CONSTRAINTS ON THE ASSEMBLY AND DYNAMICS OF GALAXIES. I. DETAILED REST-FRAME OPTICAL MORPHOLOGIES ON KILOPARSEC SCALE OF z ∼ 2 STAR-FORMING GALAXIES^*

Table 1 lists the galaxies observed along with their photometric properties. They were drawn from the initial sample of 17 rest-UV-selected objects at z ∼ 2 from the SINS survey (Förster Schreiber et al. 2006b, 2009) carried out with SINFONI (Eisenhauer et al. 2003; Bonnet et al. 2004) at the ESO VLT. The galaxies were originally part of the large optical spectroscopic survey of z ∼ 1.5–2.5 candidates selected by their $U_{n}G\mathcal {R}$ colors described by Steidel et al. (2004, see also Adelberger et al. 2004). Additional multi-wavelength data include ground-based near-IR J and K_s imaging, and space-based Spitzer mid-IR photometry at 3–8 μm with IRAC and at 24 μm with MIPS for the majority of our targets (Erb et al. 2006; Reddy et al. 2010, and Förster Schreiber et al. 2009 for the K_s-band photometry of MD 41). Prior to the SINFONI observations, near-IR long-slit spectroscopy was obtained for all of our NIC2 targets with NIRSPEC at the Keck II telescope and ISAAC at the VLT by Erb et al. (2003, 2006) and Shapley et al. (2004).

Table 1. Galaxies Observed

Object	zHαa	Kinematic Typeb	Un	G	$\mathcal {R}$	J	H160	Ks
			(mag)	(mag)	(mag)	(mag)	(mag)	(mag)
Q1623-BX528	2.2683	Major merger	24.52 ± 0.18	23.81 ± 0.14	23.56 ± 0.13	22.44 ± 0.17	22.33 ± 0.06	21.61 ± 0.20
Q1623-BX663c	2.4332	Disk	25.40 ± 0.24	24.38 ± 0.17	24.14 ± 0.15	23.41 ± 0.30	22.79 ± 0.10	21.78 ± 0.21
SSA22a-MD41	2.1704	Disk	24.81 ± 0.11	23.50 ± 0.06	23.31 ± 0.05	⋅⋅⋅	22.64 ± 0.05	22.30 ± 0.36
Q2343-BX389	2.1733	Disk	26.39 ± 0.39	25.13 ± 0.19	24.85 ± 0.16	23.82 ± 0.24	23.11 ± 0.10	22.04 ± 0.25
Q2343-BX610c	2.2103	Disk	24.67 ± 0.21	23.92 ± 0.12	23.58 ± 0.11	22.35 ± 0.13	22.09 ± 0.06	21.07 ± 0.13
Q2346-BX482	2.2571	Disk	24.44 ± 0.12	23.54 ± 0.10	23.32 ± 0.09	⋅⋅⋅	22.34 ± 0.07	⋅⋅⋅

Notes. Magnitudes are given in the AB system. Optical, J and K_s magnitudes are taken from Erb et al. (2006; with the exception of SSA22a-MD41 for which the K_s magnitude was measured on NTT/SOFI imaging available from the ESO archive). The H₁₆₀-band magnitudes were measured from the new NICMOS/NIC2 data presented in this paper. ^aSystemic vacuum redshift derived from the integrated Hα line emission in the SINFONI data (Förster Schreiber et al. 2009). ^bClassification according to the Hα kinematics from SINFONI (Shapiro et al. 2008; Förster Schreiber et al. 2006b, 2009). ^cSpectral signatures of an AGN are detected in the optical and near-IR spectrum of Q1623-BX663 and the large-scale Hα kinematics suggest that the host galaxy is a low-inclination rotating disk (Erb et al. 2006; Förster Schreiber et al. 2006b, 2009). The Spitzer/MIPS fluxes of Q1623-BX663 and Q2343-BX610 are indicative of obscured AGN activity (Reddy et al. 2010).

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The choice of our NIC2 targets was primarily driven by their kinematic nature along with their high signal-to-noise ratio (S/N), high-quality SINFONI data mapping the spatial distribution, and relative gas motions from Hα out to radii $\rm \gtrsim 10 \;kpc$ (Förster Schreiber et al. 2006b). They include five rotating disks (BX 663, MD 41, BX 389, BX 610, and BX 482) and one major merger (BX 528). The quantitative kinematic classification performed through application of kinemetry is described by Shapiro et al. (2008), and detailed dynamical modeling of the disks is presented by Genzel et al. (2008) and Cresci et al. (2009). The disks show the expected signatures of a fairly ordered two-dimensional velocity field, with a monotonic gradient across the source and flattening of the velocity curve at large radii, alignment of the Hα kinematic and morphological major axes, and peak of the velocity dispersion close to the dynamical and geometrical center. In contrast, BX 528 exhibits a reversal in velocity gradient along the major axis, as observed in nearby counterrotating binary mergers. Interestingly, the Hα morphology of this merger from the seeing-limited SINFONI data does not show features that would distinguish it from the disks; all sources have extended, more or less irregular/clumpy Hα distributions at a typical seeing-limited resolution of ≈05.

Two of our targets (BX 663 and BX 610) are candidate active galactic nucleus (AGN) hosts on the basis of their observed mid-IR spectral energy distributions (SEDs) from Spitzer IRAC and MIPS photometry (Reddy et al. 2010; N. Reddy 2010, private communication). BX 663 also exhibits spectral signatures of Type 2 AGN in its integrated rest-UV and rest-optical spectrum (Shapley et al. 2004; Erb et al. 2006). In our spatially resolved SINFONI data (as well as the new NIC2 imaging presented in this paper), the host galaxy is well detected and can be distinguished from the central compact emission peak with higher [N ii]/Hα and broad Hα velocity component associated with the AGN, underneath the narrower component dominated by star formation. In contrast, BX 610 exhibits no sign of AGN in the rest-frame UV and optical, including the spatially and spectrally resolved SINFONI data, so that its AGN is likely to be very obscured and will not affect any aspect of our analysis. Therefore, in the context of this paper, we will only consider BX 663 explicitly as an AGN source.

