by the Calzetti dust attenuation curve (Calzetti et al. 2000), with A_V varying from 0.0 to 6.0, in steps of 0.05 between 0.0 and 4.0, in steps of 0.25 between 4.0 and 5, and in steps of 0.5 between 5.0 and 6.0. The intergalactic medium (IGM) is treated using the Madau (1995) prescription. Redshifts vary between 2.0 and 2.5 in steps of 0.1.

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As shown in the top panel of Figure 11, at a fixed redshift we find a tight correlation between the observed B₄₂₈−I₈₁₄ color (approximately corresponding to the rest-frame FUV–NUV color) and A_V, with a small but significant dependence on redshift (see middle and bottom panels). These correlations are well approximated with

$$\begin{eqnarray}{{\rm{A}}}_{V} & = & (2.36\pm 0.11)+(2.11\pm 0.01)\times {(B-I)}_{{z}_{\mathrm{obs}}}\\ & & -(4.11\pm 0.40)\times \mathrm{log}(1+{z}_{\mathrm{obs}})\\ & & -(1.78\pm 0.05)\times \mathrm{log}(1+{z}_{\mathrm{obs}})\times {(B-I)}_{{z}_{\mathrm{obs}}},\end{eqnarray} \tag{ 7 }$$

where ${(B-I)}_{{z}_{\mathrm{obs}}}$ is the observed (B − I) color in mag and z_obs is the redshift of the observed galaxy.

For z_obs = 2.2, we get

$$\begin{eqnarray}&&{{\rm{A}}}_{V}=(0.28\pm 0.41)+(0.77\pm 0.05)\times {(B-I)}_{{z}_{\mathrm{obs}}=2.2},\end{eqnarray} \tag{ 8 }$$

similar to the expression suggested by Meurer et al. (1999).

For each model SED, we calculated the UV slope (β) by fitting the flux of the SED model as a function of wavelength, using only those flux points that lie within the 10 continuum windows given in Calzetti et al. (1994). The typical formal uncertainty in β, when using the 10 aforementioned windows, is Δβ ≈ 0.1.

We find a tight correlation between the (FUV−NUV) color and β, similar to above:

$$\begin{eqnarray}\beta & = & (0.41\pm 0.08)+(2.28\pm 0.01)\times {(B-I)}_{{z}_{\mathrm{obs}}}\\ & & -(5.03\pm 0.30)\times \mathrm{log}(1+{z}_{\mathrm{obs}})\\ & & -(1.86\pm 0.04)\times \mathrm{log}(1+{z}_{\mathrm{obs}})\times {(B-I)}_{{z}_{\mathrm{obs}}}.\end{eqnarray} \tag{ 9 }$$

For z_obs = 2.2, we get

$$\begin{eqnarray}&&\beta =(-2.13\pm 0.31)+(1.34\pm 0.04)\times {(B-I)}_{{z}_{\mathrm{obs}}=2.2}.\end{eqnarray} \tag{ 10 }$$

In this section we investigate the effect of varying the stellar population properties on the (FUV−NUV) color (see also, e.g., Cortese et al. 2008; Wilkins et al. 2011). In a first step, to compare the different effects, we take a reference model about which we consider deviations in the amount of dust, the previous SFH, metallicity, and IMF. This reference model assumes 1 Gyr continuous star formation, solar metallicity (Z = 0.02), a Chabrier (2003) IMF, and no dust and is constructed using the Bruzual & Charlot (2003) population synthesis model. As shown in Figure 12 (see also Wilkins et al. 2011, for a similar figure), this scenario suggests a rest-frame (FUV–NUV) color of −0.14 mag.

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By far the largest potential effect on the UV color of SFGs is the presence of dust: changing ${{\rm{A}}}_{V}=0.0\to 0.5\,\mathrm{mag}$ results in Δ(FUV−NUV) ≈ 0.4 mag. The strong wavelength dependence of typical (e.g., Calzetti et al. 2000) reddening curves results in greater extinction in the UV (relative to the optical or near-IR) and the reddening of UV colors. Therefore, reddening of the UV colors provides a good diagnostic of the magnitude of the dust attenuation. Next, we vary the second-order stellar population parameter in order to constrain the typical uncertainty that is related to estimating A_V from (FUV–NUV) color.

Variation in the SFH influences the (FUV–NUV) color since, after prolonged periods of star formation, some fraction of the most massive stars will have evolved off the stellar main sequence, which reduces the relative contribution of these stars to the UV continuum, resulting in a redder color. For example, for a given total stellar mass, reducing the age of a constantly star-forming population by a factor of 10 (i.e., from 1 Gyr to 100 Myr) makes a color by Δ(FUV–NUV) ≈ −0.1 mag bluer. Lowering the metallicity from Z = 0.02 to 0.004 results in Δ(FUV–NUV) ≈ −0.1 mag. Finally, changing the IMF from Chabrier (2003) to Salpeter (1955) makes the color redder by a small amount (Δ(FUV–NUV) = 0.01 mag) because Salpeter (1955) IMF is more bottom-heavy.

In a second step, we quantify the variation of the (B − I) color during a burst of star formation. In detail, the SFR is kept constant at 10 M_⊙ yr⁻¹ for 3 Gyr. We superimpose a burst of star formation at time 1.4 Gyr with duration of 200 Myr. We analyze two scenarios: in the first one, the peak SFR during the burst phase is SFR_burst = 50 M_⊙ yr⁻¹, while in the second one it is SFR_burst = 100 M_⊙ yr⁻¹. The SFHs are plotted as blue lines in Figure 13.

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Throughout this variation of the SFR, we compute the associated colors with the same assumptions as for our default scenario, i.e., solar metallicity (Z = 0.02), a Chabrier (2003) IMF, and no dust. The obtained colors are shown in red in Figure 13. After 1 Gyr, the (B − I) color reaches a value of −0.14 AB mag, consistent with our default scenario mentioned above. At the onset of the burst, the (B − I) color gets bluer to a value of −0.33 AB mag (−0.43 AB mag) for SFR_burst = 50 M_⊙ yr⁻¹ (SFR_burst = 100 M_⊙ yr⁻¹). While the SFR is constant during the burst phase, the (B − I) color exponentially reddens again. Shortly (≲10 Myr) after the end of the burst phase, the (B − I) color reddens significantly to 0.07 AB mag (0.19 AB mag) since the bluest and therefore most massive stars leave the stellar main sequence first. The (B − I) color then gets bluer again.

Summarizing qualitatively, a significant increase in the SFR leads to a bluer (B − I) color, while a reduction in SFR leads to a redder (B − I) color, assuming constant metallicity and dust content. Quantitatively, we find that a single burst can lead to changes in the (B − I) color of about 0.3 mag. Hence, for a given (B − I) color (FUV–NUV color) we estimate the typical uncertainty on A_V due to stellar population differences to be at most ∼0.4 mag.