component, although the interaction could explain the irregularities in the dispersion map.

8. **ZC 407302**—A bright compact source lies about 4 kpc from the center, on the northeast edge of the main body of the galaxy. Because its line-of-sight velocity is fully consistent with the extension of the velocity field of the main disk part out to this radius, it could plausibly be a massive clump that formed in situ, although we cannot rule out that it may be a small accreted satellite. The clump contains ~1/20 of the total stellar mass, which could have induced the perturbations seen in the velocity dispersion.

9. **K20-ID7**—Based on seeing-limited SINFONI data, this source had been classified as major merger mainly because of the nonaxisymmetry of the velocity dispersion map (Shapiro et al. 2008). The AO-assisted data resolve this source into a prominent ring structure with a similarly regular velocity field and little variation in velocity dispersion across the system. The Hα and rest-optical continuum emission trace extended material to the south beyond the ring, connected to a smaller source at a projected separation of 1"/6 and a relative velocity of about +350 km s⁻¹, roughly in line with the extension of the velocity gradient, and with an inferred stellar mass of ~15% that of the main source. Overall, the properties of K20-ID7 at 1.5 kpc resolution appear more consistent with a large low-inclination disk undergoing an ~1:7 minor interaction. The stellar mass map for K20-ID7 is less centrally peaked compared to the massive disks with bright, star-forming, ringlike structures, which may reflect the decrease in bulge-to-total mass ratios at lower galaxy masses (e.g., Lang et al. 2014).

10. **ZC407376**—The two components of this interacting pair have a projected separation of 1" (8 kpc), the same redshift within 20 km s⁻¹, nearly equal stellar masses, and derived dynamical masses within a factor of two of each other, making this system a major merger. Both components appeared as dispersion-dominated objects at seeing-limited resolution; the AO data resolve ZC407376N into a small disk with a projected velocity difference of 120 km s⁻¹ and V<sub>rot</sub>/σ<sub>0</sub> ~ 3, while ZC407376S still has irregular kinematics.

11. **Compact sources**—Many of the small, lower-mass sources in our sample exhibit characteristics of disk rotation in the high-resolution AO data (most notably GMASS-2363, Q1623-BX455, and ZC403741), as discussed in detail by Newman et al. (2013). Among the 18 objects with R<sub>e</sub> < 3 kpc, 55% show a monotonic velocity gradient and have V<sub>rot</sub>/σ<sub>0</sub> > 1.8. In contrast, and similar to ZC407376S, SA12-6339 and ZC409985 show the least amount of or no clear 2D velocity structure in the AO data. This may suggest that they are genuinely dispersion-dominated systems as a result of strongly dissipative mass assembly, although it is not possible to rule out that beam smearing and/or a nearly face-on orientation could cause the lack of observed structure.

## 8. Spatial Variations in [N II]/Hα Ratios

In this section, we exploit our AO-assisted data sets to characterize the spatial variations in the [N II]/Hα ratio. This ratio has been used in various studies of z ~ 0.7–2.7 SFGs to investigate radial variations in gas-phase oxygen abundances (in short, “metallicity”). The radial gradients have been found to be overall fairly flat, with some trends reported of shallower

or positive gradients among interacting/merging systems and kinematically disturbed disks and with higher redshift, lower mass, or higher specific SFR (Jones et al. 2010a, 2013, 2015; Yuan et al. 2011, 2012; Queyrel et al. 2012; Swinbank et al. 2012a; Stott et al. 2014; Leethochawalit et al. 2016; Wuyts et al. 2016; Wang et al. 2017). Results at z > 3 from bluer rest-optical strong line diagnostics still accessible from the ground suggest more prevalent positive gradients and anticorrelation with the SFR distribution (Cresci et al. 2010; Troncoso et al. 2014). By analogy with results in nearby SFGs (e.g., Kewley et al. 2006, 2010; Chien et al. 2007; Rupke et al. 2010; Rich et al. 2012; Sánchez et al. 2014; Ho et al. 2015; Belfiore et al. 2017), and in line with predictions from theoretical models and simulations (e.g., Chiappini et al. 2001; Mollá & Diáz 2005; Rahimi et al. 2011; Few et al. 2012; Kobayashi & Nakasato 2012; Pilkington et al. 2012; Torrey et al. 2012; Gibson et al. 2013; Mott et al. 2013; Ma et al. 2017), these findings have been interpreted as resulting from externally driven (interactions/mergers, enhanced halo gas accretion) or internally driven (feedback in the form of outflows, increased gas turbulence) mixing efficiently redistributing metals within galaxies and diluting the gas metallicity.

The picture remains unclear, however, because of the complicating effects of AGN and shock excitation, ISM conditions, and possible N/O abundance variations on the [N II]/Hα ratio, as amply discussed in the literature<fnref n="32" /> (e.g., Kewley & Dopita 2002; Pérez-Montero & Contini 2009; Yuan et al. 2012; Andrews & Martini 2013; Kewley et al. 2013; Steidel et al. 2014; Sanders et al. 2015, 2017; Shapley et al. 2015; Cresci et al. 2017; Kashino et al. 2017; Strom et al. 2017). In addition, high-redshift samples with gradient measurements at high spatial resolution are still small, especially at z > 2, and larger seeing-limited samples are more affected by beam smearing. Our SINS/zC-SINF AO sample enables us to significantly expand on existing measurements at 2 ≲ z ≲ 2.6 by more than doubling the number of galaxies with [N II]/Hα observations resolved on ~1 kpc scales. Despite the above limitations, the [N II]/Hα ratio has the significant advantage of being insensitive to extinction, and both lines are observed simultaneously in the same band under the same conditions.

### 8.1. Radial Gradients in [N II]/Hα

We constructed radial profiles in the [N II]/Hα ratio from the velocity-shifted spectra extracted in elliptical annuli (Section 4.4). The annuli have a width of 0"/1 and a major-axis radius *r* increasing by 0"/1 up to the largest aperture considered for the integrated measurements reported in Table 4. For reliable gradient determinations, we considered only galaxies for which at least three annuli have [N II]/Hα measured with S/N > 3. Nineteen of the targets satisfy this reliability criterion; this number increases to 21 when counting the two subcomponents ZC400569N and ZC407376S, where we can also extract a sufficiently sampled profile. The galaxies span nearly the entire range in stellar mass of our full AO sample (M<sub>⋆</sub> = 7.5 × 10<sup>9</sup> – 3.2 × 10<sup>11</sup> M<sub>☉</sub>), and the [N II]/Hα profiles extend over physical deprojected radii ranging from

<footnote n="32">³² Leethochawalit et al. (2016), however, found consistent metallicity gradients obtained from the N2 = log([N II] λ6584/Hα) and O3N2 = log({[O III] λ5007/Hβ}/[N II] λ6584/Hα) indices when employing the same set of calibrators (such as those proposed by, e.g., Pettini & Pagel 2004, hereafter PP04) for eight of their z ~ 2 lensed targets (without evidence for AGN or strong outflows) for which AO-assisted maps of all lines were obtained, suggesting no major impact from N/O and ISM condition variations within galaxies.</footnote>
<table><caption>**Table 7**

Radial [N II]/Hα Gradients</caption><thead><tr><th>Source</th><th>Observed ΔN2/Δr<sup>a</sup><br>(dex kpc<sup>-1</sup>)</th><th>Restricted<br>Observed<br>ΔN2/Δr<sup>b</sup><br>(dex kpc<sup>-1</sup>)</th><th>Corrected<br>ΔN2/Δr<sup>c</sup><br>(dex kpc<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Q2343-BX389</td><td>-0.047<sup>+0.019</sup><sub>-0.018</sub></td><td>...</td><td>-0.084<sup>+0.032</sup><sub>-0.030</sub></td></tr><tr><td>Q1623-BX455</td><td>-0.079<sup>+0.074</sup><sub>-0.098</sub></td><td>...</td><td>-0.187<sup>+0.180</sup><sub>-0.238</sub></td></tr><tr><td>Q2346-BX482</td><td>+0.005<sup>+0.023</sup><sub>-0.020</sub></td><td>...</td><td>+0.012<sup>+0.039</sup><sub>-0.034</sub></td></tr><tr><td>Q2343-BX513</td><td>+0.010 ± 0.043</td><td>...</td><td>-0.037 ± 0.075</td></tr><tr><td>Q1623-BX599</td><td>-0.032<sup>+0.022</sup><sub>-0.025</sub></td><td>...</td><td>-0.063<sup>+0.037</sup><sub>-0.042</sub></td></tr><tr><td>Q2343-BX610</td><td>-0.072<sup>+0.014</sup><sub>-0.012</sub></td><td>-0.066<sup>+0.019</sup><sub>-0.016</sub></td><td>-0.115<sup>+0.023</sup><sub>-0.020</sub></td></tr><tr><td>Deep3a-15504</td><td>-0.033 ± 0.010</td><td>-0.052<sup>+0.017</sup><sub>-0.020</sub></td><td>-0.046 ± 0.013</td></tr><tr><td>Deep3a-6004</td><td>-0.046<sup>+0.017</sup><sub>-0.021</sub></td><td>-0.004<sup>+0.039</sup><sub>-0.044</sub></td><td>-0.056<sup>+0.023</sup><sub>-0.028</sub></td></tr><tr><td>Deep3a-6397</td><td>-0.047<sup>+0.008</sup><sub>-0.011</sub></td><td>-0.041<sup>+0.019</sup><sub>-0.020</sub></td><td>-0.072<sup>+0.011</sup><sub>-0.015</sub></td></tr><tr><td>ZC400528</td><td>-0.006<sup>+0.025</sup><sub>-0.027</sub></td><td>...</td><td>-0.016<sup>+0.045</sup><sub>-0.049</sub></td></tr><tr><td>ZC400569N</td><td>-0.083<sup>+0.012</sup><sub>-0.011</sub></td><td>-0.090<sup>+0.022</sup><sub>-0.021</sub></td><td>-0.112<sup>+0.016</sup><sub>-0.014</sub></td></tr><tr><td>ZC400569</td><td>-0.052<sup>+0.008</sup><sub>-0.009</sub></td><td>-0.055<sup>+0.014</sup><sub>-0.013</sub></td><td>-0.087<sup>+0.013</sup><sub>-0.014</sub></td></tr><tr><td>ZC403741</td><td>-0.080<sup>+0.024</sup><sub>-0.030</sub></td><td>...</td><td>-0.216<sup>+0.065</sup><sub>-0.081</sub></td></tr><tr><td>ZC404221</td><td>-0.002<sup>+0.043</sup><sub>-0.049</sub></td><td>...</td><td>-0.022<sup>+0.084</sup><sub>-0.095</sub></td></tr><tr><td>ZC406690</td><td>-0.056<sup>+0.019</sup><sub>-0.018</sub></td><td>...</td><td>-0.080<sup>+0.028</sup><sub>-0.027</sub></td></tr><tr><td>ZC407302</td><td>-0.026 ± 0.012</td><td>...</td><td>-0.041 ± 0.020</td></tr><tr><td>ZC407376S</td><td>-0.035<sup>+0.042</sup><sub>-0.043</sub></td><td>...</td><td>-0.037<sup>+0.071</sup><sub>-0.073</sub></td></tr><tr><td>ZC407376</td><td>-0.050<sup>+0.027</sup><sub>-0.029</sub></td><td>...</td><td>-0.084<sup>+0.044</sup><sub>-0.048</sub></td></tr><tr><td>ZC409985</td><td>-0.091<sup>+0.079</sup><sub>-0.087</sub></td><td>...</td><td>-0.099<sup>+0.139</sup><sub>-0.153</sub></td></tr><tr><td>ZC412369</td><td>-0.058<sup>+0.032</sup><sub>-0.033</sub></td><td>...</td><td>-0.082<sup>+0.050</sup><sub>-0.051</sub></td></tr><tr><td>ZC413597</td><td>+0.135<sup>+0.110</sup><sub>-0.080</sub></td><td>...</td><td>+0.183<sup>+0.150</sup><sub>-0.109</sub></td></tr></tbody></table>

**Notes.** The gradients are expressed in terms of the [N II]/Hα ratio, the measured quantity. Gradients in terms of inferred metallicity are prone to uncertainties in calibrations, which are known to be very uncertain (e.g., Kewley & Ellison 2008; Maiolino et al. 2008). For comparison with results at z ~ 1-3 in the literature, which often use the linear calibration proposed by PP04, with 12 + log(O/H) = 8.90 + 0.57 log([N II]/Hα), the metallicity gradients would correspond to Δ(O/H)/Δr = 0.57 × Δ(O/H)/Δr.