The SINFONI data sets of our NIC2 targets are fully described by Förster Schreiber et al. (2009). They are among the deepest of the SINS survey, with on-source integration times in the K band (targeting the Hα and [N ii] λλ6548, 6584 emission lines) ranging from 3 to 7.3 hr. All galaxies were first observed using the largest pixel scale ($\rm 0\farcs 125\,pixel^{-1}$), five of them in seeing-limited mode under very good seeing conditions, and one of them (BX 663) with the aid of AO using a nearby natural guide star. The typical effective angular resolution of these SINFONI K-band data has an $\rm FWHM \approx 0\farcs 5$, corresponding to $\rm {\approx} 4.1 \;kpc$ at the redshift of the sources ($\rm FWHM = 0\farcs 39$ or 3.2 kpc for the NGS-AO data of BX 663). Seeing-limited H-band data were taken for all but BX 528 to map the [O iii] λλ4959, 5007 and Hβ emission lines, also under a very good near-IR seeing of ≈055 and using the $\rm 0\farcs 125\;pixel^{-1}$ scale. In addition, Laser Guide Star (LGS) AO-assisted K-band observations were obtained for BX 482 using the intermediate pixel scale of $\rm 0\farcs 05\;pixel^{-1}$, with a total on-source integration time of 6.8 hr and an effective resolution of 017 (1.4 kpc), very similar to that of the NIC2 1.6 μm imaging.

The central averaged Hα surface brightness (within the Hα half-light radius) of the NIC2 targets ranges from $\rm {\approx} 1 \times 10^{-17}$ to $\rm {\approx} 1 \times 10^{-16} \;erg\;s^{-1}\;cm^{-2}\;arcsec^{-2}$. Using the conversion factor of Kennicutt (1998) between the Hα luminosity and SFR, divided by 1.7 to scale from a Salpeter (1955) to a Chabrier (2003) initial mass function (IMF), and accounting for beam smearing in computing the intrinsic physical area, we calculate SFRs per unit area of ≈0.15–0.4 M_☉ yr^-1 kpc⁻² (uncorrected for dust extinction). The median S/N per pixel of the Hα maps over the regions where line emission is detected (i.e., $\rm S/N > 3$) is ≈10–15 for the six galaxies. From the velocity-integrated line maps and the noise properties of the data cubes (see details in Förster Schreiber et al. 2009), the 3σ Hα surface brightness sensitivities are typically $\rm {\approx} 10^{-17} \;erg\;s^{-1}\;cm^{-2}\;arcsec^{-2}$, corresponding to a limiting SFR of ≈0.03 M_☉ yr^-1 kpc⁻².

The NICMOS observations were carried out between 2007 April and 2007 September with the NIC2 camera onboard the HST and using the F160W filter (hereafter referred to as the H₁₆₀ bandpass). The H₁₆₀ bandpass, centered at $\rm 1.6 \;{\rm \mu m}$ ($\rm FWHM = 0.4 \;{\rm \mu m}$), probes the longest wavelengths at which the HST thermal emission is unimportant, taking full advantage of the lack of sky background that limits the sensitivity of ground-based near-IR observations. NIC2 has a pixel scale of 0075, critically sampling the HST point-spread function (PSF) at 1.6 μm, and a field of view (FOV) of 192 × 192. While the NIC3 camera has greater surface brightness sensitivity, NIC2 offers the best combination of resolution and sensitivity for our science goals, and also allows more consistent comparisons with the available HST/ACS imaging of MD 41 and SINFONI+AO observations of BX 482, which have comparable or better resolution than NIC2.

Each target was observed for four orbits, with each orbit split into four exposures with a subpixel dither pattern to ensure good sampling of the PSF and minimize the impact of hot/cold bad pixels and other such artifacts (e.g., "grot," electronic bars). The individual exposure time was 640 s, giving a total on-source integration time of 10,240 s. The read-out mode employed was the SPARS-64 MULTIACCUM sequence with $\rm NSAMP = 12$. We used a square four-point dither pattern with a step size of 15375 (20.5 pixels). We defined the starting positions of each dither sequence as the mid-points of the sides of a 09 × 045 rectangle ($\rm 12 \times 6$ pixels). Table 2 summarizes the log of the observations.

Table 2. Log of NICMOS/NIC2 Observations

Object	Date Observed	P.A.a	3σ Limit in d = 022b
		(deg)	(mag)
Q1623-BX528	2007 Apr 27	−5.43	28.07
Q1623-BX663	2007 Apr 28–29	−20.43	28.17
SSA22a-MD41	2007 May 7–8	30.13	27.98
Q2343-BX389	2007 Jul 10	16.91	28.08
Q2343-BX610	2007 Sep 24	−45.43	28.14
Q2346-BX482	2007 Jul 18	4.57	28.22

Notes. The total on-source integration time is 10,240 s for all targets. ^aPosition angle of the y-axis (in degrees east of north). ^bEffective 3σ background noise limiting magnitudes (AB system) in a "point-source" circular aperture with diameter d = 022, or 1.5 × FWHM of the NIC2 PSF as measured from stellar profiles in the data. The limiting depths were determined from the analysis of the noise properties of the reduced data presented in Section 2.6.

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We started with the pipeline-reduced data products, processed with the STSDAS task calnica, version 4.1.1, of the nicmos package within the IRAF environment. We refer to the NICMOS Data Handbook¹¹ for details and the description of specific instrumental features of NICMOS. The steps performed in this stage include bias, zero read signal, and dark current subtraction; data linearization; correction for the so-called electronic bars; flat fielding; and conversion to count rates. The task calnica also identifies cosmic ray hits and various bad pixels. These identifications missed on a significant number of obvious bad pixels present in our data, so we extended the bad pixel lists for each exposure as described below.

We then used the task pedsky in the same IRAF package to subtract a first-order estimate of the background and the quadrant-dependent residual bias (or "pedestal") in each individual exposure. We subtracted the median value along each column to correct for bias jumps. We constructed a static bad pixel mask for each galaxy based on deviant pixels in the normalized flat field and those identified by calnica with bad data quality flags. To identify remaining bad pixels and cosmic rays, we first drizzled the images for each galaxy onto a common finer pixel grid accounting for their relative shifts, the (small) NIC2 distortion, and the static bad pixel masks, using the IRAF task drizzle in the STSDAS analysis package. A clean reference image was generated by median-combining the registered drizzled images with "minmax" rejection. This image was inverse-drizzled to the original pixel scale and coordinate system of each individual exposure with the task blot in the STSDAS analysis package. We compared the "blotted" reference images with their corresponding input image and updated the static bad pixel mask to make a mask for each exposure. The background-subtracted exposures were again drizzled, now using the updated individual bad pixel masks, to create the combined drizzled image of each galaxy. For the drizzling, we chose an output pixel scale of 005, corresponding to that of the SINFONI+AO data of BX 482, and used a square kernel with 0.7 times the size of the input pixels (i.e., a "drop size" of 0.7). We found from experimentation that this combination of parameters gave the best results in terms of preserving the angular resolution and minimizing the impact on the pixel-to-pixel rms noise level of our NIC2 data.

The combined drizzled images showed substantial residual features on scales of a few tens of pixels together with residuals from vignetting at the bottom of the array. These features were successfully modeled and subtracted from the combined images using background maps generated with the SExtractor software, version 2.2.2 (Bertin & Arnouts 1996). Since our science goals require detection of low surface brightness emission of the galaxies to large radii, we took particular care in making these background maps. We masked out sufficiently large areas around each object and then ran SExtractor with a background mesh size of 24 pixels and filter size of three meshes. This combination provided the best match to the spatial frequency of the residual features, without compromising the faint extended emission from the galaxies. Further linear residual features were removed by fitting second-order polynomials (with object masking) along columns and rows. This step also resulted in a small reduction of the pixel-to-pixel rms noise.

Weight maps (for use in the determination of the noise properties and in the structural analysis) were generated in the final combination of the exposures with the task drizzle. These reflect the effective total integration time at each output pixel in the drizzling procedure (i.e., accounting for the drop size and the relative size of the input and output pixels as well as the bad pixel and cosmic ray masking). We normalized the weight maps of each galaxy to a maximum of unity. We cropped the final images and weight maps to a region 1955 × 1805 to exclude the edges with relative weight ≲0.4.

For the morphological analysis, accurate knowledge of the PSF in our data is important. We empirically determined the resulting PSF based on stellar profiles in our final reduced images. In total, there are four suitable stars (isolated, sufficiently bright but unsaturated) in three of our NIC2 pointings. Their profiles have a Gaussian core and show Airy wings at larger radii (around 023). To increase the S/N, we averaged the peak-normalized stellar profiles. From a Gaussian fit to the resulting empirical PSF, the FWHM is 0145 with an ellipticity of 0.08 (or an FWHM of 0143 and an identical ellipticity of 0.08 for a Moffat fit). Relative to the average PSF, the deviations of the radial profiles of the stars are at most 15% (on average ≈5%) out to a radius of 035, enclosing 95% of the total flux and where the profiles are at ≈1% of the peak value. The curves of growth of the individual stars differ by <10% (on average ≈3%) from that of the average PSF. We adopted this empirical average PSF for our analysis.

The quality of the final reduced data is very uniform among our targets. To characterize the effective noise properties, we followed the approach described in detail by Labbé et al. (2003) and Förster Schreiber et al. (2006a). For uncorrelated Gaussian noise, the effective standard deviation from the mean of the background for an aperture of area A is simply the pixel-to-pixel rms $\overline{\sigma }$ scaled by the linear size $N = \sqrt{A}$ of the aperture, $\sigma (N) = N\,\overline{\sigma }$. However, instrumental features, the data reduction, and the drizzling and combination procedures have added significant systematics and correlated noise in the final data. We thus derived the function σ(N) directly from the data by measuring the fluxes of ≈240 non-overlapping circular apertures. We placed the apertures at random in the maps but so as to avoid pixels associated with sources down to $\rm S/N \approx 3$, corresponding to a surface brightness of μ(H_160,AB) = 23.4 mag arcsec^-2. Series of measurements were repeated with different aperture diameters ranging from 01 to 1''.

For each aperture size, the distribution of fluxes is symmetric around the background value (about 0), and is well reproduced with a Gaussian profile. We determined the background rms variations from the width of the best-fit Gaussian to the observed distribution for each aperture size. While at any fixed spatial scale, the noise properties over the images are consistent with being Gaussian, the variations with N deviate appreciably from the scaling expected for Gaussian noise, being systematically larger and increasing nonlinearly. The real noise behavior in our NIC2 images can be approximated by the polynomial model:

$$\begin{equation} \sigma (N) = \frac{N\,\overline{\sigma }\,\left(a + b\,N\right)}{\sqrt{w}}, \end{equation} \tag{ 1 }$$

where the weight term $1/\sqrt{w}$ accounts for the spatial variations in the noise level related to the exposure time and is taken from the weight maps. The coefficient a represents the effects of correlated noise, which are dominated by the resampling of the images to the final pixel scale through the drizzling procedure. The curvature in the σ(N) relation quantified by the coefficient b indicates a noise contribution that becomes increasingly important on larger scales. For our data, this probably originates mostly from instrumental features, and residuals from the background subtraction and flat fielding. Qualitatively, the same second-order polynomial behavior is seen in ground- and space-based optical and near-IR imaging data analyzed by Labbé et al. (2003, their Figure 4), Förster Schreiber et al. (2006a, their Figure 6), and Wuyts et al. (2008, their Figure 3).

The noise properties are very similar in all NIC2 maps. The derived pixel-to-pixel rms values are identical within 3%. The mean and standard deviation of the best-fit polynomial coefficients among the six images are 1.20 and 0.15 for a and 0.039 and 0.017 for b. Limiting magnitudes and photometric uncertainties from our NIC2 data are computed through Equation (1) for the corresponding aperture size. The effective 3σ magnitude limits in a "point-source aperture" with diameter d = 1.5 × FWHM = 022 (maximizing the S/N of photometric measurements in unweighted circular apertures of point-like sources) are $\rm {\approx} 28.1 \;{\rm mag}$ (see Table 2).

Figure 1 presents the final reduced NIC2 images at a sampling of $\rm 0\farcs 05 \;pixel^{-1}$. The angular resolution from the effective PSF with $\rm FWHM = 0\farcs 145$ corresponds to a spatial resolution of $\rm 1.2 \;kpc$ at the median z = 2.2 of the targets. We computed the geometric center as the unweighted average of the x and y coordinates of pixels with $\rm S/N > 3$. Emission from the galaxies is detected out to radii of 08–12, or $\rm 6.5\hbox{--}10 \;kpc$. The averaged surface brightness of the sources over the emitting regions (with $\rm S/N > 3$) is in the range μ(H_160,AB) = 22.6–23.0 mag arcsec^-2, with typical $\rm S/N = 4\hbox{--}6$ per pixel.

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The spatial distribution of the H₁₆₀-band light in the images is characterized by a diffuse and low surface brightness component over which rich, brighter substructure is superposed. The most prominent features are the bright and compact regions, seen in all galaxies; each of the non-AGN disks contains several such clumps. BX 663 exhibits a bright central peak, and only one other and comparatively fainter clump to the southeast (SE); since the rest-UV and optical emission lines of this object indicate the presence of a Type 2 AGN, the compact central H₁₆₀-band peak may not be dominated by AGN emission and could trace in large part stellar continuum light. Detailed modeling of the optical to mid-IR SED of this galaxy will help to place constraints on the contribution of the stars and AGN (K. Hainline et al. 2011, in preparation). In BX 528, the merger components are clearly separated in our NIC2 image, with a projected distance of $\rm {\approx} 8 \;kpc$ between the compact northwestern and the more extended southeastern parts (hereafter BX 528−NW and BX 528−SE) and significant emission along a "bridge" between the two components. The fainter source ≈18 to the northeast is undetected in our SINFONI data so that its association with BX 528 is unclear. Likewise for the source ≈2'' south of BX 482, which could also result from chance alignment. In contrast, the small source ≈06 south of the main body of BX 389 corresponds to an extension in our seeing-limited Hα maps (with about three times coarser resolution) and is thus likely to be a small satellite at the same redshift and projected distance of 5 kpc (hereafter "BX 389−S"; see Sections 4 and 7). No other source is detected in the NIC2 images within ≈2'' or projected $\rm {\approx} 15 \;kpc$ of our primary targets; this area corresponds to the deeper part of the SINFONI data, where we can search for line emission to faint levels of candidate companions to determine a physical association.

Other characteristics of note include the broad curved features reminiscent of spiral arms seen in the outer isophotes of BX 610, on the northwest (NW) and southeast sides. In addition, the inner isophotes in this galaxy show a significant and systematic increase in ellipticity and change in position angle (P.A.). From fitting elliptical isophotes to the NIC2 image using the task ellipse in IRAF, the apparent (uncorrected for beam smearing) ellipticity and P.A. vary from ∼0.8 and ∼35° at radii r ≲ 05 (or 4 kpc) to ∼0.1 and ∼0° at r ∼ 1'' (8 kpc). The interpretation of the inner isophotal feature is complicated by the presence of the clumps, which are mostly aligned along a similar P.A., but it is suggestive of a bar-like structure as seen in local barred spirals.

The new H₁₆₀-band photometry from our HST/NICMOS data constitutes a significant addition to that available for our targets, especially for BX 482 without any previous near-IR imaging and MD 41 for which the existing K-band data are fairly shallow. Published data include ground-based optical $U_{n}\,G\mathcal {R}$ imaging for all sources, and near-IR JK_s imaging for a subset, presented by Erb et al. (2006; see also Steidel et al. 2004). The photometry was measured in matched isophotal apertures determined from the $\mathcal {R}$-band images and corrected to "total" magnitudes in elliptical apertures scaled based on the first moment of the $\mathcal {R}$-band light profiles (Steidel et al. 2003). Spitzer/IRAC mid-IR photometry has subsequently been obtained for all objects except BX 482 (Reddy et al. 2010). To construct the broadband SEDs and derive the global stellar and extinction properties of our targets, we however excluded the IRAC data for the following reasons. The optical and near-IR photometry provides the most uniform data sets among the six galaxies in terms of wavelength coverage whereas of the five objects with IRAC data, only three were observed in all four channels. Moreover, contamination by AGN emission in BX 663 and BX 610 becomes important at the longer wavelengths probed by IRAC and would affect the modeling results.

To include the H₁₆₀ band in the SEDs of our targets, we measured the total magnitude in a circular aperture of diameter 3'' on the NIC2 images (indicated in Figure 1). Because of the small NIC2 field of view, the accuracy of the measurements in the $\mathcal {R}$-band isophotal aperture used for the ground-based photometry on the PSF-matched H₁₆₀-band images is compromised by the difficulty of determining the local background sufficiently reliably: the area empty of sources signal after convolving to the optical seeing of ∼1'' is too small. The median difference between the total magnitudes based on the fixed circular aperture measurement on unconvolved NIC2 maps and that in the isophotal apertures on PSF-matched NIC2 maps is $\rm -0.16 \;{\rm mag}$, with the maximum for BX 389 ($\rm -0.51 \;{\rm mag}$) and best agreement for BX 528 ($\rm -0.002 \;{\rm mag}$). The photometry is given in Table 1 and the optical/near-IR SEDs are plotted in Figure 2.

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By their primary selection, all targets satisfy the $U_{n}\,G\,\mathcal {R}$ color criteria of "BX" or "MD" objects (Adelberger et al. 2004; Steidel et al. 2004). Synthetic broadband colors measured on the spectrum of the best-fitting stellar population model to the observed SEDs (described in Section 3.3 below) suggest that all targets would also satisfy the BzK = (z − K)_AB − (B − z)_AB > − 0.2 mag criterion of z > 1.4 "star-forming BzK objects" introduced by Daddi et al. (2004). In addition, two of the four sources with both J and K photometry (BX 663 and BX 389) have the red (J − K_s)_AB > 1.34 colors of "Distant Red Galaxies" (DRGs; Franx et al. 2003; van Dokkum et al. 2004), and one (BX 610, (J − K_s)_AB = 1.28 mag) is within 0.3σ of the DRG criterion. For these three sources and for BX 528, the photometry is consistent with the presence of a significant population of evolved stars along with the young stars producing the blue rest-UV SED. The best-fit models to the SEDs of these four objects imply rest-frame (U − B)_AB ≈ 0.75–0.9 mag colors, close to or just at the separation adopted by, e.g., Kriek et al. (2009), between "red" and "blue" objects. In contrast, MD 41 and BX 482 are significantly bluer with rest-frame (U − B)_AB ≈ 0.5 mag.

Our NIC2 sample is relatively bright in the near-IR; the five targets with K-band imaging have a median K_s,AB = 21.8 mag and span a range of $\rm {\approx} 1.2 \;{\rm mag}$ in the observed K band (K_s,AB = 21.1–22.3 mag) as well as in the rest-frame absolute V-band magnitude (as derived from the SED modeling below, with M_V,AB between −23.1 and $\rm -21.9 \;{\rm mag}$). In addition, the Spitzer/MIPS 24 μm measurements available for four of the targets (BX 389, BX 610, BX 528, and BX 663) indicate that they are among the brightest 3% of rest-UV-selected z ∼ 2 galaxies, in terms of rest-frame 8 μm luminosity (Reddy et al. 2010).

Stellar population synthesis modeling of BX 528, BX 663, BX 389, and BX 610 was first presented by Erb et al. (2006). The new H₁₆₀ photometry from NIC2 and K-band flux for MD 41 provide additional constraints and allow us to extend the SED modeling to BX 482 and MD 41, which had previously only three optical data points. For consistently derived stellar and dust extinction properties within our sample, we re-modeled the optical/near-IR SEDs of all six objects.¹² We followed standard procedures (e.g., Shapley et al. 2001; Erb et al. 2006; Förster Schreiber et al. 2006a), exploring also a range of parameters and model ingredients to assess possible systematics from the assumptions adopted. Our specific procedure is described in detail by Förster Schreiber et al. (2009) and is summarized here.

We used the stellar evolutionary code from Bruzual & Charlot (2003). The age, extinction, and luminosity scaling of the synthetic model SED were the free parameters in the fits. The ages were allowed to vary between 50 Myr and the age of the universe at the redshift of the source. The lower limit is set to avoid implausibly young solutions and corresponds approximately to the dynamical timescale τ_dyn = r/v from the inclination-corrected velocity v at a radius of r ∼ 10 kpc of the galaxies (e.g., Förster Schreiber et al. 2006b; Genzel et al. 2008). We employed the Chabrier (2003) IMF and the reddening curve of Calzetti et al. (2000) and assumed a solar metallicity. We fixed the star formation history (SFH), adopting a constant star formation (CSF) rate model, which we found appropriate for most galaxies (see below, and also Erb et al. 2006). We derived the formal (random) uncertainties on the best-fit parameters from 200 Monte Carlo simulations, where we varied the input photometry assuming a Gaussian probability distribution for the measurements uncertainties (see Section 2.6). To explore the impact of model assumptions and ingredients, we also used the evolutionary synthesis code of Maraston (2005) and ran suites of models with exponentially declining SFRs with e-folding timescales τ between 10 Myr and 1 Gyr, with a metallicity of 1/5 and 2.5 times solar, and with extinction laws appropriate for the Small Magellanic Cloud (Prévot et al. 1984; Bouchet et al. 1985) and the Milky Way (Allen 1976).

Table 3 lists the best-fit properties for our adopted set of Bruzual & Charlot (2003) models with CSF, solar metallicity, and Calzetti et al. (2000) law along with the formal uncertainties taken as the 68% confidence intervals from the Monte Carlo simulations around the best-fit values. Figure 2 shows the corresponding synthetic model spectra; best-fit Maraston (2005) models for the same CSF, metallicity, and reddening law are also shown for comparison. To gauge systematic uncertainties, we looked at the variations in derived properties for the other suites of model assumptions and synthesis code considered. For individual galaxies, and compared to the adopted properties, the median of the variations is as follows: the ages are mostly younger by a factor of ≈2, the extinction in V band A_V decrease by $\rm {\approx} 0.2 \;{\rm mag}$, the stellar masses M_⋆ tend to be lower by a factor of ≈1.5, the absolute and specific SFRs tend to decrease by factors of ≈2. The overall sense of these variations reflects in part the fact that, by construction, CSF models generally lead to older ages than declining SFHs. While the systematic uncertainties above are significant, the derived properties of the galaxies are robust in a relative sense. In particular, MD 41 and BX 482 remain the youngest and least massive of the sample in any case.

Table 3. Stellar and Dust Properties of the Galaxies

Object	Age	AV	M⋆	MV, ABa	SFR	sSFRb
	(Myr)	(mag)	(1010 M☉)	(mag)	(${M_{\odot }\;\rm yr^{-1}}$)	($\rm Gyr^{-1}$)
Q1623-BX528	2750+96−2110	0.6 ± 0.2	6.95+0.17−3.61	−22.90+0.04−0.12	42+29−16	0.6+1.7−0.1
Q1623-BX663	2500+147−800	0.8 ± 0.2	6.40+0.22−2.28	−22.68+0.05−0.20	42+13−12	0.7+0.3−0.2
SSA22a-MD41	50+31−0	1.2 ± 0.2	0.77+0.10−0.03	−22.37+0.04−0.09	185+3−70	24+1−9
Q2343-BX389	2750+224−1945	1.0 ± 0.2	4.12+0.77−2.16	−21.94+0.09−0.13	25+17−2	0.6+1.2−0.1
Q2343-BX610	2750+173−650	0.8 ± 0.2	10.0+2.7−0.6	−23.10+0.12−0.04	60+26−1	0.6 ± 0.2
Q2346-BX482	321+485−141	0.8 ± 0.2	1.84+0.79−0.46	−22.65+0.07−0.08	80+42−32	4.3+3.0−2.5

Notes. Results from SED modeling of the optical and near-IR photometry, with best-fitting star formation history having a constant SFR for all targets. The formal (random) fitting uncertainties are given, derived from the 68% confidence intervals based on 200 Monte Carlo simulations for the default set of Bruzual & Charlot (2003) models with solar metallicity, a Chabrier (2003) IMF, and the Calzetti et al. (2000) reddening law; systematic uncertainties (from SED modeling assumptions) are estimated to be typically a factor of ∼1.5 for the stellar masses, $\rm \pm 0.3 \;{\rm mag}$ for the extinctions, and factors of ∼2–3 for the ages as well as for the absolute and specific star formation rates. ^aRest-frame absolute V-band magnitude, uncorrected for extinction. ^bSpecific star formation rate, i.e., the ratio of the star formation rate over stellar mass.

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Our choice of CSF is obviously very simplistic. For the range of SFHs above, we find that the longest timescales ($\rm \tau = 1 \;{\rm Gyr}$ or CSF) are favored (in a minimum χ² sense) for four out of six galaxies. MD 41 and BX 482, with bluest SEDs, have best fits formally obtained for models with $\rm \tau \lesssim 50 \;{\rm Myr}$ but the age, M_⋆, and SFR are within 3σ or less of the values for CSF. Recent work has emphasized the fact that declining SFHs may well be inappropriate for high z star-forming galaxies (Renzini 2009; Maraston et al. 2010). Our exploration of constant and declining SFHs was motivated by continuity with previous work and consistency with the SED modeling assumptions for the comparison samples discussed in Section 6.

We did not account for emission line contribution in our SED modeling. The main contribution expected for our sample is from Hα in the K band, and these are in the range 7%–19% (with a median of 13%) based on our SINFONI K-band observations (see also Erb et al. 2006). The median [N ii] $\rm \lambda \,6584/H\alpha$ ratio is 0.23 (with highest ratio 0.43 for BX 610). SINFONI H-band data are available for five targets; the [O iii] doublet and Hβ are all detected in two cases and their contributions to the H₁₆₀ flux densities are smaller than for Hα in K, and 3σ upper limits for the others are at most 29% (see Section 5). The Hα-corrected K-band flux densities are indicated in Figure 2; the impact on the SED modeling results is not significant in view of the other uncertainties involved.

Our targets span over an order of magnitude in stellar mass, from 7.7 × 10⁹ to 1.0 × 10¹¹ M_☉ with median 5.3 × 10¹⁰ M_☉. The stellar populations that dominate their rest-UV to optical SEDs cover the full range allowed in our modeling (from 50 Myr to 2.75 Gyr), and are moderately obscured (with A_V between 0.6 and 1.2 mag, or equivalently E(B − V) = 0.15–0.30 mag). Four of the six targets have in fact ages consistent with the age of the universe at their redshift, indicating the presence of mature stellar populations. The median absolute and specific SFRs are ${\approx}50 {\;M_{\odot }\rm \;yr^{-1}}$ and $\rm 0.6 \;Gyr^{-1}$ (with ranges of $25\hbox{--}185 {\;M_{\odot }\rm \;yr^{-1}}$ and $0.6\hbox{--}24 \;\rm Gyr^{-1}$). Figure 3(a) compares our NIC2 sample in the M_⋆ − SFR plane with the full SINS Hα sample, and a purely K-selected sample taken from the Chandra Deep Field South (CDFS) in the same z = 1.3–2.6 interval and to the same K_s,Vega = 22 mag limit as the SINS sample (Förster Schreiber et al. 2009 and also Wuyts et al. 2008). The properties of these comparison samples were derived using the same SED fitting procedure and model assumptions as for the NIC2 sample. Clearly, and by selection, our NIC2 galaxies probe the actively star-forming part of the z ∼ 2 galaxy population (see also discussions by Erb et al. 2006; Förster Schreiber et al. 2009). Their median stellar mass and SFR are comparable to those of the SINS Hα sample (≈3 × 10¹⁰ M_☉ and ${\approx}70 {\;M_{\odot }\;\rm yr^{-1}}$).

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If our targets do not particularly stand out in terms of their stellar properties compared to the SINS Hα sample, they do more so in terms of their Hα brightness and kinematics. This distinction arises because, as described in Section 2, we chose them among the sources with highest S/N and spatially best-resolved Hα emission from our seeing-limited SINFONI data sets. Five of them were explicitly selected because of their disk-like kinematics, and BX 528 because it shows in contrast kinematic signatures expected for counterrotating mergers. The spatial extent and brightness of our targets make them particularly well suited for a detailed study of morphologies and reliable assessment of structural parameters from sensitive kpc-resolution continuum imaging.

Figure 3(b) compares the NIC2 galaxies with the SINS Hα sample in the velocity–size plane, with the half-light radii and (inclination-corrected) circular velocities derived from Hα (Genzel et al. 2008; Cresci et al. 2009; Förster Schreiber et al. 2009). The NIC2 targets lie at the high end of the v_d − r_1/2(Hα) distribution. With r_1/2(Hα) ≈ 4–5 kpc, they are all larger than the median of 3.1 kpc for the SINS Hα sample. The v_d for the disks are roughly equal to or larger than the median for SINS galaxies of $\rm {\approx} 180 \;km\;s^{-1}$, and up to $\rm {\sim} 300 \;km\;s^{-1}$. For the merger BX 528, the velocity gradient is lower and leads to a lower equivalent v_d of $\rm 145 \;km\;s^{-1}$ (see Förster Schreiber et al. 2009). The ratios of circular velocity to intrinsic local velocity dispersion of the disks are in the range v_d/σ₀ ≈ 2–6, which is significantly lower than for local spiral galaxies (values in the range ∼10–40; e.g., Dib et al. 2006; Épinat et al. 2010) and suggests comparatively larger gas turbulence and geometrical thickness. These low v_d/σ₀ ratios appear to be a characteristic feature of early disk galaxies at z ∼ 1–3 (e.g., Förster Schreiber et al. 2006b; Wright et al. 2007; Genzel et al. 2008; Stark et al. 2008; Cresci et al. 2009; Épinat et al. 2009).

The median integrated Hα flux of the NIC2 targets (uncorrected for extinction) is F(Hα) = 1.9 × 10⁻¹⁶ erg s^-1 cm⁻² (and range from 1.1 to $\rm 3.1 \times 10^{-16} \;erg\;s^{-1}\;cm^{-2}$). This places them among the brighter half of the SINS Hα sample (with median F(Hα) = 1.1 × 10⁻¹⁶ erg s^-1 cm⁻²). In terms of integrated Hα line widths, their median is σ(Hα) = 155 km s^-1 (spanning the range $\rm 120\hbox{--}245\;{\rm km\;s^{-1}}$), somewhat broader than the median for the SINS Hα sample ($\rm 130\;{\rm km\;s^{-1}}$). This difference is due in part to the large observed velocity gradients for the sources.

4.1.1. Methodology

In a first step to characterize quantitatively the morphologies of our galaxies, we followed a parametric approach. The main goal here is to derive the global structural parameters of the sources. We used the code GALFIT (Peng et al. 2002) to fit the two-dimensional surface brightness distributions with a Sérsic (1968) profile:

$$\begin{equation} I(r) = I(0)\,\exp [-b_{n}\,(r/R_{\rm e})^{1/n}], \end{equation} \tag{ 2 }$$

where I is the intensity as a function of radius r, b_n is a normalization constant, and R_e is the effective radius enclosing half of the total light of the model. In this parameterization, ellipticals with de Vaucouleurs profiles have a Sérsic index n = 4, exponential disks have n = 1, and Gaussians have n = 0.5. In the fitting procedure, GALFIT convolves the model light distribution to the effective resolution of the data and determines the best fit based on χ² minimization. We input our empirically determined PSF and the weight maps scaled by the pixel-to-pixel rms measured on the reduced images (see Section 2). To reduce the impact of large-scale residuals from flat fielding and background subtraction (Section 2.6), we performed the fits within a region 7'' × 7'' centered on the sources.

The free parameters in the fits were the Sérsic index (n), the effective radius (R_e), the axis ratio (b/a, semiminor over semimajor axis radii), the P.A. of the major axis, and the total magnitude. Given that surface brightness fitting of faint galaxies is sensitive to the background determination and that Sérsic profile parameters tend to be degenerate with the "sky" value (see, e.g., Peng et al. 2002; van Dokkum et al. 2008), we fixed the sky level S in our fits. Moreover, asymmetric and clumpy surface brightness distributions can strongly bias the results, so we also fixed the coordinates x₀ and y₀ of the center position. In order to derive realistic uncertainties, we performed a series of fits where these fixed parameters were drawn at random from plausible distributions. Specifically, for every galaxy we ran GALFIT 500 times, each time varying the x₀ and y₀ according to a uniform distribution within a squared box of 2 × 2 pixels around the geometric center as defined in Section 3.1, which corresponds closely to the dynamical center of our targets. For the background, the fixed input S values were drawn at random from the central 10% of the distribution of individual pixel values in the regions empty of sources (with this range reflecting the uncertainty in the background level). The best-fit parameters were taken as the median of the results for all 500 runs, and the 1σ uncertainties as the 68% confidence intervals about the median.

We performed additional series of fits to explore systematics from the center and sky background determinations. In all cases, the initial guesses for the center and sky values were generated as described above. In the first two series, one of the sky or center was chosen as a free parameter and the other was fixed. In a third series, both parameters were free. For BX 663, MD 41, BX 389, and BX 610, the best-fit structural parameters for these additional series are all within the 68% confidence intervals of the results for the first series with sky and center fixed to the randomly drawn values in each iteration. For BX 528 and BX 482, the two series with the free center position lead to significantly different results as expected from their particularly asymmetric morphologies, with changes in R_e and n by ≳2σ.

For the interacting system BX 528, single component fits are clearly inappropriate. When the center is free to vary, the fits are heavily influenced by the brighter BX 528−SE component: the best-fit center moves toward this component, the Sérsic index increases to match the steeper inner profile and the R_e also increases. For this system, we thus also ran a series fitting two Sérsic profiles simultaneously, fixing the respective center position and sky to random values drawn from appropriate distributions as explained above. Likewise, we performed two-component fits for BX 389 to derive the structural parameters of the small southern companion BX 389−S. The best-fit parameters for the main part of BX 389 are almost identical to those obtained with the single-component fits. For BX 482, the large and bright clump on the southeast side (which makes up ≈15% of the total light after subtracting the "background" light from the host galaxy; see Paper II) drives the center in this direction when allowed as a free parameter, and leads to a somewhat higher best-fit n index. At the same time, because the northwest side of the galaxy is overall fainter and lacks bright small-scale features, the best-fit R_e is smaller. We did not consider two-component fits for BX 482 because the kinematics as well as morphologies are more consistent with a single system.

4.1.2. Results for the NIC2 Targets

Table 4 gives the results for the main structural parameters, R_e, n, b/a, and P.A., of our targets from the single-component fits as well as from the two-component fits for BX 528 and BX 389. In Figure 4, the first two columns show the best-fit values for single-component fits along with the distributions obtained from the 500 GALFIT runs in each parameter. In the third column, ellipses are drawn on the NIC2 images showing the effective radius, axis ratio, and P.A. of the best-fit models. The fourth column shows the fit residuals, revealing the clumpy structure and large scale asymmetries in the light distributions. Figure 5 shows the same but for the two-component fits to BX 528 and BX 389. Figure 6 compares the radial light profiles of the galaxies' data and of the best-fit model (here using the two-component model for BX 528). The profiles correspond to the average along ellipses centered on the best-fit x₀ and y₀ position, and with best-fit axis ratio and P.A. of the single-component models. This tends to smooth out the small-scale structure and asymmetric features of the surface brightness distributions; the detailed substructure will be considered in the next subsection.

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Table 4. Best-fit Structural Parameters from the NIC2 H₁₆₀-band Images

Object	Re	n	b/a	P.A.
	(kpc)			(deg)
Single-component models
Q1623-BX528	4.86+0.13−0.10	0.16 ± 0.01	0.31 ± 0.01	−27.8+1.2−1.1
Q1623-BX663	4.54+7.71−0.79	2.00+2.11−0.59	0.73+0.04−0.02	−21.8+4.3−2.9
SSA22a-MD41	5.69+0.20−0.13	0.54+0.07−0.06	0.31 ± 0.01	36.5 ± 0.2
Q2343-BX389	5.93+0.17−0.12	0.36+0.07−0.05	0.30 ± 0.01	−48.6+0.3−0.5
Q2343-BX610	4.44 ± 0.08	0.57 ± 0.04	0.56 ± 0.01	16.9+0.5−0.9
Q2346-BX482	6.22+0.13−0.12	0.14 ± 0.01	0.48 ± 0.01	−60.8+1.9−1.5
Two-component models
Q1623-BX528 SE	3.18+0.18−0.25	1.20+0.15−0.19	0.35−0.08−0.03	−40.5+3.4−1.7
Q1623-BX528 NW	3.57+1.98−0.57	2.91+1.70−1.34	0.51+0.06−0.05	−10.9+9.5−5.2
Q2343-BX389 Main	5.89+0.08−0.09	0.32+0.04−0.04	0.27 ± 0.01	−49.0+0.5−0.4
Q2343-BX389 S	2.71+2.18−0.69	3.03+2.64−1.75	0.20+0.35−0.16	−41.5+2.2−5.4

Notes. Structural parameters derived from Sérsic profile fits to the two-dimensional rest-frame $\rm {\approx} 5000$ Å surface brightness distribution from the NIC2 H₁₆₀-band images. Single-component models were fitted to all targets. For BX 528, two-component fits were also performed to account for the southeast ("SE") and northwest ("NW") components. Similarly for BX 389, where the two components represent the main part of the galaxy and the small companion to the south, "Main" and "S," respectively. The results are obtained from a series of 500 GALFIT runs as described in Section 4.1. The best-fit effective radius R_e, the Sérsic index n, the ratio of minor to major axis b/a, and the position angle P.A. (in degrees east of north) correspond to the median of the distribution of results, and the uncertainties represent the 68% confidence intervals around the best fit.

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All of our targets qualify as morphologically late-type, disk-dominated systems, often defined as having n < 2–2.5 (e.g., Bell et al. 2004; Trujillo et al. 2006). The only exceptions are BX 528−NW and BX 389−S that have n ≈ 3 but the large uncertainties make them within 1σ of the above criterion. A remarkable feature of the four non-AGN galaxies with disk-like Hα kinematics is their shallow inner light profiles. With Sérsic indices in the range ≈0.15–0.6, these are significantly less centrally concentrated than exponential disks (by definition n = 1). The residuals are overall smallest for MD 41 and BX 389, the two most edge-on disks based on their axis ratios (b/a ≈ 0.30) from the fits to the H₁₆₀-band images as well as from their Hα morphologies and kinematics (Förster Schreiber et al. 2006b; Genzel et al. 2008; Cresci et al. 2009). The spiral-like features in BX 610 noted in Section 3.1 are most obvious in the outer parts beyond the effective radius. The residuals for the single- and double-component fits to BX 528 indicate that neither case provides a very good representation. There is clearly significant light emitted along the "bridge" between the SE and NW components.

BX 663 has the highest n index among our sample, reflecting the fairly prominent central peak and shallower profile of the extended emission at larger radii. We explored two-component models, meant to represent the case of a disk + bulge and of a disk + unresolved nuclear source. A free n component was considered for the disk, and the second component was taken as either a de Vaucouleurs profile with fixed n = 4 or as the empirically determined PSF. Because the central peak is accounted for by the n = 4 or PSF component, the underlying disk ends up with low n of 0.24 (disk + bulge) or 0.63 (disk + unresolved source), in the range obtained for the other five SINS targets. The disk R_e values, however, differ by 10% or less (<2.5σ) from the best-fit single-component R_e. For the disk + bulge case, the de Vaucouleurs component has R_e = 2.47^+5.03_−0.95 kpc. In terms of χ² values and of residuals, the best-fit two-component models are indistinguishable from the best-fit single Sérsic model, so we consider only the single-component model for BX 663 throughout this paper.

We find no significant correlation between structural parameters (R_e, n, and b/a) and SED derived properties (M_⋆, age, A_V, absolute and specific SFR) among our targets. Studies of larger samples based on ground-based seeing-limited or higher resolution NICMOS/NIC3 near-IR imaging (e.g., Trujillo et al. 2006; