The SINS/zC-SINF Survey of z ∼ 2 Galaxy Kinematics: SINFONI Adaptive Optics–assisted Data and Kiloparsec-scale Emission-line Properties^∗

The SINS Hα targets were drawn from large optical spectroscopic surveys of $z\sim 1.5\mbox{--}2.5$ candidates selected by their ${U}_{{\rm{n}}}G{ \mathcal R }$ optical colors ("BX/BM" objects; Steidel et al. 2004), K-band magnitudes (the "K20" survey at ${K}_{{\rm{s}},\mathrm{Vega}}\lt 20\,\mathrm{mag}$, Cimatti et al. 2002; the Gemini Deep Deep Survey (GDDS) at ${K}_{{\rm{s}},\mathrm{Vega}}\lt 20.6\,\mathrm{mag}$, Abraham et al. 2004), 4.5 μm magnitudes (the Galaxy Mass Assembly ultra-deep Spectroscopic Survey (GMASS) at ${m}_{4.5\mu {\rm{m}},\mathrm{AB}}\lt 23.0\,\mathrm{mag}$, 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 ≳5 × 10⁻¹⁷ erg s⁻¹ cm⁻² in existing long-slit spectroscopy (for the BX/BM objects) or expected based on the best-fit SFR_SED and A_V values. Fainter 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 deg² of the 2 deg² COSMOS field (Scoville et al. 2007). Reliable optical redshifts (z_opt) were derived for ∼6000 objects at 1.4 < z < 2.5, preselected at ${K}_{{\rm{s}}}\lt 23.5\,\mathrm{mag}$ and according to the BzK or BX/BM color criteria. The zC-SINF SINFONI targets were then culled among those within 30'' of a ${g}_{\mathrm{AB}}\lt 17\,\mathrm{mag}$ 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 ∼ 10 M_⊙ 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 ∼ 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).

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 ∼ 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 ∼25 sources covering the ${M}_{\star }-\mathrm{SFR}$ 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 (${R}_{\mathrm{Vega}}\lt 18\,\mathrm{mag}$ 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 ≳10⁻¹⁶ erg s⁻¹ cm⁻², although three fainter sources were included (GMASS-2303, GMASS-2363, and K20-ID6, with fluxes of (3–5) × 10⁻¹⁷ erg s⁻¹ 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 ${M}_{\star }-\mathrm{SFR}$ coverage in combination with the SINS AO 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 conjunction 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.

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 ${K}_{\mathrm{AB}}\lt 23\,\mathrm{mag}$—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 $\mathrm{SFR}\lt {t}_{{\rm{H}}}^{-1}$ are excluded, where ${t}_{{\rm{H}}}$ is the Hubble time at the redshift of each source. This cut removes a small fraction (17%) of all ${K}_{\mathrm{AB}}\lt 23\,\mathrm{mag}$ sources at 1.4 < z < 2.6 (and only 12% for the $2\lt z\lt 2.6$ interval encompassing ≥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).

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The SINS/zC-SINF AO and the parent seeing-limited samples cover nearly identical ranges in stellar mass and SFR (${M}_{\star }\sim 2\,\times {10}^{9}-3\times {10}^{11}\,{M}_{\odot }$, SFR ∼ 10–650 M_⊙ yr⁻¹). The median (mean) values in stellar mass and SFR are nearly the same, with ${M}_{\star }\sim 2\times {10}^{10}\,{M}_{\odot }$ (∼4 × 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 $\sim -0.35$ 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 × 10¹⁰ M_⊙, SFR ∼ 30 M_⊙ yr⁻¹, and ${(U-V)}_{\mathrm{rest}}\,\sim 0.82\,\mathrm{mag}$. 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 ${M}_{\star }-\mathrm{SFR}$ plane, ${\rm{\Delta }}\mathrm{log}{(\mathrm{sSFR})}_{\mathrm{MS}}$. 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 ${\rm{\Delta }}\mathrm{log}{(\mathrm{sSFR})}_{\mathrm{MS}}$ 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 ∼ 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)_rest color from Gaussian fits in stellar mass bins within a redshift slice³⁰ increases as a function of $\mathrm{log}({M}_{\star })$ with approximately constant slope. We thus defined the locus of SFGs in ${M}_{\star }-{(U-V)}_{\mathrm{rest}}$ space by fitting a line to these values, with the evolution over z ∼ 1–3 being mostly in the zero point. The color offset relative to relationship at the mass and redshift of an object is denoted Δ(U − V)_rest. The Δ(U − V)_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)_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_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 Hα 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 $z\sim 1.5\mbox{--}2.5$ 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.

The strategies for both SINS and zC-SINF relied on the detection of Hα 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 Hα surface brightness. This effect could plausibly set the upper envelope in the Hα 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_e of our SINFONI samples to those of the underlying 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 Hα. 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.

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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 ${R}_{{\rm{e}}}(H)$ 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, ${\rm{\Delta }}\mathrm{log}{({R}_{{\rm{e}}}^{5000})}_{\mathrm{SFGs}}$, 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.

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 03 or better. The emission lines targeted were Hα and [N ii] λλ6548, 6584 for z ≲ 3 objects and Hβ and [O iii] λλ4959, 5007 for those at z ≳ 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 $1\lt z\lt 1.6$ were selected based on their [O ii] λ 3727 emission-line flux and equivalent width, and one at z = 2.24 was selected based on rest-UV properties (Contini 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 for lensed sources, for 152 SFGs at 0.8 < z < 3.7 (without twice counting the objects in common between SINS and Law et al. 2009). Figure 3 illustrates the redshift coverage of the AO samples. Figure 4 shows the distribution in specific SFR relative to the MS as a function of M_⋆, excluding 17 lensed objects without an M_⋆ estimate. The stellar properties are adjusted to our adopted Chabrier (2003) IMF where relevant. The SFRs from SED modeling are plotted whenever available for the published samples; otherwise, the extinction-corrected Hα or Hβ-based SFRs are used. The reference SFG population in the COSMOS field, defined as in Section 2.3 but over 0.8 < z < 3.5, is also plotted.

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With 32 of 35 targets at 2 < z < 2.7, the SINS/zC-SINF AO survey constitutes the largest near-IR AO-assisted IFU sample in this redshift slice. In the same redshift interval, lensed galaxies form the next largest sample, comprising 22 objects. At M_⋆ ≲ 10¹⁰ M_⊙, the unlensed samples preferentially probe the galaxy population above the MS. While there is a large overlap in M_⋆ and sSFR ranges, the lensed samples unsurprisingly extend to the lowest masses and levels of star formation. Comparable efforts to those made at z ∼ 2 would be desirable at lower and higher redshift to better constrain the evolution of the kinematic, star formation, and physical properties from near-IR IFU data with 1–2 kpc resolution (or better) across the broad peak epoch of cosmic star formation activity. Future progress will benefit from improved statistics in combination with target selections that will ensure a more complete and uniform coverage in galaxy parameters.

The observations of the SINS/zC-SINF AO sample were carried out with SINFONI (Eisenhauer et al. 2003; Bonnet et al. 2004), mounted at the Cassegrain focus of the VLT UT4 telescope. The AO correction by the MACAO module (Bonnet et al. 2003) was performed in NGS or laser guide star (LGS) mode. The choice of mode depended on the brightness of the reference star and its distance to the science target; 18 targets were observed in NGS mode and 15 in LGS mode. For the two other galaxies, we used the LGS-SE mode; one of these targets had no suitable nearby AO reference star, and the other was at too high an airmass for stable tip-tilt correction during the observations. In LGS-SE mode, the higher-order wavefront distortions are corrected for on the laser spot at the position of the science target but not the tip-tilt motions that require a reference star.

For all objects, we selected the intermediate 50 mas pixel⁻¹ scale of SINFONI, with a nominal pixel size of 50 × 100 mas and total field of view FOV = 32 × 32. This pixel scale offers the best trade-off between high angular resolution and surface brightness sensitivity for our faint distant galaxies. Depending on the redshift of the sources, we used the K-band (z > 2) or H-band (z < 2) grating to map the main emission lines of interest (Hα and the [N ii] λλ6548, 6584 doublet). The nominal FWHM spectral resolution for the adopted pixel scale is $R\sim 5090$ in K and ∼2730 in H.

The data were collected between 2005 April and 2016 August as part of our ESO LP and other normal open-time programs and MPE guaranteed-time observations. Observing runs were scheduled in both Visitor and Service mode. The observing conditions were generally good to excellent, with clear to photometric sky transparency, median seeing of 087 in the optical (055 in the near-IR at the airmass of the observations), and a median atmospheric coherence time ${\tau }_{0}$ of 3.5 ms. Table 2 summarizes the observations for each target, with the band/grating, AO mode, instrument's position angle (PA) on the sky, total on-source integration time, observing strategy and angular resolution of the data (see below), and runs during which the data were taken. Table 3 lists the observing dates for every object.

Table 2.  Summary of the SINFONI AO Observations

Source	zHα	Band	AO Modea	PAb	Ditheringc	tintd	PSF FWHMe	Run IDf
				(deg)		(s)
Q1623-BX455	2.4078	K	LGS	+90	OO	12600	011	087.A-0081
Q1623-BX502	2.1557	K	NGS	0	OO	24000	015	075.A-0466, 080.A-0330, 081.B-0568
Q1623-BX543	2.5209	K	NGS	0	OO	25200	030	087.A-0081
Q1623-BX599	2.3312	K	LGS	0	OO	37200	025	183.A-0781
Q2343-BX389	2.1724	K	LGS-SE	−45	OO	25200	020	183.A-0781
Q2343-BX513	2.1082	K	LGS	0	OO	10800	015	087.A-0081
Q2343-BX610	2.2107	K	LGS-SE	+20	OS	30000	024	183.A-0781, 088.A-0202
Q2346-BX482	2.2571	K	LGS	0	OS	44400	018	080.A-0330, 080.A-0339, 183.A-0781
Deep3a-6004	2.3871	K	LGS	0	OS	19200	016	183.A-0781, 091.A-0126
Deep3a-6397	1.5133	H	LGS	0	OS	30600	019	082.A-0396
Deep3a-15504	2.3830	K	NGS	0	OO	82800	016	076.A-0527, 183.A-0781
K20-ID6	2.2348	K	LGS	+45	OO	13200	020	080.A-0339
K20-ID7	2.2240	K	LGS	+90	OS	25800	015	183.A-0781
GMASS-2303	2.4507	K	LGS	+90	OO	15600	017	080.A-0635
GMASS-2363	2.4520	K	NGS	0	OO	49200	017	080.A-0635
GMASS-2540	1.6146	H	LGS	+90	OS	36000	017	183.A-0781
SA12-6339	2.2971	K	LGS	−20	OO	28200	014	087.A-0081
ZC400528	2.3873	K	NGS	0	OO	14400	015	183.A-0781
ZC400569	2.2405	K	NGS	+30	OS	81000	015	183.A-0781, 091.A-0126
ZC401925	2.1413	K	NGS	0	OO	21000	025	183.A-0781
ZC403741	1.4457	H	NGS	0	OO	14400	016	183.A-0781
ZC404221	2.2199	K	NGS	0	OO	14400	020	183.A-0781
ZC405226	2.2870	K	NGS	0	OO	69000	024	081.A-0672, 183.A-0781
ZC405501	2.1539	K	NGS	0	OO	20400	018	183.A-0781
ZC406690	2.1950	K	NGS	0	OS	36000	017	183.A-0781
ZC407302	2.1819	K	LGS	0	OO	68400	016	079.A-0341, 183.A-0781, 088.A-0209
ZC407376	2.1729	K	NGS	0	OO	21600	022	183.A-0781
ZC409985	2.4569	K	NGS	0	OO	18000	013	081.A-0672
ZC410041	2.4541	K	NGS	0	OO	21600	016	183.A-0781
ZC410123	2.1986	K	LGS	0	OO	7200	018	081.A-0672
ZC411737	2.4442	K	LGS	0	OO	15000	019	183.A-0781
ZC412369	2.0281	K	LGS	0	OO	14400	015	183.A-0781
ZC413507	2.4800	K	NGS	0	OO	29400	014	183.A-0781
ZC413597	2.4502	K	NGS	+90	OO	21000	017	183.A-0781
ZC415876	2.4354	K	NGS	+90	OO	21000	014	183.A-0781

Notes. The SINFONI AO data for all sources were taken with the intermediate 50 mas pixel⁻¹ scale and nominal FOV of 32 × 32.

^aAO 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. ^bPA of SINFONI for the AO observations, in degrees east of north. ^cObserving 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). ^dTotal 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). ^eThe 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 ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ defined in Section 3.3). ^fESO program number under which the data were taken (see Table 3 for more details).

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The observations were carried out in series of "observing blocks" (OBs), typically consisting of six exposures. For the majority of the targets, we adopted an efficient "on-source dithering" strategy with typical nod throws between successive exposures of about half the SINFONI FOV so as to image the source in all frames and jitter box widths of about one-tenth the FOV to minimize the number of redundant positions on the detector array. Integer+fractional pixel offsets ensured adequate sampling of the AO point-spread function (PSF), which has a FWHM typically 1–2 times the largest size of the nominal rectangular pixels. For eight of the largest sources, with Hα emission extending over ≳15, we followed an "offsets-to-sky" strategy where the exposures for background subtraction were taken at positions generally 20'' away from the target. In this scheme, the telescope pointing was alternated between the object ("O") and adjacent sky regions ("S") empty of sources in an "O–S–O–O–S–O" pattern for each OB. The pointing on the object and sky positions were also varied by about one-tenth of the FOV, ensuring an adequate sampling of the sky signal subtracted from the two object frames sharing the same sky frame. The deepest area covered by all dithered exposures of a galaxy is hereafter referred to as the "effective FOV."

The individual exposure times were 600 s, optimizing the quality of the background subtraction while remaining in the background-limited regime in the wavelength regions around the emission lines of interest. The total on-source integration times ranged from 2 to 23 hr, with an average of 8.1 hr and median of 6.0 hr. Our science requirements and the Hα properties of the sources (based on the initial seeing-limited data) typically dictated on-source integration times of ≥4 hr to reach an average S/N ∼ 5 per resolution element. Only four targets were observed for shorter times. Long integration times of 10–23 hr (typically around 15 hr) for nine targets were driven by specific science goals requiring higher S/N to reliably distinguish low-contrast features (in flux, in velocity) indicative of gas outflows, fainter clumps, or perturbations in the kinematics induced by nonaxisymmetric structures (see, e.g., Genzel et al. 2006, 2011, 2017; Newman et al. 2012b; Förster Schreiber et al. 2014).

Exposures of the acquisition stars used for the AO correction and blind offsetting to the galaxies were taken to monitor the angular resolution and positional accuracy throughout the observations. For flux calibration and atmospheric transmission correction, B-type stars and early-G dwarfs with near-IR magnitudes in the range ∼7–10 mag were observed. The telluric standards data were taken every night, as close in time and airmass as possible to each target observed during the night. Acquisition stars and telluric standards were always observed with AO and the same instrument setup as for the science objects.

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, 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.

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 011 to 030, with a mean of 018 and a median of 017. 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 001). 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 020 and 024.

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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 013–033, with a mean and median of 019 and 018, 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 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 03. 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 τ₀, 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 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ and ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$, respectively, indicate the choice of PSF.

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 ⁻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.

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 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 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.

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 Hα 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 Hα at each pixel, leaving only the amplitude to vary. Since the [N ii] line is weaker than Hα, these constraints helped to extract the flux in the fainter [N ii] emission regions. The [N ii] and Hα 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 Hα kinematic maps, we masked out pixels where the S/N of Hα 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 ≳100 km s⁻¹, and a relative dispersion uncertainty of ≳50%. For the [N ii] line and [N ii]/${\rm{H}}\alpha$ ratio maps, relying on constrained fits, valid pixels were required to satisfy an S/N > 5 in both Hα and [N ii] flux, as well as the same additional criteria as for the Hα kinematic maps. We note that since [N ii] is always weaker than Hα in our SINS/zC-SINF AO sample galaxies, since the fits to [N ii] rely on the best-fit kinematic parameters to Hα, and because of the quality cuts applied to mask out the emission maps, the resulting valid regions in the [N ii]/Hα 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 Hα 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 Hα and [N ii] surface brightness distributions and the Hα 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.

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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.

We defined the Hα 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 Hα morphological center generally coincides with the kinematic center within about 2 pixels (01). 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 Hα 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 Hα 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 Hα 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 Hα 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 (03, 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 (05; 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).

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 (01), 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]/${\rm{H}}\alpha$ ratio derived from the integrated spectrum of each source in the "total" circular aperture. The table also reports the Hα flux and [N ii]/${\rm{H}}\alpha$ 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]/${\rm{H}}\alpha$ 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]/${\rm{H}}\alpha$ 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]/${\rm{H}}\alpha$ in the elliptical apertures are typically 35% lower than those in the circular apertures.

In the simplest approach, we derived the intrinsic half-light radius from the curve of growth in circular apertures, hereafter denoted ${r}_{1/2}^{\mathrm{circ}}$. We corrected the observed half-light radius for beam smearing by subtracting the PSF half-light radius in quadrature, i.e., 0.5 × FWHM of the ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ based on circular Gaussian fits (Table 2), or as determined from the curve of growth for the ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ (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 ${r}_{1/2}^{\mathrm{circ}}$ estimates obtained with the different choices of PSF agree within the formal 1σ uncertainties. As expected, however, the differences are systematic, with the values derived with the ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ lower than those obtained with the ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ by ∼10% on average and in the median. These differences depend on galaxy size and are most significant for objects with ${r}_{1/2}^{\mathrm{circ}}\lesssim 2.5\,\mathrm{kpc}$ (corresponding to the half-light radius of the ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ at z ∼ 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$.

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 ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ and ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ 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 1σ 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ are systematically lower than those with the ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$. 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 ≈1σ uncertainties. Differences in derived Sérsic indices, axis ratios, and PAs are small (on average 6%, 14%, and 2^◦, respectively) and well within the 1σ uncertainties.

Table 5 gives the ${r}_{1/2}^{\mathrm{circ}}$ 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 ${r}_{1/2}^{\mathrm{circ}}$ values derived with the ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ 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 ${r}_{1/2}^{\mathrm{circ}}$ values should be compared to the circularized effective radii ${R}_{{\rm{e}},\mathrm{circ}}\equiv {R}_{{\rm{e}}}\,\sqrt{q}$ for better consistency. The ${r}_{1/2}^{\mathrm{circ}}$ are on average (and median) 10% larger than the R_e,circ, with a scatter of 15%. When using the individual ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$, the ${r}_{1/2}^{\mathrm{circ}}$ and R_e,circ agree within 4% on average (and median), also with a scatter of 15%.

Table 5.  Hα Sizes and Global Structural Properties

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

Notes. The measurements reported are the intrinsic half-light radius computed from the Hα curve of growth in circular apertures ${r}_{1/2}^{\mathrm{circ}}$ 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.

^aMeasurements derived with the best-fit single-Gaussian fits to the PSFs associated with each individual galaxy. ^bMeasurements derived with the best-fit double-Gaussian fit to the average, high-S/N PSF.

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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 ${r}_{1/2}^{\mathrm{circ}}$ and R_e,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 simplistically (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 ${r}_{1/2}^{\mathrm{circ}}$ and R_e,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 ${r}_{1/2}^{\mathrm{circ}}/{R}_{{\rm{e}},\mathrm{circ}}$ 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ case (1.01 and 1.11, respectively, in the ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ case). We conclude that the (small) differences in Hα 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.

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 Hα light and obviously provide a poor representation 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ (and essentially identical mean and median of $n\sim 0.7$ in the ${\mathrm{PSF}}_{1{\rm{G}},\mathrm{gal}}$ 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 Hα 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 1σ of n = 2. The sample exhibits a trend of decreasing n with larger R_e (Spearman rank correlation coefficient about ρ−0.6, significant at the 3.5σ level), reflecting the qualitative trend of shallower or more ringlike profiles toward larger galaxies that is apparent from the Hα 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 Hα, 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 Hα line maps, the rest-optical and Hα 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 $n\lt 2.5$. 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 Hα maps of the same 28 objects. This differentiation is more pronounced at higher stellar masses; galaxies with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 10.7$ 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 Hα light.

The trend of increasingly more centrally peaked morphologies in the H band versus Hα 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 Hα 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 Hα (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 Hα 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 ${M}_{\star }\gt {10}^{11}\,{M}_{\odot }$ (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.

We applied the beam-smearing corrections for velocity and velocity dispersion (denoted ${C}_{\mathrm{PSF},{\rm{v}}}$ and ${C}_{\mathrm{PSF},\sigma }$) 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$. 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 σ₀ values are measured. In velocity, there is very little dependence on galaxy inclination and mass at fixed size. In contrast, the effects on σ₀ 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$.

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.

Table 6.  Kinematic Properties and Dynamical Masses

Source	Rea	$\sin (i)$ a	PAkin	ΔPAb	${\rm{\Delta }}{v}_{\mathrm{obs}}/2$	Vrot	σ0	Vrot/σ0	Vcc	Mdync	Disk Criteriad
	(kpc)		(deg)	(deg)	(km s−1)	(km s−1)	(km s−1)		(km s−1)	(1010 M⊙)
Q1623-BX455	${2.1}_{-0.4}^{+0.8}$	${0.98}_{-0.10}^{+0.01}$	65 ± 15	${10}_{-16}^{+20}$	125 ± 15	${175}_{-17}^{+54}$	${56}_{-24}^{+15}$	${3.1}_{-0.5}^{+2.4}$	${203}_{-15}^{+51}$	${3.9}_{-0.7}^{+2.1}$	1, 2, 3, 4, 5
Q1623-BX502	1.1 ± 0.7	${0.77}_{-0.18}^{+0.12}$	45 ± 15	44 ± 16	33 ± 10	${77}_{-32}^{+50}$	${40}_{-14}^{+16}$	${2.0}_{-0.8}^{+1.5}$	${106}_{-21}^{+45}$	${0.58}_{-0.21}^{+0.77}$	1, 2, 3, 5
Q1623-BX543	${3.3}_{-0.8}^{+1.2}$	0.90 ± 0.05	0 ± 25	${4}_{-25}^{+26}$	93 ± 15	${128}_{-21}^{+29}$	${70}_{-25}^{+15}$	${1.8}_{-0.3}^{+0.9}$	${181}_{-27}^{+28}$	${5.0}_{-2.0}^{+2.4}$	Irr
Q1623-BX599	2.4 ± 0.6	${0.74}_{-0.15}^{+0.12}$	−55 ± 25	2 ± 28	80 ± 20	${139}_{-36}^{+62}$	${71}_{-27}^{+18}$	${2.0}_{-0.4}^{+1.4}$	${191}_{-35}^{+55}$	${4.1}_{-1.7}^{+3.3}$	Irr
Q2343-BX389	6.2 ± 1.2	${0.98}_{-0.06}^{+0.01}$	−50 ± 5	2 ± 5	260 ± 23	${299}_{-21}^{+40}$	${56}_{-15}^{+13}$	${5.3}_{-0.7}^{+1.7}$	${316}_{-20}^{+39}$	${29}_{-6}^{+9}$	1, 2
Q2343-BX513	${2.6}_{-0.8}^{+1.5}$	${0.78}_{-0.19}^{+0.14}$	−35 ± 10	${40}_{-12}^{+11}$	60 ± 15	${102}_{-26}^{+64}$	${55}_{-28}^{+24}$	${1.8}_{-0.5}^{+2.1}$	${144}_{-30}^{+64}$	${2.5}_{-1.2}^{+3.2}$	Irr
Q2343-BX610	4.5 ± 1.1	${0.86}_{-0.12}^{+0.08}$	−10 ± 10	27 ± 10	180 ± 25	${241}_{-38}^{+62}$	${64}_{-24}^{+17}$	${3.8}_{-0.6}^{+2.0}$	${268}_{-36}^{+60}$	${15}_{-5}^{+8}$	1, 2, 3, 4, 5
Q2346-BX482	6.0 ± 0.8	${0.88}_{-0.14}^{+0.08}$	−65 ± 5	3 ± 10	225 ± 20	${287}_{-30}^{+63}$	${58}_{-15}^{+14}$	${4.9}_{-0.7}^{+1.6}$	${306}_{-29}^{+65}$	${26}_{-5}^{+12}$	1, 2, 3, 4
Deep3a-6004	5.1 ± 0.5	${0.44}_{-0.09}^{+0.23}$	−20 ± 10	75 ± 12	135 ± 10	${362}_{-126}^{+109}$	${55}_{-17}^{+11}$	${6.5}_{-1.8}^{+2.4}$	${376}_{-123}^{+106}$	${34}_{-19}^{+23}$	1, 2, 3, 5
Deep3a-6397	${5.9}_{-0.9}^{+0.6}$	${0.50}_{-0.13}^{+0.21}$	−80 ± 5	${7}_{-6}^{+7}$	150 ± 25	${351}_{-107}^{+138}$	${59}_{-17}^{+13}$	${6.0}_{-1.6}^{+2.6}$	${367}_{-101}^{+134}$	${37}_{-18}^{+33}$	1, 2, 3, 4, 5
Deep3a-15504	6.0 ± 0.4	${0.57}_{-0.16}^{+0.18}$	−35 ± 5	7 ± 5	150 ± 20	${305}_{-80}^{+138}$	${63}_{-15}^{+13}$	${4.8}_{-1.1}^{+1.8}$	${327}_{-74}^{+130}$	${30}_{-12}^{+28}$	1, 2, 3, 4, 5
K20-ID6	3.9 ± 0.3	${0.52}_{-0.14}^{+0.22}$	60 ± 10	23 ± 11	100 ± 30	${236}_{-95}^{+128}$	29 ± 13	${8.1}_{-3.1}^{+6.0}$	${242}_{-90}^{+124}$	${11}_{-6}^{+14}$	1, 2, 3, 4
K20-ID7	8.4 ± 1.1	${0.91}_{-0.16}^{+0.06}$	25 ± 5	7 ± 5	210 ± 25	${254}_{-28}^{+69}$	49 ± 15	${5.2}_{-0.8}^{+2.3}$	${270}_{-27}^{+68}$	${28}_{-6}^{+17}$	1, 2
GMASS-2303	1.6 ± 0.5	${0.78}_{-0.17}^{+0.11}$	−60 ± 20	79 ± 24	63 ± 10	${127}_{-26}^{+64}$	40 ± 14	${3.2}_{-0.7}^{+2.2}$	${146}_{-22}^{+59}$	${1.6}_{-0.4}^{+1.4}$	1, 2
GMASS-2363	2.3 ± 0.6	${0.87}_{-0.10}^{+0.07}$	55 ± 10	6 ± 10	105 ± 10	${168}_{-21}^{+45}$	${32}_{-17}^{+19}$	${5.3}_{-1.7}^{+5.0}$	${178}_{-13}^{+45}$	${3.4}_{-0.6}^{+1.9}$	1, 2, 3, 4, 5
GMASS-2540	8.5 ± 1.0	${0.52}_{-0.14}^{+0.21}$	20 ± 30	66 ± 35	125 ± 40	${266}_{-107}^{+122}$	${20}_{-9}^{+11}$	${13}_{-6}^{+9}$	${269}_{-105}^{+123}$	${29}_{-18}^{+33}$	⋯
SA12-6339	${1.2}_{-0.6}^{+1.4}$	${0.78}_{-0.23}^{+0.14}$	40 ± 20	${51}_{-37}^{+38}$	25 ± 8	${58}_{-24}^{+44}$	${25}_{-8}^{+42}$	2.3 ± 1.5	${74}_{-6}^{+81}$	${0.31}_{-0.08}^{+1.84}$	Irr
ZC400528	2.4 ± 0.7	${0.61}_{-0.18}^{+0.17}$	80 ± 20	35 ± 22	150 ± 25	${341}_{-89}^{+184}$	${28}_{-15}^{+23}$	${12}_{-5}^{+14}$	${344}_{-84}^{+186}$	${13}_{-6}^{+15}$	1, 2, 3, 5
ZC400569	${7.4}_{-1.5}^{+1.3}$	${0.98}_{-0.02}^{+0.01}$	15 ± 15	11 ± 15	263 ± 10	${312}_{-13}^{+19}$	${41}_{-21}^{+23}$	${7.6}_{-2.1}^{+5.0}$	${321}_{-12}^{+25}$	${36}_{-5}^{+8}$	Irr
ZC400569N	7.1 ± 1.4	${0.71}_{-0.17}^{+0.13}$	70 ± 15	32 ± 18	220 ± 25	${364}_{-64}^{+138}$	${43}_{-21}^{+16}$	${8.5}_{-1.8}^{+7.2}$	${372}_{-63}^{+136}$	${46}_{-16}^{+38}$	1, 2, 3, 5
ZC401925	2.6 ± 0.6	${0.78}_{-0.21}^{+0.13}$	60 ± 10	60 ± 12	55 ± 20	${96}_{-34}^{+62}$	${59}_{-19}^{+18}$	${1.6}_{-0.5}^{+1.2}$	${145}_{-30}^{+57}$	${2.5}_{-1.0}^{+2.6}$	1
ZC403741	${2.2}_{-0.3}^{+0.4}$	${0.55}_{-0.13}^{+0.11}$	25 ± 10	20 ± 19	70 ± 8	${189}_{-36}^{+73}$	${36}_{-12}^{+13}$	${5.2}_{-1.1}^{+2.9}$	${201}_{-34}^{+74}$	${4.1}_{-1.3}^{+3.4}$	1, 2, 3, 4, 5
ZC404221	0.8 ± 0.6	${0.78}_{-0.18}^{+0.14}$	90 ± 20	77 ± 20	38 ± 13	${100}_{-46}^{+44}$	${29}_{-8}^{+40}$	${3.4}_{-2.2}^{+1.1}$	${114}_{-20}^{+70}$	${0.48}_{-0.15}^{+1.43}$	Irr
ZC405226	5.4 ± 0.8	${0.82}_{-0.12}^{+0.10}$	−40 ± 10	26 ± 14	100 ± 23	${143}_{-36}^{+45}$	${58}_{-18}^{+19}$	${2.5}_{-0.6}^{+1.1}$	${178}_{-32}^{+45}$	${8.0}_{-2.6}^{+5.0}$	1, 2, 3, 4, 5
ZC405501	5.8 ± 0.9	${0.97}_{-0.07}^{+0.02}$	10 ± 5	1 ± 5	85 ± 15	${101}_{-16}^{+23}$	${52}_{-13}^{+16}$	${1.9}_{-0.4}^{+0.6}$	${139}_{-17}^{+28}$	${5.2}_{-1.4}^{+2.3}$	1, 2, 3, 4, 5
ZC406690	7.0 ± 1.2	${0.44}_{-0.09}^{+0.23}$	−70 ± 10	7 ± 12	120 ± 10	${313}_{-107}^{+88}$	${60}_{-15}^{+16}$	${5.3}_{-1.7}^{+1.6}$	${332}_{-97}^{+88}$	${36}_{-18}^{+21}$	1, 2, 3, 4
ZC407302	3.6 ± 1.2	${0.91}_{-0.09}^{+0.05}$	55 ± 5	8 ± 6	165 ± 35	${217}_{-40}^{+71}$	${56}_{-25}^{+11}$	${3.9}_{-0.6}^{+2.8}$	${240}_{-39}^{+62}$	${9.6}_{-3.8}^{+6.0}$	1, 2, 3, 4, 5
ZC407376	${5.5}_{-0.3}^{+0.7}$	${0.97}_{-0.04}^{+0.02}$	20 ± 25	5 ± 25	73 ± 18	${86}_{-20}^{+24}$	${56}_{-27}^{+28}$	${1.6}_{-0.5}^{+1.0}$	${134}_{-32}^{+46}$	${4.6}_{-2.0}^{+3.8}$	Irr
ZC407376S	1.6 ± 0.5	0.60 ± 0.18	−60 ± 10	8 ± 14	35 ± 18	${89}_{-45}^{+65}$	${77}_{-41}^{+37}$	${1.2}_{-0.5}^{+1.4}$	${167}_{-57}^{+86}$	${2.1}_{-1.3}^{+3.1}$	Irr
ZC407376N	1.4 ± 0.3	${0.83}_{-0.13}^{+0.09}$	60 ± 10	6 ± 14	58 ± 15	${113}_{-30}^{+49}$	35 ± 14	${3.2}_{-0.9}^{+2.3}$	${130}_{-24}^{+48}$	${1.1}_{-0.3}^{+0.9}$	1, 2
ZC409985	1.9 ± 0.2	${0.76}_{-0.16}^{+0.11}$	−15 ± 20	1 ± 20	20 ± 8	${38}_{-14}^{+20}$	${39}_{-13}^{+15}$	${0.97}_{-0.30}^{+0.57}$	${80}_{-20}^{+30}$	${0.57}_{-0.26}^{+0.52}$	Irr
ZC410041	4.7 ± 1.2	${1.00}_{-0.03}^{+0.00}$	−55 ± 10	9 ± 10	88 ± 10	${101}_{-9}^{+15}$	${48}_{-16}^{+14}$	${2.1}_{-0.4}^{+0.9}$	${134}_{-15}^{+22}$	${3.9}_{-1.3}^{+1.7}$	1, 2, 3, 4, 5
ZC410123	3.2 ± 0.7	${0.94}_{-0.07}^{+0.03}$	35 ± 25	19 ± 26	63 ± 15	${81}_{-17}^{+24}$	${60}_{-26}^{+25}$	${1.4}_{-0.4}^{+0.9}$	${137}_{-32}^{+44}$	${2.8}_{-1.3}^{+2.4}$	1
ZC411737	1.8 ± 0.2	${0.78}_{-0.18}^{+0.14}$	−60 ± 10	41 ± 12	73 ± 18	${139}_{-36}^{+56}$	${38}_{-18}^{+20}$	${3.7}_{-1.1}^{+2.8}$	${156}_{-32}^{+61}$	${2.0}_{-0.8}^{+2.0}$	1, 2
ZC412369	3.1 ± 1.1	${0.90}_{-0.08}^{+0.05}$	−70 ± 20	16 ± 22	80 ± 20	${120}_{-27}^{+49}$	${75}_{-27}^{+13}$	${1.6}_{-0.3}^{+1.0}$	${182}_{-27}^{+37}$	${4.8}_{-1.9}^{+2.8}$	1
ZC413507	2.6 ± 0.5	${0.77}_{-0.20}^{+0.13}$	−35 ± 10	13 ± 12	70 ± 20	${132}_{-40}^{+69}$	${42}_{-19}^{+21}$	${3.1}_{-0.9}^{+2.5}$	${153}_{-35}^{+70}$	${2.8}_{-1.2}^{+3.1}$	1, 2
ZC413597	1.6 ± 0.5	${0.78}_{-0.18}^{+0.13}$	45 ± 40	30 ± 41	48 ± 10	${92}_{-24}^{+52}$	${38}_{-18}^{+21}$	${2.4}_{-0.8}^{+2.6}$	${115}_{-19}^{+54}$	${0.98}_{-0.34}^{+1.24}$	Irr
ZC415876	2.4 ± 1.0	${0.64}_{-0.19}^{+0.16}$	−50 ± 15	30 ± 41	73 ± 15	${153}_{-41}^{+105}$	${47}_{-19}^{+13}$	${3.2}_{-0.7}^{+3.0}$	${176}_{-34}^{+98}$	${3.5}_{-1.3}^{+4.4}$	1, 2, 3, 4, 5

Notes.

^aAdopted 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 ${\mathrm{PSF}}_{2{\rm{G}},\mathrm{ave}}$ 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. ^bKinematic misalignment, based on the PA derived from the structural fits to HST H-band imaging, when available, or to the Hα maps otherwise. ^cCircular velocity and total dynamical mass in the rotating disk framework. Arguably, the V_rot and σ₀ 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 = σ_tot(Hα)/0.8 sin(i) would yield the following values of V_c and ${M}_{\mathrm{dyn}}/{10}^{10}\,{M}_{\odot }$: Q1623-BX543: ${227}_{-46}^{+22}$, ${7.9}_{-4.1}^{+0.4};$ Q1623-BX599: ${305}_{-90}^{+37}$, ${10}_{-6}^{+2};$ Q2343-BX513: ${224}_{-66}^{+17}$, ${6.1}_{-3.7}^{+0.2};$ SA12-6339: ${180}_{-51}^{+11}$, ${1.8}_{-1.1}^{+0.7};$ ZC400569 (full system): ${254}_{-57}^{+3}$, ${22}_{-10}^{+1};$ ZC404221: ${138}_{-42}^{+7}$, ${0.71}_{-0.40}^{+0.24};$ ZC407376 (full system): ${170}_{-29}^{+10}$, ${7.4}_{-2.4}^{+0.7};$ ZC407376S: ${311}_{-126}^{+52}$, ${7.2}_{-5.0}^{+1.7};$ ZC409985: ${116}_{-38}^{+9}$, ${1.2}_{-0.7}^{+0.1};$ ZC413597: ${147}_{-44}^{+8}$, ${1.6}_{-0.9}^{+0.1}$. ^dList 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.

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