# The SINS/zC-SINF Survey of $z \sim 2$ Galaxy Kinematics: SINFONI Adaptive Optics-assisted Data and Kiloparsec-scale Emission-line Properties

N. Forster Schreiber, A. Renzini, C. Mancini, R. Genzel, N. Bouché, G.

Cresci, E. Hicks, S. Lilly, Y. Peng, A. Burkert, et al.

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## To cite this version:

N. Forster Schreiber, A. Renzini, C. Mancini, R. Genzel, N. Bouché, et al. The SINS/zC-SINF Survey of $z \sim 2$ Galaxy Kinematics: SINFONI Adaptive Optics-assisted Data and Kiloparsec-scale Emission-line Properties. The Astrophysical Journal Supplement, 2018, 238 (2), pp.21. 10.3847/1538-4365/aadd49. hal-02380665

HAL Id: hal-02380665

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# The SINS/zC-SINF Survey of $z \sim 2$ Galaxy Kinematics: SINFONI Adaptive Optics-assisted Data and Kiloparsec-scale Emission-line Properties*

N. M. Förster Schreiber¹, A. Renzini², C. Mancini²,³, R. Genzel¹,⁴,⁵, N. Bouche⁶, G. Cresi⁷, E. K. S. Hicks⁸, S. J. Lilly⁹, Y. Peng¹⁰, A. Burkert¹,¹¹, C. M. Carollo⁹, A. Cimatti⁷,¹², E. Daddi¹³, R. I. Davies¹, S. Genel¹⁴,¹⁵, J. D. Kurk¹, P. Lang¹⁶, D. Lutz¹, V. Mainieri¹⁷, H. J. McCracken¹⁸, M. Mignoli¹⁹, T. Naab²⁰, P. Oesch²¹, L. Pozzetti¹⁹, M. Scodeggio²², K. Shapiro Griffin²³, A. E. Shapley²⁴, A. Sternberg²⁵, S. Tacchella²⁶, L. J. Tacconi¹, S. Wuyts²⁷, and G. Zamorani¹⁹

¹Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse, D-85748 Garching, Germany

²INAF-Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy

³Dipartimento di Fisica e Astronomia, Università di Padova, Vicolo dell'Osservatorio 2, I-35122 Padova, Italy

⁴Department of Physics, Le Conte Hall, University of California, Berkeley, CA 94720, USA

⁵Department of Astronomy, Hearst Field Annex, University of California, Berkeley, CA 94720, USA

⁶Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, F-31400 Toulouse, France

⁷INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50157 Firenze, Italy

⁸Department of Physics and Astronomy, University of Alaska, Anchorage, AK 99508-4664, USA

⁹Institute of Astronomy, Department of Physics, Eidenössische Technische Hochschule, Zürich, CH-8093, Switzerland

¹⁰Kavli Institute for Astronomy and Astrophysics, Peking University, 100871 Beijing, People's Republic of China

¹¹Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, Scheinerstr. 1, D-81679 Munich, Germany

¹²Department of Physics and Astronomy (DIFA), Università di Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy

¹³Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/Service d'Astrophysique, Bât. 709, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France

¹⁴Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

¹⁵Columbia Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY 10027, USA

¹⁶Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany

¹⁷European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany

¹⁸Institut d'Astrophysique de Paris, 98bis Boulevard Arago, F-75014 Paris, France

¹⁹INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Piero Gobetti 93/3, I-40129 Bologna, Italy

²⁰Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, D-85741 Garching, Germany

²¹Observatoire de Genève, 51 Ch. des Maillettes, 1290 Versoix, Switzerland

²²INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, I-20133 Milano, Italy

²³Northrop Grumman Aerospace Systems, San Diego, CA 92150, USA

²⁴Department of Physics & Astronomy, University of California, Los Angeles, 430 Portola Plaza, Los Angeles, CA 90095, USA

²⁵Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel

²⁶Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

²⁷Department of Physics, University of Bath, Claverton Down, Bath, BA2 7AY, UK

Received 2018 February 19; revised 2018 August 14; accepted 2018 August 17; published 2018 October 4

## Abstract

We present the “SINS/zC-SINF AO survey” of 35 star-forming galaxies, the largest sample with deep adaptive optics (AO)-assisted near-infrared integral field spectroscopy at $z \sim 2$. The observations, taken with SINFONI at the Very Large Telescope, resolve the $H\alpha$ and [N II] emission and kinematics on scales of $\sim 1.5$ kpc. The sample probes the massive ($M_* \sim 2 \times 10^9 - 3 \times 10^{11} M_\odot$), actively star-forming (SFR $\sim 10-600 M_\odot$ yr$^{-1}$) part of the $z \sim 2$ galaxy population over a wide range of colors ($(U-V)_{\text{rest}} \sim 0.15-1.5$ mag) and half-light radii ($R_{e,H} \sim 1-8.5$ kpc). The sample overlaps largely with the “main sequence” of star-forming galaxies in the same redshift range to a similar $K_{AB} = 23$ mag limit; it has $\sim 0.3$ dex higher median specific SFR, $\sim 0.1$ mag bluer median $(U-V)_{\text{rest}}$ color, and $\sim 10\%$ larger median rest-optical size. We describe the observations, data reduction, and extraction of basic flux and kinematic properties. With typically 3–4 times higher resolution and 4–5 times longer integrations (up to 23 hr) than the seeing-limited data sets of the same objects, the AO data reveal much more detail in morphology and kinematics. The complete AO observations confirm the majority of kinematically classified disks and the typically elevated disk velocity dispersions previously reported based on subsets of the data. We derive typically flat or slightly negative radial [N II]/$H\alpha$ gradients, with no significant trend with global galaxy properties, kinematic nature, or the presence of an AGN. Azimuthal variations in [N II]/$H\alpha$ are seen in several sources and are associated with ionized gas outflows and possibly more metal-poor star-forming clumps or small companions. The reduced AO data are made publicly available (http://www.mpe.mpg.de/ir/SINS/SINS-zcSINF-data).

**Key words:** galaxies: high-redshift – galaxies: ISM – galaxies: kinematics and dynamics – galaxies: structure

## 1. Introduction

The advent of high-throughput near-infrared (near-IR) integral field unit (IFU) spectrometers mounted on 8–10 m class telescopes in the past 15 yr has made it possible to spatially resolve the kinematics and distribution of the warm ionized gas in galaxies at redshift $z \gtrsim 1$. Near-IR IFU surveys have been

<footnote>* Based on observations obtained at the Very Large Telescope of the European Southern Observatory, Paranal, Chile (ESO Programme IDs 075.A-0466, 076. A-0527, 079.A-0341, 080.A-0330, 080.A-0339, 080.A-0635, 081.B-0568, 081.A-0672, 082.A-0396, 183.A-0781, 087.A-0081, 088.A-0202, 088.A-0209, 091.A-0126).</footnote>
instrumental in revealing that a significant proportion (≥50%) of massive $z \sim 1-3$ star-forming galaxies (SFGs) are disks, characterized by high intrinsic local velocity dispersions of $\sigma_0 \sim 25-100 \text{ km s}^{-1}$ and typically irregular, often clumpy emission-line morphologies (e.g., Buitrago et al. 2014; Cresci et al. 2009; Épinat et al. 2009, 2012; Förster Schreiber et al. 2006, 2009; Genzel et al. 2006, 2008; Gnerucci et al. 2011a, 2011b; Jones et al. 2010b; Law et al. 2009; Leethochawalit et al. 2016; Mancini et al. 2011, hereafter M11; Molina et al. 2017; Newman et al. 2013; Shapiro et al. 2008; Stott et al. 2014, 2016; Swinbank et al. 2012a, 2012b; Wisnioski et al. 2011, 2012, 2015; Wright et al. 2009). High-resolution rest-UV/optical and Hα imaging of large mass-selected samples out to $z \sim 2.5$ obtained with the Hubble Space Telescope (HST) confirmed the prevalence of disklike morphologies among massive SFGs, with an increasingly important central stellar bulge-like component at higher galaxy masses and clumpier appearances toward shorter wavelengths (e.g., Wuyts et al. 2011b, 2012, 2013; Nelson et al. 2013, 2016b; Lang et al. 2014; see also Elmegreen et al. 2007, 2009; Law et al. 2012a; Tacchella et al. 2015b, 2018). Mapping and kinematics of the cold molecular gas in star-forming disks via low-lying CO line emission also revealed clumpy distributions and elevated intrinsic local velocity dispersions, showing that these characteristics are not just a property of the ionized gas layer but of the entire interstellar medium (ISM; e.g., Daddi et al. 2010; Tacconi et al. 2010, 2013; Swinbank et al. 2011; Genzel et al. 2013; Übler et al. 2018). From surveys of CO line and cold dust continuum emission, it is now well established that $z \sim 1-3$ SFGs have high gas mass fractions of ~30%-50% (see Carilli & Walter 2013; Tacconi et al. 2013, 2018; Genzel et al. 2015; Scoville et al. 2016 and references therein).

A widely invoked theoretical framework to interpret these properties is that of gas-rich, turbulent disks in which kpc-scale clumps form through violent disk instabilities, and bulge formation takes place via efficient secular processes and inward clump migration on timescales $\lesssim 1$ Gyr (e.g., Noguchi 1999; Immeli et al. 2004a, 2004b; Bournaud et al. 2007, 2008, 2014; Genzel et al. 2008; Dekel et al. 2009; Jones et al. 2010b; Cacciato et al. 2012; Ceverino et al. 2012; Genel et al. 2012; Hopkins et al. 2012; Dekel & Burkert 2014). Theory and numerical simulations indicate that telltale signatures of physical processes at play appear on scales of ~1 kpc and ~10–100 km s⁻¹ or less. Both high resolution and high sensitivity are needed to separate different components from each other in space and velocity, such as bulges and clumps in disks, perturbations induced by mergers, disk clumps or bar streaming, and narrow line profiles tracing the potential well versus broader components associated with gas outflows.

Most of the near-IR IFU data at $z \sim 1-3$ published to date comprise seeing-limited observations. Good near-IR seeing conditions of ~0.5' correspond to a spatial resolution of ~4 kpc at $z = 1-3$. Observations aided by adaptive optics (AO) typically reach 3–4 times higher resolution or ~1 kpc (and even better in the source plane for rare, strongly lensed sources). An important practical limitation for AO-assisted near-IR IFU observations is that targets must have both (1) an accurate redshift to ensure the lines of interest fall within atmospheric windows and away from the numerous bright night-sky lines in the near-IR and (2) a sufficiently bright nearby star providing a reference signal for the AO correction. Adding to the challenge, observing conditions must be

favorable (good seeing, long atmospheric turbulence coherence time) to achieve significant image quality improvement with AO, and long integration times are required for faint distant galaxies. As a consequence, $z \sim 1-3$ near-IR IFU AO samples are typically small and form a rather heterogeneous collection, and few objects benefit from very sensitive data.

Using SINFONI at the ESO Very Large Telescope (VLT), we carried out a substantial effort to collect a sizable sample of 35 typical massive $z \sim 2$ SFGs with deep AO observations. The largest part of the data was obtained through an ESO Large Program (LP) and a small pilot program, building on two previous major programs: the “SINS” survey of $z \sim 1.5-3$ galaxies with SINFONI and the “zCOSMOS” optical spectroscopic survey of $0 < z < 3$ galaxies. The SINS survey observed a total of 80 galaxies, mostly in seeing-limited mode, and provided the first and largest near-IR IFU sample at $z \sim 2$ at the time (Förster Schreiber et al. 2009, hereafter FS09). The galaxies were drawn from spectroscopically confirmed subsets of various samples selected by diverse photometric criteria. While three-quarters of the sources have a suitable AO reference star, routine AO operations with SINFONI began roughly midway into the 5 yr spanned by the SINS survey observing campaigns, so that only a handful of targets were initially followed up with AO. To expand and improve on the initial SINFONI+AO sample, we collected an additional 30 $z \sim 2$ sources from the “zCOSMOS-deep” spectroscopic survey, which spans $1.4 < z < 3$ and was conducted with VIMOS at the VLT (Lilly et al. 2007, 2009). This “zC-SINF” sample was selected with uniform criteria and such that all objects had an AO reference star and accurate spectroscopic redshift (M11), capitalizing on the wide area (the central ~1 deg² of the COSMOS field) and high sampling rate (~50% to $B_{AB} = 25$ mag) of the zCOSMOS-Deep survey (Diener et al. 2013).

Taken together, the SINS and zC-SINF samples comprise a total of 110 massive $z \sim 1-3$ SFGs with seeing-limited SINFONI data, 35 of which were followed up with sensitive, high-resolution AO-assisted observations targeting the Hα and [N II] emission lines. After the initial no-AO observations of the 30 new zC-SINF objects, the major part of our SINFONI LP (and its pilot program) was devoted to the AO observations of 26 targets. The AO data of a further nine SINS targets were obtained as part of complementary SINFONI+AO normal, open-time programs. The underlying strategy for all these programs was ultimately to collect high-quality AO data for a reliable overview of kpc-scale kinematics and emission-line properties over a wide range in stellar mass ($M_\star$) and star formation rate (SFR) and to obtain very deep AO data of a subset most suitable to investigate particular dynamical/physical processes.

This strategy was motivated by a specific set of science goals: (1) to quantify the fraction and structure of disks and mergers, (2) to investigate what dynamical processes drive the early evolution of galaxies, (3) to determine the origin of the large turbulence in high-z disks, (4) to constrain the relative importance of gas accretion and mass and metals redistribution, (5) to map the strength of galactic winds on galactic and subgalactic (clump) scales and investigate the mechanisms and energetics of feedback from star formation and active galactic nuclei (AGNs), (6) to unveil the nature of compact dispersion-dominated objects, and (7) to shed light on the relative growth of bulges and supermassive black holes. The SINS/zC-SINF
project motivated three dedicated HST imaging follow-up programs (Förster Schreiber et al. 2011a; Tacchella et al. 2015b, 2018) to map the stellar light at a resolution comparable to that of the SINFONI+AO data, enhancing the exploitation of the line emission and kinematics data.

Over the 12 yr during which the SINFONI+AO data were taken, key science results addressing the goals listed above based on a subset of targets and/or the observations were published in several papers, which we summarize here.

1. Our first and deepest AO-assisted observations of a $z \sim 2$ galaxy to date revealed for the first time the prototypical properties of massive high-redshift SFGs: a large rotating disk with elevated intrinsic gas velocity dispersion, several distinct star-forming clumps, and evidence for a powerful gas outflow driven by AGN activity (Genzel et al. 2006, 2008, 2011, 2014a; Förster Schreiber et al. 2014).

2. The disk dynamics, disk versus merger structure of the galaxies, and nature of dispersion-dominated objects were further explored in several papers (Bouché et al. 2007; Shapiro et al. 2008; Cresci et al. 2009; FS09; Newman et al. 2013; Genzel et al. 2014a, 2017; Burkert et al. 2016).

3. Bulge formation and incipient quenching of star formation in the most massive galaxies of the sample rapidly became a scientific focus, together with the nature and evolutionary role of the massive star-forming clumps (Genzel et al. 2008, 2011, 2014a; Tacchella et al. 2015a).

4. The detection and characterization of the physical properties of the ubiquitous star formation- and AGN-driven winds in typical $z \sim 2$ massive SFGs on galactic and subgalactic scales—as diagnosed by the $H\alpha+[N\II] ([+S\II])$ line profiles—was uniquely enabled by the sensitive SINFONI data (Shapiro et al. 2009; Genzel et al. 2011, 2014b; Newman et al. 2012a, 2012b; Förster Schreiber et al. 2014).

5. The SINFONI+AO data combined with HST imaging further elucidated the structure of the galaxies through mapping of the distribution of stellar mass, SFR, and dust extinction (Förster Schreiber et al. 2011a, 2011b; Tacchella et al. 2015a, 2015b, 2018).

6. Most recently, intriguing evidence was found for the largest galaxies in the sample having falling rotation curves at large galactocentric radii, at variance with the typically flat outer disk rotation curves that are characteristic of local spiral galaxies (Genzel et al. 2017; Lang et al. 2017).

We present here the complete sample of 35 SINS/zC-SINF objects with SINFONI+AO observations, the survey strategy, and the characteristics of the data sets. The paper is organized as follows. We describe the selection and global properties of the sample in Section 2, the observations and data reduction in Section 3, and the extraction of maps and spectra in Section 4. We present the measurements of $H\alpha$ sizes and global surface brightness distributions in Section 5 and the kinematic properties in Section 6. In Section 7, we revisit the nature of the galaxies (i.e., disks versus nondisks) based on their kinematics and morphologies, and in Section 8, we exploit the AO data to constrain spatial variations in $[N\II]/H\alpha$ ratio. The paper is summarized in Section 9. Several technical aspects of the AO observations and data analysis can be found in the appendices, including the presentation of the full data set and a comparison of the results obtained from the SINFONI AO and

no-AO data. Throughout, we assume a $\Lambda$-dominated cosmology with $H_0 = 70\ h_0\ km\ s^{-1}\ Mpc^{-1}$, $\Omega_m = 0.3$, and $\Omega_\Lambda = 0.7$. For this cosmology, $1''$ corresponds to $8.3\ kpc$ at $z = 2.2$. Magnitudes are given in the AB photometric system unless otherwise specified.

## 2. SINS/zC-SINF AO Sample

The SINFONI AO targets form a subset of the SINS and zC-SINF $H\alpha$ samples at $z \sim 2$ initially observed in natural seeing. Table 1 lists the galaxies of the AO sample, their $H\alpha$ redshifts, K-band magnitudes, and several other global properties. An exhaustive description of the selection of the parent sample and the derivation of stellar properties is given by FS09 and M11 (with updated results for six objects using new H-band photometry presented by Förster Schreiber et al. 2011a). We refer the reader to these papers for details and highlight the salient points in this section.

The stellar mass, visual extinction ($A_V$), and SFR (SFR$_{SED}$) of the galaxies were derived from evolutionary synthesis modeling of their optical to near-IR broadband spectral energy distributions (SEDs) supplemented with mid-IR 3–8 µm photometry when available. Model assumptions dominate the uncertainties of the derived stellar properties. In general, however, for observed SEDs covering up to at least near-IR wavelengths, and for similar model evolutionary tracks and star formation histories, the relative ranking of galaxies in these properties is fairly robust (e.g., Förster Schreiber et al. 2004; Shapley et al. 2005; Wuyts et al. 2007, 2011a; Maraston et al. 2010; M11). For consistency, we adopted best-fit results for the SINS and zC-SINF samples obtained with the same Bruzual & Charlot (2003) code, a Chabrier (2003) IMF, solar metallicity, the Calzetti et al. (2000) reddening law, and constant or exponentially declining SFRs.<fnref n="28" />

Table 1 also lists the rest-frame *U* − *V* color of the galaxies and, for objects in fields with mid- or far-IR coverage with the *Spitzer*/MIPS or *Herschel*/PACS instruments (COSMOS, GOODS-South, and Deep3a) and detected in at least one of the 24, 70, 100, or 160 µm bands, the SFR from the emergent rest-UV and IR emission (SFR$_{UV+IR}$). The rest-frame photometry was computed from interpolation of the observed photometry using the code EAZY (Brammer et al. 2008). The SFR$_{UV+IR}$ estimates were derived following the prescriptions of Wuyts et al. (2011a): the UV contribution was calculated from the rest-frame 2800 Å luminosity, and the IR contribution was derived from the longest wavelength at which an object is detected.<fnref n="29" /> Throughout the paper, we use the SFR$_{UV+IR}$ when available and the SFR$_{SED}$ otherwise.

The SINS/zC-SINF AO sample includes six galaxies with evidence for a Type 2 AGN, noted in Table 1. Two of them were known to host an AGN based on the detection of rest-UV spectral signatures and a 1.4 GHz radio emission excess (Genzel et al. 2006; Förster Schreiber et al. 2014). As

<footnote n="28">²⁸ Declining star formation histories may not be appropriate for $z \sim 2$ SFGs (e.g., Renzini 2009; Maraston et al. 2010). The objects modeled with an exponentially declining SFR of e-folding timescale $\tau = 300$ Myr by FS09 have age/$\tau \sim 1$, on average, with a central 68% distribution between 0.3 and 2 and, in most cases, cannot be statistically distinguished from fits with a constant SFR. The resulting typically young ages indicate that most stars formed in the recent past of these galaxies, meaning that exponentially declining models are actually trying to mimic a secularly increasing SFR.</footnote>

<footnote n="29">²⁹ IR photometry was taken from the PEP survey catalog in GOODS-South and COSMOS (Berta et al. 2011; Lutz et al. 2011) with updated MIPS data from the COSMOS2015 catalog (Laigle et al. 2016) where relevant.</footnote>
<table><caption>**Table 1**
SINS/zC-SINF AO Survey: Sample Galaxies</caption><thead><tr><th>Source</th><th>R.A.</th><th>Decl.</th><th>K<sub>AB</sub><sup>a</sup><br>(mag)</th><th>z<sub>Hα</sub><sup>b</sup></th><th>M<sub>*</sub><br>(10<sup>10</sup> M<sub>☉</sub>)</th><th>A<sub>V</sub><br>(mag)</th><th>SFR<sub>SED</sub><br>(M<sub>☉</sub> yr<sup>-1</sup>)</th><th>sSFR<sub>SED</sub><br>(Gyr<sup>-1</sup>)</th><th>SFR<sub>UV+IR</sub><sup>c</sup><br>(M<sub>☉</sub> yr<sup>-1</sup>)</th><th>sSFR<sub>UV+IR</sub><br>(Gyr<sup>-1</sup>)</th><th>(U - V)<sub>rest</sub><sup>d</sup><br>(mag)</th><th>Notes<sup>e</sup></th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>16:25:51.7</td><td>+26:46:55</td><td>23.41</td><td>2.4078</td><td>1.03</td><td>0.6</td><td>15</td><td>1.5</td><td>...</td><td>...</td><td>0.67</td><td>...</td></tr><tr><td>Q1623-BX502</td><td>16:25:54.4</td><td>+26:44:09</td><td>23.89</td><td>2.1557</td><td>0.23</td><td>0.4</td><td>14</td><td>6.0</td><td>...</td><td>...</td><td>0.14</td><td>...</td></tr><tr><td>Q1623-BX543</td><td>16:25:57.7</td><td>+26:50:09</td><td>22.39</td><td>2.5209</td><td>0.94</td><td>0.8</td><td>145</td><td>15.5</td><td>...</td><td>...</td><td>0.24</td><td>...</td></tr><tr><td>Q1623-BX599</td><td>16:26:02.6</td><td>+26:45:32</td><td>21.78</td><td>2.3312</td><td>5.66</td><td>0.4</td><td>34</td><td>0.6</td><td>...</td><td>...</td><td>0.93</td><td>...</td></tr><tr><td>Q2343-BX389</td><td>23:46:28.9</td><td>+12:47:34</td><td>22.04</td><td>2.1724</td><td>4.12</td><td>1.0</td><td>25</td><td>0.6</td><td>...</td><td>...</td><td>1.29</td><td>...</td></tr><tr><td>Q2343-BX513</td><td>23:46:11.1</td><td>+12:48:32</td><td>21.95</td><td>2.1082</td><td>2.70</td><td>0.2</td><td>10</td><td>0.4</td><td>...</td><td>...</td><td>0.93</td><td>...</td></tr><tr><td>Q2343-BX610</td><td>23:46:09.4</td><td>+12:49:19</td><td>21.07</td><td>2.2107</td><td>10.0</td><td>0.8</td><td>60</td><td>0.6</td><td>...</td><td>...</td><td>0.93</td><td>1</td></tr><tr><td>Q2346-BX482</td><td>23:48:13.0</td><td>+00:25:46</td><td>(22.34)<sup>f</sup></td><td>2.2571</td><td>1.84</td><td>0.8</td><td>80</td><td>4.3</td><td>...</td><td>...</td><td>0.77</td><td>...</td></tr><tr><td>Deep3a-6004</td><td>11:25:03.8</td><td>-21:45:33</td><td>20.79</td><td>2.3871</td><td>31.6</td><td>1.8</td><td>214</td><td>0.7</td><td>355</td><td>1.1</td><td>1.52</td><td>1</td></tr><tr><td>Deep3a-6397</td><td>11:25:10.5</td><td>-21:45:06</td><td>19.96</td><td>1.5133</td><td>12.0</td><td>2.2</td><td>563</td><td>4.7</td><td>214</td><td>1.8</td><td>1.28</td><td>1</td></tr><tr><td>Deep3a-15504</td><td>11:24:15.6</td><td>-21:39:31</td><td>21.03</td><td>2.3830</td><td>10.9</td><td>1.0</td><td>150</td><td>1.4</td><td>146</td><td>1.3</td><td>0.71</td><td>1</td></tr><tr><td>K20-ID6</td><td>03:32:29.1</td><td>-27:45:21</td><td>22.13</td><td>2.2348</td><td>2.67</td><td>1.0</td><td>45</td><td>1.7</td><td>47</td><td>1.8</td><td>0.91</td><td>...</td></tr><tr><td>K20-ID7</td><td>03:32:29.1</td><td>-27:46:29</td><td>21.47</td><td>2.2240</td><td>3.95</td><td>1.0</td><td>112</td><td>2.8</td><td>101</td><td>2.6</td><td>0.49</td><td>...</td></tr><tr><td>GMASS-2303</td><td>03:32:38.9</td><td>-27:43:22</td><td>22.78</td><td>2.4507</td><td>0.72</td><td>0.4</td><td>21</td><td>2.9</td><td>IR-undet</td><td>IR-undet</td><td>0.46</td><td>...</td></tr><tr><td>GMASS-2363</td><td>03:32:39.4</td><td>-27:42:36</td><td>22.67</td><td>2.4520</td><td>2.16</td><td>1.2</td><td>64</td><td>2.9</td><td>45</td><td>2.1</td><td>0.87</td><td>...</td></tr><tr><td>GMASS-2540</td><td>03:32:30.3</td><td>-27:42:40</td><td>21.80</td><td>1.6146</td><td>1.89</td><td>0.6</td><td>21</td><td>1.1</td><td>32</td><td>1.7</td><td>0.96</td><td>...</td></tr><tr><td>SA12-6339</td><td>12:05:32.7</td><td>-07:23:38</td><td>22.00</td><td>2.2971</td><td>2.57</td><td>2.0</td><td>620</td><td>24</td><td>...</td><td>...</td><td>0.61</td><td>...</td></tr><tr><td>ZC400528</td><td>09:59:47.6</td><td>+01:44:19</td><td>21.08</td><td>2.3873</td><td>11.0</td><td>0.9</td><td>148</td><td>1.3</td><td>556</td><td>5.1</td><td>0.84</td><td>1</td></tr><tr><td>ZC400569</td><td>10:01:08.7</td><td>+01:44:28</td><td>20.69</td><td>2.2405</td><td>16.1</td><td>1.4</td><td>241</td><td>1.5</td><td>239</td><td>1.5</td><td>1.29</td><td>1,2</td></tr><tr><td>ZC400569N</td><td>10:01:08.7</td><td>+01:44:28</td><td>...</td><td>2.2432</td><td>12.9</td><td>...</td><td>157</td><td>1.2</td><td>156</td><td>1.2</td><td>...</td><td>1,2</td></tr><tr><td>ZC401925</td><td>10:01:01.7</td><td>+01:48:38</td><td>22.74</td><td>2.1413</td><td>0.58</td><td>0.7</td><td>47</td><td>8.2</td><td>IR-undet</td><td>IR-undet</td><td>0.40</td><td>...</td></tr><tr><td>ZC403741</td><td>10:00:18.4</td><td>+01:55:08</td><td>21.02</td><td>1.4457</td><td>4.45</td><td>1.6</td><td>113</td><td>2.5</td><td>IR-undet</td><td>IR-undet</td><td>0.99</td><td>...</td></tr><tr><td>ZC404221</td><td>10:01:41.3</td><td>+01:56:43</td><td>22.44</td><td>2.2199</td><td>1.57</td><td>0.7</td><td>61</td><td>3.9</td><td>IR-undet</td><td>IR-undet</td><td>0.40</td><td>...</td></tr><tr><td>ZC405226</td><td>10:02:19.5</td><td>+02:00:18</td><td>22.33</td><td>2.2870</td><td>0.93</td><td>1.0</td><td>117</td><td>12.6</td><td>IR-undet</td><td>IR-undet</td><td>0.56</td><td>...</td></tr><tr><td>ZC405501</td><td>09:59:53.7</td><td>+02:01:09</td><td>22.25</td><td>2.1539</td><td>0.84</td><td>0.9</td><td>85</td><td>10.1</td><td>IR-undet</td><td>IR-undet</td><td>0.33</td><td>...</td></tr><tr><td>ZC406690</td><td>09:58:59.1</td><td>+02:05:04</td><td>20.81</td><td>2.1950</td><td>4.14</td><td>0.7</td><td>200</td><td>4.8</td><td>296</td><td>7.2</td><td>0.56</td><td>...</td></tr><tr><td>ZC407302</td><td>09:59:56.0</td><td>+02:06:51</td><td>21.48</td><td>2.1819</td><td>2.44</td><td>1.3</td><td>340</td><td>13.9</td><td>358</td><td>14.7</td><td>0.50</td><td>...</td></tr><tr><td>ZC407376</td><td>10:00:45.1</td><td>+02:07:05</td><td>21.79</td><td>2.1729</td><td>2.53</td><td>1.2</td><td>89</td><td>3.5</td><td>124</td><td>4.9</td><td>0.80</td><td>3</td></tr><tr><td>ZC407376S</td><td>10:00:45.1</td><td>+02:07:05</td><td>...</td><td>2.1730</td><td>1.39</td><td>...</td><td>67</td><td>4.8</td><td>93</td><td>6.7</td><td>...</td><td>3</td></tr><tr><td>ZC407376N</td><td>10:00:45.2</td><td>+02:07:06</td><td>...</td><td>2.1728</td><td>1.14</td><td>...</td><td>22</td><td>1.9</td><td>31</td><td>2.7</td><td>...</td><td>3</td></tr><tr><td>ZC409985</td><td>09:59:14.2</td><td>+02:15:47</td><td>22.30</td><td>2.4569</td><td>1.61</td><td>0.6</td><td>51</td><td>3.2</td><td>IR-undet</td><td>IR-undet</td><td>0.64</td><td>...</td></tr><tr><td>ZC410041</td><td>10:00:44.3</td><td>+02:15:59</td><td>23.16</td><td>2.4541</td><td>0.46</td><td>0.6</td><td>47</td><td>10.2</td><td>IR-undet</td><td>IR-undet</td><td>0.36</td><td>...</td></tr><tr><td>ZC410123</td><td>10:02:06.5</td><td>+02:16:16</td><td>22.80</td><td>2.1986</td><td>0.42</td><td>0.8</td><td>59</td><td>13.9</td><td>IR-undet</td><td>IR-undet</td><td>0.31</td><td>...</td></tr><tr><td>ZC411737</td><td>10:00:32.4</td><td>+02:21:21</td><td>22.81</td><td>2.4442</td><td>0.34</td><td>0.6</td><td>48</td><td>13.9</td><td>IR-undet</td><td>IR-undet</td><td>0.53</td><td>...</td></tr><tr><td>ZC412369</td><td>10:01:46.9</td><td>+02:23:25</td><td>21.39</td><td>2.0281</td><td>2.17</td><td>1.0</td><td>94</td><td>4.3</td><td>IR-undet</td><td>IR-undet</td><td>0.88</td><td>...</td></tr><tr><td>ZC413507</td><td>10:00:24.2</td><td>+02:27:41</td><td>22.52</td><td>2.4800</td><td>0.88</td><td>1.1</td><td>111</td><td>12.6</td><td>IR-undet</td><td>IR-undet</td><td>0.57</td><td>...</td></tr><tr><td>ZC413597</td><td>09:59:36.4</td><td>+02:27:59</td><td>22.58</td><td>2.4502</td><td>0.75</td><td>1.0</td><td>84</td><td>11.3</td><td>IR-undet</td><td>IR-undet</td><td>0.51</td><td>...</td></tr><tr><td>ZC415876</td><td>10:00:09.4</td><td>+02:36:58</td><td>22.38</td><td>2.4354</td><td>0.92</td><td>1.0</td><td>94</td><td>10.2</td><td>IR-undet</td><td>IR-undet</td><td>0.68</td><td>...</td></tr></tbody></table>

Notes. The stellar properties are taken from Förster Schreiber et al. (2009, 2011a) and M11 and were derived using Bruzual & Charlot (2003) models with a Chabrier (2003) IMF, solar metallicity, the Calzetti et al. (2000) reddening law, and either constant or exponentially declining SFRs (see text). Stellar masses correspond to those in live stars and remnants. Uncertainties for the stellar properties derived from SEDs are dominated by systematics from model assumptions; for this sample and the analyses throughout this paper, we adopt typical uncertainties of 0.2 dex in log(M<sub>*</sub>), 0.3 mag in A<sub>V</sub>, and 0.47 dex in log(SFR<sub>SED</sub>).

<sup>a</sup> Typical uncertainties on the K-band magnitudes range from 0.05 mag for the brightest quartile (mean and median K<sub>AB</sub> ≈ 21.0 mag) to 0.15 mag for the faintest quartile (mean and median K<sub>AB</sub> ≈ 22.9 mag).

<sup>b</sup> Spectroscopic redshift based on the source-integrated Hα emission.

<sup>c</sup> For sources in fields observed in the mid- or far-IR with Spitzer/MIPS and/or Herschel/PACS (GOODS-South, COSMOS, Deep3a) and detected in at least one band, the SFR is also computed from the emergent rest-frame 2800 Å and IR luminosities following Wuyts et al. (2011a). Sources undetected with MIPS and PACS are indicated explicitly with “IR-undet,” to distinguish them from objects in fields without MIPS and PACS observations. For the analysis, we adopt typical uncertainties of 0.47 dex in log(SFR<sub>UV+IR</sub>).

<sup>d</sup> Rest-frame U - V colors derived following the procedure described by Wuyts et al. (2012; see also Taylor et al. 2009; Brammer et al. 2011). Uncertainties are dominated by those of the observed photometry and systematics from the set of templates used for interpolation and are typically estimated to be 0.1 mag.

<sup>e</sup> (1) These objects have evidence for an AGN (Section 2.2). (2) ZC400569 has a complex morphology characterized by a brighter northern source and a southern clumpy extension; the stellar mass and SFR of the dominant northern component are scaled from the total values according to the fractions estimated from the stellar mass map (based on HST/WFC3 near-IR imaging) and the observed Hα line map, respectively. (3) ZC407376 is an interacting pair; the stellar mass and SFR of each component are scaled from those of the total system according to the fractions estimated from the HST/WFC3-based stellar mass map and the observed Hα line map, respectively.

<sup>f</sup> For Q2346-BX482, no K-band photometry is available; here we give the H-band magnitude from HST/NICMOS imaging through the F160W filter (Förster Schreiber et al. 2011a).
discussed by Förster Schreiber et al. (2014; see also Newman et al. 2014), the high-resolution SINFONI+AO Hα+[N II] data, supplemented with seeing-limited maps of [O III] and Hβ obtained for four objects, further indicate the presence of an AGN through the line ratios and high-velocity gas outflow signatures in the central few kpc of all of the AO targets more massive than $M_* \gtrsim 10^{11} M_\odot$, including four cases previously unidentified as hosting an AGN.

## 2.1. Selection of the Parent SINS/zC-SINF Seeing-limited Sample

The SINS Hα targets were drawn from large optical spectroscopic surveys of $z \sim 1.5-2.5$ candidates selected by their $U_nGR$ optical colors (“BX/BM” objects; Steidel et al. 2004), K-band magnitudes (the “K20” survey at $K_{s,\text{Vega}} < 20$ mag, Cimatti et al. 2002; the Gemini Deep Deep Survey (GDDS) at $K_{s,\text{Vega}} < 20.6$ mag, Abraham et al. 2004), 4.5 µm magnitudes (the Galaxy Mass Assembly ultra-deep Spectroscopic Survey (GMASS) at $m_{4.5 \mu m,AB} < 23.0$ mag, Cimatti et al. 2008; Kurk et al. 2013), or a combination of K-band and BzK color criteria (from the survey by Kong et al. 2006 of the “Deep3a” field of the ESO Imaging Survey; Renzini & Da Costa 1997). The SINS BX/BM targets were more specifically taken from the near-IR long-slit spectroscopic follow-up with NIRSPEC at the Keck II telescope of Erb et al. (2006b), and the SINS K20 objects comprised all five $z > 2$ sources discussed by Daddi et al. (2004). In addition to a reliable optical redshift, the selection criteria common to all SINS targets were that Hα falls in wavelength intervals of high atmospheric transmission and away from bright night-sky lines, object visibility during the observing runs, and an observed integrated line flux of $\gtrsim 5 \times 10^{-17} \text{erg s}^{-1} \text{cm}^{-2}$ in existing long-slit spectroscopy (for the BX/BM objects) or expected based on the best-fit SFR<sub>SED</sub> and A<sub>V</sub> values. Faintier sources were discarded because of prohibitively long integration times for detection, but we note that this criterion, applied last in the selection, removed very few objects. As argued by FS09, the diversity of criteria employed for the surveys from which the SINS targets were drawn makes the resulting sample less biased than any of its constituent subsamples.

The zC-SINF sample was drawn from the spectroscopic zCOSMOS-Deep survey carried out with VLT/VIMOS (Lilly et al. 2007, 2009), covering the central $1 \text{ deg}^2$ of the $2 \text{ deg}^2$ COSMOS field (Scoville et al. 2007). Reliable optical redshifts ($z_{\text{opt}}$) were derived for $\sim 6000$ objects at $1.4 < z < 2.5$, preselected at $K_s < 23.5$ mag and according to the BzK or BX/BM color criteria. The zC-SINF SINFONI targets were then culled among those within $30''$ of a $g_{AB} < 17$ mag star enabling natural guide star (NGS) AO (with one exception), a sufficiently secure redshift, avoidance of spectral regions with bright night-sky lines and/or low atmospheric transmission for the Hα line, and a minimum SFR of $\sim 10 M_\odot \text{ yr}^{-1}$ (see M11 for details). This SFR roughly matches the minimum Hα flux criterion for the SINS galaxies at $z = 2$ assuming $A_V = 1$ mag, and, as for the SINS sample, this cut removes only a few objects. Of the 62 viable SINFONI targets thus culled, the best 30 in terms of all criteria combined were observed. Of this zC-SINF sample, 29 belong to the zCOSMOS-Deep subset preselected with the BzK criteria, and one is from the “BX” subset.

The resulting SINS and zC-SINF Hα seeing-limited samples range in redshift from 1.35 to 2.58, with median $z = 2.22; 76\%$

of the targets are at $z > 2$. The fraction of objects with Hα detected in the seeing-limited data is 84%. Although non-AGN targets were preferentially selected, six of the galaxies observed were known to host an AGN based on diagnostic features in their rest-UV spectra, their strong mid-IR excess, or their brightness in X-ray or radio emission depending on the multiwavelength and spectroscopic coverage of the sources in different fields. As noted above, our SINFONI data added four cases with evidence for an AGN from their rest-optical emission-line properties. The different diagnostics available among the fields prevent a reliable assessment of AGN fraction and biases with respect to this population for the SINS/zC-SINF sample. The increase in AGN fraction with higher galaxy mass is, however, fully consistent with the trends observed from much larger multiwavelength and spectroscopic surveys at $z \sim 2$ (e.g., Reddy et al. 2005; Daddi et al. 2007; Brusa et al. 2009; Bongiorno et al. 2012; Hainline et al. 2012; Mancini et al. 2015).

## 2.2. Selection of the SINS/zC-SINF AO Sample

For the SINFONI+AO observations, 17 targets were taken from the parent SINS seeing-limited survey and 18 from the zC-SINF sample. They were mostly chosen to lie at $z > 2$, although three objects at $z \sim 1.5$ were considered. The redshifts range from 1.45 to 2.52, with a median $z = 2.24$, approximately the same as for the parent seeing-limited sample. The goal of the SINFONI LP was to collect AO data of $\sim 25$ sources covering the $M_* - \text{SFR}$ plane as widely as possible and obtain a set of “benchmark objects” to relate resolved kinematics, star formation, and physical conditions with global properties of the massive SFG population. Some of the objects had been previously observed with AO as part of other programs; for them, the additional LP observations aimed at a substantial increase in the sensitivity of the data sets. In addition to the final 26 AO targets of the LP, nine other galaxies were observed during the course of various SINFONI+AO programs addressing more specific, though related, science goals. The total number of targets results from the trade-off between sample size and S/N of the data within the constraints set by the available observing time.

The SINS objects were taken among those with a suitable AO reference star ($R_{V,\text{Vega}} < 18$ mag and distance from the galaxy <60"), except for one without a nearby bright star that was observed in the so-called “Seeing Enhancer” (SE) mode (see Section 3.1). Some preference was given to brighter SINS objects with a source-integrated Hα flux $\gtrsim 10^{-16} \text{ erg s}^{-1} \text{cm}^{-2}$, although three fainter sources were included (GMASS-2303, GMASS-2363, and K20-ID6, with fluxes of (3–5) $\times 10^{-17} \text{ erg s}^{-1} \text{cm}^{-2}$). In general, for these SINS AO targets, emphasis was given to larger disklike systems or compact objects with velocity dispersion-dominated kinematics in seeing-limited data. One object identified as a merger from seeing-limited kinematics (K20-ID7; see Shapiro et al. 2008) was also observed. These choices were driven by the aim of obtaining very deep kpc-scale-resolution IFU data of objects in different kinematic classes, unveiling the nature of the most compact sources, and studying in detail the dynamical and star formation processes in early disks (see Genzel et al. 2006, 2008, 2011, 2014a; Newman et al. 2012b, 2013).

The choice of zC-SINF objects for the AO observations was more objective and dictated by the targets being detected in the 1–2 hr natural seeing observations and the goal of ensuring wide $M_* - \text{SFR}$ coverage in combination with the SINS AO
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Distributions in stellar and color properties of the SINS/zC-SINF AO sample and the parent Hα sample observed with SINFONI in seeing-limited mode. The SINFONI samples are compared to 1.4 < *z* < 2.6 SFGs in the COSMOS field at $K_{S,AB} < 23.0$ mag and with inverse specific SFR lower than the Hubble time at the redshift of each object. The SINS/zC-SINF galaxies are plotted as large circles ($z > 2$) and squares ($z < 2$), with red symbols showing those observed with AO. The density distribution of COSMOS SFGs is shown in green, with contours corresponding to fractions of 0.1, 0.3, 0.5, 0.7, 0.9, and 0.98 of the maximum. The green filled, gray hatched, and red hatched histograms show the fractional distributions projected onto each axis for the reference SFG population and the SINFONI seeing-limited and AO samples, respectively (with median *z* of 1.73, 2.22, and 2.24). Left: stellar mass vs. SFR. The solid line indicates the MS of SFGs at *z* = 2.2 from Whitaker et al. (2014); dashed and dotted lines correspond to offsets in SFR relative to the MS, as labeled in the plot. The inset shows the distributions of the offsets in specific SFR (in logarithmic units) of the reference SFG sample and the SINS/zC-SINF no-AO and AO targets relative to the MS at the mass and redshift of each individual source. Right: stellar mass vs. rest-frame *U* − *V* color. The solid line indicates the mean (*U* − *V*)<sub>rest</sub> as a function of *M*<sub>⋆</sub> of the reference SFG sample around *z* = 2.2 (see Section 2.3). The inset shows the distributions of the reference SFG, SINFONI no-AO, and AO samples in color offset from the *M*<sub>⋆</sub> versus (*U* − *V*)<sub>rest</sub> relation accounting for its zero-point evolution (∝ −0.24 × *z*). The SINS/zC-SINF AO sample covers similar ranges in *M*<sub>⋆</sub>, SFR, Δlog(sSFR)<sub>MS</sub>, and (*U* − *V*)<sub>rest</sub> as the parent no-AO sample and somewhat emphasizes the bluer targets at fixed stellar mass. The SINS/zC-SINF objects have a similar coverage in *M*<sub>⋆</sub> as the reference SFG sample but preferentially probe the more actively star-forming and bluer part of this population.</figcaption></figure>

targets. No explicit Hα flux or S/N cut was applied for the zC-
SINF AO targets; their integrated Hα fluxes are in the range
~4 × 10⁻¹⁷⁻⁶ × 10⁻¹⁶ erg s⁻¹ cm⁻². The Hα morphology
and kinematics were not considered, except to exclude two
candidate Type 1 AGNs based on their bright and point-like
morphologies in Hα and HST broadband imaging in conjunc-
tion with their X-ray emission and rest-UV spectral features.
For both SINS and zC-SINF AO targets, no explicit
requirement on the averaged Hα surface brightness was used;
instead, the integration times were adjusted to optimize the
S/N per resolution element.

## 2.3. Global Stellar and Color Properties of the Samples

In terms of stellar mass, SFR, and color, the SINS/zC-SINF
AO sample is fairly representative of its parent seeing-limited
sample. This is shown in Figure 1, which compares their
distributions in M* versus SFR and (U-V)rest color diagrams.
To place the samples in a broader context, Figure 1 also shows
the distributions of the underlying galaxy population in the
COSMOS field at 1.4 < z < 2.6 to KAB < 23 mag—similar to
the ranges for the SINS/zC-SINF objects. Since here we are
primarily interested in massive SFGs, objects in the reference
sample with a specific SFR < tH-1 are excluded, where tH is the
Hubble time at the redshift of each source. This cut removes a
small fraction (17%) of all KAB < 23 mag sources at 1.4 <
z < 2.6 (and only 12% for the 2 < z < 2.6 interval encom-
passing ≥80% of the parent SINS/zC-SINF sample and the
AO subset). The stellar properties and colors for the reference
sample are taken from Wuyts et al. (2011b), where they were

computed using the source catalog of Ilbert et al. (2009)
supplemented with Spitzer/MIPS and Herschel/PACS mid-
and far-IR photometry (Le Floc’h et al. 2009; Berta et al. 2011;
Lutz et al. 2011) in a similar fashion as for the SINS/zC-SINF
objects. Because the reference SFG sample is magnitude-
limited, it is dominated by galaxies toward lower redshifts
(median z = 1.7) compared to the SINS/zC-SINF samples
(median z = 2.2). The different redshift distributions are
reflected in the small vertical shift between the peak in density
distribution for the reference population and the M* versus SFR
and (U − V)rest relationships at z = 2.2 in Figure 1. To account
for evolutionary effects, the inset in each panel shows the
distributions in terms of offsets in specific SFR and color from
the relationships at the redshift and mass of the individual
galaxies (see below).

The SINS/zC-SINF AO and the parent seeing-limited samples
cover nearly identical ranges in stellar mass and SFR (M* ~ 2 x
10⁹ - 3 x 10¹¹ M☉, SFR ~ 10–650 M☉ yr⁻¹). The median
(mean) values in stellar mass and SFR are nearly the same, with
M* ~ 2 x 10¹⁰ M☉ (~4 x 10¹⁰ M☉) and SFR ~ 80 M☉ yr⁻¹
(~125 M☉ yr⁻¹). The (U − V)rest colors of the AO targets range
from ~0.15 to ~1.5 mag, compared to ~−0.35 to ~2.1 mag for
the full seeing-limited sample. The median and mean colors of the
AO sample are 0.67 and 0.71 mag, slightly bluer than those for the
parent no-AO sample (0.83 and 0.82, respectively). For
comparison, the reference SFG sample has median values of
M* ~ 1.5 x 10¹⁰ M☉, SFR ~ 30 M☉ yr⁻¹, and (U − V)rest ~
0.82 mag. The ranges in properties for the SINS/zC-SINF
samples overlap largely with those of the more general z ~ 2 SFG
population. It is, however, apparent from Figure 1 that they probe preferentially higher specific SFRs and bluer colors at fixed stellar mass, as illustrated by the distributions in the inset of each panel and obtained as follows.

The trend in specific SFR can be quantified through the offset relative to the “main sequence” (MS) delineated by the distribution of SFGs in the $M_*$ − SFR plane, $\Delta \log(\text{sSFR})_{\text{MS}}$. For this purpose, we used the MS parameterization of Whitaker et al. (2014) and calculated the offsets at the redshift and stellar mass of each individual object. The SINS/zC-SINF no-AO sample extends down to 0.7 dex below and up to 1.2 dex above the MS, with a median (mean) ~0.35 dex (~0.30 dex) above the MS. The $\Delta \log(\text{sSFR})_{\text{MS}}$ distribution for the AO sample spans a similar range, from 0.7 dex below up to 1.0 dex above the MS, with a median (mean) offset of ~0.35 dex (~0.25 dex). About 75% of the SINS/zC-SINF seeing-limited and AO targets lie above the MS at their redshift and mass; several of them have an sSFR >4 times larger than the MS and would qualify as “starbursts” according to Rodighiero et al. (2011). The bias toward higher sSFRs is more important at lower $M_*$ (a result of the target selection introducing an effective lower SFR limit of ~10 $M_*$ yr$^{-1}$).

The trend in colors of the SINS/zC-SINF samples relative to the bulk of $z \sim 2$ SFGs can be quantified in an analogous manner. At fixed stellar mass and redshift, the distribution of the reference SFG sample is well approximated by a Gaussian. The mean $(U-V)_{\text{rest}}$ color from Gaussian fits in stellar mass bins within a redshift slice<fnref n="30" /> increases as a function of $\log(M_*)$ with approximately constant slope. We thus defined the locus of SFGs in $M_* - (U-V)_{\text{rest}}$ space by fitting a line to these values, with the evolution over $z \sim 1-3$ being mostly in the zero point. The color offset relative to relationship at the mass and redshift of an object is denoted $\Delta(U-V)_{\text{rest}}$. The $\Delta(U-V)_{\text{rest}}$ values of the SINS/zC-SINF seeing-limited sample span −0.6 to 0.9 mag, with a small median and mean offset of ~−0.03 mag. The AO subset covers a narrower range of −0.55 to 0.25 mag, with median and mean offsets of ≈−0.10 mag. Accounting for the redshift and mass of the targets, about 65% of the no-AO sample lies on the blue side of the SFG locus in $M_*$ versus $(U-V)_{\text{rest}}$, and 70% of the AO targets do.

The preferentially higher sSFRs and bluer rest-optical colors of the SINS/zC-SINF samples compared to the underlying population of massive SFGs results from the combination of selection criteria, as extensively discussed by FS09 and M11. In particular, even for a primary selection at near-/mid-IR wavelengths (as for the majority of our targets), the mandatory $z_{\text{opt}}$ means in practice an optical magnitude cut to ensure sufficient S/N for a reliable redshift determination. This limit is typically ~25–26 mag for the spectroscopic surveys from which the galaxies were drawn and implies that on average, the objects have bluer colors than an unbiased, purely K- (or mass-) selected sample in the same redshift range. In addition, the requirement of minimum H$\alpha$ flux (or SFR) likely emphasizes younger, less obscured, and more actively star-forming systems, but we note again that few objects were discarded as SINFONI targets by this criterion, applied last in the selection process. An examination of the optical brightness and SFR distributions of photometrically selected candidate

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Distribution in stellar mass vs. size of the SINS/zC-SINF AO sample and the parent H$\alpha$ sample observed in seeing-limited mode. The SINFONI samples are compared to $1.4 < z < 2.6$ SFGs in the CANDELS/3D-HST fields at $K_{S,AB} < 23.0$ mag and with inverse specific SFR lower than the Hubble time at the redshift of each object. Symbols and colors are the same as in Figure 1. In the main plot, the sizes are the major-axis effective radii derived from HST H-band imaging, available for 51 targets in the full SINS/zC-SINF sample and 29 targets from the AO subset. The solid and dashed lines indicate the mass–size relation for SFGs at $z = 2.2$ from van der Wel et al. (2014b) and the offsets by factors of two around it. The inset shows the distributions of the offsets in log($R_c$) from the mass–size relation at the mass and redshift of each individual source, where the sizes are corrected to a reference rest-frame wavelength of 5000 Å to account for the (small) effects of color gradients. The SINS/zC-SINF AO sample covers similar ranges in $R_c(H)$ and $\Delta \log(R_c^{5000})_{\text{SFGs}}$ as the parent no-AO sample and the reference population of SFGs, with only a small shift toward larger sizes at fixed mass (by ~10% on average).</figcaption></figure>

$z \sim 1.5–2.5$ galaxies and spectroscopically confirmed subsets in public data sets for popular deep fields (GOODS, COSMOS) confirms that biases toward higher sSFRs and bluer colors result largely from the optical magnitude limits of the spectroscopic surveys.

## 2.4. Rest-optical Size Distribution of the Samples

The strategies for both SINS and zC-SINF relied on the detection of H$\alpha$ emission in 1–2 hr on-source integrations in natural seeing. Therefore, while no surface brightness criterion was applied, there is an implicit bias toward galaxies with at least some regions above a minimum H$\alpha$ surface brightness. This effect could plausibly set the upper envelope in the H$\alpha$ size versus flux distribution of the parent no-AO sample (FS09; M11), and, consequently, the AO sample may be missing the largest objects at any given integrated line flux. It is also possible that the most extended objects at a given optical magnitude are underrepresented because a low surface brightness may have prevented reliable redshift measurements. On the other hand, some of the more subjective choices made in particular for the AO follow-up of the SINS targets may have favored overall larger-than-average objects (see Section 2.2).

Figure 2 compares the distributions in $M_*$ versus effective radius $R_c$ of our SINFONI samples to those of the underlying

<footnote n="30">³⁰ We used a bin width in $\log(M_*)$ of 0.3 dex, but the result is not very sensitive to this choice as long as each bin contains $\ge$1000 sources; our approach is inspired by that of Rodighiero et al. (2011) in deriving their MS relationship in $M_*$ − SFR. For the redshift bins, we used a width of 0.5.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Redshift distributions of $z \sim 1–3$ SFGs observed and detected with AO-assisted near-IR IFUs. The different samples are plotted with color and filling schemes as labeled in the legend. The samples are split in redshift slices corresponding to the near-IR band in which the main lines of interest were observed ($H\alpha$ for $0.8 < z < 2.8$, $H\beta+[OIII]$ for $2.8 < z < 3.5$), and the bin width spans the redshift range of the sources within each band. In addition to SINS/zC-SINF, the samples shown include the galaxies observed with SINFONI+AO from the LSD (Mannucci et al. 2009; Troncoso et al. 2014), MASSIV (Contini et al. 2012), and sHiZELS (Swinbank et al. 2012a, 2012b; Molina et al. 2017) surveys and with OSIRIS+AO from the work of Law et al. (2009, 2012a), Wright et al. (2007, 2009), the IROCKS survey (Mieda et al. 2016), and the WiggleZ sample (Wisnioski et al. 2011, 2012). A collection of strongly lensed objects observed with AO using SINFONI, OSIRIS, and Gemini/NIFS is also plotted (Stark et al. 2008; Jones et al. 2010a, 2010b, 2013; Yuan et al. 2011, 2012; Wuys et al. 2014b; Livermore et al. 2015; Leethochawalit et al. 2016). With 32 of 35 SFGs at $2 < z < 2.7$, SINS/zC-SINF is the largest near-IR IFU AO sample in this redshift slice.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Distributions in stellar mass and offset in specific SFR from the MS of $z \sim 1–3$ SFGs obtained with AO-assisted near-IR IFUs. The samples are the same as plotted in Figure 3, with symbols and median redshifts as labeled in the legend (excluding the 17 lensed objects without an $M_*$ estimate). The density distribution of COSMOS SFGs at $0.8 < z < 3.5$, $K_{S,AB} < 23.0$ mag, and $sSFR > t_H^{-1}$ is shown in green, with contours marking fractions of 0.1, 0.3, 0.5, 0.7, 0.9, and 0.98 of the maximum value. The MS population is fairly well probed by all AO surveys down to ~$10^{10} M_\odot$. Below this mass, nonlensed samples are biased toward higher specific SFRs, while lensed samples more easily reach the lower-mass population also below the MS.</figcaption></figure>

population of SFGs. We considered rest-frame optical continuum sizes obtained from H-band observations, less prone to the effects of extinction and localized star formation than the rest-UV or $H\alpha$. Here the reference SFG population is taken from the CANDELS/3D-HST surveys (Grogin et al. 2011; Koekemoer et al. 2011; Skelton et al. 2014; Momcheva et al. 2016), which provide the largest sample with sizes measured in the near-IR from HST imaging (van der Wel et al. 2012, 2014b). The same redshift, K magnitude, and sSFR cuts are applied as for the COSMOS reference sample in the previous subsection (the 3D-HST reference sample has similar median $z = 1.8$). The H-band sizes are available for 51 objects in our full SINS/zC-SINF sample and 29 of the AO targets; we use the measurements presented by Förster Schreiber et al. (2011a) and Tacchella et al. (2015b), as well as van der Wel et al. (2012), for the other objects that fall within the CANDELS/3D-HST fields.

The size distribution of the SINS/zC-SINF galaxies overlaps well with that of the underlying SFG population. The full and AO samples cover the same range in $R_e(H)$ from 0.8 to 8.5 kpc with the same average of 4.1 kpc and comparable median values of 4.0 and 3.6 kpc, respectively. These average and median sizes are modestly larger than those of the reference SFG sample, which are 3.4 and 3.2 kpc, respectively.

To further quantify possible size biases, we considered the offsets in effective radius relative to the mass–size relation for SFGs at the redshift and stellar mass of individual objects, as parameterized by van der Wel et al. (2014b). For consistency with this relation, we accounted for the effects of average color gradients following the prescriptions given by van der Wel et al. to derive effective radii at rest frame 5000 Å. The offsets, $\Delta \log(R_e^{5000})_{SFGs}$, range from –0.6 to 0.4 dex for the parent seeing-limited SINS/zC-SINF sample and the AO subset. The mean and median offsets are ~0.07 dex for the full sample and 0.05 dex for the AO targets (with a scatter of 0.24 dex, identical to that of the reference SFG sample used here). Based on the comparison presented here, there is no substantial size bias for our SINS/zC-SINF samples relative to the underlying SFG population, at least for the objects (in majority) with HST H-band imaging.

## 2.5. Comparison to Other AO Samples

To further place our SINS/zC-SINF AO sample in context, we compare it here with several other published near-IR IFU AO samples at $0.8 < z < 3.5$. We consider galaxies that were detected with AO observations obtained with comparable pixel scales of 50–100 mas, i.e., with data usable for analysis and well-sampled angular resolution of 0.′′3 or better. The emission lines targeted were $H\alpha$ and [N II] $\lambda\lambda6548, 6584$ for $z \lesssim 3$ objects and $H\beta$ and [O III] $\lambda\lambda4959, 5007$ for those at $z \gtrsim 3$. Because such observations are time-consuming, the samples are still fairly modest in size.

Using SINFONI, Mannucci et al. (2009; see also Gnerucci et al. 2011a, 2011b; Troncoso et al. 2014) obtained deep AO data and detected nine Lyman-break galaxies (LBGs) at $2.9 < z < 3.4$ from the “Lyman-break galaxies Stellar populations and Dynamics” (LSD) project. In the “Mass Assembly Survey with SINFONI in VVDS” (MASSIV) survey, five of the 11 AO targets were observed at the 50 mas pixel scale and detected, four at $1 < z < 1.6$ were selected based on their [O II] $\lambda 3727$ emission-line flux and equivalent width, and one at $z = 2.24$ was selected based on rest-UV properties (Contini
<table><caption>**Table 2**
Summary of the SINFONI AO Observations</caption><thead><tr><th>Source</th><th>z<sub>Hα</sub></th><th>Band</th><th>AO Mode<sup>a</sup></th><th>PA<sup>b</sup><br>(deg)</th><th>Dithering<sup>c</sup></th><th>t<sub>int</sub><sup>d</sup><br>(s)</th><th>PSF FWHM<sup>e</sup></th><th>Run ID<sup>f</sup></th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>2.4078</td><td>K</td><td>LGS</td><td>+90</td><td>OO</td><td>12600</td><td>0".11</td><td>087.A-0081</td></tr><tr><td>Q1623-BX502</td><td>2.1557</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>24000</td><td>0".15</td><td>075.A-0466, 080.A-0330, 081.B-0568</td></tr><tr><td>Q1623-BX543</td><td>2.5209</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>25200</td><td>0".30</td><td>087.A-0081</td></tr><tr><td>Q1623-BX599</td><td>2.3312</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>37200</td><td>0".25</td><td>183.A-0781</td></tr><tr><td>Q2343-BX389</td><td>2.1724</td><td>K</td><td>LGS-SE</td><td>-45</td><td>OO</td><td>25200</td><td>0".20</td><td>183.A-0781</td></tr><tr><td>Q2343-BX513</td><td>2.1082</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>10800</td><td>0".15</td><td>087.A-0081</td></tr><tr><td>Q2343-BX610</td><td>2.2107</td><td>K</td><td>LGS-SE</td><td>+20</td><td>OS</td><td>30000</td><td>0".24</td><td>183.A-0781, 088.A-0202</td></tr><tr><td>Q2346-BX482</td><td>2.2571</td><td>K</td><td>LGS</td><td>0</td><td>OS</td><td>44400</td><td>0".18</td><td>080.A-0330, 080.A-0339, 183.A-0781</td></tr><tr><td>Deep3a-6004</td><td>2.3871</td><td>K</td><td>LGS</td><td>0</td><td>OS</td><td>19200</td><td>0".16</td><td>183.A-0781, 091.A-0126</td></tr><tr><td>Deep3a-6397</td><td>1.5133</td><td>H</td><td>LGS</td><td>0</td><td>OS</td><td>30600</td><td>0".19</td><td>082.A-0396</td></tr><tr><td>Deep3a-15504</td><td>2.3830</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>82800</td><td>0".16</td><td>076.A-0527, 183.A-0781</td></tr><tr><td>K20-ID6</td><td>2.2348</td><td>K</td><td>LGS</td><td>+45</td><td>OO</td><td>13200</td><td>0".20</td><td>080.A-0339</td></tr><tr><td>K20-ID7</td><td>2.2240</td><td>K</td><td>LGS</td><td>+90</td><td>OS</td><td>25800</td><td>0".15</td><td>183.A-0781</td></tr><tr><td>GMASS-2303</td><td>2.4507</td><td>K</td><td>LGS</td><td>+90</td><td>OO</td><td>15600</td><td>0".17</td><td>080.A-0635</td></tr><tr><td>GMASS-2363</td><td>2.4520</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>49200</td><td>0".17</td><td>080.A-0635</td></tr><tr><td>GMASS-2540</td><td>1.6146</td><td>H</td><td>LGS</td><td>+90</td><td>OS</td><td>36000</td><td>0".17</td><td>183.A-0781</td></tr><tr><td>SA12-6339</td><td>2.2971</td><td>K</td><td>LGS</td><td>-20</td><td>OO</td><td>28200</td><td>0".14</td><td>087.A-0081</td></tr><tr><td>ZC400528</td><td>2.3873</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>14400</td><td>0".15</td><td>183.A-0781</td></tr><tr><td>ZC400569</td><td>2.2405</td><td>K</td><td>NGS</td><td>+30</td><td>OS</td><td>81000</td><td>0".15</td><td>183.A-0781, 091.A-0126</td></tr><tr><td>ZC401925</td><td>2.1413</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>21000</td><td>0".25</td><td>183.A-0781</td></tr><tr><td>ZC403741</td><td>1.4457</td><td>H</td><td>NGS</td><td>0</td><td>OO</td><td>14400</td><td>0".16</td><td>183.A-0781</td></tr><tr><td>ZC404221</td><td>2.2199</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>14400</td><td>0".20</td><td>183.A-0781</td></tr><tr><td>ZC405226</td><td>2.2870</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>69000</td><td>0".24</td><td>081.A-0672, 183.A-0781</td></tr><tr><td>ZC405501</td><td>2.1539</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>20400</td><td>0".18</td><td>183.A-0781</td></tr><tr><td>ZC406690</td><td>2.1950</td><td>K</td><td>NGS</td><td>0</td><td>OS</td><td>36000</td><td>0".17</td><td>183.A-0781</td></tr><tr><td>ZC407302</td><td>2.1819</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>68400</td><td>0".16</td><td>079.A-0341, 183.A-0781, 088.A-0209</td></tr><tr><td>ZC407376</td><td>2.1729</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>21600</td><td>0".22</td><td>183.A-0781</td></tr><tr><td>ZC409985</td><td>2.4569</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>18000</td><td>0".13</td><td>081.A-0672</td></tr><tr><td>ZC410041</td><td>2.4541</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>21600</td><td>0".16</td><td>183.A-0781</td></tr><tr><td>ZC410123</td><td>2.1986</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>7200</td><td>0".18</td><td>081.A-0672</td></tr><tr><td>ZC411737</td><td>2.4442</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>15000</td><td>0".19</td><td>183.A-0781</td></tr><tr><td>ZC412369</td><td>2.0281</td><td>K</td><td>LGS</td><td>0</td><td>OO</td><td>14400</td><td>0".15</td><td>183.A-0781</td></tr><tr><td>ZC413507</td><td>2.4800</td><td>K</td><td>NGS</td><td>0</td><td>OO</td><td>29400</td><td>0".14</td><td>183.A-0781</td></tr><tr><td>ZC413597</td><td>2.4502</td><td>K</td><td>NGS</td><td>+90</td><td>OO</td><td>21000</td><td>0".17</td><td>183.A-0781</td></tr><tr><td>ZC415876</td><td>2.4354</td><td>K</td><td>NGS</td><td>+90</td><td>OO</td><td>21000</td><td>0".14</td><td>183.A-0781</td></tr></tbody></table>

Notes. The SINFONI AO data for all sources were taken with the intermediate 50 mas pixel⁻¹ scale and nominal FOV of 3".2 × 3".2.

a AO mode used, either with an NGS or LGS. For two objects, the LGS observations were carried out in SE mode, with higher-order corrections performed on the laser spot but without correction for tip-tilt motions on a reference star.

b PA of SINFONI for the AO observations, in degrees east of north.

c Observing strategy followed for adequate sampling of the background. “OO” refers to on-source dithering in which the object is present in all individual exposures, and “OS” refers to the scheme applied for the largest galaxies, in which the background emission is sampled away from the target in one-third of the exposures (see Section 3.1).

d Total on-source integration time of the combined data sets used for the analysis, excluding low-quality exposures for some sources (e.g., taken under poorer observing conditions leading to poorer AO correction).

e The PSF FWHM corresponds to the effective resolution of all observations for a given object. It is estimated from the combined data of the acquisition star taken regularly during the observations of a science target, fitting a circularly symmetric 2D Gaussian profile (i.e., it is the PSF<sub>t G,gal</sub> defined in Section 3.3).

f ESO program number under which the data were taken (see Table 3 for more details).

et al. 2012; see also Épinat et al. 2012; Queyrel et al. 2012; Vergani et al. 2012). Twenty Hα-selected galaxies from the HiZELS narrowband survey were observed with AO as part of the “sHiZELS” project, with six $z \approx 0.8$, eight $z \approx 1.47$, and six $z \approx 2.23$ galaxies (Swinbank et al. 2012a, 2012b; Molina et al. 2017). Using OSIRIS+AO at the Keck II telescope, Law et al. (2009, 2012a) presented data for $13 < 2 < z < 2.5$ BX-selected objects and one LBG at $z = 3.32$; three of the BX objects are in common with our SINS AO subset. At lower redshifts, Wright et al. (2007, 2009) studied seven $1.5 < z < 1.7$ BX/BM-selected objects. Mieda et al. (2016) analyzed the data of 16 galaxies at $0.8 < z < 1.0$ and one at $z = 1.4$ drawn from optical spectroscopic surveys in

well-studied extragalactic fields in their “Intermediate Redshift OSIRIS Chemo-Kinematic Survey” (IROCKS). Thirteen SFGs at $1.2 < z < 1.5$ selected from the WiggleZ Dark Energy Survey based on their [O II] λ3727 strength and rest-UV colors were detected with sufficient S/N for analysis (Wisnioski et al. 2011, 2012). In addition, AO data obtained with OSIRIS, SINFONI, and NIFS on Gemini North of a collection of 35 strongly lensed objects at $1.0 < z < 3.7$ have been published (Stark et al. 2008; Jones et al. 2010a, 2010b, 2013; Yuan et al. 2011, 2012; Wuyts et al. 2014b; Livermore et al. 2015; Leethochawalit et al. 2016).

Including our SINS/zC-SINF survey, these samples provide near-IR AO-assisted IFU data at kpc-scale resolution, or better
<table><caption>**Table 3**
Log of the Observations</caption><thead><tr><th>Source</th><th>Run ID<sup>a</sup></th><th>Observing Dates<sup>b</sup></th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>087.A-0081(B)</td><td>2011 Jul 24</td></tr><tr><td>Q1623-BX502</td><td>075.A-0466(A)</td><td>2005 Apr 07</td></tr><tr><td>...</td><td>080.A-0330(B)</td><td>2008 Mar 25, 26</td></tr><tr><td>...</td><td>081.B-0568(A)</td><td>2008 Apr 04</td></tr><tr><td>Q1623-BX543</td><td>087.A-0081(A)</td><td>2011 Apr 28, 29, 30</td></tr><tr><td>Q1623-BX599</td><td>183.A-0781(E)</td><td>2010 Apr 11, 12; 2013 May 03; 2013 Aug 15; 2014 Jul 13; 2015 Jun 06, 15; 2016 Jun 22; 2016 Jul 27, 29, 31; 2016 Aug 01</td></tr><tr><td>Q2343-BX389</td><td>183.A-0781(E)</td><td>2012 Sep 10, 11, 12; 2012 Oct 09; 2012 Dec 12</td></tr><tr><td>Q2343-BX513</td><td>087.A-0081(B)</td><td>2011 Jul 24</td></tr><tr><td>Q2343-BX610</td><td>183.A-0781(D)</td><td>2011 Sep 27; 2012 Aug 09, 10, 13</td></tr><tr><td>...</td><td>088.A-0202(A)</td><td>2011 Oct 24, 26</td></tr><tr><td>Q2346-BX482</td><td>080.A-0330(A)</td><td>2007 Oct 28, 29</td></tr><tr><td>...</td><td>080.A-0339(A)</td><td>2007 Oct 31; 2008 Jul 27, 28, 30</td></tr><tr><td>...</td><td>183.A-0781(D)</td><td>2009 Nov 10, 11, 12, 17; 2010 Sep 07, 08; 2010 Nov 04; 2011 Nov 25</td></tr><tr><td>Deep3a-6004</td><td>183.A-0781(B)</td><td>2010 Jan 09, 13, 14; 2010 Mar 15; 2011 Jan 01; 2011 Mar 26, 27, 30; 2012 Mar 19</td></tr><tr><td>...</td><td>091.A-0126(A)</td><td>2013 Apr 04</td></tr><tr><td>Deep3a-6397</td><td>082.A-0396(B)</td><td>2008 Dec 23; 2009 Feb 21; 2009 Mar 21, 24; 2009 Jun 18; 2010 Jan 08, 10; 2010 Feb 09; 2010 Mar 09</td></tr><tr><td>Deep3a-15504</td><td>076.A-0527(B)</td><td>2006 Mar 19, 20</td></tr><tr><td>...</td><td>183.A-0781(B)</td><td>2009 Apr 29, 30; 2009 May 15; 2009 Jun 15; 2010 Apr 01; 2011 Mar 26, 31; 2011 Apr 12, 19</td></tr><tr><td>...</td><td>183.A-0781(G)</td><td>2010 Feb 10, 11, 12; 2010 Mar 04, 08</td></tr><tr><td>K20-ID6</td><td>080.A-0339(A)</td><td>2008 Jan 01; 2008 Dec 11, 20, 22</td></tr><tr><td>K20-ID7</td><td>183.A-0781(F)</td><td>2012 Sep 11; 2013 Oct 27, 30; 2013 Nov 05, 12, 21, 22</td></tr><tr><td>GMASS-2303</td><td>080.A-0635(A)</td><td>2007 Nov 13, 14</td></tr><tr><td>GMASS-2363</td><td>080.A-0635(B)</td><td>2007 Dec 17; 2008 Jan 19; 2008 Feb 03, 08, 09, 12, 13, 14, 21, 22</td></tr><tr><td>GMASS-2540</td><td>183.A-0781(F)</td><td>2010 Nov 01; 2010 Dec 05; 2011 Oct 27; 2011 Nov 27, 30; 2011 Dec 01, 19, 21</td></tr><tr><td>SA12-6339</td><td>087.A-0081(A)</td><td>2011 Apr 29, 30</td></tr><tr><td>ZC400528</td><td>183.A-0781(B)</td><td>2010 Jan 15, 24, 25</td></tr><tr><td>ZC400569</td><td>183.A-0781(B)</td><td>2010 Feb 12; 2010 Mar 09, 14; 2012 Jan 18; 2012 Feb 15, 25, 26</td></tr><tr><td>...</td><td>183.A-0781(I)</td><td>2012 Jan 31; 2012 Feb 16, 22, 23</td></tr><tr><td>...</td><td>091.A-0126(A)</td><td>2013 Apr 04, 05, 06, 07, 08, 09</td></tr><tr><td>ZC401925</td><td>183.A-0781(I)</td><td>2011 Jan 25; 2011 Apr 04, 17; 2011 Dec 18, 28</td></tr><tr><td>ZC403741</td><td>183.A-0781(B)</td><td>2009 May 15, 24, 25, 27</td></tr><tr><td>ZC404221</td><td>183.A-0781(G)</td><td>2011 Feb 14</td></tr><tr><td>...</td><td>183.A-0781(H)</td><td>2012 Dec 14; 2013 Jan 07</td></tr><tr><td>ZC405226</td><td>081.A-0672(B)</td><td>2008 Jun 01, 04, 05; 2009 Jan 08, 20</td></tr><tr><td>...</td><td>183.A-0781(G)</td><td>2011 Feb 12; 2012 Jan 06, 07, 16, 17</td></tr><tr><td>...</td><td>183.A-0781(H)</td><td>2013 Jan 12, 15, 17, 24</td></tr><tr><td>ZC405501</td><td>183.A-0781(G)</td><td>2011 Jan 06, 17, 18</td></tr><tr><td>ZC406690</td><td>183.A-0781(G)</td><td>2010 Apr 17; 2010 May 24; 2010 Nov 30</td></tr><tr><td>...</td><td>183.A-0781(H)</td><td>2010 Dec 07, 10, 29, 30; 2011 Jan 02, 03, 17</td></tr><tr><td>ZC407302</td><td>079.A-0341(A)</td><td>2007 Apr 17, 22</td></tr><tr><td>...</td><td>183.A-0781(B)</td><td>2009 Apr 17; 2010 Jan 08, 12; 2010 Feb 09</td></tr><tr><td>...</td><td>088.A-0209(A)</td><td>2012 Mar 14, 15, 16, 17</td></tr><tr><td>ZC407376</td><td>183.A-0781(H)</td><td>2012 Jan 17, 23, 27; 2012 Feb 20, 22</td></tr><tr><td>ZC409985</td><td>081.A-0672(B)</td><td>2008 May 09, 24, 26, 31</td></tr><tr><td>ZC410041</td><td>183.A-0781(H)</td><td>2011 Jan 16; 2011 Feb 10, 23; 2011 May 25</td></tr><tr><td>ZC410123</td><td>081.A-0672(B)</td><td>2009 Mar 22</td></tr><tr><td>ZC411737</td><td>183.A-0781(E)</td><td>2011 Feb 26; 2011 Mar 03; 2011 Dec 19</td></tr><tr><td>ZC412369</td><td>183.A-0781(E)</td><td>2010 Dec 03, 06; 2011 Jan 04, 27</td></tr><tr><td>ZC413507</td><td>183.A-0781(I)</td><td>2011 Mar 28; 2011 Dec 29; 2012 Mar 03; 2012 May 19; 2013 Jan 08, 17</td></tr><tr><td>ZC413597</td><td>183.A-0781(I)</td><td>2011 Jan 04, 27; 2011 Mar 04, 05</td></tr><tr><td>ZC415876</td><td>183.A-0781(I)</td><td>2011 Jan 06, 19, 29</td></tr></tbody></table>

**Notes.**

## 3.2. SINFONI Data Reduction

We reduced the data using the software package SPRED developed for SINFONI (Schreiber et al. 2004; Abuter et al. 2006), complemented with additional custom routines to optimize the reduction for faint high-redshift targets. We followed the same

steps as described by FS09, to which we refer for details. Key features of the procedure include the method developed by Davies (2007) for accurate wavelength registration and background subtraction, which helps to reduce residuals from the night-sky emission lines. Each individual exposure was background-subtracted, flat-fielded, wavelength-calibrated, distortion-corrected,

<footnote><sup>a</sup> ESO observing run under which the data were taken.</footnote>

<footnote><sup>b</sup> The date corresponds to when the observing night started.</footnote>
and reconstructed into a three-dimensional cube with spatial sampling of 50 × 50mas pixel⁻¹. These preprocessed cubes were then corrected for atmospheric transmission, flux-calibrated, spatially aligned, and coaveraged (with a 2.5σ clipping algorithm) to produce the final reduced cube of a given science target. A “noise cube” was also generated, containing the rms deviation over all combined cubes of each pixel corresponding to the same spatial and spectral coordinates (see Section 4.2 and Appendix C of FS09).

The data of the telluric standard stars and acquisition (i.e., PSF calibration) stars were reduced in a similar way as the science data. Flux calibration of the galaxies' data was performed on a night-by-night basis using the broadband magnitudes of the telluric standards. The integrated spectrum of the telluric standard stars was used to correct the science data for atmospheric transmission. The reduced cubes of the acquisition star's data associated with all OBs of a target were coaveraged (with σ-clipping) into a final PSF cube. Broadband images were made by averaging all wavelength channels of the reduced cubes to create the final PSF image.

As described in detail in Appendix C of FS09, the noise behavior of our SINFONI data is consistent with being Gaussian for a given aperture size and spectral channel but scales with aperture size faster than for pure Gaussian noise due to correlations present in the data. The noise scaling was derived for each galaxy individually from the analysis of the fluctuations of the fluxes in apertures placed randomly over regions empty of source emission within the effective FOV and with a range of sizes. This analysis was carried out for each spectral channel separately and represents the average behavior over the FOV at each wavelength. For all measurements in apertures larger than a pixel, the noise spectrum was calculated from the average pixel-to-pixel rms multiplied by the aperture scaling factor derived from the noise analysis.

### 3.3. Effective Angular Resolution

We characterized the effective angular resolution of our AO-assisted data by fitting a two-dimensional (2D) Gaussian profile to the final PSF image associated with the combined OBs of each galaxy. As reported in Table 2, the FWHMs of the best-fit circular Gaussians range from 0.′′11 to 0.′′30, with a mean of 0.′′18 and a median of 0.′′17. Figure 5 shows the distribution of the PSF FWHMs. Overall, there is no significant difference in FWHMs between the PSFs observed in NGS or LGS mode (the mean and median are identical within 0.′′01). Perhaps more remarkably, the resolution for the two LGS-SE data sets, taken under similar typical (median) seeing, coherence time, and airmass conditions as the NGS and LGS data sets, is very comparable with PSF FWHMs of 0.′′20 and 0.′′24.

Due to a combination of the instrument's optics, the nominal rectangular pixel shape, and anisoplanatism (e.g., Cresci et al. 2005; Davies & Kasper 2012), the PSF deviates slightly from circularity. To quantify these deviations, we also fitted 2D elliptical Gaussians. The major-axis FWHM, minor-to-major axis ratio, and PA of these fits are given in Appendix A (Table 8). The major-axis FWHMs are in the range 0.′′13–0.′′33, with a mean and median of 0.′′19 and 0.′′18, respectively. On average, the axis ratios are 0.88 (median of 0.89), implying that a circular Gaussian provides a good approximation of the effective PSF shape.

Since the PSF calibrations were not obtained simultaneously with the science data and the AO correction for the objects is

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Distribution of the PSF FWHMs for the SINS/zC-SINF AO sample. Each histogram bin shows in different colors the number of galaxies observed in NGS, LGS, and LGS-SE AO modes added vertically on top of each other (dark, medium, and light green, respectively). The FWHMs correspond to the single-component 2D circular Gaussian fit to the PSF image associated with each galaxy.</figcaption></figure>

not fully on-axis (except in LGS-SE mode), the PSF characteristics approximately represent the effective angular resolution of the data sets. Inspection of the individual exposures of the stars indicates typical OB-to-OB variations of ~30% in PSF FWHM and ~10% in axis ratio for our AO data sets. Examination of the light profile of the most compact sources and the smallest substructures seen in our galaxies' data (bright clumps, nuclei) suggest that the degradation in FWHM resolution due to tilt anisoplanatism is modest and within the typical OB-to-OB variations.

In Appendix A, we analyze the PSF properties in more detail based on higher-S/N coaveraged images of the individual PSFs. The high-S/N profiles better reveal the broad halo from the uncorrected seeing underneath the AO-corrected narrow core component. The peak amplitude of the narrow core is five times higher than that of the broad halo, its width is three times narrower, and it contains about 40% of the total flux. The best-fit parameters of the PSF core component are very close to those derived from a single 2D Gaussian fit to the PSFs associated with individual galaxies. Although significant in terms of photometry, the broad halo only dominates the total enclosed flux at radii larger than 0.′′3. Despite the limitations on AO performance stemming from practicalities when observing faint high-z galaxies (i.e., the choice of pixel scale driven by the trade-off between resolution and surface brightness sensitivity and the brightness of AO reference stars around the scientifically selected targets), the gain from the PSF core/halo contrast for our data is important in terms of revealing substructure on physical scales as small as 1–2 kpc.

We further examined the impact of the reference star brightness, seeing, atmospheric coherence time $τ_0$, and airmass on the AO performance from the PSF images. The analysis is presented in Appendix A, where the star properties and average conditions during the PSF observations associated with each target are also given. The AO star brightness most importantly influenced the angular resolution (and Strehl ratio). The airmass (affecting the actual seeing at a target's elevation) and coherence time played a noticeable but lesser role. The AO performance for our observations is weakly, if at all, coupled to
<figure><img src="image_9.png" /><figcaption>1"), or about 8 kpc at z = 2; north is up and east is to the left for all objects. The mean and median FWHM resolution of the maps is 0.20, or 1.65 kpc, shown by the white filled circle.</figcaption></figure>

the seeing as measured in the optical at zenith from the DIMM telescope at the VLT.

While the PSFs associated with individual galaxies more closely track variations in angular resolution among the objects and are appropriate to characterize the substructure within them, the scatter in best-fit FWHMs is ~25% of the average, somewhat smaller than the typical OB-to-OB variations of 30%. For the quantitative analyses presented in this paper, we adopted the results derived with the double-Gaussian model of the average PSF to account for the extended and photometrically important halo and compared with results obtained with the individual single-Gaussian PSFs where relevant. For conciseness, the notations PSF<sub>2 G,ave</sub> and PSF<sub>1 G,gal</sub>, respectively, indicate the choice of PSF.

### 3.4. Effective Spectral Resolution

We determined the resulting spectral resolution of the reduced data based on night-sky line measurements, described in Appendix B. The empirical line-spread function (LSF) is well approximated by a Gaussian profile, and fits give an effective spectral resolution corresponding to a velocity FWHM of about

85 km s⁻¹ across the K band and 120 km s⁻¹ across the H band for the SINFONI 50 mas pixel⁻¹ scale. The LSFs show a small excess in low-amplitude wings, which, however, contain only about 12% and 5% of the total flux in K and H, respectively.

## 4. Extraction of Emission-line and Kinematic Maps and Profiles

In this section, we describe the methodology followed to extract the Hα and [N II] emission-line flux and kinematic maps, position–velocity (p–v) diagrams, axis and radial profiles, and integrated spectra. The main products of the extraction are presented in Figures 6 and 7 and in the series of figures described in more detail in Appendices D–F. The source-integrated spectral properties are reported in Table 4.

### 4.1. Fitting Methodology

We extracted the emission-line properties and kinematics following procedures similar to those described by FS09 and M11. We employed the code LINEFIT developed for SINFONI applications (Davies et al. 2011). The core of the
<figure><img src="image_10.png" /><figcaption>**Figure 7.** The Hα velocity fields for all 35 galaxies of the SINS/zC-SINF AO sample. The galaxies are displayed in the stellar mass vs. SFR plane, as in Figure 6. The $z = 2$ MS of Whitaker et al. (2014) and offsets thereof in SFR by factors of 4 and 10 are overplotted with solid, dashed, and dotted lines for reference. The color coding is such that blue to red colors correspond to the blueshifted to redshifted line emission with respect to the systemic velocity, scaled from the minimum to maximum value of each galaxy. All sources are shown on the same angular scale, with north up and east to the left. The mean and median FWHM resolution of the maps is 0.′′20, or 1.65 kpc.</figcaption></figure>

algorithm fits a Gaussian line profile to an input spectrum within a specified wavelength interval after continuum subtraction and 2σ-clipping rejection of outliers. The line flux, velocity, and velocity dispersion correspond to the area, centroid, and width of the best-fit Gaussian profile, respectively. The continuum corresponds to the best-fit first-order polynomial through adjacent spectral intervals free from possible line emission from the sources. The line fits are weighted based on the input noise spectrum (we used Gaussian weighting, appropriate for our data) to account for the variations with wavelength of the noise due to the near-IR night-sky line emission. The instrumental spectral resolution is implicitly taken into account by convolving the template profile derived from sky lines with the assumed intrinsic Gaussian prior to the fitting.

Formal fitting uncertainties were computed from 100 Monte Carlo simulations, where the points of the input spectrum are perturbed according to a Gaussian distribution of dispersion given by the associated noise spectrum (with scaling accounting for correlated noise in apertures with size > 1 pixel; see Section 3.2). For the objects with undetected [N II] line emission, upper limits were computed based on the noise spectrum for the appropriate

aperture size and wavelength interval. Throughout this paper, we quote the formal measurement uncertainties and limits thus derived. The uncertainties from the absolute flux calibration are estimated to be ~10%, and those from the wavelength calibration are estimated to be <5%. Other sources of uncertainties include the continuum placement and the wavelength intervals used for line and continuum fits, which were gauged by varying the continuum and line intervals and inspecting the curve-of-growth behavior at large radii (see Section 4.4). These tests suggest that the associated uncertainties typically amount to 20% and up to ~50% in some data sets with the lowest S/N or potentially missing faint extended emission falling close to the edges or outside of the effective FOV of the AO data.

With the assumption of a single-Gaussian profile, the fits are primarily sensitive to the narrower line emission component dominated by star formation, but the fluxes and line widths may be overestimated due to the presence of an underlying broader, lower-amplitude component tracing, for instance, outflowing gas (e.g., Shapiro et al. 2009; Genzel et al. 2011, 2014b; Newman et al. 2012a, 2012b; Förster Schreiber et al. 2014). This component is generally not noticeable in the lower-S/N spectra of individual pixels or small apertures. In Appendix C, we quantify the possible
<table><caption>**Table 4**
Integrated Line Emission Properties</caption><thead><tr><th rowspan="2">Source</th><th rowspan="2">z<sub>Hα</sub><sup>c</sup></th><th colspan="4">Circular Apertures<sup>a</sup></th><th colspan="5">Elliptical Apertures<sup>b</sup></th></tr><tr><th>r<sub>ap</sub></th><th>F(Hα)<br>(10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup>)</th><th>σ<sub>tot</sub>(Hα)<br>(km s<sup>-1</sup>)</th><th>[N II]/Hα</th><th>r<sub>maj,ap</sub></th><th>q<sub>ap</sub></th><th>PA<sub>ap</sub><br>(deg)</th><th>F(Hα)<br>(10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup>)</th><th>[N II]/Hα</th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>2.4078</td><td>0.60</td><td>9.5<sup>+0.5</sup><sub>-0.4</sub></td><td>145<sup>+15</sup><sub>-16</sub></td><td>&lt;0.22</td><td>0.50</td><td>0.55</td><td>+65</td><td>6.9<sup>+0.3</sup><sub>-0.2</sub></td><td>0.26<sup>+0.05</sup><sub>-0.04</sub></td></tr><tr><td>Q1623-BX502</td><td>2.1557</td><td>0.60</td><td>12.7 ± 0.6</td><td>66 ± 5</td><td>&lt;0.08</td><td>0.40</td><td>0.80</td><td>+45</td><td>10.2 ± 0.3</td><td>&lt;0.05</td></tr><tr><td>Q1623-BX543</td><td>2.5209</td><td>0.85</td><td>16.8<sup>+0.5</sup><sub>-0.6</sub></td><td>163<sup>+8</sup><sub>-11</sub></td><td>&lt;0.14</td><td>0.60</td><td>0.67</td><td>0</td><td>12.1 ± 0.3</td><td>&lt;0.10</td></tr><tr><td>Q1623-BX599</td><td>2.3312</td><td>0.90</td><td>28.7<sup>+0.9</sup><sub>-0.8</sub></td><td>180<sup>+8</sup><sub>-10</sub></td><td>0.19<sup>+0.02</sup><sub>-0.02</sub></td><td>0.60</td><td>0.85</td><td>-55</td><td>22.7<sup>+0.5</sup><sub>-0.4</sub></td><td>0.19<sup>+0.02</sup><sub>-0.01</sub></td></tr><tr><td>Q2343-BX389</td><td>2.1724</td><td>0.95</td><td>21.0<sup>+0.8</sup><sub>-0.9</sub></td><td>258<sup>+23</sup><sub>-27</sub></td><td>0.21<sup>+0.03</sup><sub>-0.04</sub></td><td>1.10</td><td>0.35</td><td>-50</td><td>14.1<sup>+0.4</sup><sub>-0.3</sub></td><td>0.19<sup>+0.03</sup><sub>-0.02</sub></td></tr><tr><td>Q2343-BX513</td><td>2.1082</td><td>0.60</td><td>13.9<sup>+0.6</sup><sub>-0.7</sub></td><td>139 ± 11</td><td>0.22<sup>+0.03</sup><sub>-0.03</sub></td><td>0.40</td><td>0.81</td><td>-35</td><td>9.3<sup>+0.4</sup><sub>-0.3</sub></td><td>0.21<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>Q2343-BX610</td><td>2.2107</td><td>0.90</td><td>15.4 ± 0.5</td><td>164<sup>+9</sup><sub>-10</sub></td><td>0.40<sup>+0.04</sup><sub>-0.03</sub></td><td>1.00</td><td>0.60</td><td>-10</td><td>14.9<sup>+0.5</sup><sub>-0.3</sub></td><td>0.37<sup>+0.03</sup><sub>-0.02</sub></td></tr><tr><td>Q2346-BX482</td><td>2.2571</td><td>1.00</td><td>13.5<sup>+0.6</sup><sub>-0.5</sub></td><td>123<sup>+6</sup><sub>-7</sub></td><td>0.14<sup>+0.04</sup><sub>-0.02</sub></td><td>1.10</td><td>0.50</td><td>-65</td><td>14.8<sup>+0.4</sup><sub>-0.2</sub></td><td>0.14<sup>+0.02</sup><sub>-0.01</sub></td></tr><tr><td>Deep3a-6004</td><td>2.3871</td><td>1.10</td><td>11.7<sup>+1.1</sup><sub>-0.9</sub></td><td>142<sup>+18</sup><sub>-19</sub></td><td>0.48<sup>+0.11</sup><sub>-0.08</sub></td><td>0.90</td><td>0.95</td><td>-20</td><td>10.8<sup>+0.8</sup><sub>-0.6</sub></td><td>0.46<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>Deep3a-6397</td><td>1.5133</td><td>1.10</td><td>12.7<sup>+0.8</sup><sub>-0.6</sub></td><td>142<sup>+9</sup><sub>-14</sub></td><td>0.44<sup>+0.05</sup><sub>-0.04</sub></td><td>1.20</td><td>0.85</td><td>-80</td><td>13.6<sup>+0.8</sup><sub>-0.6</sub></td><td>0.39<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>Deep3a-15504</td><td>2.3830</td><td>0.95</td><td>15.7 ± 0.4</td><td>181<sup>+8</sup><sub>-9</sub></td><td>0.35<sup>+0.03</sup><sub>-0.02</sub></td><td>1.00</td><td>0.75</td><td>-35</td><td>14.2<sup>+0.4</sup><sub>-0.3</sub></td><td>0.34<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>K20-ID6</td><td>2.2348</td><td>1.00</td><td>6.5<sup>+0.7</sup><sub>-0.8</sub></td><td>91<sup>+14</sup><sub>-13</sub></td><td>&lt;0.30</td><td>0.70</td><td>0.90</td><td>+60</td><td>4.5<sup>+0.5</sup><sub>-0.4</sub></td><td>0.25<sup>+0.06</sup><sub>-0.06</sub></td></tr><tr><td>K20-ID7</td><td>2.2240</td><td>1.00</td><td>8.2 ± 0.7</td><td>148<sup>+14</sup><sub>-15</sub></td><td>0.27<sup>+0.08</sup><sub>-0.08</sub></td><td>1.40</td><td>0.50</td><td>+25</td><td>9.2<sup>+0.6</sup><sub>-0.4</sub></td><td>0.20<sup>+0.06</sup><sub>-0.04</sub></td></tr><tr><td>GMASS-2303</td><td>2.4507</td><td>0.60</td><td>7.6<sup>+0.6</sup><sub>-0.7</sub></td><td>107 ± 9</td><td>&lt;0.24</td><td>0.40</td><td>0.70</td><td>-60</td><td>4.4<sup>+0.3</sup><sub>-0.2</sub></td><td>&lt;0.18</td></tr><tr><td>GMASS-2363</td><td>2.4520</td><td>0.65</td><td>4.3<sup>+0.4</sup><sub>-0.3</sub></td><td>111 ± 10</td><td>&lt;0.29</td><td>0.50</td><td>0.67</td><td>+55</td><td>3.4<sup>+0.1</sup><sub>-0.2</sub></td><td>0.16<sup>+0.04</sup><sub>-0.05</sub></td></tr><tr><td>GMASS-2540</td><td>1.6149</td><td>1.25</td><td>4.3<sup>+0.7</sup><sub>-0.5</sub></td><td>76<sup>+17</sup><sub>-18</sub></td><td>&lt;0.56</td><td>0.60</td><td>0.86</td><td>+20</td><td>1.1 ± 0.1</td><td>&lt;0.54</td></tr><tr><td>SA12-6339</td><td>2.2971</td><td>0.75</td><td>7.4 ± 0.2</td><td>112<sup>+5</sup><sub>-6</sub></td><td>0.18<sup>+0.04</sup><sub>-0.03</sub></td><td>0.30</td><td>0.80</td><td>+40</td><td>4.7 ± 0.1</td><td>0.15<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>ZC400528</td><td>2.3873</td><td>0.85</td><td>15.7 ± 0.8</td><td>187 ± 19</td><td>0.69<sup>+0.05</sup><sub>-0.06</sub></td><td>0.40</td><td>0.85</td><td>+80</td><td>9.2 ± 0.3</td><td>0.70<sup>+0.04</sup><sub>-0.04</sub></td></tr><tr><td>ZC400569</td><td>2.2405</td><td>1.00</td><td>10.0<sup>+0.7</sup><sub>-0.8</sub></td><td>199<sup>+23</sup><sub>-29</sub></td><td>0.41<sup>+0.07</sup><sub>-0.06</sub></td><td>1.30</td><td>0.35</td><td>+15</td><td>9.6<sup>+0.4</sup><sub>-0.3</sub></td><td>0.44<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>ZC400569N</td><td>2.2432</td><td>1.00</td><td>9.1 ± 0.9</td><td>185 ± 15</td><td>0.45 ± 0.06</td><td>1.00</td><td>0.95</td><td>+70</td><td>10.5<sup>+0.4</sup><sub>-0.3</sub></td><td>0.42<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>ZC401925</td><td>2.1412</td><td>0.75</td><td>6.9<sup>+0.7</sup><sub>-0.4</sub></td><td>99 ± 13</td><td>&lt;0.25</td><td>0.40</td><td>0.75</td><td>+60</td><td>3.9<sup>+0.3</sup><sub>-0.2</sub></td><td>&lt;0.16</td></tr><tr><td>ZC403741</td><td>1.4457</td><td>0.80</td><td>12.3 ± 0.6</td><td>93<sup>+8</sup><sub>-7</sub></td><td>0.46<sup>+0.04</sup><sub>-0.04</sub></td><td>0.60</td><td>0.85</td><td>+25</td><td>10.7<sup>+0.4</sup><sub>-0.3</sub></td><td>0.43<sup>+0.02</sup><sub>-0.03</sub></td></tr><tr><td>ZC404221</td><td>2.2199</td><td>1.00</td><td>10.5<sup>+0.8</sup><sub>-0.7</sub></td><td>86<sup>+8</sup><sub>-9</sub></td><td>0.26<sup>+0.06</sup><sub>-0.07</sub></td><td>1.00</td><td>0.40</td><td>-10</td><td>8.9 ± 0.3</td><td>0.18<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>ZC405226</td><td>2.2870</td><td>0.90</td><td>6.2<sup>+0.4</sup><sub>-0.3</sub></td><td>97<sup>+5</sup><sub>-6</sub></td><td>0.15<sup>+0.05</sup><sub>-0.04</sub></td><td>0.90</td><td>0.65</td><td>-40</td><td>6.0<sup>+0.3</sup><sub>-0.2</sub></td><td>0.17<sup>+0.04</sup><sub>-0.03</sub></td></tr><tr><td>ZC405501</td><td>2.1539</td><td>0.90</td><td>6.9 ± 0.4</td><td>85<sup>+5</sup><sub>-6</sub></td><td>&lt;0.14</td><td>1.00</td><td>0.30</td><td>+10</td><td>5.3 ± 0.2</td><td>&lt;0.09</td></tr><tr><td>ZC406690</td><td>2.1950</td><td>1.00</td><td>30.1 ± 0.5</td><td>140 ± 3</td><td>0.12<sup>+0.01</sup><sub>-0.01</sub></td><td>1.10</td><td>0.75</td><td>-70</td><td>29.0<sup>+0.5</sup><sub>-0.4</sub></td><td>0.12<sup>+0.01</sup><sub>-0.01</sub></td></tr><tr><td>ZC407302</td><td>2.1819</td><td>0.80</td><td>16.8<sup>+0.4</sup><sub>-0.3</sub></td><td>168 ± 7</td><td>0.25<sup>+0.02</sup><sub>-0.02</sub></td><td>0.80</td><td>0.60</td><td>+55</td><td>14.7<sup>+0.3</sup><sub>-0.2</sub></td><td>0.23<sup>+0.01</sup><sub>-0.01</sub></td></tr><tr><td>ZC407376</td><td>2.1729</td><td>0.95</td><td>13.6<sup>+0.6</sup><sub>-0.5</sub></td><td>131<sup>+7</sup><sub>-10</sub></td><td>0.25<sup>+0.05</sup><sub>-0.04</sub></td><td>0.90</td><td>0.35</td><td>+20</td><td>9.2<sup>+0.3</sup><sub>-0.2</sub></td><td>0.21<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>ZC407376S</td><td>2.1730</td><td>0.60</td><td>9.9<sup>+0.4</sup><sub>-0.3</sub></td><td>149<sup>+9</sup><sub>-10</sub></td><td>0.23<sup>+0.04</sup><sub>-0.03</sub></td><td>0.50</td><td>0.90</td><td>-60</td><td>8.1 ± 0.2</td><td>0.20<sup>+0.03</sup><sub>-0.03</sub></td></tr><tr><td>ZC407376N</td><td>2.1728</td><td>0.40</td><td>3.2 ± 0.2</td><td>95<sup>+5</sup><sub>-8</sub></td><td>0.26<sup>+0.07</sup><sub>-0.05</sub></td><td>0.40</td><td>0.70</td><td>+60</td><td>2.6<sup>+0.2</sup><sub>-0.1</sub></td><td>0.21<sup>+0.06</sup><sub>-0.05</sub></td></tr><tr><td>ZC409985</td><td>2.4569</td><td>0.75</td><td>11.2<sup>+0.8</sup><sub>-0.7</sub></td><td>70<sup>+11</sup><sub>-7</sub></td><td>0.18<sup>+0.04</sup><sub>-0.05</sub></td><td>0.40</td><td>0.85</td><td>-15</td><td>8.5 ± 0.3</td><td>0.15<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>ZC410041</td><td>2.4541</td><td>0.85</td><td>9.1<sup>+0.8</sup><sub>-0.7</sub></td><td>86<sup>+11</sup><sub>-8</sub></td><td>&lt;0.25</td><td>0.80</td><td>0.35</td><td>-55</td><td>6.5 ± 0.3</td><td>&lt;0.14</td></tr><tr><td>ZC410123</td><td>2.1986</td><td>0.85</td><td>7.0<sup>+0.8</sup><sub>-0.7</sub></td><td>118<sup>+20</sup><sub>-18</sub></td><td>&lt;0.36</td><td>0.60</td><td>0.60</td><td>+35</td><td>4.4<sup>+0.4</sup><sub>-0.3</sub></td><td>&lt;0.22</td></tr><tr><td>ZC411737</td><td>2.4442</td><td>0.65</td><td>7.5<sup>+0.7</sup><sub>-0.6</sub></td><td>105<sup>+13</sup><sub>-11</sub></td><td>&lt;0.24</td><td>0.40</td><td>0.75</td><td>-60</td><td>5.0 ± 0.3</td><td>&lt;0.14</td></tr><tr><td>ZC412369</td><td>2.0281</td><td>0.70</td><td>18.0<sup>+0.6</sup><sub>-0.4</sub></td><td>152<sup>+8</sup><sub>-7</sub></td><td>0.21<sup>+0.02</sup><sub>-0.02</sub></td><td>0.60</td><td>0.70</td><td>-70</td><td>13.1 ± 0.3</td><td>0.19<sup>+0.02</sup><sub>-0.02</sub></td></tr><tr><td>ZC413507</td><td>2.4800</td><td>0.85</td><td>10.1<sup>+1.1</sup><sub>-0.8</sub></td><td>114 ± 17</td><td>&lt;0.27</td><td>0.50</td><td>0.75</td><td>-35</td><td>6.2 ± 0.4</td><td>&lt;0.16</td></tr><tr><td>ZC413597</td><td>2.4502</td><td>0.80</td><td>8.6<sup>+0.7</sup><sub>-0.6</sub></td><td>91<sup>+11</sup><sub>-8</sub></td><td>&lt;0.22</td><td>0.50</td><td>0.75</td><td>+45</td><td>6.3 ± 0.3</td><td>0.16<sup>+0.03</sup><sub>-0.04</sub></td></tr><tr><td>ZC415876</td><td>2.4354</td><td>0.65</td><td>14.1<sup>+0.8</sup><sub>-0.7</sub></td><td>105<sup>+8</sup><sub>-7</sub></td><td>0.15<sup>+0.04</sup><sub>-0.05</sub></td><td>0.50</td><td>0.80</td><td>-50</td><td>11.5<sup>+0.5</sup><sub>-0.4</sub></td><td>0.14<sup>+0.03</sup><sub>-0.03</sub></td></tr></tbody></table>

### Notes.

a Properties from Gaussian line profile fits to the spatially integrated spectrum of each galaxy extracted in a circular aperture. The radius of the adopted “total” aperture and the total Hα flux, velocity dispersion, and [N II]/Hα ratio are listed. The velocity dispersion is corrected for the instrumental LSF. The uncertainties correspond to the formal 68% confidence intervals from 100 Monte Carlo simulations; 3σ upper limits are given when the [N II] 6584 Å emission line is undetected.

b Properties from Gaussian line profile fitting to the spatially integrated spectrum extracted in an elliptical aperture, corrected for velocity shifts across the aperture. The major-axis radius, axis ratio, and PA of the elliptical aperture and the Hα flux and [N II]/Hα ratio are listed. Uncertainties and upper limits were computed as for the properties in the circular apertures.

c Redshift (vacuum) from the Hα line fits to the spectrum of each galaxy integrated in the circular aperture.

impact of such a component on our measurements and conclude that it is unlikely to significantly affect the overall results. We thus neglect these effects throughout this paper but discuss potential biases where relevant.

We neglected the impact of potential Balmer absorption from the stellar populations on our Hα emission-line fits. As argued by FS09, the stellar absorption at Hα is always <5 Å

for a wide range of stellar ages, star formation histories, and plausible IMFs (see also, e.g., Brinchmann et al. 2004). This value is small compared to the equivalent widths of the feature in emission for the SINS/zC-SINF AO sample, which are typically ~140 Å in the rest frame based on the Hα fluxes and continuum flux densities derived from the broadband magnitudes. The lowest equivalent widths are ~50 Å in three sources.
Neglecting stellar absorption is unlikely to importantly affect our line measurements and would imply an error that is smaller than other sources of uncertainties.

## 4.2. Emission and Kinematics Maps

To extract the flux, velocity, and velocity dispersion maps, we fitted the spectra of individual pixels. Prior to the fitting, the data cubes were lightly smoothed with a median filter width of 3 pixels spectrally and, for all but five objects, 3 × 3 pixels spatially to increase the S/N without significant loss of resolution (see below). For five of the largest low surface brightness sources (Deep3a-6004, Deep3a-6397, K20-ID6, K20-ID7, and GMASS-2540), a 5 × 5 pixel spatial filter was used. We first fitted the $H\alpha$ emission line, with the amplitude, central wavelength, and width of the Gaussian profile as free parameters. We then performed fits to the neighboring [N II] λ6584 line, fixing the central wavelength and width based on the fit to $H\alpha$ at each pixel, leaving only the amplitude to vary. Since the [N II] line is weaker than $H\alpha$, these constraints helped to extract the flux in the fainter [N II] emission regions. The [N II] and $H\alpha$ lines are expected to originate from the same regions within our SINS/zC-SINF galaxies and thus to have similar kinematics, justifying this approach. We verified this assumption by comparing the results from these constrained fits to those where amplitude, central wavelength, and width were left free for several of the galaxies with higher overall S/N on [N II]. We found no significant difference within the uncertainties between the respective line flux, velocity, and dispersion maps.

In the resulting $H\alpha$ kinematic maps, we masked out pixels where the S/N of $H\alpha$ drops below 5. We further masked out pixels for which the line center and width were clearly unreliable based on inspection of the velocity and velocity dispersion maps. These outliers were identified with the following criteria: velocity and dispersion of a given pixel exceeding by a factor of at least two the typical maximum value over the maps, a velocity uncertainty of $\ge 100$ km s⁻¹, and a relative dispersion uncertainty of $\ge 50\%$. For the [N II] line and [N II]/$H\alpha$ ratio maps, relying on constrained fits, valid pixels were required to satisfy an S/N > 5 in both $H\alpha$ and [N II] flux, as well as the same additional criteria as for the $H\alpha$ kinematic maps. We note that since [N II] is always weaker than $H\alpha$ in our SINS/zC-SINF AO sample galaxies, since the fits to [N II] rely on the best-fit kinematic parameters to $H\alpha$, and because of the quality cuts applied to mask out the emission maps, the resulting valid regions in the [N II]/$H\alpha$ maps are biased toward higher ratios, more so for the fainter regions of a galaxy. This bias is important to keep in mind when interpreting variations in line ratio maps, as done in Section 8.

We also derived continuum maps obtained by summing over the emission-line free wavelength channels of the SINFONI data cubes, applying a 2σ clipping to reduce the impact of elevated noise due to night-sky lines. In contrast to the line emission, the continuum in our IFU data is more sensitive to systematic uncertainties from the background subtraction and flat-fielding. The SINFONI-based continuum maps for our targets are generally of limited usefulness, except for the objects with bright or more centrally concentrated continuum emission. High-resolution HST imaging is available in the H band for 31 of our SINS/zC-SINF AO targets and in at least one additional band for 29 of them, which provides more sensitive and reliable maps of the stellar continuum emission, as well as color- or SED-based stellar mass maps (Förster Schreiber et al. 2011a; Lang et al. 2014; Tacchella et al. 2015a, 2015b, 2018).

Figures 6 and 7 show the $H\alpha$ emission-line maps and velocity fields for all 35 SINS/zC-SINF AO targets. Additional maps are presented in Appendix D (Figure 16), showing for each galaxy the $H\alpha$ and [N II] surface brightness distributions and the $H\alpha$ velocity and velocity dispersion maps. For 13 objects, the [N II] emission is too weak to reliably extract 2D maps. The near-IR H- or K-band images (from HST observations where available, otherwise from SINFONI) are also shown for comparison.

We quantified the impact of the smoothing applied when extracting the 2D maps as follows. We remeasured the characteristics of the effective PSFs associated with individual galaxies after subjecting them to the same spatial median filtering as the science cubes. The average increase in the smoothed stellar PSF FWHMs with a 3 × 3 pixel filter width is only about 10%, and the axis ratios vary by <2%, significantly smaller than the OB-to-OB variations in PSF properties. For the five data sets with 5 × 5 pixel median filtering, the FWHMs and axis ratios are, on average, about 50% and 5% larger, respectively. Spectrally, the 3 pixel wide median filtering broadens the line profiles by about 10% in the K band and 5% in the H band, as determined by a Gaussian fit to the smoothed templates. In all measurements of galaxy properties based on the 2D maps, we accounted for the spatial and spectral broadening introduced by the median filtering.

## 4.3. Centers, p-v Diagrams, and Axis Profiles

We defined the $H\alpha$ morphological center of each galaxy as the center of ellipses matching the outer isophotes of the emission-line maps. This choice makes the morphological center position less sensitive to bright asymmetric or small-scale features such as clumps and is more robust in cases where the line emission is not centrally concentrated (e.g., ZC406690). For the objects with the most regular (disklike) velocity fields and dispersion maps, the kinematic center, corresponding to the position of steepest velocity gradient and central peak in dispersion (e.g., van der Kruit & Allen 1978; Genzel et al. 2014a), is well constrained and is our preferred center position, as it is sensitive to the total mass distribution. In those cases (the majority of the sample; see Section 7.1), the $H\alpha$ morphological center generally coincides with the kinematic center within about 2 pixels (0.′′1). The rest-optical continuum centroid based on the H- or K-band images from HST observations or synthesized from the SINFONI+AO cubes, and the central peak or mass-weighted center in the stellar mass maps when available, also generally lie within the same distance of the kinematic center. For the objects with irregular kinematic maps, our adopted center position relied on the centroid determined from the morphologies and stellar mass maps (which typically also agree within 2 pixels). The overall good agreement between the $H\alpha$ morphological center as defined above and the other measures of the center position gives confidence that the choice of ellipse is not importantly affected by irregularities in the intrinsic surface brightness or low S/N of the outer $H\alpha$ isophotes. In summary, we adopted the kinematic center as the center position, except for the objects with irregular kinematics, and hence an ill-defined kinematic center, for which we adopted the $H\alpha$ morphological center.

We identified the kinematic major axis as the direction of the largest observed velocity difference across the source and passing through the adopted center position. For most of the galaxies, this axis agrees well with the direction of the largest extent in $H\alpha$ and rest-optical continuum emission, although there are some notable exceptions (discussed in Section 6.3).
For some objects with more complex morphologies or irregular kinematics, the velocity extrema are not always symmetrically located along a given axis through the center (e.g., ZC410123). For the purpose of extracting *p*-*v* diagrams, we nevertheless used the kinematic PA as defined here, noting that for the more irregular cases, this does not always probe the full velocity difference across a source. We estimated the uncertainty on the kinematic PA from the difference in angle between lines passing through the center and the positions of the blue- and redshifted velocity extrema.

We extracted the *p*-*v* diagrams from the unsmoothed reduced data cubes in synthetic slits, integrating the light along the spatial direction perpendicular to the slit orientation. We used a slit width of 6 pixels (0.′′3, or about two spatial resolution elements), except for four large disks with low Hα surface brightness along the major axis, where we used a 10 pixel wide slit (0.′′5; Deep3a-6004, Deep3a-6397, GMASS-2540, and K20-ID7). The *p*-*v* diagrams are shown in Appendix E (Figure 17).

We computed axis profiles based on spectra integrated in circular apertures equally spaced along the kinematic major and minor axes. For the objects with the most irregular velocity fields, we also considered axes passing through the center and the positions of the blue- and redshifted velocity extrema to better sample the full velocity difference. We used apertures with diameters of 6 pixels, separated by 3 pixels. No median filtering was applied to the cubes or the aperture spectra. The fits to Hα and [N II] in the aperture spectra were performed as described in Section 4.2. The resulting axis profiles were truncated where the S/N on Hα drops below 3, and 3σ upper limits on [N II] were calculated for the positions where the line is formally undetected (S/N < 3).

### 4.4. Integrated Spectra and Radial Profiles

For each galaxy, we measured the global emission-line properties and radial profiles from spatially integrated spectra extracted from the unsmoothed reduced data cubes. We followed two approaches, differing in the shape of the apertures employed and the coaddition of the spectra of individual pixels within the apertures. In both cases, the apertures were positioned at the center of the galaxies as defined in Section 4.3. Again, no spectral smoothing was applied to the spectra, and the flux, central wavelength, and width were left free for Hα, while constrained fits were performed for [N II]; 3σ upper limits were calculated when [N II] is formally undetected.

In the first approach, measurements were made in circular apertures of increasing radius, summing the spectra of pixels within the apertures to obtain the integrated spectrum. From a curve-of-growth analysis, we determined the total Hα flux and corresponding total aperture radius. The curve of growth does not always converge within the formal 1σ measurement uncertainties at large radii, although it always exhibits a clear flattening at a radius roughly encompassing most of the emission seen in the line maps. In those cases, the choice of total aperture was guided by the Hα line map. Possible reasons for this divergence could be real signal from the source at low surface brightness that gets buried in the noisier edges on an individual pixel basis or is cut off by the effective FOV, or systematics that affect the accuracy of the line measurements. This effect is, however, typically small; the largest difference between the adopted total Hα flux and the flux in the largest aperture considered (with diameter typically 1.2× and up to

1.7× larger, generally limited by the effective FOV) is on average and median ~10% (at most 25%), within ≲2σ of the formal measurement uncertainties.

In the second approach, we used elliptical apertures with a major axis aligned with the kinematic PA determined in Section 4.3. The axis ratio was based on the value from the rest-frame optical continuum maps when available or the Hα maps otherwise, accounting for average beam-smearing effects at the half-light radius of each galaxy. For most objects, these aperture parameters match the outer isophotes of the Hα line maps well (see Section 5). The spectra of individual pixels were coadded after shifting them (through interpolation) to a common peak Hα wavelength based on the velocity field. We refer to these spectra as “velocity-shifted spectra” to distinguish them from those extracted in circular apertures. By better matching the apertures to the line-emitting regions and concentrating the light in wavelength space, this approach leads to higher S/N, optimizes measurements of fainter lines such as [N II], and increases the contrast between narrow and broad emission components when present. The improvement in S/N is most noticeable for the sources with the largest velocity gradients and low axis ratios. On the other hand, since this method involves velocity shifting, the resulting spectra probe the line emission in the regions where the velocity field is reliable and misses some of the outer parts of galaxies. A suite of elliptical apertures and corresponding annuli was employed, with major-axis radius $r_{maj}$ increasing in steps of 2 pixels (0.′′1), up to the annulus at which >40% of the area becomes masked out based on the velocity field. Radial profiles in [N II]/Hα line ratios were computed from the velocity-shifted spectra in the elliptical annuli. Because the outer annuli exclude some fraction of the pixels, the corresponding ratios are assumed to be representative of the average ratio along these annuli.

Table 4 lists the aperture radius $r_{ap}$, the Hα vacuum redshift $z_{Hα}$, flux $F(Hα)$, velocity dispersion $σ_{tot}(Hα)$, and [N II]/Hα ratio derived from the integrated spectrum of each source in the “total” circular aperture. The table also reports the Hα flux and [N II]/Hα ratio measurements obtained from the velocity-shifted spectra in the largest elliptical apertures, along with the parameters of these apertures (major-axis radius $r_{maj,ap}$, minor-to-major axis ratio $q_{ap}$, and position angle PA$_{ap}$). For ZC407376, an interacting system, the table lists the measurements for each of the clearly separated pair components. For ZC400569, which exhibits a chain of bright Hα clumps, measurements centered on the northern component that dominates the stellar light and mass (Section 5.4) are given separately as well. All uncertainties reported correspond to the formal fitting uncertainties.

On average (and median), the Hα flux enclosed in the largest elliptical aperture is about 80% of that measured in the total circular aperture, because of the smaller area covered by the former apertures. The [N II]/Hα ratios for the 24 sources for which [N II] is detected in both circular and elliptical aperture spectra agree to within 10% on average (and median). For four objects, [N II] is undetected in the circular aperture spectrum, and the 3σ upper limits on [N II]/Hα are consistent within about 30% (mean and median) with the ratio measured in the higher-S/N elliptical aperture spectrum. For the 10 remaining sources, the upper limits on [N II]/Hα in the elliptical apertures are typically 35% lower than those in the circular apertures.
**5. Measurements of the Hα Sizes and Global Surface Brightness Profiles**

In this section, we describe the measurements of the Hα sizes and global surface brightness distributions of the SINS/zC-SINF AO sample. It is obvious from, e.g., Figure 6 that the observed Hα morphologies of the galaxies are more complex than smooth single-component models. Examination of the azimuthally averaged radial profiles in elliptical annuli indicates that a majority of the objects (26/35) exhibit a clear off-center bump or upturn, reflecting ringlike structures or bright clumps within the galaxies, and asymmetric extensions or possible faint companions around the outer isophotes. For 16 sources, these features are superposed on an otherwise centrally peaked profile, whereas for the other 10 objects, the central surface brightness drops toward the center<fnref n="31" /> (see also Genzel et al. 2014a; Tacchella et al. 2015a).

In view of these morphologies, we followed two different approaches to derive the Hα sizes of the objects. The first method is based on curve-of-growth analysis; the second one is based on parametric fits to the Hα surface brightness distribution. Although the choice of method and the interpretation of the results should be tailored to the particular aim of an analysis, we preliminarily note that the two approaches give very consistent results for our SINS/zC-SINF AO galaxies. To assess the impact of the PSF, we derived the sizes and global profile properties using the parameters of the PSF associated with each individual galaxy and of the higher-S/N average PSF.

**5.1. Size Estimates from Curve-of-growth Analysis**

In the simplest approach, we derived the intrinsic half-light radius from the curve of growth in circular apertures, hereafter denoted $r_{1/2}^{\text{circ}}$. We corrected the observed half-light radius for beam smearing by subtracting the PSF half-light radius in quadrature, i.e., $0.5 \times \text{FWHM of the PSF}_{\text{1 G,gal}}$ based on circular Gaussian fits (Table 2), or as determined from the curve of growth for the PSF$_2$$_{G,ave}$ (Appendix A). The uncertainties take into account those stemming from the curve-of-growth behavior at large radii and those of the effective PSF parameters. The maximum deviation from the convergence of the curve of growth of individual galaxies beyond the radius adopted for the total Hα flux measurement (Section 4.4) implies an average and median difference of about 5% in beam-smeared half-light radius (maximum difference of 22%). The uncertainties of the PSF are more important, and we adopt a conservative 30% to account for the fact that the PSF stars are not observed simultaneously with and along the same optical path as the galaxies and for the deviations of the PSF shape from a pure circular Gaussian profile (Section 3.3).

Overall, the $r_{1/2}^{\text{circ}}$ estimates obtained with the different choices of PSF agree within the formal $1\sigma$ uncertainties. As expected, however, the differences are systematic, with the values derived with the PSF$_2$$_{G,ave}$ lower than those obtained with the PSF$_1$$_{G,gal}$ by ~10% on average and in the median. These differences depend on galaxy size and are most significant for objects with $r_{1/2}^{\text{circ}} \lesssim 2.5$ kpc (corresponding to the half-light radius of the PSF$_2$$_{G,ave}$ at $z \sim 2$), for which the mean and median differences are about 15%. The largest

difference is 35% for BX502; SA12-6339, the smallest source, is formally unresolved when using the PSF$_2$$_{G,ave}$.

**5.2. Parametric Fits to the Hα Line Maps**

In the alternative approach, we derived the sizes by fitting intrinsic 2D Sérsic (1968) profiles convolved with the PSF to the observed Hα surface brightness distributions. We followed a similar procedure as described by Förster Schreiber et al. (2011a). We used the code GALFIT (Peng et al. 2002) and, for simplicity, considered single-component models. The free parameters in the fits were the major-axis effective radius $R_e$, the Sérsic index $n$, the projected minor-to-major axis ratio $q$, the PA of the major axis, and the total flux. The Sérsic index was allowed to vary in the range $0.1 < n < 4.0$. The input error maps accounted for the background rms noise, as well as the Poisson noise from the sources. The input PSFs were noiseless models created with the parameters derived for the PSF$_1$$_{G,gal}$ and PSF$_2$$_{G,ave}$ cases based on elliptical Gaussian fits (see Appendix A). Since asymmetric and/or clumpy distributions can heavily bias the results, and the profile parameters tend to be degenerate with the background level (e.g., Peng et al. 2002; van Dokkum et al. 2008; Förster Schreiber et al. 2011a), we fixed the center position and the “sky” level in the fits.

For realistic estimates of the uncertainties on the derived parameters, we ran 200 fits for every galaxy, varying in each iteration the center position, sky level, and PSF. The center coordinates were drawn randomly from a uniform distribution in a square box of typically 4 × 4 pixels around the adopted position (Section 4.3). An accurate determination of the background level in our Hα maps is complicated by the limited FOV and by possible residual systematics (as discussed in Section 4.4). The sky values were conservatively drawn from a Gaussian distribution based on the fluxes of pixels sufficiently well outside of the regions where Hα is formally detected at S/N > 3. The input PSFs were generated by varying the FWHM$_{maj}$ and axis ratio according to Gaussian distributions centered on the nominal values, and with dispersions of 30% and 10% of these values, respectively, and the PAs were drawn from a Gaussian distribution with a dispersion of 50° around the nominal PA (the parameters of the narrow and broad PSF$_2$$_{G,ave}$ components were varied independently).

The best-fit parameters for a given galaxy were taken as the median of the results for all 200 iterations and the $1\sigma$ uncertainties from the central 68% of the distribution. For the northern component of ZC407376, fits were unsuccessful because of the faintness of the source. For GMASS-2540, the fits were unreliable because of its low average surface brightness; its strongly asymmetric, clumpy, ringlike Hα morphology; and the fact that its large extent is not fully covered by the effective SINFONI FOV. The parametric fit results for both objects were thus excluded in our subsequent quantitative analysis. As for the size estimates from the Hα curve of growth, the $R_e$ values from the Sérsic model fits with the PSF$_2$$_{G,ave}$ are systematically lower than those with the PSF$_1$$_{G,gal}$. The differences are approximately 10% on average and median and increase toward smaller sources (mean and median of around 15% and up to 45%) but remain within the formal ≈$1\sigma$ uncertainties. Differences in derived Sérsic indices, axis ratios, and PAs are small (on average 6%, 14%, and 2°, respectively) and well within the $1\sigma$ uncertainties.

<footnote n="31">³¹ For ZC407376, an interacting system, the profiles of the compact individual components are centrally peaked, and we also derived the sizes for each of them separately. For ZC400569, we measured the sizes for the entire Hα emission, as well as the mass-dominating northern component.</footnote>
<table><caption>**Table 5**
Hα Sizes and Global Structural Properties</caption><thead><tr><th rowspan="2">Source</th><th colspan="5">Single-Gaussian PSF<sup>a</sup></th><th colspan="5">Double-Gaussian PSF<sup>b</sup></th></tr><tr><th>r<sub>1/2</sub><sup>circ</sup><br>(kpc)</th><th>R<sub>e</sub><br>(kpc)</th><th>n</th><th>q</th><th>PA<br>(deg)</th><th>r<sub>1/2</sub><sup>circ</sup><br>(kpc)</th><th>R<sub>e</sub><br>(kpc)</th><th>n</th><th>q</th><th>PA<br>(deg)</th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>1.9<sup>+0.2</sup><sub>-0.3</sub></td><td>2.6<sup>+1.2</sup><sub>-0.5</sub></td><td>0.80<sup>+0.69</sup><sub>-0.28</sub></td><td>0.49<sup>+0.08</sup><sub>-0.04</sub></td><td>+77<sup>+10</sup><sub>-5</sub></td><td>1.4 ± 0.6</td><td>2.0<sup>+0.8</sup><sub>-0.4</sub></td><td>0.90<sup>+2.37</sup><sub>-0.55</sub></td><td>0.27<sup>+0.16</sup><sub>-0.20</sub></td><td>+75<sup>+13</sup><sub>-5</sub></td></tr><tr><td>Q1623-BX502</td><td>1.7 ± 0.3</td><td>2.1<sup>+0.4</sup><sub>-0.4</sub></td><td>1.02<sup>+0.66</sup><sub>-0.27</sub></td><td>0.82<sup>+0.07</sup><sub>-0.08</sub></td><td>-23<sup>+20</sup><sub>-22</sub></td><td>1.1<sup>+0.6</sup><sub>-0.4</sub></td><td>1.7<sup>+0.7</sup><sub>-0.5</sub></td><td>0.96<sup>+1.47</sup><sub>-0.67</sub></td><td>0.70<sup>+0.17</sup><sub>-0.13</sub></td><td>-20<sup>+31</sup><sub>-19</sub></td></tr><tr><td>Q1623-BX543</td><td>2.5 ± 0.3</td><td>3.7<sup>+1.5</sup><sub>-0.9</sub></td><td>1.64<sup>+1.40</sup><sub>-0.64</sub></td><td>0.48<sup>+0.10</sup><sub>-0.14</sub></td><td>-4<sup>+6</sup><sub>-4</sub></td><td>2.4<sup>+0.3</sup><sub>-0.4</sub></td><td>3.3<sup>+1.2</sup><sub>-0.8</sub></td><td>1.37<sup>+1.02</sup><sub>-0.43</sub></td><td>0.48<sup>+0.08</sup><sub>-0.11</sub></td><td>-4<sup>+6</sup><sub>-4</sub></td></tr><tr><td>Q1623-BX599</td><td>2.5 ± 0.2</td><td>2.6 ± 0.4</td><td>0.67<sup>+0.28</sup><sub>-0.15</sub></td><td>0.87<sup>+0.08</sup><sub>-0.12</sub></td><td>-33<sup>+16</sup><sub>-13</sub></td><td>2.3<sup>+0.3</sup><sub>-0.4</sub></td><td>2.2<sup>+0.4</sup><sub>-0.5</sub></td><td>0.64<sup>+0.22</sup><sub>-0.29</sub></td><td>0.87<sup>+0.08</sup><sub>-0.10</sub></td><td>-31<sup>+29</sup><sub>-16</sub></td></tr><tr><td>Q2343-BX389</td><td>4.0 ± 0.2</td><td>5.9<sup>+0.4</sup><sub>-0.2</sub></td><td>0.29<sup>+0.07</sup><sub>-0.11</sub></td><td>0.41<sup>+0.04</sup><sub>-0.03</sub></td><td>-47 ± 2</td><td>3.9<sup>+0.3</sup><sub>-0.4</sub></td><td>5.8<sup>+0.2</sup><sub>-0.1</sub></td><td>0.16<sup>+0.14</sup><sub>-0.06</sub></td><td>0.39<sup>+0.05</sup><sub>-0.08</sub></td><td>-47 ± 2</td></tr><tr><td>Q2343-BX513</td><td>2.1 ± 0.3</td><td>3.2<sup>+0.9</sup><sub>-0.6</sub></td><td>1.11<sup>+0.48</sup><sub>-0.26</sub></td><td>0.63<sup>+0.04</sup><sub>-0.05</sub></td><td>+5<sup>+4</sup><sub>-10</sub></td><td>1.7<sup>+0.6</sup><sub>-1.1</sub></td><td>2.6<sup>+1.5</sup><sub>-0.8</sub></td><td>1.71<sup>+2.19</sup><sub>-0.73</sub></td><td>0.48<sup>+0.12</sup><sub>-0.15</sub></td><td>+5<sup>+5</sup><sub>-6</sub></td></tr><tr><td>Q2343-BX610</td><td>3.6<sup>+0.1</sup><sub>-0.2</sub></td><td>4.7<sup>+0.1</sup><sub>-0.3</sub></td><td>0.13<sup>+0.09</sup><sub>-0.03</sub></td><td>0.56 ± 0.04</td><td>+14<sup>+1</sup><sub>-2</sub></td><td>3.5<sup>+0.2</sup><sub>-0.3</sub></td><td>4.6<sup>+0.1</sup><sub>-0.2</sub></td><td>0.10<sup>+0.05</sup><sub>-0.01</sub></td><td>0.50<sup>+0.06</sup><sub>-0.08</sub></td><td>+14 ± 2</td></tr><tr><td>Q2346-BX482</td><td>4.1 ± 0.3</td><td>5.3<sup>+0.2</sup><sub>-0.3</sub></td><td>0.10<sup>+0.04</sup><sub>-0.01</sub></td><td>0.61 ± 0.03</td><td>-57<sup>+2</sup><sub>-3</sub></td><td>3.9 ± 0.4</td><td>5.4 ± 0.3</td><td>0.10 ± 0.01</td><td>0.55<sup>+0.04</sup><sub>-0.06</sub></td><td>-56<sup>+3</sup><sub>-4</sub></td></tr><tr><td>Deep3a-6004</td><td>4.7 ± 0.5</td><td>5.1<sup>+0.4</sup><sub>-1.6</sub></td><td>0.16<sup>+0.55</sup><sub>-0.06</sub></td><td>0.59<sup>+0.20</sup><sub>-0.08</sub></td><td>+58<sup>+5</sup><sub>-8</sub></td><td>4.5 ± 0.6</td><td>5.1<sup>+0.3</sup><sub>-1.5</sub></td><td>0.10<sup>+0.62</sup><sub>-0.01</sub></td><td>0.49<sup>+0.11</sup><sub>-0.21</sub></td><td>+61<sup>+4</sup><sub>-6</sub></td></tr><tr><td>Deep3a-6397</td><td>4.9 ± 0.1</td><td>6.1<sup>+0.5</sup><sub>-0.6</sub></td><td>0.76<sup>+0.32</sup><sub>-0.46</sub></td><td>0.56 ± 0.05</td><td>-74 ± 3</td><td>4.8 ± 0.2</td><td>5.9<sup>+0.6</sup><sub>-0.9</sub></td><td>0.52<sup>+0.57</sup><sub>-0.38</sub></td><td>0.54<sup>+0.08</sup><sub>-0.16</sub></td><td>-73<sup>+4</sup><sub>-3</sub></td></tr><tr><td>Deep3a-15504</td><td>3.7 ± 0.2</td><td>6.6<sup>+1.5</sup><sub>-1.0</sub></td><td>1.01<sup>+0.28</sup><sub>-0.23</sub></td><td>0.46<sup>+0.02</sup><sub>-0.03</sub></td><td>-13<sup>+3</sup><sub>-2</sub></td><td>3.5<sup>+0.3</sup><sub>-0.4</sub></td><td>6.4<sup>+2.4</sup><sub>-1.3</sub></td><td>1.25<sup>+0.69</sup><sub>-0.42</sub></td><td>0.40<sup>+0.06</sup><sub>-0.09</sub></td><td>-12<sup>+3</sup><sub>-2</sub></td></tr><tr><td>K20-ID6</td><td>4.0 ± 0.1</td><td>4.3<sup>+1.6</sup><sub>-1.1</sub></td><td>0.51<sup>+0.43</sup><sub>-0.39</sub></td><td>0.53<sup>+0.26</sup><sub>-0.17</sub></td><td>+50<sup>+7</sup><sub>-6</sub></td><td>3.8 ± 0.2</td><td>4.2<sup>+1.2</sup><sub>-1.3</sub></td><td>0.37<sup>+0.94</sup><sub>-0.26</sub></td><td>0.43<sup>+0.21</sup><sub>-0.20</sub></td><td>+50 ± 6</td></tr><tr><td>K20-ID7</td><td>5.1 ± 0.3</td><td>5.5<sup>+0.3</sup><sub>-1.2</sub></td><td>0.10<sup>+0.36</sup><sub>-0.01</sub></td><td>0.75<sup>+0.12</sup><sub>-0.04</sub></td><td>-2<sup>+37</sup><sub>-6</sub></td><td>5.0 ± 0.4</td><td>5.5<sup>+0.4</sup><sub>-1.2</sub></td><td>0.10<sup>+0.92</sup><sub>-0.01</sub></td><td>0.72<sup>+0.16</sup><sub>-0.07</sub></td><td>0<sup>+27</sup><sub>-5</sub></td></tr><tr><td>GMASS-2303</td><td>2.2 ± 0.6</td><td>2.4<sup>+1.3</sup><sub>-0.6</sub></td><td>1.00<sup>+0.63</sup><sub>-0.42</sub></td><td>0.58<sup>+0.12</sup><sub>-0.08</sub></td><td>-12<sup>+6</sup><sub>-14</sub></td><td>1.9<sup>+0.8</sup><sub>-1.6</sub></td><td>2.2<sup>+1.0</sup><sub>-0.9</sub></td><td>0.91<sup>+1.67</sup><sub>-0.71</sub></td><td>0.47<sup>+0.13</sup><sub>-0.12</sub></td><td>-10<sup>+9</sup><sub>-13</sub></td></tr><tr><td>GMASS-2363</td><td>2.0<sup>+0.3</sup><sub>-0.4</sub></td><td>2.1<sup>+1.2</sup><sub>-0.2</sub></td><td>0.50<sup>+0.87</sup><sub>-0.14</sub></td><td>0.70<sup>+0.21</sup><sub>-0.07</sub></td><td>+37<sup>+13</sup><sub>-32</sub></td><td>1.5<sup>+0.6</sup><sub>-1.3</sub></td><td>1.9<sup>+2.0</sup><sub>-0.4</sub></td><td>0.50<sup>+2.75</sup><sub>-0.40</sub></td><td>0.53<sup>+0.17</sup><sub>-0.15</sub></td><td>+34<sup>+14</sup><sub>-12</sub></td></tr><tr><td>GMASS-2540</td><td>7.9 ± 0.2</td><td>...</td><td>...</td><td>...</td><td>...</td><td>7.8<sup>+0.2</sup><sub>-0.3</sub></td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>SA12-6339</td><td>1.5 ± 0.3</td><td>2.3<sup>+1.0</sup><sub>-0.6</sub></td><td>2.18<sup>+2.20</sup><sub>-0.92</sub></td><td>0.81<sup>+0.12</sup><sub>-0.11</sub></td><td>-3<sup>+29</sup><sub>-33</sub></td><td>&lt;1.4</td><td>1.2<sup>+1.4</sup><sub>-0.6</sub></td><td>3.75<sup>+1.25</sup><sub>-2.23</sub></td><td>0.65<sup>+0.20</sup><sub>-0.26</sub></td><td>-11<sup>+32</sup><sub>-31</sub></td></tr><tr><td>ZC400528</td><td>2.4 ± 0.2</td><td>3.2<sup>+1.6</sup><sub>-0.5</sub></td><td>1.03<sup>+0.67</sup><sub>-0.36</sub></td><td>0.54<sup>+0.08</sup><sub>-0.06</sub></td><td>-25<sup>+7</sup><sub>-5</sub></td><td>2.1<sup>+0.4</sup><sub>-0.5</sub></td><td>2.7<sup>+1.5</sup><sub>-0.8</sub></td><td>1.50<sup>+1.35</sup><sub>-0.52</sub></td><td>0.40<sup>+0.12</sup><sub>-0.17</sub></td><td>-24<sup>+7</sup><sub>-5</sub></td></tr><tr><td>ZC400569</td><td>4.4 ± 0.5</td><td>7.6<sup>+0.8</sup><sub>-1.8</sub></td><td>0.40<sup>+0.26</sup><sub>-0.09</sub></td><td>0.33<sup>+0.05</sup><sub>-0.03</sub></td><td>+4<sup>+4</sup><sub>-3</sub></td><td>4.2<sup>+0.6</sup><sub>-0.7</sub></td><td>7.4<sup>+1.3</sup><sub>-1.5</sub></td><td>0.44<sup>+0.46</sup><sub>-0.15</sub></td><td>0.28<sup>+0.06</sup><sub>-0.05</sub></td><td>+5 ± 3</td></tr><tr><td>ZC400569N</td><td>3.9<sup>+1.1</sup><sub>-1.2</sub></td><td>3.2<sup>+0.4</sup><sub>-0.4</sub></td><td>0.76<sup>+0.21</sup><sub>-0.13</sub></td><td>0.98<sup>+0.02</sup><sub>-0.09</sub></td><td>+70<sup>+7</sup><sub>-6</sub></td><td>3.7<sup>+1.3</sup><sub>-1.5</sub></td><td>2.8<sup>+0.9</sup><sub>-0.6</sub></td><td>0.95<sup>+0.37</sup><sub>-0.24</sub></td><td>0.95<sup>+0.06</sup><sub>-0.11</sub></td><td>+70<sup>+7</sup><sub>-6</sub></td></tr><tr><td>ZC401925</td><td>2.2<sup>+0.4</sup><sub>-0.5</sub></td><td>2.6<sup>+1.3</sup><sub>-0.5</sub></td><td>0.88<sup>+0.74</sup><sub>-0.45</sub></td><td>0.65 ± 0.09</td><td>-9 ± 7</td><td>1.9<sup>+0.5</sup><sub>-0.9</sub></td><td>2.5<sup>+1.2</sup><sub>-0.5</sub></td><td>0.65<sup>+0.98</sup><sub>-0.55</sub></td><td>0.62<sup>+0.09</sup><sub>-0.10</sub></td><td>-10<sup>+8</sup><sub>-11</sub></td></tr><tr><td>ZC403741</td><td>2.5<sup>+0.1</sup><sub>-0.2</sub></td><td>2.5<sup>+0.3</sup><sub>-0.2</sub></td><td>0.42<sup>+0.23</sup><sub>-0.07</sub></td><td>0.89 ± 0.04</td><td>+52<sup>+23</sup><sub>-21</sub></td><td>2.2<sup>+0.3</sup><sub>-0.5</sub></td><td>2.2<sup>+0.4</sup><sub>-0.3</sub></td><td>0.29<sup>+0.39</sup><sub>-0.19</sub></td><td>0.84<sup>+0.07</sup><sub>-0.10</sub></td><td>+45 ± 16</td></tr><tr><td>ZC404221</td><td>1.7<sup>+0.1</sup><sub>-0.2</sub></td><td>2.2<sup>+1.6</sup><sub>-0.5</sub></td><td>1.89<sup>+2.81</sup><sub>-0.68</sub></td><td>0.70<sup>+0.14</sup><sub>-0.15</sub></td><td>-9<sup>+6</sup><sub>-7</sub></td><td>1.3<sup>+0.4</sup><sub>-0.8</sub></td><td>1.5<sup>+1.1</sup><sub>-0.5</sub></td><td>1.71<sup>+2.79</sup><sub>-1.06</sub></td><td>0.68 ± 0.20</td><td>-9<sup>+13</sup><sub>-12</sub></td></tr><tr><td>ZC405226</td><td>3.6 ± 0.2</td><td>5.2<sup>+0.7</sup><sub>-0.6</sub></td><td>0.56<sup>+0.14</sup><sub>-0.14</sub></td><td>0.67<sup>+0.05</sup><sub>-0.02</sub></td><td>-42<sup>+4</sup><sub>-2</sub></td><td>3.4 ± 0.3</td><td>5.1<sup>+0.7</sup><sub>-0.5</sub></td><td>0.53<sup>+0.26</sup><sub>-0.14</sub></td><td>0.65 ± 0.05</td><td>-43 ± 2</td></tr><tr><td>ZC405501</td><td>4.1 ± 0.2</td><td>6.2<sup>+0.7</sup><sub>-0.9</sub></td><td>0.10<sup>+0.69</sup><sub>-0.01</sub></td><td>0.29<sup>+0.14</sup><sub>-0.05</sub></td><td>+13 ± 2</td><td>3.9<sup>+0.3</sup><sub>-0.4</sub></td><td>6.3<sup>+0.3</sup><sub>-0.6</sub></td><td>0.10<sup>+0.81</sup><sub>-0.01</sub></td><td>0.23 ± 0.09</td><td>+12 ± 3</td></tr><tr><td>ZC406690</td><td>4.8 ± 0.1</td><td>5.4 ± 0.1</td><td>0.10 ± 0.01</td><td>0.76 ± 0.02</td><td>-87 ± 2</td><td>4.6<sup>+0.1</sup><sub>-0.2</sub></td><td>5.3 ± 0.1</td><td>0.10 ± 0.01</td><td>0.73<sup>+0.03</sup><sub>-0.06</sub></td><td>-86<sup>+2</sup><sub>-3</sub></td></tr><tr><td>ZC407302</td><td>3.1 ± 0.2</td><td>4.1<sup>+0.4</sup><sub>-0.3</sub></td><td>0.47<sup>+0.14</sup><sub>-0.11</sub></td><td>0.53<sup>+0.04</sup><sub>-0.03</sub></td><td>+28<sup>+3</sup><sub>-5</sub></td><td>2.9<sup>+0.3</sup><sub>-0.4</sub></td><td>3.9 ± 0.3</td><td>0.35<sup>+0.22</sup><sub>-0.25</sub></td><td>0.46<sup>+0.07</sup><sub>-0.09</sub></td><td>+29 ± 4</td></tr><tr><td>ZC407376</td><td>4.0 ± 0.1</td><td>5.5<sup>+0.5</sup><sub>-0.3</sub></td><td>0.10<sup>+0.34</sup><sub>-0.01</sub></td><td>0.38<sup>+0.10</sup><sub>-0.05</sub></td><td>+15<sup>+3</sup><sub>-2</sub></td><td>3.9 ± 0.2</td><td>5.5<sup>+0.7</sup><sub>-0.3</sub></td><td>0.10<sup>+0.34</sup><sub>-0.01</sub></td><td>0.32<sup>+0.08</sup><sub>-0.10</sub></td><td>+15 ± 2</td></tr><tr><td>ZC407376S</td><td>2.1<sup>+0.3</sup><sub>-0.4</sub></td><td>3.1<sup>+2.6</sup><sub>-0.7</sub></td><td>1.16<sup>+1.33</sup><sub>-0.58</sub></td><td>0.58 ± 0.12</td><td>-23<sup>+19</sup><sub>-13</sub></td><td>1.8<sup>+0.5</sup><sub>-0.8</sub></td><td>2.6<sup>+3.5</sup><sub>-0.9</sub></td><td>1.17<sup>+1.89</sup><sub>-0.56</sub></td><td>0.55<sup>+0.14</sup><sub>-0.15</sub></td><td>-19<sup>+21</sup><sub>-13</sub></td></tr><tr><td>ZC407376N</td><td>1.6<sup>+0.4</sup><sub>-0.6</sub></td><td>...</td><td>...</td><td>...</td><td>...</td><td>1.2<sup>+0.7</sup><sub>-1.0</sub></td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>ZC409985</td><td>1.9 ± 0.1</td><td>2.5<sup>+0.9</sup><sub>-0.4</sub></td><td>0.86<sup>+0.56</sup><sub>-0.29</sub></td><td>0.60<sup>+0.16</sup><sub>-0.04</sub></td><td>-10<sup>+9</sup><sub>-5</sub></td><td>1.4<sup>+0.4</sup><sub>-0.8</sub></td><td>2.1<sup>+0.6</sup><sub>-0.4</sub></td><td>0.81<sup>+1.17</sup><sub>-0.61</sub></td><td>0.46<sup>+0.18</sup><sub>-0.14</sub></td><td>-11<sup>+8</sup><sub>-5</sub></td></tr><tr><td>ZC410041</td><td>3.8 ± 0.3</td><td>5.2<sup>+0.6</sup><sub>-0.4</sub></td><td>0.22<sup>+0.46</sup><sub>-0.12</sub></td><td>0.31<sup>+0.12</sup><sub>-0.07</sub></td><td>-55 ± 3</td><td>3.6<sup>+0.4</sup><sub>-0.5</sub></td><td>5.3<sup>+0.5</sup><sub>-0.6</sub></td><td>0.10<sup>+0.63</sup><sub>-0.01</sub></td><td>0.25<sup>+0.11</sup><sub>-0.14</sub></td><td>-56<sup>+3</sup><sub>-2</sub></td></tr><tr><td>ZC410123</td><td>3.3<sup>+0.1</sup><sub>-0.2</sub></td><td>4.0<sup>+0.9</sup><sub>-0.5</sub></td><td>0.38<sup>+0.50</sup><sub>-0.20</sub></td><td>0.38<sup>+0.12</sup><sub>-0.06</sub></td><td>+36<sup>+3</sup><sub>-4</sub></td><td>3.1 ± 0.3</td><td>3.8<sup>+0.6</sup><sub>-1.3</sub></td><td>0.33<sup>+1.08</sup><sub>-0.23</sub></td><td>0.31<sup>+0.28</sup><sub>-0.12</sub></td><td>+36<sup>+4</sup><sub>-6</sub></td></tr><tr><td>ZC411737</td><td>2.0<sup>+0.2</sup><sub>-0.3</sub></td><td>2.8<sup>+1.2</sup><sub>-0.4</sub></td><td>0.57<sup>+0.74</sup><sub>-0.40</sub></td><td>0.56<sup>+0.13</sup><sub>-0.07</sub></td><td>-6<sup>+8</sup><sub>-6</sub></td><td>1.7<sup>+0.5</sup><sub>-0.8</sub></td><td>2.4<sup>+0.9</sup><sub>-0.3</sub></td><td>0.18<sup>+1.46</sup><sub>-0.08</sub></td><td>0.45<sup>+0.14</sup><sub>-0.18</sub></td><td>-6<sup>+7</sup><sub>-9</sub></td></tr><tr><td>ZC412369</td><td>2.5 ± 0.3</td><td>3.7<sup>+0.9</sup><sub>-0.6</sub></td><td>0.93<sup>+0.35</sup><sub>-0.25</sub></td><td>0.54<sup>+0.09</sup><sub>-0.06</sub></td><td>-35<sup>+4</sup><sub>-3</sub></td><td>2.1<sup>+0.5</sup><sub>-0.7</sub></td><td>3.1<sup>+1.0</sup><sub>-0.9</sub></td><td>1.22<sup>+1.00</sup><sub>-0.64</sub></td><td>0.41<sup>+0.13</sup><sub>-0.14</sub></td><td>-34<sup>+6</sup><sub>-4</sub></td></tr><tr><td>ZC413507</td><td>2.8 ± 0.2</td><td>3.3<sup>+1.6</sup><sub>-0.6</sub></td><td>0.64<sup>+0.38</sup><sub>-0.32</sub></td><td>0.79<sup>+0.14</sup><sub>-0.10</sub></td><td>-35<sup>+78</sup><sub>-10</sub></td><td>2.5<sup>+0.3</sup><sub>-0.4</sub></td><td>2.9<sup>+1.1</sup><sub>-0.5</sub></td><td>0.65<sup>+0.65</sup><sub>-0.55</sub></td><td>0.72 ± 0.17</td><td>-31<sup>+50</sup><sub>-13</sub></td></tr><tr><td>ZC413597</td><td>2.1 ± 0.1</td><td>2.4<sup>+1.4</sup><sub>-0.5</sub></td><td>1.09<sup>+0.67</sup><sub>-0.44</sub></td><td>0.66<sup>+0.18</sup><sub>-0.12</sub></td><td>+54<sup>+17</sup><sub>-5</sub></td><td>1.8<sup>+0.3</sup><sub>-0.5</sub></td><td>2.1<sup>+0.9</sup><sub>-0.6</sub></td><td>0.98<sup>+1.51</sup><sub>-0.66</sub></td><td>0.52<sup>+0.23</sup><sub>-0.18</sub></td><td>+51<sup>+6</sup><sub>-15</sub></td></tr><tr><td>ZC415876</td><td>2.0 ± 0.2</td><td>2.2<sup>+0.5</sup><sub>-0.3</sub></td><td>0.70<sup>+0.44</sup><sub>-0.21</sub></td><td>0.77<sup>+0.11</sup><sub>-0.08</sub></td><td>-74 ± 8</td><td>1.5<sup>+0.4</sup><sub>-0.8</sub></td><td>1.8<sup>+0.6</sup><sub>-0.4</sub></td><td>0.52<sup>+1.04</sup><sub>-0.42</sub></td><td>0.70<sup>+0.15</sup><sub>-0.17</sub></td><td>-74<sup>+19</sup><sub>-24</sub></td></tr></tbody></table>

**Notes.** The measurements reported are the intrinsic half-light radius computed from the Hα curve of growth in circular apertures $r_{1/2}^{\text{circ}}$ and the intrinsic major-axis effective radius $R_e$, Sérsic index $n$, projected minor-to-major axis ratio $q$, and PA of the major axis (in degrees east of north) from 2D Sérsic model fits to the Hα surface brightness distributions.

a Measurements derived with the best-fit single-Gaussian fits to the PSFs associated with each individual galaxy.

b Measurements derived with the best-fit double-Gaussian fit to the average, high-S/N PSF.

## 5.3. Consistency of the Hα Size Estimates

Table 5 gives the $r_{1/2}^{\text{circ}}$ estimates from the curve-of-growth analysis and the $R_e$, $n$, $q$, and PA obtained from the Sérsic profile fits to the Hα line maps. The results are reported for both choices of PSF for comparison. The $r_{1/2}^{\text{circ}}$ values derived with the PSF$_2$$_{G,ave}$ are in the range 1.1–5.0 kpc, with a mean of 2.8 kpc and median of 2.5 kpc. The major-axis effective radii $R_e$ are between 1.2 and 7.4 kpc, with a mean and median of 3.7 and 3.0 kpc, respectively. Since the curves of growth were measured in circular apertures, the $r_{1/2}^{\text{circ}}$ values should be

compared to the circularized effective radii $R_{e,\text{circ}} \equiv R_e \sqrt{q}$ for better consistency. The $r_{1/2}^{\text{circ}}$ are on average (and median) 10% larger than the $R_{e,\text{circ}}$, with a scatter of 15%. When using the individual PSF$_1$$_{G,gal}$, the $r_{1/2}^{\text{circ}}$ and $R_{e,\text{circ}}$ agree within 4% on average (and median), also with a scatter of 15%.

The size estimates obtained from the curve of growth and parametric fits are thus in very good agreement, in particular considering some of the inherent differences between the two approaches. The curves of growth were computed directly from the data cubes and so rely on Hα line fits from higher-S/N spectra than those at the individual pixel level when making the
line maps, although they are more prone to limitations due to
the small effective FOV of our SINFONI+AO data sets for the
largest sources (see Appendix E). The parametric fits can
mitigate both the S/N and FOV limitations at large radii if the
global profiles are sufficiently well represented by a simple
(single-component) model. Both methods are sensitive to
uncertainties from the background subtraction. The tight
correlation between the $r_1^{\text{circ}}$ and $R_{e,\text{circ}}$ estimates suggests that
these sources of uncertainty do not importantly affect our
measurements.

The curve-of-growth method has the main advantage of
properly accounting for all the light irrespective of the details
of (potentially complex) surface brightness distributions. On
the other hand, in this approach, we treated the beam smearing
simplystically (subtracting in quadrature the PSF half-light
radius), and the use of circular apertures would overestimate
the sizes because projection effects from galaxy inclination are
neglected. The parametric approach more accurately accounts
for projected axis ratios and the impact of beam smearing for
non-Gaussian intrinsic galaxy profiles and non-Gaussian PSFs,
although single-component Sérsic models as adopted here
obviously do not account for the detailed substructure of the
galaxies. Based on a large suite of 2D Sérsic models created
with varying $R_e$, $n$, $q$, PSF parameters, and spatial sampling in
the ranges spanned by our AO sample, we found that
differences between $r_1^{\text{circ}}$ and $R_{e,\text{circ}}$ are mostly affected by the
projected axis ratio, with little dependence on galaxy profile
and little impact of the simplistic beam-smearing correction in
the curve-of-growth approach. The trend in $r_1^{\text{circ}}/R_{e,\text{circ}}$ among
the galaxies is consistent with the model expectations, with an
average ratio of 1.04 for the sources with $q > 0.5$ and 1.15 for
those with $q < 0.5$ in the PSF<sub>2 G,ave</sub> case (1.01 and 1.11,
respectively, in the PSF<sub>1 G,gal</sub> case). We conclude that the
(small) differences in $H\alpha$ sizes obtained from the two methods
for our sample can be attributed partly to galaxy inclination
effects, along with other factors, such as complex morphologies
that are more difficult to quantify.

## 5.4. Global $H\alpha$ Surface Brightness Distributions and Comparison to H-band Continuum Results

The simple Sérsic models adopted in Section 5.2 lead in many
cases to significant fit residuals on small scales left as the imprint of
bright clumps, ringlike features, or other prominent irregular
substructure in $H\alpha$ light and obviously provide a poor representa-
tion of systems with spatially resolved interacting units. In
particular, rings and bright off-center clumps drive the best-fit
Sérsic indices to low values. The mean and median indices are
$n \sim 0.7$ and 0.5, respectively, using the PSF<sub>2 G,ave</sub> (and essentially
identical mean and median of $n \sim 0.7$ in the PSF<sub>1 G,gal</sub> case). Best-
fit indices of around 0.1, the lower limit allowed in our parametric
fits, are reached by eight objects with the most prominent rings or
off-center clumps (Q2343-BX610, Q2346-BX482, Deep3a-6004,
K20-ID7, ZC405501, ZC406690, ZC410041, and the merger
ZC407376 when modeled as a single system). Only SA12-6339
has $n > 2$ (though with large uncertainties because of the
compactness of this source). Taken at face value, these results
imply that the SINS/zC-SINF AO galaxies have global observed
$H\alpha$ surface brightness distributions consistent with morphologically
late-type, disk-dominated systems, usually defined as having
$n < 2-2.5$ (e.g., Bell et al. 2004; Trujillo et al. 2006). Even for
SA12-6339, the derived $n$ for either PSF choice is within $1\sigma$ of
$n = 2$. The sample exhibits a trend of decreasing $n$ with larger

$R_e$ (Spearman rank correlation coefficient about $\rho$-0.6, significant at the 3.5$\sigma$ level), reflecting the qualitative trend of shallower or more ringlike profiles toward larger galaxies that is apparent from the $H\alpha$ maps and profiles.

A similar parametric analysis was performed on the H-band maps for the subset of 29 galaxies with high-resolution HST near-IR imaging (Förster Schreiber et al. 2011a; Tacchella et al. 2015b). Qualitatively, the H-band morphologies often exhibit similar noticeable substructure as seen in $H\alpha$, but they tend to be overall smoother and more centrally peaked (see Appendix D). For ZC400569 and ZC407376, the H-band parameters refer to the northern and southern components, respectively. Quantitatively, and excluding GMASS-2540 because of the unreliable fits to the $H\alpha$ line maps, the rest-optical and $H\alpha$ sizes are essentially identical within about 5% on average, both in terms of major axis and circularized effective radius. The axis ratios and PAs agree on average within about 10% and 18°, respectively. For a majority of the sources, the rest-optical light also globally follows a disklike profile, with 80% having a best-fit $n < 2.5$. However, systematically higher Sérsic indices are derived, with a mean $n = 1.6$ (median $n = 1.2$) compared to $n = 0.7$ (median $n = 0.5$) from the $H\alpha$ maps of the same 28 objects. This differentiation is more pronounced at higher stellar masses; galaxies with $\log(M_*/M_\odot) > 10.7$ have an average $n$ of 2.5 (median $n \approx 2.3$) in rest-optical light and an average and median $n$ of about 0.8 in $H\alpha$ light.

The trend of increasingly more centrally peaked morphol-
ogies in the H band versus $H\alpha$ toward higher masses is
consistent with the presence of a significant bulge along with
suppressed star formation activity in the central regions of these
massive galaxies, as discussed by Genzel et al. (2014a) and
Tacchella et al. (2015a, 2018). This trend also echoes findings
from the average $H\alpha$ and rest-optical continuum profiles from
much larger samples of SFGs, albeit at lower $z \sim 1$, from the
3D-HST HST/WFC3 grism survey (Nelson et al. 2012, 2013,
2016b; Wuyts et al. 2013). Such differences in global light
profiles could be indicative of quenching in the central regions
of high-mass galaxies, caused by a massive bulge stabilizing
the gas against the formation of massive star-forming clumps
(e.g., Martig et al. 2009; Genzel et al. 2014a), efficient removal
of gas via powerful nuclear outflows (Förster Schreiber
et al. 2014; Genzel et al. 2014b; see also Cano-Díaz et al.
2012; Brusa et al. 2015, 2016; Cresci et al. 2015; Perna et al.
2015; Carniani et al. 2016), or central gas consumption (e.g.,
Tacchella et al. 2016; Tadaki et al. 2017).

An important uncertainty in interpreting the sizes and global
profiles from $H\alpha$ (and continuum) emission is the possible
effects of spatially variable dust extinction (e.g., Wuyts
et al. 2013; Nelson et al. 2016a). Higher extinction in the
inner regions would imply more centrally peaked intrinsic
profiles than observed, such that the effective radii inferred here
would overestimate the true intrinsic sizes. This overestimate
could be more important for the $H\alpha$ emission if the H II regions
were more attenuated relative to the stellar continuum light
along the line of sight (e.g., Calzetti et al. 2000; FS09; M11; Ly
et al. 2012; Kashino et al. 2013; Wuyts et al. 2013; Price
et al. 2014; Koyama et al. 2015; Puglisi et al. 2016). Spatially
resolved maps of the extinction toward the stars and the nebular
line emission are very challenging to obtain for distant
galaxies. Exploiting new HST imaging probing the near- and
far-UV emission of 10 of the SINS/zC-SINF AO galaxies
together with the Hα maps, Tacchella et al. (2018) showed that the dust attenuation peaks at the center, with an $A_V$ on average ~1 mag higher than in the outer disk regions. Most importantly, while the central dust attenuation is higher in the four galaxies with $M_* > 10^{11} M_\odot$ (Q2343-BX610, Deep3a-15504, ZC400569, and ZC400528), the dust-corrected specific SFR profiles still drop in the inner regions and thus support quenching of star formation at the center of these galaxies.

# 6. Measurements of the Hα Kinematic Properties

In this section, we present the measurements of the intrinsic rotation velocity and local velocity dispersion from the Hα data of the SINS/zC-SINF AO sample, after summarizing the choice of galaxy parameters necessary for the beam-smearing and inclination corrections. These measurements assume a rotating disk framework, which is justified in more detail in the next section (see also Shapiro et al. 2008; Cresci et al. 2009; FS09; Genzel et al. 2014a).

## 6.1. Beam-smearing and Inclination Corrections

We applied the beam-smearing corrections for velocity and velocity dispersion (denoted $C_{PSF,v}$ and $C_{PSF,\sigma}$) presented by Burkert et al. (2016, Appendix A). These corrections were derived from rotating disk models ($n=1$) with a range of sizes, inclinations, and masses appropriate for our sample and convolved with the PSF$_2$ G,ave. As discussed in Section 5 and further in Section 7, the disk assumption is valid for the vast majority of our galaxies, but the corrections are necessarily more uncertain for the few nondisk systems. The beam smearing depends on the ratio of galaxy to PSF sizes, as well as the radius at which the observed velocity and $\sigma_0$ values are measured. In velocity, there is very little dependence on galaxy inclination and mass at fixed size. In contrast, the effects on $\sigma_0$ also depend fairly sensitively on galaxy inclination and mass. It is also important to account for the extended wings of the AO PSF. For instance, the beam-smearing corrections in velocity for our objects are 10%–40% larger than those for a single-Gaussian PSF with FWHM equal to that of the core component of the PSF$_2$ G,ave.

For the purpose of beam-smearing corrections (and kinematic analysis), we adopted the $R_e$ values from the single-component Sérsic model fits to the HST H-band imaging, when available (from Tacchella et al. 2015b), and from the Hα maps for the other sources (from Section 5.2). The H-band light being dominated by the continuum from stars making up the bulk of the stellar mass, it is less likely to be affected by sites of ongoing intense star formation, and the parametric fits to H-band maps are arguably more robust because of the higher Strehl ratio, simultaneous PSF, and much wider FOV of the HST imaging compared to the SINFONI Hα data. As noted in the previous section, the difference in sizes between Hα and H-band emission is small, such that the choice made here has little consequence for the results. For reference, the $R_e$ adopted here for each galaxy is given in Table 6.

Similarly, we adopted the inclinations inferred from the axis ratios $q$ from the fits to the H-band maps whenever possible and from the Hα maps otherwise, with the exceptions detailed below (and indicated in Table 6). We assumed a disk geometry with finite intrinsic thickness $q_0$ and computed the inclination $i$ via $\sin^2(i) = (1-q^2)/(1-q_0^2)$. We used $q_0 = 0.20$, motivated by the typical local random motions relative to rotational motions in previous work and structural studies from deep high-resolution rest-UV/optical imaging of $z \sim 2$ disks (e.g., Elmegreen

et al. 2005, 2017; Genzel et al. 2008; Cresci et al. 2009; Law et al. 2012b, 2012a; Newman et al. 2013; van der Wel et al. 2014a; Wisnioski et al. 2015). The differences with inclination corrections in the thin-disk approximation are, however, <5%, so the exact choice has little impact on our analysis. For eight of the most compact sources, the $q$ estimates are quite uncertain. We assigned to these objects the average for a distribution of randomly inclined disks corresponding to $\langle \sin(i) \rangle = \pi/4$ (e.g., Law et al. 2009). For four large disks with bright off-center clumps and nonaxisymmetric features in both Hα and H-band emission, the inclinations implied by the morphological axis ratios lead to models that do not reproduce the observed kinematics well and poorly match the mass priors from the stellar and gaseous components (Genzel et al. 2014a, 2017). For those cases, which include Deep3a-6004 with nearly orthogonal kinematic and morphological major axes, we adopted the inclination from the best-fit disk modeling.

## 6.2. Intrinsic Rotation Velocity and Velocity Dispersion

We determined the maximum observed velocity difference across the galaxies, $\Delta v_{obs}$, based on the profiles extracted along the kinematic major axis as defined in Section 4.3. For objects that do not exhibit regular disklike kinematics, we evaluated the $\Delta v_{obs}$ from the velocity maps and the identification of the bluest and reddest spectral channels at which Hα emission is still detected over at least one spatial resolution element. We then calculated the intrinsic rotation velocity through $V_{rot} \times \sin(i) = C_{PSF,v} \times \Delta v_{obs}/2$. The beam-smearing correction factors $C_{PSF,v}$ for our galaxies are 1.3 on average (and median) and at most 2 for the smallest objects (Q1623-BX502, SA12-6339, ZC404221).

In the framework of rotating disks, the observed line width at a given position reflects the intrinsic local velocity dispersion $\sigma_0$ (related to the disk thickness), as well as the beam-smearing line-of-sight velocity distribution. For the galaxies with the most regular kinematics, we determined $\sigma_{0,obs}$ from the velocity dispersion profiles along the kinematic major axis at the largest radii possible, away from the central peak caused by the steep inner disk velocity gradient. For the other sources, we estimated $\sigma_{0,obs}$ from the dispersion maps and line widths in the outer parts of the galaxies from inspection of the data cubes. We then computed the intrinsic $\sigma_0 = C_{PSF,\sigma} \times \sigma_{0,obs}$, where the correction factors also take into account galaxy inclination, size, and mass relevant to the spatial beam smearing in dispersion. The corrections for our sample have an average and median of ≈0.85 and range between 0.3 and 1.0 (three objects have $C_{PSF,\sigma} < 0.6$, driven by their compactness: ZC400528, ZC404221, and SA12-6339).

Two underlying assumptions in our $\sigma_0$ estimates (and beam-smearing corrections) are that the intrinsic velocity dispersion is isotropic and that it is constant throughout the regions probed by our SINFONI+AO data. The latter assumption is motivated by the detailed analysis of the residuals in velocity dispersion between the data and disk models for several SINS/zC-SINF galaxies with the highest-quality AO and seeing-limited observations (see Genzel et al. 2006, 2008, 2017; Cresci et al. 2009). Although the impact of beam smearing is reduced at the higher resolution of AO-assisted data compared to seeing-limited observations, the derived $\sigma_0$ can still include contributions from noncircular motions on ≲1–2 kpc scales. Naturally, for nondisk systems, $\sigma_0$ may also be more related to kinematic perturbations than to support from random motions in a disklike geometry.
<table><caption>**Table 6**
Kinematic Properties and Dynamical Masses</caption><thead><tr><th>Source</th><th>R<sub>e</sub><sup>a</sup><br>(kpc)</th><th>sin(i)<sup>a</sup></th><th>PA<sub>kin</sub><br>(deg)</th><th>ΔPA<sup>b</sup><br>(deg)</th><th>Δv<sub>obs</sub>/2<br>(km s<sup>-1</sup>)</th><th>V<sub>rot</sub><br>(km s<sup>-1</sup>)</th><th>σ<sub>0</sub><br>(km s<sup>-1</sup>)</th><th>V<sub>rot</sub>/σ<sub>0</sub></th><th>V<sub>c</sub><sup>c</sup><br>(km s<sup>-1</sup>)</th><th>M<sub>dyn</sub><sup>c</sup><br>(10<sup>10</sup>M<sub>☉</sub>)</th><th>Disk<br>Criteria<sup>d</sup></th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>2.1<sup>+0.8</sup><sub>-0.4</sub></td><td>0.98<sup>+0.01</sup><sub>-0.10</sub></td><td>65 ± 15</td><td>10<sup>+20</sup><sub>-16</sub></td><td>125 ± 15</td><td>175<sup>+54</sup><sub>-17</sub></td><td>56<sup>+15</sup><sub>-24</sub></td><td>3.1<sup>+2.4</sup><sub>-0.5</sub></td><td>203<sup>+51</sup><sub>-15</sub></td><td>3.9<sup>+2.1</sup><sub>-3.7</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>Q1623-BX502</td><td>1.1 ± 0.7</td><td>0.77<sup>+0.12</sup><sub>-0.18</sub></td><td>45 ± 15</td><td>44 ± 16</td><td>33 ± 10</td><td>77<sup>+50</sup><sub>-32</sub></td><td>40<sup>+16</sup><sub>-14</sub></td><td>2.0<sup>+1.5</sup><sub>-0.8</sub></td><td>106<sup>+45</sup><sub>-21</sub></td><td>0.58<sup>+0.77</sup><sub>-0.21</sub></td><td>1, 2, 3, 5</td></tr><tr><td>Q1623-BX543</td><td>3.3<sup>+1.2</sup><sub>-0.8</sub></td><td>0.90 ± 0.05</td><td>0 ± 25</td><td>4<sup>+26</sup><sub>-25</sub></td><td>93 ± 15</td><td>128<sup>+29</sup><sub>-21</sub></td><td>70<sup>+15</sup><sub>-25</sub></td><td>1.8<sup>+0.9</sup><sub>-0.3</sub></td><td>181<sup>+28</sup><sub>-27</sub></td><td>5.0<sup>+2.4</sup><sub>-2.0</sub></td><td>Irr</td></tr><tr><td>Q1623-BX599</td><td>2.4 ± 0.6</td><td>0.74<sup>+0.12</sup><sub>-0.15</sub></td><td>-55 ± 25</td><td>2 ± 28</td><td>80 ± 20</td><td>139<sup>+62</sup><sub>-36</sub></td><td>71<sup>+18</sup><sub>-27</sub></td><td>2.0<sup>+1.4</sup><sub>-0.4</sub></td><td>191<sup>+55</sup><sub>-35</sub></td><td>4.1<sup>+3.3</sup><sub>-1.7</sub></td><td>Irr</td></tr><tr><td>Q2343-BX389</td><td>6.2 ± 1.2</td><td>0.98<sup>+0.01</sup><sub>-0.06</sub></td><td>-50 ± 5</td><td>2 ± 5</td><td>260 ± 23</td><td>299<sup>+40</sup><sub>-21</sub></td><td>56<sup>+13</sup><sub>-15</sub></td><td>5.3<sup>+1.7</sup><sub>-0.7</sub></td><td>316<sup>+39</sup><sub>-20</sub></td><td>29<sup>+9</sup><sub>-6</sub></td><td>1, 2</td></tr><tr><td>Q2343-BX513</td><td>2.6<sup>+1.5</sup><sub>-0.8</sub></td><td>0.78<sup>+0.14</sup><sub>-0.19</sub></td><td>-35 ± 10</td><td>40<sup>+11</sup><sub>-12</sub></td><td>60 ± 15</td><td>102<sup>+64</sup><sub>-26</sub></td><td>55<sup>+24</sup><sub>-28</sub></td><td>1.8<sup>+2.1</sup><sub>-0.5</sub></td><td>144<sup>+64</sup><sub>-30</sub></td><td>2.5<sup>+3.2</sup><sub>-1.2</sub></td><td>Irr</td></tr><tr><td>Q2343-BX610</td><td>4.5 ± 1.1</td><td>0.86<sup>+0.08</sup><sub>-0.12</sub></td><td>-10 ± 10</td><td>27 ± 10</td><td>180 ± 25</td><td>241<sup>+62</sup><sub>-36</sub></td><td>64<sup>+17</sup><sub>-24</sub></td><td>3.8<sup>+2.0</sup><sub>-0.6</sub></td><td>268<sup>+60</sup><sub>-36</sub></td><td>15<sup>+8</sup><sub>-5</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>Q2346-BX482</td><td>6.0 ± 0.8</td><td>0.88<sup>+0.08</sup><sub>-0.14</sub></td><td>-65 ± 5</td><td>3 ± 10</td><td>225 ± 20</td><td>287<sup>+63</sup><sub>-30</sub></td><td>58<sup>+14</sup><sub>-15</sub></td><td>4.9<sup>+1.6</sup><sub>-0.7</sub></td><td>306<sup>+65</sup><sub>-29</sub></td><td>26<sup>+12</sup><sub>-5</sub></td><td>1, 2, 3, 4</td></tr><tr><td>Deep3a-6004</td><td>5.1 ± 0.5</td><td>0.44<sup>+0.23</sup><sub>-0.09</sub></td><td>-20 ± 10</td><td>75 ± 12</td><td>135 ± 10</td><td>362<sup>+109</sup><sub>-126</sub></td><td>55<sup>+11</sup><sub>-17</sub></td><td>6.5<sup>+2.4</sup><sub>-1.8</sub></td><td>376<sup>+106</sup><sub>-123</sub></td><td>34<sup>+23</sup><sub>-19</sub></td><td>1, 2, 3, 5</td></tr><tr><td>Deep3a-6397</td><td>5.9<sup>+0.6</sup><sub>-0.9</sub></td><td>0.50<sup>+0.21</sup><sub>-0.13</sub></td><td>-80 ± 5</td><td>7<sup>+7</sup><sub>-6</sub></td><td>150 ± 25</td><td>351<sup>+138</sup><sub>-107</sub></td><td>59<sup>+13</sup><sub>-17</sub></td><td>6.0<sup>+2.6</sup><sub>-1.6</sub></td><td>367<sup>+134</sup><sub>-101</sub></td><td>37<sup>+33</sup><sub>-18</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>Deep3a-15504</td><td>6.0 ± 0.4</td><td>0.57<sup>+0.18</sup><sub>-0.16</sub></td><td>-35 ± 5</td><td>7 ± 5</td><td>150 ± 20</td><td>305<sup>+138</sup><sub>-80</sub></td><td>63<sup>+13</sup><sub>-15</sub></td><td>4.8<sup>+1.8</sup><sub>-1.1</sub></td><td>327<sup>+130</sup><sub>-74</sub></td><td>30<sup>+28</sup><sub>-12</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>K20-ID6</td><td>3.9 ± 0.3</td><td>0.52<sup>+0.22</sup><sub>-0.14</sub></td><td>60 ± 10</td><td>23 ± 11</td><td>100 ± 30</td><td>236<sup>+128</sup><sub>-95</sub></td><td>29 ± 13</td><td>8.1<sup>+6.0</sup><sub>-3.1</sub></td><td>242<sup>+124</sup><sub>-90</sub></td><td>11<sup>+14</sup><sub>-6</sub></td><td>1, 2, 3, 4</td></tr><tr><td>K20-ID7</td><td>8.4 ± 1.1</td><td>0.91<sup>+0.06</sup><sub>-0.16</sub></td><td>25 ± 5</td><td>7 ± 5</td><td>210 ± 25</td><td>254<sup>+69</sup><sub>-28</sub></td><td>49 ± 15</td><td>5.2<sup>+2.3</sup><sub>-0.8</sub></td><td>270<sup>+68</sup><sub>-27</sub></td><td>28<sup>+17</sup><sub>-5</sub></td><td>1, 2</td></tr><tr><td>GMASS-2303</td><td>1.6 ± 0.5</td><td>0.78<sup>+0.11</sup><sub>-0.17</sub></td><td>-60 ± 20</td><td>79 ± 24</td><td>63 ± 10</td><td>127<sup>+64</sup><sub>-26</sub></td><td>40 ± 14</td><td>3.2<sup>+2.2</sup><sub>-0.7</sub></td><td>146<sup>+59</sup><sub>-22</sub></td><td>1.6<sup>+1.4</sup><sub>-0.4</sub></td><td>1, 2</td></tr><tr><td>GMASS-2363</td><td>2.3 ± 0.6</td><td>0.87<sup>+0.07</sup><sub>-0.10</sub></td><td>55 ± 10</td><td>6 ± 10</td><td>105 ± 10</td><td>168<sup>+45</sup><sub>-21</sub></td><td>32<sup>+19</sup><sub>-17</sub></td><td>5.3<sup>+5.0</sup><sub>-1.7</sub></td><td>178<sup>+45</sup><sub>-13</sub></td><td>3.4<sup>+1.9</sup><sub>-0.6</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>GMASS-2540</td><td>8.5 ± 1.0</td><td>0.52<sup>+0.21</sup><sub>-0.14</sub></td><td>20 ± 30</td><td>66 ± 35</td><td>125 ± 40</td><td>266<sup>+122</sup><sub>-107</sub></td><td>20<sup>+11</sup><sub>-9</sub></td><td>13<sup>+9</sup><sub>-6</sub></td><td>269<sup>+123</sup><sub>-105</sub></td><td>29<sup>+33</sup><sub>-18</sub></td><td>...</td></tr><tr><td>SA12-6339</td><td>1.2<sup>+1.4</sup><sub>-0.6</sub></td><td>0.78<sup>+0.14</sup><sub>-0.23</sub></td><td>40 ± 20</td><td>51<sup>+38</sup><sub>-37</sub></td><td>25 ± 8</td><td>58<sup>+44</sup><sub>-24</sub></td><td>25<sup>+42</sup><sub>-8</sub></td><td>2.3 ± 1.5</td><td>74<sup>+81</sup><sub>-6</sub></td><td>0.31<sup>+1.84</sup><sub>-0.08</sub></td><td>Irr</td></tr><tr><td>ZC400528</td><td>2.4 ± 0.7</td><td>0.61<sup>+0.17</sup><sub>-0.18</sub></td><td>80 ± 20</td><td>35 ± 22</td><td>150 ± 25</td><td>341<sup>+184</sup><sub>-89</sub></td><td>28<sup>+23</sup><sub>-15</sub></td><td>12<sup>+14</sup><sub>-5</sub></td><td>344<sup>+186</sup><sub>-84</sub></td><td>13<sup>+15</sup><sub>-6</sub></td><td>1, 2, 3, 5</td></tr><tr><td>ZC400569</td><td>7.4<sup>+1.3</sup><sub>-1.5</sub></td><td>0.98<sup>+0.01</sup><sub>-0.02</sub></td><td>15 ± 15</td><td>11 ± 15</td><td>263 ± 10</td><td>312<sup>+19</sup><sub>-13</sub></td><td>41<sup>+23</sup><sub>-21</sub></td><td>7.6<sup>+5.0</sup><sub>-2.1</sub></td><td>321<sup>+25</sup><sub>-12</sub></td><td>36<sup>+8</sup><sub>-6</sub></td><td>Irr</td></tr><tr><td>ZC400569N</td><td>7.1 ± 1.4</td><td>0.71<sup>+0.13</sup><sub>-0.17</sub></td><td>70 ± 15</td><td>32 ± 18</td><td>220 ± 25</td><td>364<sup>+138</sup><sub>-64</sub></td><td>43<sup>+16</sup><sub>-21</sub></td><td>8.5<sup>+7.2</sup><sub>-1.8</sub></td><td>372<sup>+136</sup><sub>-63</sub></td><td>46<sup>+38</sup><sub>-16</sub></td><td>1, 2, 3, 5</td></tr><tr><td>ZC401925</td><td>2.6 ± 0.6</td><td>0.78<sup>+0.13</sup><sub>-0.21</sub></td><td>60 ± 10</td><td>60 ± 12</td><td>55 ± 20</td><td>96<sup>+62</sup><sub>-34</sub></td><td>59<sup>+18</sup><sub>-19</sub></td><td>1.6<sup>+1.2</sup><sub>-0.5</sub></td><td>145<sup>+57</sup><sub>-30</sub></td><td>2.5<sup>+2.6</sup><sub>-1.0</sub></td><td>1</td></tr><tr><td>ZC403741</td><td>2.2<sup>+0.4</sup><sub>-0.3</sub></td><td>0.55<sup>+0.11</sup><sub>-0.13</sub></td><td>25 ± 10</td><td>20 ± 19</td><td>70 ± 8</td><td>189<sup>+73</sup><sub>-36</sub></td><td>36<sup>+13</sup><sub>-12</sub></td><td>5.2<sup>+2.9</sup><sub>-1.1</sub></td><td>201<sup>+74</sup><sub>-34</sub></td><td>4.1<sup>+1.4</sup><sub>-1.3</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>ZC404221</td><td>0.8 ± 0.6</td><td>0.78<sup>+0.14</sup><sub>-0.18</sub></td><td>90 ± 20</td><td>77 ± 20</td><td>38 ± 13</td><td>100<sup>+44</sup><sub>-46</sub></td><td>29<sup>+40</sup><sub>-8</sub></td><td>3.4<sup>+1.1</sup><sub>-2.2</sub></td><td>114<sup>+70</sup><sub>-20</sub></td><td>0.48<sup>+1.43</sup><sub>-0.15</sub></td><td>Irr</td></tr><tr><td>ZC405226</td><td>5.4 ± 0.8</td><td>0.82<sup>+0.10</sup><sub>-0.12</sub></td><td>-40 ± 10</td><td>26 ± 14</td><td>100 ± 23</td><td>143<sup>+45</sup><sub>-36</sub></td><td>58<sup>+19</sup><sub>-18</sub></td><td>2.5<sup>+1.1</sup><sub>-0.6</sub></td><td>178<sup>+45</sup><sub>-32</sub></td><td>8.0<sup>+5.0</sup><sub>-2.6</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>ZC405501</td><td>5.8 ± 0.9</td><td>0.97<sup>+0.02</sup><sub>-0.07</sub></td><td>10 ± 5</td><td>1 ± 5</td><td>85 ± 15</td><td>101<sup>+23</sup><sub>-16</sub></td><td>52<sup>+16</sup><sub>-13</sub></td><td>1.9<sup>+0.6</sup><sub>-0.4</sub></td><td>139<sup>+28</sup><sub>-17</sub></td><td>5.2<sup>+2.3</sup><sub>-1.4</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>ZC406690</td><td>7.0 ± 1.2</td><td>0.44<sup>+0.23</sup><sub>-0.09</sub></td><td>-70 ± 10</td><td>7 ± 12</td><td>120 ± 10</td><td>313<sup>+88</sup><sub>-107</sub></td><td>60<sup>+16</sup><sub>-15</sub></td><td>5.3<sup>+1.6</sup><sub>-1.7</sub></td><td>332<sup>+88</sup><sub>-97</sub></td><td>36<sup>+21</sup><sub>-18</sub></td><td>1, 2, 3, 4</td></tr><tr><td>ZC407302</td><td>3.6 ± 1.2</td><td>0.91<sup>+0.05</sup><sub>-0.09</sub></td><td>55 ± 5</td><td>8 ± 6</td><td>165 ± 35</td><td>217<sup>+71</sup><sub>-40</sub></td><td>56<sup>+11</sup><sub>-25</sub></td><td>3.9<sup>+2.8</sup><sub>-0.6</sub></td><td>240<sup>+62</sup><sub>-39</sub></td><td>9.6<sup>+6.0</sup><sub>-3.8</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>ZC407376</td><td>5.5<sup>+0.7</sup><sub>-0.3</sub></td><td>0.97<sup>+0.02</sup><sub>-0.04</sub></td><td>20 ± 25</td><td>5 ± 25</td><td>73 ± 18</td><td>86<sup>+24</sup><sub>-20</sub></td><td>56<sup>+28</sup><sub>-27</sub></td><td>1.6<sup>+1.0</sup><sub>-0.5</sub></td><td>134<sup>+46</sup><sub>-32</sub></td><td>4.6<sup>+3.8</sup><sub>-2.0</sub></td><td>Irr</td></tr><tr><td>ZC407376S</td><td>1.6 ± 0.5</td><td>0.60 ± 0.18</td><td>-60 ± 10</td><td>8 ± 14</td><td>35 ± 18</td><td>89<sup>+65</sup><sub>-49</sub></td><td>77<sup>+37</sup><sub>-41</sub></td><td>1.2<sup>+1.4</sup><sub>-0.5</sub></td><td>167<sup>+86</sup><sub>-57</sub></td><td>2.1<sup>+3.1</sup><sub>-1.3</sub></td><td>Irr</td></tr><tr><td>ZC407376N</td><td>1.4 ± 0.3</td><td>0.83<sup>+0.09</sup><sub>-0.13</sub></td><td>60 ± 10</td><td>6 ± 14</td><td>58 ± 15</td><td>113<sup>+45</sup><sub>-30</sub></td><td>35 ± 14</td><td>3.2<sup>+2.3</sup><sub>-0.9</sub></td><td>130<sup>+48</sup><sub>-24</sub></td><td>1.1<sup>+0.9</sup><sub>-0.2</sub></td><td>1, 2</td></tr><tr><td>ZC409985</td><td>1.9 ± 0.2</td><td>0.76<sup>+0.11</sup><sub>-0.16</sub></td><td>-15 ± 20</td><td>1 ± 20</td><td>20 ± 8</td><td>38<sup>+20</sup><sub>-14</sub></td><td>39<sup>+15</sup><sub>-13</sub></td><td>0.97<sup>+0.57</sup><sub>-0.30</sub></td><td>80<sup>+30</sup><sub>-20</sub></td><td>0.57<sup>+0.52</sup><sub>-0.26</sub></td><td>Irr</td></tr><tr><td>ZC410041</td><td>4.7 ± 1.2</td><td>1.00<sup>+0.00</sup><sub>-0.03</sub></td><td>-55 ± 10</td><td>9 ± 10</td><td>88 ± 10</td><td>101<sup>+15</sup><sub>-9</sub></td><td>48<sup>+14</sup><sub>-16</sub></td><td>2.1<sup>+0.9</sup><sub>-0.4</sub></td><td>134<sup>+22</sup><sub>-15</sub></td><td>3.9<sup>+1.7</sup><sub>-1.3</sub></td><td>1, 2, 3, 4, 5</td></tr><tr><td>ZC410123</td><td>3.2 ± 0.7</td><td>0.94<sup>+0.03</sup><sub>-0.07</sub></td><td>35 ± 25</td><td>19 ± 26</td><td>63 ± 15</td><td>81<sup>+24</sup><sub>-17</sub></td><td>60<sup>+25</sup><sub>-26</sub></td><td>1.4<sup>+0.9</sup><sub>-0.4</sub></td><td>137<sup>+44</sup><sub>-32</sub></td><td>2.8<sup>+2.4</sup><sub>-1.3</sub></td><td>1</td></tr><tr><td>ZC411737</td><td>1.8 ± 0.2</td><td>0.78<sup>+0.14</sup><sub>-0.18</sub></td><td>-60 ± 10</td><td>41 ± 12</td><td>73 ± 18</td><td>139<sup>+36</sup><sub>-36</sub></td><td>38<sup>+20</sup><sub>-18</sub></td><td>3.7<sup>+2.8</sup><sub>-1.1</sub></td><td>156<sup>+61</sup><sub>-32</sub></td><td>2.0<sup>+2.0</sup><sub>-0.8</sub></td><td>1, 2</td></tr><tr><td>ZC412369</td><td>3.1 ± 1.1</td><td>0.90<sup>+0.05</sup><sub>-0.08</sub></td><td>-70 ± 20</td><td>16 ± 22</td><td>80 ± 20</td><td>120<sup>+49</sup><sub>-27</sub></td><td>75<sup>+13</sup><sub>-27</sub></td><td>1.6<sup>+1.0</sup><sub>-0.3</sub></td><td>182<sup>+37</sup><sub>-27</sub></td><td>4.8<sup>+2.8</sup><sub>-1.9</sub></td><td>1</td></tr><tr><td>ZC413507</td><td>2.6 ± 0.5</td><td>0.77<sup>+0.13</sup><sub>-0.20</sub></td><td>-35 ± 10</td><td>13 ± 12</td><td>70 ± 20</td><td>132<sup>+69</sup><sub>-40</sub></td><td>42<sup>+27</sup><sub>-19</sub></td><td>3.1<sup>+2.5</sup><sub>-0.9</sub></td><td>153<sup>+70</sup><sub>-35</sub></td><td>2.8<sup>+3.1</sup><sub>-1.2</sub></td><td>1, 2</td></tr><tr><td>ZC413597</td><td>1.6 ± 0.5</td><td>0.78<sup>+0.13</sup><sub>-0.18</sub></td><td>45 ± 40</td><td>30 ± 41</td><td>48 ± 10</td><td>92<sup>+52</sup><sub>-24</sub></td><td>38<sup>+21</sup><sub>-18</sub></td><td>2.4<sup>+2.6</sup><sub>-0.8</sub></td><td>115<sup>+54</sup><sub>-19</sub></td><td>0.98<sup>+1.24</sup><sub>-0.34</sub></td><td>Irr</td></tr><tr><td>ZC415876</td><td>2.4 ± 1.0</td><td>0.64<sup>+0.16</sup><sub>-0.19</sub></td><td>-50 ± 15</td><td>30 ± 41</td><td>73 ± 15</td><td>153<sup>+105</sup><sub>-41</sub></td><td>47<sup>+13</sup><sub>-19</sub></td><td>3.2<sup>+3.0</sup><sub>-0.7</sub></td><td>176<sup>+98</sup><sub>-34</sub></td><td>3.5<sup>+4.4</sup><sub>-1.3</sub></td><td>1, 2, 3, 4, 5</td></tr></tbody></table>

### Notes.

a Adopted half-light radius and galaxy inclination, from the best-fit Sérsic model to HST H-band imaging, when available (Tacchella et al. 2015b), or to the Hα maps otherwise (Table 5, using the PSF<sub>2 G,ave</sub> case). Exceptions are five compact sources (Q2343-BX513, ZC401925, ZC404221, ZC411737, and ZC413597) for which we adopted the average $\langle \sin(i) \rangle = \pi/4$ for randomly inclined disks, and four large disks (Deep3a-6004, Deep3a-6397, Deep3a-15504, and ZC406690) for which we adopted the values inferred from detailed kinematic modeling (Genzel et al. 2014a, 2017), as discussed in Section 6.1.

b Kinematic misalignment, based on the PA derived from the structural fits to HST H-band imaging, when available, or to the Hα maps otherwise.

c Circular velocity and total dynamical mass in the rotating disk framework. Arguably, the $V_{rot}$ and $\sigma_0$ estimates become more uncertain for the smallest sources due to large beam smearing or for objects with observed irregular kinematics. Assuming that rotational motions still intrinsically dominate the gravitational support for the 10 objects with irregular kinematics (indicated in the rightmost column), an alternative estimate based on the integrated Hα line width with $V_c = \sigma_{rot}(H\alpha)/0.8 \sin(i)$ would yield the following values of $V_c$ and $M_{dyn}/10^{10} M_{\odot}$: Q1623-BX543: 227<sup>+22</sup><sub>-46</sub>, 7.9<sup>+0.4</sup><sub>-3.1</sub>; Q1623-BX599: 305<sup>+37</sup><sub>-90</sub>, 10<sup>+2</sup><sub>-6</sub>; Q2343-BX513: 224<sup>+17</sup><sub>-66</sub>, 6.1<sup>+0.2</sup><sub>-3.7</sub>; SA12-6339: 180<sup>+11</sup><sub>-51</sub>, 1.8<sup>+0.7</sup><sub>-1.1</sub>; ZC400569 (full system): 254<sup>+3</sup><sub>-57</sub>, 22<sup>+1</sup><sub>-10</sub>; ZC404221: 138<sup>+7</sup><sub>-42</sub>, 0.71<sup>+0.24</sup><sub>-0.40</sub>; ZC407376 (full system): 170<sup>+10</sup><sub>-29</sub>, 7.4<sup>+0.7</sup><sub>-2.4</sub>; ZC407376S: 311<sup>+52</sup><sub>-26</sub>, 7.2<sup>+1.7</sup><sub>-5.0</sub>; ZC409985: 116<sup>+9</sup><sub>-38</sub>, 1.2<sup>+0.1</sup><sub>-0.7</sub>; ZC413597: 147<sup>+8</sup><sub>-44</sub>, 1.6<sup>+0.1</sup><sub>-0.9</sub>.

d List of disk criteria fulfilled by each galaxy, as described in Section 7.1. Sources for which the observed velocity field is irregular and without a clear monotonic gradient (our disk criterion 1) are indicated with “Irr.” GMASS-2540 is not classified because of the FOV and S/N limitations of the SINFONI AO data.

Table 6 reports the derived $\Delta v_{obs}$, $\sin(i)$, $V_{rot}$, and $\sigma_0$ values along with the $V_{rot}/\sigma_0$ ratios as a measure of the relative amount of dynamical support from ordered rotation (or orbital

motions) versus random (and noncircular) motions. The uncertainties are taken as the 68% confidence intervals derived from a Monte Carlo approach (with 1000 realizations),
propagating the errors of the measurements, galaxy inclinations, sizes, masses, and PSF<sub>2 G,ave</sub> parameters to better account for the non-Gaussian nature of the uncertainties of input properties and the nonlinear functions involved. For our sample, V<sub>rot</sub> ranges from 38 to 364 km s<sup>-1</sup>, with a mean and median of 181 and 141 km s<sup>-1</sup>, respectively. The σ<sub>0</sub> estimates are between 20 and 77 km s<sup>-1</sup>, with a mean of 49 and nearly identical median of 51 km s<sup>-1</sup>. The V<sub>rot</sub>/σ<sub>0</sub> ratios span the range from 0.97 to 13, with an average of 4.1 and median of 3.2. These values compare well with the ensemble properties of 1.4 < z < 2.6 disks that are sufficiently resolved in the seeing-limited data of the parent SINS/zC-SINF sample and the KMOS<sup>3D</sup> survey with the VLT/KMOS multi-IFU (FS09; M11; Wisnioski et al. 2015; Burkert et al. 2016; Wuyts et al. 2016; Übler et al. 2017). Thus, our AO sample does not stand out in its global kinematic properties from larger and more complete SFG samples at z ~ 2.

## 6.3. Kinematic and Morphological Alignment

From simple geometrical arguments, the line of nodes of an axisymmetric oblate rotating disk with a smooth light distribution is expected to be aligned with its projected morphological major axis. The coincidence in PAs from the kinematics and morphology is thus generally a criterion in determining the nature of a galaxy. In practice, complications arise for a variety of physical reasons (e.g., presence of nonaxisymmetric structures, nearby companions with overlapping outer isophotes, spatially nonuniform extinction), compounded by surface brightness sensitivity and spatial resolution limitations for high-redshift galaxies.

We examined the agreement between the derived kinematic position angle PA<sub>kin</sub> (Section 4.3) and the morphological position angle PA<sub>morph</sub>, quantified via the “kinematic misalignment” ΔPA = |PA<sub>kin</sub> - PA<sub>morph</sub>|. We exclude GMASS-2540 here because it is not fully covered by the SINFONI AO data and because of its low Hα surface brightness emission hampering a reliable PA<sub>kin</sub> determination. Following the same motivation as in Section 6.1, we adopted as PA<sub>morph</sub> the PA from the H-band morphologies, when available, and from the Hα maps otherwise. As noted in Section 5.4, the PA<sub>Hα</sub> and PA<sub>H</sub> are similar within 1.5σ, and we verified that our conclusions would not be affected by instead adopting PA<sub>Hα</sub> for all objects.

For our sample, the mean and median ΔPA are 23° and 13°, respectively. For 73% of the galaxies, the alignment is better than 30°. Figure 8 shows the PA offsets as a function of the adopted axis ratio q and effective radius R<sub>e</sub>. Not unexpectedly, and as seen in other high-redshift samples (e.g., Wisnioski et al. 2015; Harrison et al. 2017), our galaxies broadly follow a trend of increasing ΔPA for more face-on and smaller sources. Of the 10 objects with ΔPA > 30°, eight are compact sources with distortions/extensions in their outer isophotes, asymmetric light distributions in their inner brighter regions, or little or irregular velocity structure (Q1623-BX502, Q1623-BX513, GMASS-2303, SA12-6339, ZC400528, ZC401925, ZC404221, and ZC411737). The other two sources are large, massive, and fairly face-on disks for which the misalignment can be attributed to morphological features (a noncircular ring with a clump on one side for Deep3a-6004 and clumps in a tail-like structure for ZC400569N; see Section 7.2 for more details).

From the case-by-case inspection of our galaxies, it is clear that while it provides a useful indication, the kinematic misalignment should be used with caution when classifying high-redshift objects as disks versus nondisks. Asymmetric morphological features can

<figure><img src="image_11.png" /><figcaption>**Figure 8.** Kinematic misalignment ΔPA as a function of morphological axis ratio q for the SINS/zC-SINF AO sample. The symbols are color-coded and sized according to the effective radius R<sub>e</sub> of the galaxies. The five compact objects with ill-defined axis ratios and to which we assigned q = 0.64, corresponding to the ⟨sin(i)⟩ = π/4 for randomly oriented disks (Section 6.1), are plotted as squares connected with red dotted lines to their nominal best-fit q, shown as circles with a red arrow pointing toward the adopted value. Most of the well-resolved objects show very good agreement between their kinematic and morphological PAs, especially for the more edge-on systems. A larger proportion of the compact sources have ΔPA > 30°, reflecting ill-defined PAs due to irregular or fairly featureless morphologies and/or velocity fields.</figcaption></figure>

drive up the ΔPA in otherwise kinematically regular disks. The finite angular resolution and S/N will limit the ability to determine reliable PAs for compact objects. For similar reasons, the inclinations based on morphological axis ratios, in particular for cases with a large misalignment or a more face-on orientation, may be very uncertain or even wrong (see also, e.g., the discussions by Wuyts et al. 2016 and Rodrigues et al. 2017). Ideally, inclinations should be validated with kinematic modeling when possible, as done in Section 6.1.

## 6.4. Circular Velocities and Dynamical Masses

With the intrinsic structural and kinematic properties derived in the previous sections, we calculated the circular velocities and dynamical masses in the rotating disk framework as

$$V_c = (V_{\text{rot}}^2 + 3.36 \sigma_0^2)^{0.5} \quad (1)$$

and

$$M_{\text{dyn}} = 2 \times R_e V_c^2 / G \quad (2)$$

(Binney & Tremaine 2008; Burkert et al. 2010, 2016), where G is the gravitational constant. In Equation (1), the dispersion term accounts for pressure support in an exponential distribution, which is significant for our galaxies given their typically low V<sub>rot</sub>/σ<sub>0</sub> ~ 3–4 ratios. Equation (2) corresponds to the total disk mass in the spherical approximation (for an infinitely thin Freeman disk, the M<sub>dyn</sub> values would scale down by a factor of 0.8; Binney & Tremaine 2008). The circular velocities and dynamical masses are reported in Table 6, with uncertainties
derived from a Monte Carlo approach, as for the $V_{rot}$ and $\sigma_0$ estimates.

Equations (1) and (2) rely on two simplifying but important assumptions. First, it is assumed that all galaxies are rotating disks. As discussed in more detail in Section 7, the kinematic properties of the majority of the galaxies are disklike. If rotational motions still intrinsically dominate the gravitational support (either disk rotation or orbital motions) for the 10 objects with observed irregular (or featureless) kinematics, estimates can be obtained, for instance, from the integrated $H\alpha$ line width with $V_c = \sigma_{tot}(H\alpha)/0.8 \sin(i)$ (following, e.g., van Dokkum et al. 2015; Wisnioski et al. 2018 but neglecting the contribution from outflowing gas and the explicit split of pressure support; see also, e.g., Rix et al. 1997; Weiner et al. 2006). The $V_c$ values in that case are typically a factor of 1.4 higher, and the $M_{dyn}$ are about twice higher.

Second, it is assumed that the mass distribution is exponential. Again, this is roughly the case for most of the galaxies in our sample (see Section 5). To gauge the impact of deviations from $n=1$, we recomputed $V_c$ and $M_{dyn}$, applying the corrections for Sérsic index and dispersion truncation described by Romanowsky & Fall (2012) and Burkert et al. (2016). The $V_c$ and $M_{dyn}$ values scale by factors in the range 0.6–1.9 and 0.4–3.6, respectively, but the overall changes are small, with an average increase of 8% in $V_c$ and 22% in $M_{dyn}$ and a median increase of only ~1% in both quantities (reflecting the mean and median $n$ close to 1 of the sample).

The $M_{dyn}$ estimates derived here agree well with the results obtained from the more detailed kinematic modeling of 19 of the galaxies presented by Genzel et al. (2014a, 2017). Excluding GMASS-2540, the average (median) differences amount to 0.11 (0.17) dex, smaller than the typical uncertainties of our estimates (0.34 dex) and comparable to those of the modeling results (0.15 dex). Whereas a modeling approach is more accurate by better taking into account details of the mass distribution (such as possible bulge and disk components), the agreement between the simpler approach and the modeling-based results is reassuring and indicates that the beam-smearing corrections applied and the galaxy parameters adopted (Sections 6.1 and 6.2) are overall satisfactory.

## 7. Nature of the Galaxies

In this section, we revisit the classification of the SINS/zC-SINF AO targets and highlight features of interest in several of the targets. This analysis updates previous results with the now-complete sample and SINFONI AO data sets and summarizes findings from more detailed case studies presented elsewhere (Cresci et al. 2009; FS09; Genzel et al. 2006, 2008, 2011, 2014a, 2017; Newman et al. 2013; Shapiro et al. 2008; Tacchella et al. 2015a, 2015b, 2018).

### 7.1. Kinematic Classification

The higher resolution of the AO observations allows us to better assess the nature of compact objects and reveals more detail in the $H\alpha$ morphologies and kinematics of the larger sources. To characterize these details quantitatively and accurately relies on very high S/N over many resolution elements such that all components of the mass model (e.g., bulge and disk) can be well determined and perturbations can be well constrained (e.g., Krajnović et al. 2006). This is only possible for a small subset of our sample (e.g., Shapiro

et al. 2008; Genzel et al. 2014a, 2017). We focus here on a simpler approach that can be applied to every galaxy, with the aim of distinguishing between disks and nondisks. The full system ZC400569 and its massive northern component ZC400569N are considered individually, and so are the full ZC407376 and its two clearly separated components. The very large and low surface brightness GMASS-2540 is excluded, but we note that despite the FOV and S/N limitations, the SINFONI AO data suggest that it is a large, low-inclination clumpy disk.

We classified an object as disklike (hereafter simply “disk”) if at least one of the following criteria is satisfied (analogous to the set presented by Wisnioski et al. 2015).

1. The velocity field exhibits a monotonic gradient with well-defined kinematic PA; in the larger systems with high-S/N data, this corresponds to the detection of a “spider” diagram (van der Kruit & Allen 1978).

2. The ratio $V_{rot}/\sigma_0$ is above $\sqrt{3.36}$, corresponding to the value at which rotation starts to dominate over velocity dispersion in the dynamical support within $R_c$ for $n=1$ turbulent disks (Section 6.4).

3. The position of the steepest velocity gradient, at the midpoint between the velocity extrema along the kinematic axis, coincides with the observed peak of velocity dispersion within the uncertainties (≈2 pixels); this position defines the kinematic center (Section 4.3).

4. The morphological and kinematic PAs agree, with $\Delta PA \le 30^\circ$.

5. The kinematic center coincides within 2 pixels (0.1 arcsec) with the light-weighted center of the continuum emission (or mass-weighted center of the stellar mass distribution, when available) as a proxy for the gravitational potential; in most cases, the continuum and stellar mass maps are fairly smooth and regular, such that the weighted center is located at/near the central peak and usually corresponds to a bulge-like component in the more massive galaxies.

Table 6 lists the disk criteria fulfilled by each galaxy; in cases in which a source does not meet the necessary first criterion, it is marked as irregular (“Irr”).

Not counting the full systems ZC400569 and ZC407376, 27 of the other 35 classified objects satisfy the first criterion of a disklike velocity gradient. In a majority of them (16), a flattening or even a turnover is observed in the velocity curve along the kinematic axis; the more demanding detection of a spider diagram is typically—but not exclusively—fulfilled by the larger objects with higher S/N. When adding the second criterion, 24 of the objects are rotation-dominated disks. Various thresholds in $V_{rot}/\sigma_0$ have been used in the literature; all objects with disklike velocity gradients in our sample have a ratio above 1, and a large majority (20) still have a ratio above 3. Among the 24 rotation-dominated disks, 15 exhibit a clear peak in their velocity dispersion at/near the position of steepest velocity gradient and thus meet the third criterion. In three additional cases, the dispersion profile is fairly flat, which can be attributed primarily to the low mass and low-to-modest central mass concentration of these objects.

Considering the last two criteria involving morphologies, 14 of the 18 rotation-dominated disks with centrally peaked or flat dispersion profiles satisfy $\Delta PA \le 30^\circ$, and 11 of them also have their kinematic and continuum/mass centers coincident. However, the four galaxies that drop because of a large PA
misalignment show nearly coincident centers. The misalign-
ment is driven by extended low-level emission affecting the
outer isophotes (Q1623-BX502, ZC400528, and ZC400569N)
or bright off-center clumps and possible deviations from disk
circularity (Deep3a-6004). Two of the three galaxies that have
aligned PAs but offset centers exhibit a prominent clumpy
ringlike structure even in H-band light and stellar mass maps
(Q2346-BX482 and ZC406690); the light-weighted center is
just marginally off the kinematic center (by about 2.5 pixels, or
0.′′13) and obviously affected by the asymmetric clump
distribution along the ring. When considering the geometric
center (i.e., unweighted) or the center of the outer isophotes,
these two galaxies would then satisfy the fifth criterion as well.
The third source that meets all but this criterion has a
significant projected neighboring source in continuum light and
overall lower Hα S/N ratio such that the center positions are
more uncertain (K20-ID6).

Ten objects do not exhibit a disklike velocity gradient, including the full systems ZC400569 and ZC407376 (although one component of each is classified as a disk). The other eight objects tend to lack any kinematic structure, with some of them having nearby companions and others showing little morphological structure. The lack of kinematic structure could reflect an intrinsic dynamical property or result from projection effects (e.g., in nearly face-on disks) and beam smearing. All eight of these sources are compact ($R_e = 0.8–3.3$ kpc), with low $\Delta v_{\text{obs}}/2 \sim 20–90$ km s$^{-1}$ and inferred $V_{\text{rot}}/\sigma_0$ ratios below or within $1\sigma$ of 1.8.

In summary, ~70% of the objects in our AO sample satisfy criteria 1–3 and are thus kinematically classified rotation-dominated disks. The other ~30% have observed properties that are not compatible with signatures of rotation in an inclined disk, i.e., exhibit clearly irregular or fairly featureless 2D kinematics in the data.

7.2. Features of Note in Individual Galaxies

Obviously, the set of disk criteria above is somewhat simplistic. It is designed assuming ideal smooth rotating disks and neglects the signatures of internally or externally driven perturbations caused by nonaxisymmetric substructures such as massive disk clumps, bars, and spiral arms or induced by minor mergers and interactions (e.g., Bournaud et al. 2007; Ceverino et al. 2012; Genel et al. 2012), which may also be difficult to disentangle from each other. Low-inclination disks may appear as fairly featureless in their velocity field and dispersion maps, and the kinematic misalignment may be more affected by asymmetric features, star-forming clumps, or possible deviations from circularity (e.g., Wuyts et al. 2016). Some merger configurations can mimic the smooth monotonic disklike velocity gradients of ordered disk rotation, or out-of-equilibrium disks can form in late merger stages (e.g., Law et al. 2006; Robertson et al. 2006; Robertson & Bullock 2008; Shapiro et al. 2008).

Equally importantly, however, the simple classification does
not capture the richness of information about individual
 galaxies provided by the high-quality AO data sets. The
comparison presented in Appendix E illustrates the gain in
detail for each galaxy between the seeing-limited and AO data,
from both the higher resolution and our observing strategy
emphasizing S/N. Figure 9 further demonstrates the impor-
tance of sensitivity in recovering the nature and properties of a

<figure><img src="image_12.png" /></figure>

**Figure 9.** SINFONI AO-assisted maps of K20-ID7 as a function of integration time. Each row shows the Hα line map (left panel) and the velocity field (right panel) extracted from the data cube after each hour of integration, up to the total time of 7 hr obtained for this source. The (linear) color coding for the line maps and velocity fields is the same for all rows. The angular scale and PSF FWHM are indicated in each panel by the vertical bar and white filled circle, respectively. With just a few hours of integration, only the brightest regions are detected, and one would infer that this object is morphologically and kinematically irregular. The full extent of the source and its nature become apparent only after ~5 hr.
source, especially when surface brightness variations are large and asymmetric. The figure shows the Hα line map and velocity field of K20-ID7 extracted from data cubes in a sequence of increasing on-source integration time. With a few hours of integration, the source would be classified as irregular and rather small; only after 5 hr or more does the large extent and overall regular velocity field of the main source become apparent, along with the connection to the small physically associated low-mass companion to the south.

Given the amount of detail seen in many of the AO data sets, attempting a more refined classification as done in Section 7.1 becomes arguably subjective without detailed quantitative analysis and modeling, which is beyond the scope of the present paper. Nonetheless, it is instructive to highlight selected objects that most prominently exhibit several of the features mentioned above and whose nature is best revealed by the high-resolution AO data.

1. Deep3a-15504—This galaxy was the first object we observed with SINFONI+AO and has the deepest data of our survey (23 hr). It is a large, high-mass, rotating disk with a massive bulge seen in the rest-optical continuum light and stellar mass maps, causing a steep inner velocity gradient, several modestly bright Hα-emitting star-forming clumps are distributed across the disk, and an AGN revealed by diagnostic rest-UV and optical line emission drives a nuclear outflow that is spatially extended and anisotropic in broad Hα+[N II] emission (Genzel et al. 2006, 2008, 2014a; Förster Schreiber et al. 2014; Tacchella et al. 2015a). It is one of the objects for which the detected emission extends sufficiently far out to probe the decline in the outer disk rotation curve recently discovered in $z \sim 1-2.5$ SFGs (Genzel et al. 2017; Lang et al. 2017). The kinematics show a strong velocity gradient along the minor axis toward the center, characteristic of gas inflow in the disk and/or outflow. A small, faint, low-mass source is detected in continuum and Hα at the north edge of the disk, redshifted by $140 \text{ km s}^{-1}$ relative to the disk rotation at that location, consistent with an $\sim 1:30$ minor merging event (Genzel et al. 2017).

2. ZC 400569—This target is one with most complex structure in Hα among our sample and also one of the deepest SINFONI+AO data sets (22.5 hr). The velocity difference across the full extent of the source reaches $570 \text{ km s}^{-1}$, with a change of orientation of the isovelocity contours from north to south and a chain of Hα knots southward of the brightest northern peak. The northern component is a massive rotating disk hosting a significant bulge, while the main southern knots $1''$0 and $1''$5 to the south are associated with lower-mass satellites with $\sim 5\%$ and $2.3\%$, respectively, of the stellar mass of the main disk (Tacchella et al. 2015a; Genzel et al. 2017). It is another of the individual galaxies with the best evidence for a dropping outer rotation curve discussed in detail by Genzel et al. (2017), and it is also one of the objects where broad line emission signatures of an AGN-driven wind are detected and spatially resolved in the AO data (Förster Schreiber et al. 2014).

3. ZC 406690—This disk has the most prominent clumpy ring among our targets, with very little Hα and continuum emission detected inside the ring. Intense star formation in the clumps drives powerful outflows, whose broad and blueshifted emission in the southwest part of the ring

(Newman et al. 2012b) causes the local perturbations apparent in our velocity and dispersion maps (extracted with single-Gaussian line fits). The kinematics in the inner regions of the galaxy suggest the presence of a significant central mass concentration, although its nondetection at rest-optical wavelengths would imply that it is very highly dust-obscured or mostly in cold gas form (Tacchella et al. 2015b; Genzel et al. 2017). ZC406690 exhibits the steepest falloff detected in the outer disk rotation curve among the sample discussed by Genzel et al. (2017). The properties of the faint continuum and Hα source $1''$6 west of the center imply that it is a small satellite with $\sim 15\%$ of the stellar mass of the main disk.

4. Q2343-BX610—Another of the best rotating disk examples among our sample, Q2343-BX610 also has no evidence of a physically associated neighbor in the available data. It exhibits signatures of gas outflows driven by a weak or obscured AGN in the center and by star formation at the location of the bright southern clump (Förster Schreiber et al. 2014). Its rest-optical morphology shows bar- and spiral-like features (Förster Schreiber et al. 2011a), which could cause the deviations from pure rotation along the minor axis observed in the kinematics.

5. Deep3a-6004—This massive galaxy exhibits very compelling characteristics of a disk but with nearly orthogonal kinematic and morphological major axes ($\Delta PA = 75^\circ \pm 12^\circ$). The inclination inferred from kinematic disk modeling (Genzel et al. 2008, 2014a) is significantly different from that implied by the Hα axis ratio and indicates a quite face-on orientation ($i \sim 25^\circ$), such that the bright clumpy ringlike structure and possible deviations from circularity affect the kinematic misalignment more importantly. Broad Hα + [N II] with an elevated [N II]/Hα ratio associated with an AGN-driven outflow strongly dominates the line emission inside the star-forming ring, causing the apparent twist in isovelocity contours and the high-velocity dispersions at the center, where a massive bulge component is in place (Förster Schreiber et al. 2014; Tacchella et al. 2015a).

6. Q2346-BX482—This galaxy is another example of a disk with a prominent star-forming ring strongly dominated by one bright large clump, although stellar light and mass at faint levels is detected around the kinematic center based on the near-IR HST data (Genzel et al. 2008; Förster Schreiber et al. 2011a; Genzel et al. 2014a; Tacchella et al. 2015b). It is associated with a source $27 \text{ kpc}$ in projection to the southeast at a relative velocity of $+630 \text{ km s}^{-1}$, which is detected in Hα in the wider FOV of the seeing-limited SINFONI data and in CO $3-2$ line emission in IRAM Plateau de Bure interferometric observations (Tacconi et al. 2013). With a stellar mass of $\sim 25\%$ that of Q2346-BX482, this companion may have induced the small kinematic perturbations on the northwestern edge of the main galaxy discussed by Genzel et al. (2008).

7. Q2343-BX389—This large, nearly edge-on disk has a small southern companion at a projected distance of $5 \text{ kpc}$ and the same redshift within $20 \text{ km s}^{-1}$ with estimated mass $\sim 10$ times lower than that of the main northern component (Förster Schreiber et al. 2011a; Tacchella et al. 2015b). It thus represents a minor merger, consistent with the regular velocity field of the primary