<sup>a</sup> Full-range radial [N II]/Hα gradient based on integrated spectra in elliptical apertures.

<sup>b</sup> Radial [N II]/Hα gradient fitted over the restricted range r > 0.3 for sources with evidence of an AGN.

<sup>c</sup> Full-range radial gradients corrected for beam-smearing effects.

3.2 to 10.7 kpc, and 6.5 kpc on average (and median). The radial profiles are presented in Appendix F (Figure 20), together with the Hα and [N II]/Hα maps and the velocity-shifted integrated spectra of these sources.

We quantified the gradients ΔN2/Δr from linear regression with censored data to account for upper limits, where N2 = log([N II]/Hα) and r is in physical units. We derived the uncertainties from 500 Monte Carlo iterations. For the galaxies with evidence of an AGN, we also fitted the gradients restricted to the outer r > 0.3 parts only, motivated by the extent of broad Hα +[N II] line emission associated with nuclear outflows in the most massive galaxies (Förster Schreiber et al. 2014); this radius corresponds to 2.5 kpc and encloses ~80% of the total light for a point-like source with the average PSF<sub>2 G,ave</sub>.

Beam smearing has a small but nonnegligible effect in our AO data because of the broad halo of the PSF (Appendix A). To estimate its impact, we followed a forward-modeling approach analogous to that presented by Wuyts et al. (2016; see also Carton et al. 2017). We created for each galaxy a suite of simulated Hα +[N II] data cubes consisting of model rotating disks with intrinsic ΔN2/Δr between -0.2 and +0.2 dex kpc⁻¹ using the IDL code DYSMAL (Davies et al. 2011). The models were

generated for the size, Sérsic index, inclination, and dynamical mass derived from the data, with the line emission normalized to the source-integrated Hα flux and [N II]/Hα ratio and assuming [N II]λ 6548/[N II]λ 6584 = 0.34 (Storey & Zeppen 2000). The intrinsic models were convolved with the LSF and PSF<sub>2 G,ave</sub>, noise was added based on the reduced cubes, and the ΔN2/Δr were measured from the mock data in the same way as for the observations. Corrected gradients and their uncertainties were then derived from the relation between mock-observed and intrinsic values of each galaxy (equivalent to a multiplicative factor applied to the observed gradients and associated 68% confidence intervals). Although these simulations are simplistic, they highlight cases for which corrections may become quite important.

The best-fit slopes and 68% confidence intervals for the full, restricted, and corrected gradients are given in Table 7. Figure 10 (left and middle panels) compares the full observed and beam-smearing-corrected ΔN2/Δr for all sources and those over the restricted radial range for the AGN sources. The full observed gradients range from -0.091 to +0.135 dex kpc⁻¹, with a mean of -0.035 and median of -0.047 dex kpc⁻¹. All sources have a best-fit slope that is negative or consistent with zero within the 1σ uncertainties, with the exception of the compact and kinematically irregular ZC413597. The inferred intrinsic gradients are on average (and median) only modestly steeper by about 0.025 dex kpc⁻¹, which is comparable to the typical measurement uncertainties (0.030 dex kpc⁻¹). As expected, the largest corrections are for the smaller sources, reaching differences of -0.11 and -0.14 dex kpc⁻¹ for Q1623-BX455 and ZC403741, respectively, implying that our observations recover ≈40% of the gradient for these objects, assuming it is intrinsically smooth and monotonic. Among the seven sources with an AGN, the restricted gradients remain overall the same (mean difference of +0.004 dex kpc⁻¹); the largest difference is for Deep3a-6004, where the inner regions are strongly dominated by the broad line emission from its AGN-driven outflow (Förster Schreiber et al. 2014).

For our sample, we find no significant trend in ΔN2/Δr with galaxy stellar, star formation, and structural properties or global [N II]/Hα ratio.<sup>33</sup> Considering the kinematic nature and nuclear activity of the sources, while the mean and median ΔN2/Δr (observed or corrected) may suggest shallower or more positive gradients among kinematically irregular systems versus disks and among non-AGNs versus AGNs, the differences have <1σ significance (and Kolmogorov-Smirnov (K-S) tests do not support that the ΔN2/Δr distributions between these subsets significantly differ).

## 8.2. Comparison with Other z ~ 2 AO Samples

Figure 11 plots the source-integrated [N II]/Hα ratio and ΔN2/Δr measurements as a function of galaxy stellar mass for our sample along with those of other published AO samples. The comparison is restricted to the redshift range 1.4 < z < 2.6

<footnote n="33"><sup>33</sup> In observed ΔN2/Δr, there may be weak trends of shallower ΔN2/Δr at lower M<sub>∗</sub>, (U-V)<sub>rest</sub>, sSFR, and size, with Spearman rank correlation coefficient ρ ≈ 0.2-0.3 and low 1σ significance. However, the trends are driven by one object with positive ΔN2/Δr, the AGN-hosting galaxies, and beam-smearing effects, since, for our sample, mass, color, and specific sSFR vary with effective radius. In corrected ΔN2/Δr, the trend with R<sub>e</sub> disappears, while the strength and significance of those with M<sub>∗</sub>, (U-V)<sub>rest</sub>, and sSFR marginally increase (ρ ≈ 0.25-0.4 at the 1-2σ level), but they all weaken again when using the restricted gradients for the AGN or removing them altogether from the sample and excluding ZC413597.</footnote>
<figure><img src="image_13.png" /></figure>

**Figure 10.** Comparison of measurements of $\Delta N_2/\Delta r$ for the SINS/zC-SINF AO sample. In all panels, the dashed line shows the 1:1 relation, and dotted lines indicate a flat slope. Error bars show the formal fitting uncertainties corresponding to the 68% confidence intervals derived from a Monte Carlo approach (Section 8.1). Left: observed vs. beam-smearing-corrected gradients over the full radial range. Different symbols correspond to galaxies with disklike or irregular kinematics and with or without evidence for an AGN, as labeled in the plot. The gradients are modestly negative or flat for all but one galaxy (the compact ZC413597), and beam-smearing effects are overall small (typically $-0.024 \text{ dex kpc}^{-1}$, with the largest differences reaching about $-0.1 \text{ dex kpc}^{-1}$ for two of the smaller galaxies). Middle: full radial gradients vs. gradients fitted over the restricted $r > 0.0^{\prime\prime}3$ range for the galaxies with AGNs. Disklike and irregular systems are distinguished by different symbol shapes, and observed and beam-smearing-corrected gradients are plotted as filled and open symbols following the legend in the panel. The full and restricted gradients are essentially identical except for one object (Deep3a-6004, strongly dominated by broad $H\alpha$ + [N II] emission from an AGN-driven outflow in the central regions). Right: full radial gradients derived from the spectra in elliptical annuli vs. gradients fitted to the distribution of pixels with $H\alpha$ flux above the threshold avoiding the bias toward higher [N II]/$H\alpha$ ratios (see Section 8.3). No beam-smearing correction is applied here (and ZC413597 is omitted because too few pixels can be included). The kinematic nature and presence or not of an AGN are indicated with different symbols and colors as in the left panel. The largest differences between annuli- and pixel-based gradients are driven by the limited spatial coverage of the unbiased pixels in some of the objects, probing brighter regions that are less representative of the global trend across the galaxy captured by the annuli data.

<figure><img src="image_14.png" /></figure>

**Figure 11.** The [N II]/$H\alpha$ properties vs. stellar mass for $1.4 < z < 2.6$ galaxies with a $\Delta N_2/\Delta r$ measurement from IFU observations. Large symbols represent measurements from AO-assisted data, and small open symbols show those from seeing-limited data, as labeled at the bottom of each panel. The SINS/zC-SINF AO results are compared to those of the KMOS$^{3D}$ (Wuyts et al. 2016), HiZELS (Swinbank et al. 2012a; Molina et al. 2017), and MASSIV (Queyrel et al. 2012) surveys and from the lensed samples presented by Yuan et al. (2011), Jones et al. (2013), and Leethochawalit et al. (2016). Different colors distinguish between systems with disklike or irregular kinematics and those hosting or not hosting an AGN, as shown by the legend at the top of the panels. Left: global [N II]/$H\alpha$ ratios and corresponding O/H abundance inferred from the linear N2 calibration of PP04. In addition, we plot the [N II]/$H\alpha$ versus $M_*$ relationships derived from stacked spectra in mass bins from 124 $1.9 < z < 2.7$ galaxies from the KMOS$^{3D}$ multi-IFU survey (Wuyts et al. 2016, including AGNs; gray shaded area) and 642 $1.4 < z < 1.7$ galaxies from the FMOS multislit spectroscopic survey (Kashino et al. 2017; green hatched areas), along with the linear fit to the stacking results from 195 $z < z < 2.5$ galaxies from the MOSDEF multislit spectroscopic survey (Sanders et al. 2018; pink dashed line). The latter fit was used to assign a stellar mass to the lensed objects from Leethochawalit et al. (2016; plotted as asterisks; see text). Right: observed $\Delta N_2/\Delta r$ measurements. Beam-smearing corrections cannot be applied to all samples because for some of them, sizes and other relevant galaxy properties are not available. Overall, the radial gradients are tightly clustered around a flat slope of zero, with large overlap between the various samples. The SINS/zC-SINF sample roughly doubles the number of published $\Delta N_2/\Delta r$ measurements from AO-assisted IFU data at $2 < z < 2.6$ and covers more than an order of magnitude in stellar mass.

spanned by the SINS/zC-SINF AO galaxies to mitigate evolutionary effects (e.g., Erb et al. 2006a; Jones et al. 2010a, 2013; Troncoso et al. 2014; Wuyts et al. 2014a, 2016; Zahid et al. 2014; Sanders et al. 2015; Leethochawalit et al. 2016) and to

results obtained from the same N2 indicator as used here for consistency. The relevant published AO samples include 16 lensed objects (Yuan et al. 2011; Jones et al. 2013; Leethochawalit et al. 2016), eight galaxies drawn from the HiZELS survey
(Swinbank et al. 2012a; Molina et al. 2017), and one observed as part of the MASSIV survey (Queyrel et al. 2012). For the lensed galaxy of Yuan et al. (2011), the quoted dynamical mass is used as an upper limit on the stellar mass. For the Leethochawalit et al. (2016) sample, no mass estimate is listed or can be inferred based on the published data; the range of $log(M_*/M_\odot) \sim 9-9.6$ is mentioned for the subset of galaxies with available near-IR photometry. For the purpose of Figure 11, we assigned $M_*$ values for the 11 objects of Leethochawalit et al. calculated from their [N II]/H$\alpha$ ratios using the linear $N2-M_*$ relation for $z \sim 2.3$ SFGs given by Sanders et al. (2018), yielding a range of $log(M_*/M_\odot) \sim 9-10.6$.

In Figure 11, we show the data in terms of [N II]/H$\alpha$ ratio and gradient, the measured quantities. As an indication, the right-hand axes show the corresponding values for oxygen abundance adopting the linear calibration of (PP04) that is commonly used in high-redshift studies: $12 + \log(O/H) = 8.90 + 0.57 \times \text{N2}$. Since galaxy sizes are not available for all of the literature samples considered here but would be essential for beam-smearing corrections, the comparison is made for the observed (uncorrected) $\Delta N2/\Delta r$. As a further comparison, we include results derived based on seeing-limited observations from the KMOS$^{3D}$ survey, the largest sample with $\Delta N2/\Delta r$ measurements (Wuyts et al. 2016), and the four $z \sim 1.5$ galaxies from the MASSIV survey that fall in the redshift range considered here (Queyrel et al. 2012). In the background of the galaxy-integrated [N II]/H$\alpha - M_*$ panel, we further plot the relationships derived from stacked spectra in mass bins of much larger samples from the KMOS$^{3D}$ (including AGNs; Wuyts et al. 2016) and MOSDEF (excluding AGNs; Sanders et al. 2018) surveys and at $z \sim 1.6$ from the FMOS survey (excluding AGNs; Kashino et al. 2017).

The objects with $\Delta N2/\Delta r$ measurements broadly follow the [N II]/H$\alpha$ versus $M_*$ relationships delineated by KMOS$^{3D}$, MOSDEF, and FMOS SFGs down to $log(M_*/M_\odot) \sim 10$. Objects around and below this mass almost all lie above these relationships, a trend that partly reflects the observational surface brightness limitations associated with the [N II]/H$\alpha$ employed for the gradient measurements.

In $\Delta N2/\Delta r$, the distributions between the various AO samples at $1.4 < z < 2.6$ largely overlap. Our SINS/zC-SINF AO sample represents an important extension and strengthens the previous findings of typically weak radial variations in [N II]/H$\alpha$. It dominates at the higher masses and extends down to the regime probed so far largely by lensed and/or lower-$z$ galaxies; 19 of our sources are at $2 < z < 2.6$, compared to 15 of the published AO targets (the other 10 discussed here are at $1.4 < z < 1.8$). From the combined AO samples (46 objects), the average and median $\Delta N2/\Delta r$ are $-0.053$ and $-0.044 \text{ dex kpc}^{-1}$, with a scatter of $0.115 \text{ dex kpc}^{-1}$; excluding the five galaxies with the steepest negative and positive gradients ($>1.5\sigma$ away from the mean) increases the average to $-0.036$ and reduces the scatter to $0.054 \text{ dex kpc}^{-1}$. The most prominent feature in the $\Delta N2/\Delta r$ distributions is the wider range spanned by the lensed objects, which Leethochawalit et al. (2016) argued could reflect large variations in gas and metal mixing due to feedback between different galaxies, which are better probed with the aid of gravitational magnification.

Even with the increased statistics, no strong trend with galaxy properties emerges when adding the published AO targets to ours. There is a possible distinction between disks and nondisks, with a median $\Delta N2/\Delta r$ of $-0.047$ and

$-0.009 \text{ dex kpc}^{-1}$, respectively, but the difference is at the $1.8\sigma$ level, and a K-S test does not indicate that the distributions are significantly distinct. The nine galaxies with evidence for an AGN differ even less from the non-AGN ones (median of $-0.047$ and $-0.033 \text{ dex kpc}^{-1}$, respectively, a $1.2\sigma$ difference). No significant correlation is seen in $\Delta N2/\Delta r$ as a function of $M_*$ (excluding the Leethochawalit et al. 2016 sample, for which no stellar mass is given, as explained above). Although the AO and seeing-limited measurements overlap, the latter have fairly uniformly flatter $\Delta N2/\Delta r$ at fixed stellar mass over the better-sampled $log(M_*/M_\odot) \gtrsim 10$ range (the mean, median, and scatter are $-0.001, 0.000$, and $0.037 \text{ dex kpc}^{-1}$, respectively), consistent with expectations from beam smearing (see also Appendix E).

Comparisons between different samples as presented in Figure 11 still have important caveats. In particular, the physical resolution between the data sets varies widely, from $\sim 100 \text{ pc}$ for the most strongly magnified objects, to $\sim 1-2 \text{ kpc}$ for the nonlensed AO samples, and up to $\sim 5 \text{ kpc}$ for the seeing-limited data (see also the discussions by Yuan et al. 2013 and Carton et al. 2017). Even for strongly lensed galaxies, the stretch is generally nonuniform and can be negligible along the least-magnified direction, such that beam smearing may still play a role for these sources.

### 8.3. Pixel Distributions in [N II]/H$\alpha$ Ratio

The [N II]/H$\alpha$ maps presented in Appendix F suggest possibly more complex spatial variations than simple smooth gradients. We examined the distributions of the [N II]/H$\alpha$ ratio of individual pixels as a function of radius to assess the degree of azimuthal scatter and the consistency between azimuthally averaged and pixel-based gradients.

Before interpreting the data, it is important to account for the surface brightness effects that can bias the [N II]/H$\alpha$ ratio toward higher values in regions of fainter H$\alpha$ line emission. We empirically derived the $3\sigma$ limit in [N II]/H$\alpha$ as a function of H$\alpha$ flux based on the S/N(H$\alpha$) versus F(H$\alpha$) relationship for each galaxy. We then determined the threshold in H$\alpha$ flux, F(H$\alpha$)$_{pix,thresh}$, below which the pixel distribution in [N II]/H$\alpha$ becomes biased toward higher values, i.e., where the range of ratio values starts to extend below the $3\sigma$ limiting curve. This process is illustrated in the rightmost panels of Figure 20. The pixels with a ratio measurement $>3\sigma$ but an H$\alpha$ flux $<F(H\alpha)_{pix,thresh}$ are marked on the ratio maps and distinguished from those in the unbiased regime in the radial distributions of pixel ratios shown in the fifth column of the figures. It is apparent from these figures that accounting for the biased regime is essential in discussing trends in 2D and with line flux based on [N II]/H$\alpha$. For instance, an anticorrelation between [N II]/H$\alpha$ and the observed F(H$\alpha$) is seen in many objects but is largely driven by this bias.

Keeping in mind the bias just described, the data nonetheless reveal the presence of an important scatter in [N II]/H$\alpha$ at a fixed radius in several of the galaxies. This scatter may arise from the contribution of shock excitation in ionized gas outflows, reflect localized enrichment or dilution of the ISM in metals on short timescales, or be caused by the possible presence of recently accreted, metal-poor low-mass companions. One particularly striking example is ZC406690, where the H$\alpha$+[N II] emission from star formation-driven outflows exhibits different properties (line widths and ratios) between different clumps along the bright ringlike structure, at least in part due to shocks (Newman et al. 2012b). Another interesting
example is ZC400528, where the broad H$\alpha$+[N II] component associated with an AGN-driven outflow is anisotropic and extends along one side of the kinematic minor axis (Förster Schreiber et al. 2014) opposite an off-center clump or close-by low-mass satellite with very weak [N II] emission.

We compared the $\Delta N2/\Delta r$ derived from the spectra of elliptical annuli with those from the distributions of unbiased pixels following a similar fitting procedure (denoted $\Delta N2/\Delta r_{pix}$). The right panel of Figure 10 shows the comparison, and the best-fit $\Delta N2/\Delta r_{pix}$ are overplotted in the fifth column of Figure 20. In half of the cases, the annuli- and pixel-based gradients agree within about $1\sigma$. The largest differences (at the 1.5–3$\sigma$ level) occur for six objects and can be attributed to (i) the smaller radial coverage of the pixels missing the decrease in [N II]/H$\alpha$ compared to the measurements in annuli extending further out in compact objects with significantly negative gradients (ZC407376S, ZC412369, and especially ZC403741, where the more abrupt drop in the outermost annulus is not probed by the pixels), (ii) the brighter asymmetric regions with outflow emission dominating the off-center pixel distribution in ZC400528, and (iii) the limited spatial coverage of the pixels being particularly affected by the bright asymmetric features in the full systems ZC407376 and ZC400569.

We conclude from the comparison presented here that while the more detailed information from 2D maps allows, in principle, a more direct association of [N II]/H$\alpha$ variations with specific subgalactic regions, surface brightness limitations inherent to this ratio can still make the interpretation quite challenging, even for our deep AO data sets, especially when seeking to constrain radial variations. Although the summation of the spectra of individual pixels applied in extracting the spectra in annuli (Section 4.4) is inherently light-weighted, it better probes the regions of fainter line emission. The [N II]/H$\alpha$ profiles derived from these spectra thus enable a more reliable estimate of $\Delta N2/\Delta r$, albeit in an azimuthally averaged sense and with the potential caveats of annuli binning (e.g., Yuan et al. 2013).

## 9. Summary

We presented sensitive, high-resolution SINFONI+AO observations of 35 star-forming, high-redshift galaxies, the result of a 12 yr series of observing campaigns at the ESO VLT carried out between 2005 April and 2016 August. Most galaxies (32 out of 35) are at $2 < z < 2.6$ and constitute the largest sample of galaxies with AO-assisted, near-IR integral field spectroscopy targeting this specific redshift range. As a legacy to the community, we make the reduced data cubes publicly available.

Some of the targets were selected from the literature for having both a suitable redshift and a nearby star usable for the AO wavefront correction. Others, those coming from the zCOSMOS-Deep project (Lilly et al. 2007), were specifically targeted as fulfilling the above AO requirements and provide targets for this SINS/zC-SINF survey. As such, the whole sample was not assembled following a single selection criterion. However, we demonstrated that this sample is largely representative in terms of SFR, size, and rest-optical colors of main-sequence SFGs in the same redshift and mass ranges (as illustrated in Section 2.3; but see also discussions by FS09 and M11). The angular resolution of the AO data spans a fairly narrow range, with PSF FWHM from 0.13 to 0.33 and a median of 0.18, corresponding to 1.5 kpc at the redshift of

these galaxies. The prime target of the observations was the line emission from H$\alpha$ and [N II], allowing us to construct high-resolution maps of the SFR surface density, velocity field, and velocity dispersion for all galaxies and [N II]/H$\alpha$ maps for a subset of 19 of them.

About 70% of the galaxies show ordered disk rotation patterns in their kinematics, including several of the compact sources, as well as individual components in two larger interacting systems. The other sources have irregular or nearly featureless kinematics on resolved scales of 1–2 kpc. In the larger disks, the AO data reveal second-order features that are reminiscent of perturbations induced by massive bulges and star-forming disk clumps, possible bar-/spiral-like structure, or low-mass nearby satellite galaxies or that are related to the presence of strong ionized gas outflows driven by star formation or AGNs. The sensitive AO data from our survey highlight the richness of detail and diversity of processes that become apparent at higher angular resolution. Simple classification schemes will not capture this richness, but it is nonetheless clear that the majority of the galaxies are observed in a disk configuration (further supported in most cases by the global stellar light and H$\alpha$ structure). This result implies a fairly stable dynamical state, consistent with the notion that the mere existence of the “main sequence” requires SFGs to be in a quasi-steady state equilibrium between gas accretion, ejection, and star formation (e.g., Lilly et al. 2013).

Our SINS/zC-SINF AO sample more than doubled the number of galaxies with high-resolution [N II]/H$\alpha$ gradient measurements at $2 < z < 2.7$. The radial gradients are fairly shallow (similar to findings from other studies) and almost exclusively negative. The shallow slopes may reflect efficient gas and metal mixing from various internal and external processes but can also be directly affected by the contribution from shock and AGN excitation, as seen in some of the galaxies. The maps and pixel distributions show that azimuthal variations are present in several cases, associated with ionized gas outflows or more metal-poor regions in the disks or nearby companions. Future progress will rely primarily on fully mapping multiple diagnostic line ratios in 2D to disentangle metallicity, excitation, and physical conditions.

It will be important to take the next steps not only by increasing the sample size and coverage of galaxy parameter space but also by pushing quantitative analyses to the characterization of substructure in kinematics, morphologies, and line ratio properties and to establish connections with variations in stellar population and reddening within galaxies. For instance, a robust identification of distinct residuals in velocity and dispersion maps, together with the breaking of age-reddening degeneracies in the central regions of high-redshift galaxies, will be crucial in mapping the emergence of galactic bulges. Also, future efforts to map outflows from disks, clumps, and nuclear regions on ~1 kpc scales are crucially needed for many more typical high-redshift SFGs in order to more accurately constrain physical parameters such as the mass-loading factor and establish the time-averaged impact of feedback. Our work and other IFU studies show that it is feasible given sufficient integration time to reach the necessary sensitivity. Such observations will be critical in providing much-needed quantitative constraints for theory and numerical simulations of galaxy evolution. Another key goal includes the systematic exploration of the properties of the progenitor population of $z \sim 2$ galaxies, using the same diagnostics for consistency.
Such studies will be facilitated by upcoming instruments
such as ERIS at the VLT and NIRSpec on board the *James
Webb Space Telescope*, affording near-IR IFU capabilities with
improved sensitivity, AO performance, and wavelength cover-
age. Combining the resolved distribution and kinematics of the
warm (~10⁴ K) ionized gas as probed by Hα with those of the
dominant (and unobscured) cold molecular and atomic gas with
NOEMA and ALMA will be essential to assess the baryonic
mass budget and the extent to which outflows are able to
entrain the neutral ISM phase.

Given the 12 yr period it took to complete the SINFONI AO-
assisted observations of our 35 targets, it appears unlikely that
another comparable sample with similar deep and high-quality
kinematic and structural information will be produced anytime
soon. Accordingly, this sample offers the best candidate targets
at z ~ 2 for further investigation at other wavelengths and
higher spatial resolution.

We wish to thank the ESO staff for excellent support during
the many observing campaigns over which the SINFONI data
were obtained. Special thanks to J. Navarrete for always
enthusiastic help and discussions. We also thank the SINFONI
and PARSEC teams for their hard work on the instrument and
laser, which allowed our programs to be carried out success-
fully. We thank the referee for a careful reading of the
manuscript and useful suggestions that helped improve the
quality and presentation of the paper. This paper and the SINS/
zC-SINF survey have benefited from many stimulating
discussions with many colleagues, especially M. Franx,
P. van Dokkum, M. Bureau, S. Courteau, L. Kewley, A.
Dekel, and E. Wisnioski. NMFS acknowledges support by the
Minerva Program of the Max-Planck-Gesellschaft and the
Schwerpunkt Programme SPP1177 of the Deutsche For-
schungsgemeinschaft. AR and CM acknowledge support from
INAF-PRIN 2008 and 2012; AR also acknowledges support
from INAF-PRIN 2014 and 2017 and is grateful for the kind
hospitality of the Excellence Cluster universe (Garching) and
the Max-Planck-Institut für Extraterrestrische Physik while
working on the early and final versions of this paper. YP
acknowledges support from the National Key Program for
Science and Technology Research and Development under
grant No. 2016YFA0400702 and NSFC grant No. 11773001.
AC acknowledges the grants ASI n.I/023/12/0 "Attività
relative alla fase B2/C per la missione Euclid" and PRIN
MIUR 2015 "Cosmology and Fundamental Physics: illuminat-
ing the Dark universe with Euclid."

# Appendix A
## AO Performance and Point-spread Function

A.1. *Impact of Reference Star Brightness and Observing Conditions on the AO Performance*

We inspected variations of the effective angular resolution of
our data sets with the properties of the AO reference star and
with the seeing at visible wavelengths, atmospheric coherence
time τ₀, and airmass during the observations. The seeing, τ₀,
and airmass are taken from the Paranal observatory's data
recorded for all individual exposures. For this trending
analysis, we use the conditions during the PSF star observa-
tions, noting that variations between the PSF star and science
target observations are very similar to those within individual
OBs and between different OBs. We also estimated the Strehl

ratio from the peak-to-total flux ratio of the effective PSF
image, accounting for the pixel sampling, the seeing at the
observed wavelength of Hα and average airmass of each
object, and the outer scale correction for the VLT pupil of 8 m
(following Sarazin 2000).

Table 8 lists the reference star's R-band magnitude and separation from the science target and the average and standard deviation of the observing conditions (seeing, τ₀, and airmass), along with the parameters derived from 2D elliptical Gaussian fits to the effective PSF image and estimated Strehl ratio. Figure 12 shows the distributions of effective PSF parameters and Strehl ratio as a function of the reference AO star brightness, average airmass, optical seeing, and coherence time.

As expected, the effective PSF major-axis FWHM (FWHM<sub>major</sub>) and the Strehl ratio are tightly coupled. The estimated Strehl ratios range from 5.8% to 32%, with an average of 17% and median of 16%. As for the angular resolution (see Section 3.3), there is no significant distinction in Strehl ratio between the data taken in NGS and LGS mode (the mean and median differ by <5%) except for the two LGS-SE data sets (Strehl ratio of 7% and 14%). The FWHM<sub>major</sub> correlates most strongly with the magnitude of the star (the Spearman rank correlation is ρ = 0.55 with a significance of 3.2σ), and so does the Strehl ratio (ρ = 0.42 and 2.5σ). Both quantities also vary with τ₀ and airmass, but less significantly (ρ = 0.2–0.3 at the 1.2σ–1.9σ level). There is no trend with the seeing for our data, either in the optical at zenith or corrected to the near-IR wavelength and airmass of the observations.

A.2. *Averaged AO Point-spread Function*

Because of the nonideal AO performance reflected in the
Strehl ratios from the AO reference star images, broad wings
in the PSF shape are expected from the uncorrected seeing.
While the wings can be discerned in most of the PSF images,
the data of individual stars are too noisy for an accurate profile
characterization. To obtain a high-S/N PSF profile, we thus
spatially registered, normalized by the peak flux, and
coaveraged (with 3.5σ clipping) the PSF images associated
with the different galaxies. We excluded the PSF associated
with Deep3a-15504 because the star is in a double system, and,
while it is resolved in our data, the secondary component is
relatively bright and may affect the average. We fitted a single
and a double-component 2D elliptical Gaussian model to the
resulting averaged AO PSF. Instead averaging the PSFs with an
FWHM within the central 68% of the distribution, or the NGS
or LGS subsets, makes no significant difference (≤0.01 and
≤0.07 in FWHM for the narrow core and broad halo,
respectively, and <5% in their total flux contributions). We
also tested PSF models consisting of a single and a double-
component 2D elliptical Moffat profile. While these models
match the observed averaged AO PSF better than a single
Gaussian, they do so more poorly than the double Gaussian,
with deviations from the empirical curve of growth of 5%–7%
on average (at most ≈10%) for the Moffat models compared to
2% on average (at most 5%) for the adopted double-Gaussian
model.

The images and axis profiles of the adopted average PSF,
best-fit models, and residuals, along with the curves of growth,
are shown in Figure 13. The best-fit parameters are given in the
figure panels. Even in the high-S/N average PSF, a single-
Gaussian fit provides a reasonable description of the inner PSF
profile, and the core component in the double-Gaussian fit has
<table><caption>**Table 8**
Observational Parameters and AO Performance</caption><thead><tr><th colspan="2">Science Target</th><th colspan="2">Reference Star<sup>a</sup></th><th colspan="4">Observing Conditions<sup>b</sup></th><th colspan="3">Effective PSF<sup>c</sup></th></tr><tr><th>Source</th><th>AO Mode</th><th>R<sub>Vega</sub><br>(mag)</th><th>Distance</th><th>Optical Seeing</th><th>τ<sub>0</sub><br>(ms)</th><th>Airmass</th><th>FWHM<sub>major</sub></th><th>Axis Ratio</th><th>PA<br>(deg)</th><th>Strehl Ratio<br>(%)</th></tr></thead><tbody><tr><td>Q1623-BX455</td><td>LGS</td><td>10.9</td><td>48"</td><td>0"84 (0"00)</td><td>2.0 (0.0)</td><td>1.78 (0.00)</td><td>0"13</td><td>0.71</td><td>-3</td><td>20</td></tr><tr><td>Q1623-BX502</td><td>NGS</td><td>15.5</td><td>8"</td><td>0"61 (0"27)</td><td>4.9 (2.9)</td><td>1.65 (0.05)</td><td>0"16</td><td>0.91</td><td>+71</td><td>16</td></tr><tr><td>Q1623-BX543</td><td>NGS</td><td>16.3</td><td>25"</td><td>1"05 (0"46)</td><td>3.6 (2.0)</td><td>1.79 (0.16)</td><td>0"33</td><td>0.84</td><td>+51</td><td>5.8</td></tr><tr><td>Q1623-BX599</td><td>LGS</td><td>17.0</td><td>50"</td><td>0"76 (0"17)</td><td>9.6 (11.9)</td><td>1.64 (0.02)</td><td>0"18</td><td>0.97</td><td>+75</td><td>13</td></tr><tr><td>Q2343-BX389</td><td>LGS-SE</td><td>...</td><td>...</td><td>0"77 (0"13)</td><td>4.6 (1.9)</td><td>1.31 (0.05)</td><td>0"21</td><td>0.92</td><td>+19</td><td>14</td></tr><tr><td>Q2343-BX513</td><td>LGS</td><td>13.6</td><td>51"</td><td>0"85 (0"00)</td><td>2.3 (0.0)</td><td>1.28 (0.00)</td><td>0"16</td><td>0.88</td><td>+1</td><td>20</td></tr><tr><td>Q2343-BX610</td><td>LGS-SE</td><td>...</td><td>...</td><td>0"94 (0"24)</td><td>2.8 (0.9)</td><td>1.33 (0.06)</td><td>0"24</td><td>0.95</td><td>+47</td><td>6.7</td></tr><tr><td>Q2346-BX482</td><td>LGS</td><td>15.4</td><td>50"</td><td>0"83 (0"25)</td><td>3.2 (1.8)</td><td>1.17 (0.07)</td><td>0"19</td><td>0.91</td><td>-85</td><td>13</td></tr><tr><td>Deep3a-6004</td><td>LGS</td><td>15.8</td><td>49"</td><td>0"87 (0"16)</td><td>3.2 (1.0)</td><td>1.17 (0.17)</td><td>0"16</td><td>0.98</td><td>+87</td><td>24</td></tr><tr><td>Deep3a-6397</td><td>LGS</td><td>16.8</td><td>26"</td><td>0"81 (0"22)</td><td>6.5 (4.1)</td><td>1.09 (0.08)</td><td>0"22</td><td>0.77</td><td>+83</td><td>12</td></tr><tr><td>Deep3a - 15504</td><td>NGS</td><td>16.3</td><td>17"</td><td>1"02 (0"38)</td><td>6.2 (5.5)</td><td>1.08 (0.07)</td><td>0"16</td><td>0.74</td><td>+75</td><td>5.8</td></tr><tr><td>K20-ID6</td><td>LGS</td><td>15.3</td><td>55"</td><td>0"90 (0"21)</td><td>3.2 (0.9)</td><td>1.13 (0.10)</td><td>0"22</td><td>0.88</td><td>-71</td><td>13</td></tr><tr><td>K20-ID7</td><td>LGS</td><td>17.8</td><td>39"</td><td>0"70 (0"22)</td><td>4.2 (1.6)</td><td>1.06 (0.07)</td><td>0"16</td><td>0.88</td><td>+90</td><td>23</td></tr><tr><td>GMASS-2303</td><td>LGS</td><td>17.2</td><td>25"</td><td>0"76 (0"14)</td><td>3.1 (0.5)</td><td>1.23 (0.30)</td><td>0"19</td><td>0.81</td><td>+17</td><td>25</td></tr><tr><td>GMASS-2363</td><td>NGS</td><td>13.5</td><td>16"</td><td>0"88 (0"27)</td><td>5.0 (3.6)</td><td>1.45 (0.26)</td><td>0"17</td><td>0.94</td><td>+84</td><td>13</td></tr><tr><td>GMASS-2540</td><td>LGS</td><td>16.5</td><td>42"</td><td>1"24 (0"43)</td><td>3.0 (1.3)</td><td>1.10 (0.11)</td><td>0"18</td><td>0.88</td><td>-8</td><td>20</td></tr><tr><td>SA12-6339</td><td>LGS</td><td>14.5</td><td>57"</td><td>1"05 (0"24)</td><td>2.7 (0.8)</td><td>1.14 (0.08)</td><td>0"15</td><td>0.89</td><td>+58</td><td>19</td></tr><tr><td>ZC400528</td><td>NGS</td><td>15.1</td><td>7"</td><td>1"02 (0"31)</td><td>2.5 (0.7)</td><td>1.18 (0.06)</td><td>0"16</td><td>0.94</td><td>+30</td><td>22</td></tr><tr><td>ZC400569</td><td>NGS</td><td>15.2</td><td>20"</td><td>0"86 (0"26)</td><td>3.9 (3.3)</td><td>1.26 (0.13)</td><td>0"16</td><td>0.89</td><td>-73</td><td>18</td></tr><tr><td>ZC401925</td><td>NGS</td><td>16.1</td><td>24"</td><td>0"82 (0"31)</td><td>5.2 (5.9)</td><td>1.46 (0.22)</td><td>0"27</td><td>0.85</td><td>+71</td><td>10</td></tr><tr><td>ZC403741</td><td>NGS</td><td>14.3</td><td>15"</td><td>0"79 (0"23)</td><td>4.7 (3.5)</td><td>1.13 (0.00)</td><td>0"17</td><td>0.89</td><td>+51</td><td>15</td></tr><tr><td>ZC404221</td><td>NGS</td><td>15.9</td><td>8"</td><td>0"97 (0"12)</td><td>3.4 (0.5)</td><td>1.31 (0.12)</td><td>0"21</td><td>0.96</td><td>+89</td><td>14</td></tr><tr><td>ZC405226</td><td>NGS</td><td>16.7</td><td>5"</td><td>0"92 (0"24)</td><td>4.5 (4.1)</td><td>1.25 (0.13)</td><td>0"25</td><td>0.96</td><td>+83</td><td>8.7</td></tr><tr><td>ZC405501</td><td>NGS</td><td>15.2</td><td>21"</td><td>0"94 (0"22)</td><td>5.4 (0.9)</td><td>1.23 (0.15)</td><td>0"22</td><td>0.60</td><td>+76</td><td>15</td></tr><tr><td>ZC406690</td><td>NGS</td><td>14.9</td><td>18"</td><td>0"87 (0"36)</td><td>5.0 (2.6)</td><td>1.36 (0.20)</td><td>0"18</td><td>0.89</td><td>+69</td><td>20</td></tr><tr><td>ZC407302</td><td>LGS</td><td>14.2</td><td>39"</td><td>0"86 (0"16)</td><td>4.1 (1.1)</td><td>1.23 (0.12)</td><td>0"17</td><td>0.89</td><td>+75</td><td>23</td></tr><tr><td>ZC407376</td><td>NGS</td><td>16.6</td><td>22"</td><td>0"92 (0"24)</td><td>4.9 (3.0)</td><td>1.30 (0.20)</td><td>0"23</td><td>0.88</td><td>+82</td><td>13</td></tr><tr><td>ZC409985</td><td>NGS</td><td>13.4</td><td>17"</td><td>0"75 (0"29)</td><td>3.6 (1.6)</td><td>1.25 (0.07)</td><td>0"14</td><td>0.90</td><td>+78</td><td>27</td></tr><tr><td>ZC410041</td><td>NGS</td><td>14.0</td><td>21"</td><td>0"97 (0"23)</td><td>4.2 (1.6)</td><td>1.33 (0.21)</td><td>0"17</td><td>0.93</td><td>+60</td><td>24</td></tr><tr><td>ZC410123</td><td>LGS</td><td>17.6</td><td>25"</td><td>0"64 (0"08)</td><td>5.7 (0.6)</td><td>1.26 (0.13)</td><td>0"20</td><td>0.88</td><td>+76</td><td>14</td></tr><tr><td>ZC411737</td><td>LGS</td><td>14.6</td><td>29"</td><td>1"14 (0"32)</td><td>9.6 (9.0)</td><td>1.22 (0.14)</td><td>0"20</td><td>0.95</td><td>+40</td><td>13</td></tr><tr><td>ZC412369</td><td>LGS</td><td>11.8</td><td>29"</td><td>1"04 (0"16)</td><td>4.5 (3.3)</td><td>1.24 (0.10)</td><td>0"16</td><td>0.85</td><td>+48</td><td>23</td></tr><tr><td>ZC413507</td><td>NGS</td><td>12.7</td><td>29"</td><td>1"15 (0"41)</td><td>3.5 (1.4)</td><td>1.19 (0.06)</td><td>0"15</td><td>0.93</td><td>+40</td><td>32</td></tr><tr><td>ZC413597</td><td>NGS</td><td>15.6</td><td>28"</td><td>0"88 (0"17)</td><td>8.5 (5.5)</td><td>1.36 (0.19)</td><td>0"18</td><td>0.93</td><td>+12</td><td>19</td></tr><tr><td>ZC415876</td><td>NGS</td><td>13.5</td><td>27"</td><td>0"86 (0"28)</td><td>6.9 (3.9)</td><td>1.17 (0.07)</td><td>0"15</td><td>0.91</td><td>-83</td><td>25</td></tr></tbody></table>

**Notes.**

<sup>a</sup> The R-band magnitude of the reference star used for the AO correction in NGS mode or tip-tilt correction in LGS mode. In LGS-SE mode (used for Q2343-BX389 and Q2343-BX610), no tip-tilt correction was applied.

<sup>b</sup> The average optical seeing measured at zenith, coherence time τ₀, and airmass over all individual exposures of the PSF calibration star, with the standard deviation given in parentheses (a standard deviation of zero indicates that only a single measurement/exposure is available).

<sup>c</sup> Characteristics of the PSF associated with the final reduced data of each source (see Section 3.3): the major-axis FWHM, axis ratio, and PA (in degrees east of north) of the best-fit 2D elliptical Gaussian and the Strehl ratio measured based on the PSF star's image.

an amplitude about 5 times higher than the broad component. For aperture diameters larger than 0"6, the three-times-wider broad component starts to dominate the enclosed flux and reaches a total of 63%. Because of the significant power in the PSF halo, it is important to assess its impact in the derivation of intrinsic galaxy properties from the data (such as sizes, rotation velocities, and intrinsic velocity dispersions), albeit in an average sense, since it does not capture galaxy-to-galaxy PSF variations.

## Appendix B
Line-spread Functions

To characterize the effective spectral resolution of our SINFONI 50 mas pixel⁻¹ K- and H-band data, we extracted spectra of the night-sky emission in circular apertures of

1" radius in "sky" cubes, obtained by reducing the data but without background subtraction (see FS09). We coaveraged the profiles in velocity space of several of the brighter emission features in each of K and H that have no neighboring line within ±300 km s⁻¹ with peak amplitude greater than 1% of the lines considered. Most of these features consist of blended pairs, but their separations are <5 km s⁻¹ in K and <18 km s⁻¹ in H such that they approximate a single line at SINFONI's resolution. The average LSFs are plotted in Figure 14. Their profile is close to Gaussian with FWHM = 85 and 120 km s⁻¹ in K and H, respectively. Slight deviations from a pure Gaussian are nonetheless apparent, but the power in these wings compared to the total in the empirical profile is small: about 12% in K and 5% in H. Variations in the best-fit FWHM of the effective LSFs are <15% across the K band and <10% across the H band. We note that the low-level wings have a
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Impact of tip-tilt star brightness and observing conditions on the AO performance for our data sets. Individual elliptical symbols have sizes proportional to the major- and minor-axis FWHMs of the PSF and orientation corresponding to its PA. The color coding scales linearly with the estimated Strehl ratio, as shown by the color bar in each panel. Top left: PSF properties as a function of the AO star R-band magnitude. Top right: PSF properties as a function of the average airmass of the individual PSF star observations. Bottom left: PSF properties as a function of the average optical ($\lambda = 0.5$ µm) seeing measured at zenith. Bottom right: PSF properties as a function of the average atmospheric coherence time $\tau_0$. The vertical error bars correspond to the OB-to-OB variations in PSF FWHMs, and the horizontal error bars indicate the standard deviation of the observing conditions recorded for the individual PSF star exposures. Data taken in NGS, LGS, and LGS-SE modes are indicated with gray, black, and pink symbol outlines, respectively. The FWHM and Strehl ratio are more closely coupled with the brightness of the AO star, less with the airmass and $\tau_0$, and little if at all with the optical seeing at zenith.</figcaption></figure>

negligible impact on single-Gaussian spectral fits as used throughout this paper, but their effects should be considered when investigating detailed line profile properties.

## Appendix C

### Impact of Broad Underlying Emission on the Extracted Emission-line Properties

Our line fits assumed a single-Gaussian component for the emission lines of interest. This approach provides a satisfactory representation of the observed line profiles for most sources on an individual basis. The typical line widths, profiles, and [N II]/Hα ratios indicate that the emission is generally dominated by star-forming regions across the galaxies. However, a broader underlying component attributed to ionized gas outflows discovered in our SINS/zC-SINF galaxies and driven by star formation and/or an AGN (Shapiro et al. 2009; Genzel et al. 2011, 2014b; Newman et al. 2012a, 2012b; Förster Schreiber et al. 2014) is thus not taken into account. Because of its large width and low amplitude, the broad component is generally unnoticed in the spectrum of individual pixels or small regions within the galaxies. It becomes more clearly

apparent in the spatially integrated spectrum of some galaxies or brightest clumps individually and in coadded spectra of galaxies. From the latter higher-S/N data, the derived flux and width relative to the narrow component, together with the modest velocity offsets by up to several tens of km s⁻¹, indicate that such a broad component could make up a significant fraction of the fluxes from single-component fits and affect the inferred line widths.

To estimate the possible impact of a broad component to our Hα measurements, we generated sets of 5000–6000 simulated spectra as follows. We created mock line profiles consisting of a narrow and broad component with ranges of intrinsic line widths $\sigma_{narrow}$ and $\sigma_{broad}$, velocity offsets $dv_{broad}$ of the broad component relative to the narrow component, and broad-to-narrow flux ratios $F_{broad}/F_{narrow}$. The values were drawn randomly from uniform distributions based on our analyses of the best individual cases and stacked spectra with high S/N exhibiting broad emission (Newman et al. 2012a; Förster Schreiber et al. 2014; Genzel et al. 2014b): $\sigma_{narrow} = 50–120$ km s⁻¹, $\sigma_{broad} = 130–1300$ km s⁻¹, $dv_{broad} = -100$ to +100 km s⁻¹, and $F_{broad}/F_{narrow} = 0–3$. In order to simulate realistic noise properties, we inserted the mock line profiles convolved with the instrumental LSF at random
<figure><img src="image_16.png" /><figcaption>**Figure 13.** Detailed profile characteristics derived from the high-S/N averaged image of all PSFs associated with the combined data cubes of the sample. From left to right, the panels in each row show the average PSF image, best-fitting model, fit residuals, and curves of growth of the data and model. Top row: results for a single-component 2D elliptical Gaussian fit. In the middle left panel, cuts through the PSF image (white solid line) and best-fit model (red solid line) are plotted on the bottom and left axes. In the middle right panel, cuts on the residual image are plotted (red solid line) on the same scale as for the PSF image profiles (white solid line). In the right panel, the normalized curves of growth in circular apertures of the average PSF and the single-component model are plotted in black and red, respectively. Bottom row: similar series of panels showing the results for a double-component 2D elliptical Gaussian fit. In the middle left panel, the axis profiles for the observed average PSF, total model fit, and individual narrow core and broad halo components are plotted (white, red, yellow, and green solid lines, respectively). In the right panel, the individual curves of growth of the core and halo are shown (yellow and green solid lines) along with those of the observed and total model fit (black and red solid lines). In addition, the variations of the fractional contributions to the total flux of the core and halo are plotted (yellow and green dashed lines). The double-component model provides a much better representation of the PSF profile and curve of growth, and the low-amplitude but wide halo dominates the total flux for aperture diameters >0.6".</figcaption></figure>

wavelength positions in actual spectra taken from our data sets, avoiding the intervals with emission lines from the real galaxies. The total line fluxes were scaled randomly so as to uniformly cover the typical ranges of fluxes and S/Ns of our Hα maps and aperture spectra (S/N ~ 3–50). We then fitted the resulting mock spectra assuming a single-Gaussian line profile following the method applied for the real data (Section 4.1).

The results are shown in Figure 15 for one set of 6000 simulations inserted into the real data of Q2343-BX610 (results using the data of other galaxies observed in the K or H bands are very similar). The plots show the effects on the flux, LSF-corrected width, and velocity centroid from the single-Gaussian fits to the mock spectra ($F_{1comp}$, $\sigma_{1comp}$, $dv_{1comp}$) relative to the input narrow-component parameters as a function of the broad-component width and broad-to-narrow flux ratio. The line fluxes and widths are most affected by the underlying broad component when it is not explicitly accounted for in the fitting. As expected, the impact becomes more important toward higher broad-to-narrow flux ratios and narrower widths of the broad component. For broad emission with $F_{broad}/F_{narrow} \sim 0.7$ and $\sigma_{broad} \sim 200$ km s$^{-1}$, characteristic of star formation-driven outflows as derived from coadded spectra of clumps, $log(M_*/M_\odot) \lesssim 10.6$ galaxies, and outer disk regions of $log(M_*/M_\odot) \gtrsim 10.6$ galaxies (Newman et al. 2012a, 2012b; Förster Schreiber et al. 2014; Genzel et al. 2014b), the $F_{1comp}$ typically overestimates $F_{narrow}$ by 50%, and the $\sigma_{1comp}$ typically is 30% larger than $\sigma_{narrow}$. In the presence of a broader AGN-driven nuclear outflow with representative

$F_{broad}/F_{narrow} \sim 0.7$ and $\sigma_{broad} \sim 700$ km s$^{-1}$ based on coadded nuclear spectra of $log(M_*/M_\odot) \gtrsim 10.6$ galaxies (Förster Schreiber et al. 2014; Genzel et al. 2014b), the $F_{1comp}$ and $\sigma_{1comp}$ are typically 20% larger than the $F_{narrow}$ and $\sigma_{narrow}$. The largest effects are seen for $F_{broad}/F_{narrow} > 1$ and $\sigma_{broad} \sim 200–500$ km s$^{-1}$, where $F_{1comp}$ typically exceeds $F_{narrow}$ by factors of at least 1.5 and $\sigma_{1comp}$ exceeds $\sigma_{narrow}$ by factors of 1.3 or more. In contrast, the impact on $dv_{1comp}$ is small and comparable to half the resolution element in velocity; a larger (but still typically modest) velocity offset requires $F_{broad}/F_{narrow} > 2$. There is no strong trend with input $\sigma_{narrow}$ or with the flux level and S/N, although the scatter in $F_{1comp}/F_{narrow}$, $\sigma_{1comp}/\sigma_{narrow}$, and $v_{1comp} - v_{narrow}$ increases by a factor of ~2–4 from the highest to lowest S/N ratios.

Despite the sensitivity of our AO data sets, the S/N is still insufficient to reliably fit double Gaussians to the line emission at the pixel level and for small apertures. The analysis above suggests that the impact of a broad component on our single-Gaussian fits could be nonnegligible but overall modest, and it is not expected to strongly bias the sample results. Indeed, from stacking analysis, the broad emission from star formation-driven outflows was found to depend most strongly on the SFR surface density and become important ($F_{broad}/F_{narrow} > 0.5$) at $\Sigma(\text{SFR}) \gtrsim 1 M_\odot \text{ yr}^{-1} \text{ kpc}^{-2}$ (Newman et al. 2012a). For our SINS/zC-SINF AO sample, SFR surface densities are below this threshold over $\gtrsim 70\%$ of the area. Nuclear AGN-driven outflows are only detected in the inner $r \lesssim 0.6$" regions of the
<figure><img src="image_17.png" /><figcaption>**Figure 14.** The LSFs of our reduced SINFONI data at 50 mas pixel⁻¹ from the average profile of several telluric OH lines. Left: LSF in *K* band. Right: LSF in *H* band. In each panel, the average observed profile from the data (black line), the best-fit single-Gaussian profile (cyan filled curve), and the residuals (orange line) are plotted. The best-fit Gaussian has a velocity FWHM = 85 km⁻¹ in *K* and 120 km⁻¹ in *H*. Broader wings are apparent in the observed LSFs, which contain 12% and 5% of the total flux in *K* and *H*, respectively.</figcaption></figure>

six most massive galaxies of our AO sample (Förster Schreiber et al. 2014).

Two examples from our sample where the broad emission noticeably affects the emission and kinematic maps as extracted in this paper are ZC406690 and Deep3a-6004. In the former galaxy, the brightest among our AO sample, particularly strong, broad, blueshifted emission with FWHM ~500–600km s⁻¹ tracing outflowing gas in/around clumps on the southwest side of the Hα and rest-UV/optical ringlike structure visibly distorts the velocity and dispersion maps obtained from single-Gaussian fits (see Figure 16), leading to significant local residuals relative to the best-fit kinematic disk model (Genzel et al. 2011, 2017). For Deep3a-6004, our most massive galaxy, broad FWHM ~900 km s⁻¹ and high-excitation ([N II]/Hα ~1) emission tracing an AGN-driven outflow dominates around the kinematic center, causing the twist of the isovelocity lines and the slight asymmetry in the flux and dispersion maps presented here (see Figure 16). This object has by far the largest nuclear F_broad/F_narrow ratio (~3), such that narrower line emission that would trace star formation around the center is comparatively very weak (Förster Schreiber et al. 2014; Genzel et al. 2014a). In other galaxies of our sample where broad emission is detected, its effects are less important.

## Appendix D
### Presentation of the Full AO Data Sets

Figure 16 shows the main line emission and kinematic maps extracted from the SINFONI data cubes for our SINS/zC-SINF AO sample, along with high-resolution near-IR broadband maps and, when available, stellar mass maps. Each row presents the maps of a given galaxy. The leftmost panels show near-IR broadband maps, probing the rest-optical continuum at ~0.′′2 resolution. For 31 objects, the imaging was obtained with HST in the *H* band using either the WFC3/IR or the NICMOS/NIC2 camera (Tacchella et al. 2015b; see also Förster Schreiber et al. 2011a; Law et al. 2012b). For the other four objects, the maps were synthesized from the SINFONI+AO data cubes (see Section 4.2) in the *H* band for *z* < 2 sources (D3a-6397 and ZC403741) and in the *K* band for sources at *z* > 2 (Q2343-BX513 and SA12-6339). The next two panels show the velocity-integrated flux for Hα and [N II] λ6584 at each pixel position. The fourth and

fifth panels show the velocity field (relative to the systemic velocity) and velocity dispersion maps of Hα. The velocity dispersion map is corrected for the instrumental spectral resolution. The rightmost panels show the distribution of stellar mass surface density, Σ(M_★), from Tacchella et al. (2015b), available for 29 of the galaxies. These mass maps were derived from *J* − *H* color maps obtained with the HST WFC3/IR and/or NICMOS/NIC2 cameras.

The galaxy, its Hα redshift, the AO observing mode, and the total on-source integration time with SINFONI and HST are given at the top of the two first panels on the left. The color coding for the emission maps scales linearly with flux from dark blue to red/white for the minimum to maximum levels displayed (varying for each galaxy). The scaling between the Hα and [N II] maps is tied such that the minimum is the same and the maximum level of the [N II] map is half that of the Hα map. The color coding for the velocity and dispersion maps scales linearly from blue to red following the color bar in the respective panels. The color coding for the stellar mass maps scales linearly from blue to red with log(Σ(M_★)) following the color bar in each panel and where the surface density is in units of M☉ kpc⁻². Black contours in all maps correspond to Hα fractional flux levels relative to the maximum of 0.2, 0.4, 0.6, 0.8, and 0.95. The FWHM spatial resolution is represented by the filled circle at the bottom left of the HST maps and the filled ellipse for the SINFONI+AO maps; the latter reflects the slightly asymmetric AO PSFs and represents the effective resolution, including the effects of the median filtering applied spatially in extracting the maps from the data cubes. The angular scale is indicated by the vertical bars in the leftmost panels. The black crosses indicate the center of the galaxy.

## Appendix E
### Comparison of Data and Measurements from AO-assisted and Seeing-limited Observations

Since every galaxy of our SINS/zC-SINF AO sample was first observed under natural seeing conditions, we examined the consistency of the basic data and measurements obtained at a different resolution. This comparison entails different integration times (hence sensitivities) and often long time periods covered by the observations of an object (in between which instrumental interventions were carried out). Therefore, it is not
<figure><img src="image_18.png" /><figcaption>**Figure 15.** Impact of the presence of a broad emission component underneath narrow line emission on measurements based on single-Gaussian profile fits. The results plotted are for a subset of the simulations carried out for the case of the spectral resolution of the SINFONI K-band data taken in the 50 mas pixel⁻¹ scale, with simulated double-Gaussian profiles inserted at random wavelengths in the real data of Q2343-BX610 and other assumed line parameters as described in the text of Appendix C. Left: ratio of the measured line flux from the single-Gaussian fit to the input flux in the narrow component ($F_{1comp}/F_{narrow}$) vs. input velocity width of the broad component ($\sigma_{broad}$). Middle: same as the left panel but for the ratio of the measured velocity width (corrected for LSF smearing) to the input velocity width of the narrow component ($\sigma_{1comp}/\sigma_{narrow}$). Right: same as the other panels but for the absolute value of the velocity offset in measured line centroid relative to the input narrow component ($dv_{1comp}$). In all panels, individual points show the results of 6000 simulated spectra, color-coded according to the input broad-to-narrow component flux ratio as labeled in the top right. Large white filled circles with error bars show the median and central 68% of the full distribution in bins of input $\sigma_{broad}$; large white filled squares show the average in the same bins. Thick colored lines indicate the median trends split in bins of broad-to-narrow component flux ratios ($F_b/F_n$) centered on the values labeled in the plots. The gray hatched band shows the dispersion corresponding to the LSF. In the left and middle panels, black horizontal lines indicate ratios of 1, 1.3, and 1.5; in the right panel, they show velocity offsets of 0, 0.5, and 1.0 times the spectral-resolution element. The presence of a broad component leads to overestimates in line flux and width exceeding 30% only when $F_{broad}/F_{narrow}$ approaches or exceeds unity, and $\sigma_{broad} \sim 200–500$ km s⁻¹.</figcaption></figure>

strictly an assessment of the effects of resolution, but it also provides an instructive view on how various observational factors may impact data obtained with different strategies or IFU instruments.

### E.1. Visual Inspection

Figure 17 compares the SINFONI Hα line, velocity, and velocity dispersion maps; p-v diagrams along the major axis; and source-integrated spectra extracted in circular apertures obtained with AO-assisted observations and in seeing-limited mode. Successive rows are grouped pairwise for each galaxy, with the AO and seeing-limited data shown in the top and bottom row of a pair, respectively. Q1623-BX502 is excluded, as it was only observed in AO mode. The area covered by the AO maps is outlined with a dotted yellow square on the seeing-limited maps. The labels, color coding, contour levels, and orientation of the maps follow the same scheme as used in Figure 16. In addition, the dashed rectangle and solid circle overlaid on the Hα line maps show the synthetic slit and the aperture used to extract the p-v diagrams and the integrated spectra, respectively. In the p-v diagrams, the horizontal axis corresponds to the velocity relative to the systemic velocity, and the vertical axis corresponds to the spatial position along the synthetic slit, with bottom to top running from the south to the north end of the slit. The angular scale is indicated by the vertical bar on the left, and the color scale is identical to that of the Hα line map of the object. The wavelength range displayed for the integrated spectra corresponds to the velocity range shown for the p-v diagrams (±2500 km s⁻¹ around Hα). The error bars show the 1σ uncertainties derived from the noise properties of each data set and include the scaling with aperture size described in Section 3.2, which accounts for the fact that the effective noise is not purely Gaussian. The continuum emission has been subtracted in the spectra. Green hatched bars show the location of bright night-sky lines with widths

corresponding to the FWHM of the effective spectral resolution of the data.

In general, and considering the differences in angular resolution and integration times, the AO and seeing-limited results are very consistent with each other. In all cases, the integrated line profile shapes agree well, more so for the objects with the highest-S/N spectra. Clearly, the level to which the maps and p-v diagrams agree depends primarily on the S/N achieved, resulting from the combination of integration time and surface brightness distribution of the galaxies. The typically 3 times higher resolution and roughly 3.5 times higher sensitivity of the AO data sets obviously reveal in more detail the morphology and kinematics of the Hα line emission. On the other hand, the wider FOV of the no-AO data probes the extended emission (or lack thereof) out to 1.5–2 times larger radii. As long as a source is sufficiently well resolved in the no-AO data ($r_{1/2}^{\text{circ}} \gtrsim 3$ kpc, about half of the galaxies), the broad features of the velocity field can be recognized (presence and direction of velocity gradients), and the p-v diagrams show qualitatively similar spatial variations in velocities and line widths along the major axis. Lower S/N sometimes also leads to more important differences in the Hα morphologies (e.g., ZC410041, ZC400569).

The largest diversity of changes in the appearance of the maps and p-v diagrams occurs (unsurprisingly) for the smaller sources, with $r_{1/2}^{\text{circ}} \lesssim 3$ kpc. These cases can be split as follows. For six objects, significant velocity gradients were detected in the no-AO data and are confirmed in the AO data, which further resolve clumps and/or more diffuse extensions in the Hα maps (Q1623-BX543, GMASS-2363, ZC400528, ZC403741, ZC412369, and ZC415876). For eight other objects, structure is resolved in the Hα morphology and/or velocity field and p-v diagrams from the AO data that were not, or only marginally, apparent in the no-AO observations (Q1623-BX455, Q1623-BX599, Q2343-BX513, GMASS-2303, ZC401925, ZC409985, ZC411737, and ZC413507).
<figure><img src="image_19.png" /><figcaption>**Figure 16.** High-resolution near-IR broadband images (in the H or K band), Hα and [N II] emission-line maps, Hα velocity and velocity dispersion maps, and stellar mass maps, when available (based on HST imaging), of the SINS/zC-SINF AO sample, as described in Appendix D.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure 16. (Continued.)</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure 16. (Continued.)</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure 16. (Continued.)</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure 16. (Continued.)</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>**Figure 17.** The Hα line flux, velocity, and velocity dispersion maps; *p*–*v* diagrams; and integrated spectra of the SINS/zC-SINF AO sample. Rows are grouped pairwise for each galaxy, showing the AO and seeing-limited data (top and bottom row, respectively) as described in Appendix E.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>
<figure><img src="image_32.png" /><figcaption>Figure 17. (Continued.)</figcaption></figure>

For the remaining three objects, both AO and no-AO data show compact and fairly featureless $H\alpha$ morphologies and kinematics (SA12-6339, ZC404221, and ZC413597).

## E.2. Quantitative Comparison of Extracted Properties

Figure 18 compares the results derived from the AO and seeing-limited data for selected basic measurements: the total $H\alpha$ flux and line width from the integrated spectrum, the half-light radius from the curve-of-growth analysis, and the maximum observed velocity difference, all extracted following the procedures described in Sections 4–6.

The best agreement is seen for the integrated $H\alpha$ line widths. On average (and median), the same values are obtained within 5% from the AO and seeing-limited data. The objects with the largest differences (up to a factor of ≈2) typically have short (1 hr) integrations and higher noise in their no-AO data. The AO-based total $H\alpha$ fluxes tend to be lower (by 10% on average and 14% on median), and the half-light radii $r_{1/2}^{\text{circ}}$ are smaller (by 20% on average and median) than those measured in the no-AO data. These differences are comparable to the measurement uncertainties, typically dominated by those of the flux calibration and continuum subtraction (Section 4.1) and PSF determination (Section 3.3). Part of the bulk offsets is driven by the smaller effective FOV of the AO-assisted observations limiting measurements of the most extended line emission in larger targets, notably for K20-ID7, GMASS-2540, and ZC406690, where the fluxes from the AO data miss up to roughly half the total flux. Another factor is the impact of the broad wings of the PSF$_{2\,G,\text{ave}}$ used in computing the intrinsic

radii, possibly leading to underestimates in the intrinsic size of the smallest sources. Using the PSF$_{1\,G,\text{gal}}$ associated with individual galaxies for the AO data instead brings the $r_{1/2}^{\text{circ}}$ for the compact objects in better agreement with those from the no-AO data, resulting in a smaller average (and median) size difference of 10% for the full sample. The choice of circular apertures to derive the total fluxes and half-light radii may also introduce some differences. Although they were chosen to enclose as well as possible the total $H\alpha$ emission based mainly on the curve-of-growth behavior (see Section 4.4), they may miss more of the extended emission for sources with the highest isophotal ellipticity and were different between the AO and seeing-limited data in most cases. To gauge the impact of these factors on the measurements, we estimated aperture corrections based on the 2D Sérsic models described in Section 5.3 for the $H\alpha$ structural parameters derived in Section 5.2 and convolved with the appropriate PSFs. With these corrections, the AO-based fluxes are then on average 4% (median 8%) lower than the no-AO-based ones, while the size differences remain essentially the same. The largest discrepancies are only modestly reduced because such simple aperture corrections do not capture the impact of S/N differences and clumpy irregular morphologies.

The comparison in observed velocity difference shows the expected effects of beam smearing. The agreement is best among the largest sources, with AO-based $\Delta v_{\text{obs}}$ on average ≈1.4 times higher (median ≈1.2) for the targets with $r_{1/2}^{\text{circ}} \gtrsim 3$ kpc. The difference among the smaller sources increases to an average and median factor of ≈1.7. Two of the most compact objects
<figure><img src="image_33.png" /><figcaption>**Figure 18.** Comparison of global galaxy properties measured from the AO-assisted vs. seeing-limited SINFONI data sets. Top left: $H\alpha$ fluxes from the integrated spectra in the total circular apertures. Top right: $H\alpha$ half-light radii from the curve-of-growth analysis in circular apertures. Bottom left: velocity dispersions from the line widths measured in the integrated spectra in the total circular apertures. Bottom right: observed maximum velocity difference from the $H\alpha$ kinematics. In all panels, the solid line corresponds to equality between the quantities compared, and the dashed lines indicate the range by a factor of two about the one-to-one relationship. The symbols are color-coded according to the logarithm of the ratio of integration times in AO and no-AO mode, as shown by the color bars. For the comparisons of total fluxes, velocity dispersions, and maximum observed velocity differences, the size of the symbols is proportional to the logarithm of the $H\alpha$ half-light radii measured from the AO data using the PSF<sub>2 G,ave</sub>; reference symbol sizes are plotted at the top left of the panels for three values of $r_{1/2}^{\text{eire}}$. For the comparison of half-light radii, the large circles correspond to the AO-based sizes derived using the PSF<sub>2 G,ave</sub> parameters for every galaxy, and the small squares represent those computed with the parameters of the PSF<sub>1 G,gal</sub> associated with each individual galaxy.</figcaption></figure>

(SA12-6339 and ZC409985) deviate from this beam-smearing-driven trend: the same low $\Delta v_{\text{obs}}$ is measured within the $1\sigma$ uncertainties between the AO and no-AO data, suggesting that these sources are genuinely dispersion-dominated or have very low inclination. With the beam-smearing corrections described in Section 6.1, the systematic offset is reduced to a mean and median factor of ≈1.2 and ≈1.6 for the larger and smaller sources, respectively. The AO versus no-AO differences also reflect in part the shallower seeing-limited data not fully

probing the velocity gradients in fainter or lower surface brightness objects (explaining, for instance, the nearly twice higher AO-based $\Delta v_{\text{obs}}$ for GMASS-2540 despite its large extent).

As a last comparison, Figure 19 shows the radial [N II]/$H\alpha$ gradients obtained from the AO and no-AO data sets. The measurements from the seeing-limited data were made in elliptical annuli with the same PA and similar axis ratio as used for the AO data and 2 pixel width and separation giving a 2.5 times coarser
<figure><img src="image_34.png" /><figcaption>**Figure 19.** Comparison of radial [N II]/H$\alpha$ gradients measured from the AO-assisted vs. seeing-limited SINFONI data sets. The gradients are derived from the [N II]/H$\alpha$ ratio measured in the coaveraged spectra of individual pixels within elliptical annuli. The data are shown for the nine targets for which the ratio can be measured over at least three annuli in both the AO and no-AO data. The solid line corresponds to the one-to-one relationship, and the dashed lines indicate offsets by $\pm 0.04$ dex kpc$^{-1}$, or factors of 0.9 and 1.1, about this relationship. The symbols are color-coded according to the logarithm of the ratio of AO to no-AO integration times as shown by the color bar, and their size is proportional to the logarithm of the curve-of-growth-based H$\alpha$ half-light radii measured from the AO data using the PSF$_{2\,G,ave}$; reference symbol sizes are plotted at the top left of the panel.</figcaption></figure>

sampling (i.e., 0.′′25). The comparison is restricted to the nine objects for which an [N II]/H$\alpha$ ratio can be measured in at least three annuli for both observing modes (Q2343-BX389, Q2343-BX599, Q2343-BX610, Deep3a-6004, Deep3a-6397, Deep3a-15504, ZC400569, ZC403741, and ZC407302). The $\Delta$N2/$\Delta$r from the higher-resolution observations are on average (and median) more negative by $\approx 0.035$ dex kpc$^{-1}$. The one exception is Deep3a-15504, where the gradient derived from the AO data is shallower ($-0.033 \pm 0.010$ compared to $-0.060 \pm 0.014$ dex kpc$^{-1}$). The strong, spatially resolved, and asymmetric broad H$\alpha$+[N II] emission associated with the AGN-driven outflow in this galaxy (Förster Schreiber et al. 2014) could cause this difference, given the simple single-Gaussian fits to the lines applied here. Aperture positioning may be an issue; for instance, small offsets could flatten a steep inner gradient, but we verified that this has little impact for this galaxy, and the restricted gradient (at $r > 0.′′3$; Section 8.1) is also shallower in the AO data.

In summary, the comparisons between AO and seeing-limited data presented in this appendix show an overall good agreement, with differences consistent with expectations from beam smearing and from varying S/N and effective FOV between the observations obtained in each mode. Although the agreement generally improves when applying aperture and beam-smearing corrections, there still remain noticeable differences. These corrections obviously do not, or poorly, account for emission components that may be undetected in the data. In addition, they are derived from simple models that do not capture the complexity of the galaxies that appears most prominently in the higher-resolution, and typically higher-S/N, AO-assisted data sets.

## Appendix F
MAPS and Radial Profiles of the [N II]/H$\alpha$ Ratio

Figure 20 shows the spatially resolved and integrated information from the [N II]/H$\alpha$ ratios extracted from the SINFONI AO data for the individual galaxies.

The first two panels from left to right show the velocity-integrated H$\alpha$ flux and [N II]/H$\alpha$ ratio maps. The galaxy, its H$\alpha$ redshift, the AO observing mode, and the total on-source integration time are given at the top of the H$\alpha$ line map. Galaxies hosting an AGN have the corresponding label at the top left of the [N II]/H$\alpha$ ratio map. The color coding for the H$\alpha$ maps scales linearly with flux from dark blue to red for the minimum to maximum levels displayed (varying for each galaxy). The color coding for the [N II]/H$\alpha$ ratio maps scales linearly from blue to red following the color bar in the respective panels. In the [N II]/H$\alpha$ maps, pixels for which the ratio has an S/N < 3 are masked out, and those for which the ratio has an S/N $\ge$ 3 but the H$\alpha$ flux is in the regime where the ratio distribution is biased toward high values (as described in Section 8.3; see below) are marked with a cross. Black contours in both maps correspond to H$\alpha$ fractional flux levels relative to the maximum of 0.2, 0.4, 0.6, 0.8, and 0.95. The spatial resolution is represented by the filled ellipse at the bottom left; the diameters along each axis correspond to the FWHMs and characterize the effective PSF, including the median filtering applied spatially in extracting the maps from the data cubes. The angular scale is indicated by the vertical bars on the left of the H$\alpha$ line map. The solid white ellipse overlaid on the maps shows the aperture used to extract the spectrum in the third panel. The black cross indicates the center of the galaxy. In all maps, north is up and east is to the left.

The third panel from the left shows the velocity-shifted, continuum-subtracted integrated spectrum extracted in the elliptical aperture marked on the maps. Before coadding the spectra of individual pixels, they are shifted according to the velocity field (see Figure 16) to bring the H$\alpha$ line centroid at zero offset relative to the systemic redshift. The elliptical apertures roughly trace the outer H$\alpha$ isophotes, further enhancing the resulting S/N compared to circular apertures. The error bars correspond to the $1\sigma$ uncertainties derived from the noise properties of each data set and include the scaling with aperture size following the model described in Section 3.2, which accounts for the fact that the effective noise is not purely Gaussian. Green hatched bars show the locations of bright night-sky lines, with width corresponding to the FWHM of the effective spectral resolution of the data.

The fourth panel from the left shows the radial variations of the [N II]/H$\alpha$ ratio, measured from velocity-shifted spectra extracted in elliptical annuli of the same axis ratio and PA as for the integrated spectrum plotted in the previous panel. The width of the annuli is two pixels, or 0.′′1. The half width at half maximum of the PSF core is plotted in units of the physical radius of the horizontal axis. The black dots and error bars give the [N II]/H$\alpha$ ratio measurements and $1\sigma$ uncertainties; downward arrows correspond to $3\sigma$ upper limits. In the fifth panel, the [N II]/H$\alpha$ ratio or upper limits thereof are plotted for individual pixels as a function of the deprojected radius from the center, where the parameters of the ellipse shown on the maps define the projection assuming a disk geometry. Ratios are plotted at the $3\sigma$ level if the formal S/N < 3. The color coding corresponds to the same flux levels as used for the H$\alpha$ maps. In both these panels, the horizontal thin orange and thick yellow lines indicate the [N II]/H$\alpha$ ratio and $1\sigma$ uncertainties
<figure><img src="image_35.png" /><figcaption>**Figure 20.** The Hα line maps, [N II]/Hα ratio maps, velocity-shifted integrated spectra, [N III]/Hα radial profiles in elliptical apertures, and distribution of [N II]/Hα ratios in individual pixels vs. (deprojected) radius and measured Hα line flux, as described in Appendix F. The color coding for the symbols in the two rightmost columns corresponds to the linear color scale used for the Hα maps in the leftmost column. In the [N II]/Hα map (second column from left), pixels with S/N < 3 in [N II]/Hα (below the 3σ curve in the rightmost column) are masked out; those with S/N ≥ 3 in [N II]/Hα but with Hα flux below the threshold where the pixel distribution becomes biased toward higher ratios (above the 3σ curve and within the gray hatched flux regime) are shown with a cross symbol overplotted.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Figure 20. (Continued.)</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>Figure 20. (Continued.)</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Figure 20. (Continued.)</figcaption></figure>
derived from the velocity-shifted integrated spectrum. The black line and gray shaded areas correspond to the best-fit linear gradient in $N2 \equiv \log([N\text{II}]/H\alpha)$ versus radius $r$ and range of slopes from the 68% confidence intervals obtained from a linear regression with censored data. The integrated $[N\text{II}]/H\alpha$ ratio and the best-fit linear gradient are labeled in each plot. For objects with evidence of an AGN, fits were also performed excluding the central $r < 0.3''$ regions (shown as hatched vertical bars in the fourth and fifth panels and indicated with a dashed magenta circle on the $H\alpha$ and $[N\text{II}]/H\alpha$ maps); the best-fit line and its uncertainties are overplotted, and the slope is labeled in magenta.

In the rightmost panel, the $[N\text{II}]/H\alpha$ ratios of the pixels are plotted versus their $H\alpha$ flux, with $1\sigma$ uncertainties. The black-and-white curve shows the $3\sigma$ limiting $[N\text{II}]/H\alpha$ ratio as a function of the $H\alpha$ flux derived for each object. The flux at which the pixel distribution starts to scatter below this limit then corresponds to the level at/below which the measurements become biased toward the higher $[N\text{II}]/H\alpha$ ratios; the hatched region marks this flux regime. In this and the fifth panel, the large filled symbols show the pixels in the unbiased flux regime, and the small filled and open symbols show those in the biased regime with a $>3\sigma$ and $<3\sigma$ $[N\text{II}]/H\alpha$ measurement, respectively. The average ratio for the unbiased pixels is labeled in the fifth panel. Pixels with a formal $>3\sigma$ $[N\text{II}]/H\alpha$ measurement but an $F(H\alpha)$ flux in the biased regime are those indicated with a superposed cross in the ratio maps of the second panel.

We note that here, as throughout the paper, the formal uncertainties on the line flux measurements are derived through a Monte Carlo procedure, where the input spectrum is perturbed according to the noise spectrum that includes the contribution from correlated noise on scales $>1$ pixel (Sections 3.2 and 4.1). Thus, the uncertainties on the $[N\text{II}]$ and $H\alpha$ fluxes in elliptical annuli are larger than would be expected from a simple $\propto\sqrt{N_{\text{pix}}}$ scaling for purely Gaussian uncorrelated noise, where $N_{\text{pix}}$ represents the number of pixels within a given annulus. This effect is reflected in the relative size of the error bars on the $[N\text{II}]/H\alpha$ ratios in annuli versus individual pixels (fourth to sixth panels in Figure 20).

## ORCID iDs

N. M. Förster Schreiber https://orcid.org/0000-0003-4264-3381

A. Renzini https://orcid.org/0000-0002-7093-7355

C. Mancini https://orcid.org/0000-0002-4297-0561

R. Genzel https://orcid.org/0000-0002-2767-9653

G. Cresci https://orcid.org/0000-0002-5281-1417

S. J. Lilly https://orcid.org/0000-0002-6423-3597

C. M. Carollo https://orcid.org/0000-0003-1624-7609

A. Cimatti https://orcid.org/0000-0002-4409-5633

E. Daddi https://orcid.org/0000-0002-3331-9590

S. Genel https://orcid.org/0000-0002-3185-1540

P. Lang https://orcid.org/0000-0002-5681-3575

D. Lutz https://orcid.org/0000-0003-0291-9582

H. J. McCracken https://orcid.org/0000-0002-9489-7765

M. Mignoli https://orcid.org/0000-0002-9087-2835

T. Naab https://orcid.org/0000-0002-7314-2558

P. Oesch https://orcid.org/0000-0001-5851-6649

S. Tacchella https://orcid.org/0000-0002-8224-4505

L. J. Tacconi https://orcid.org/0000-0002-1485-9401

S. Wuys https://orcid.org/0000-0003-3735-1931

G. Zamorani https://orcid.org/0000-0002-2318-301X

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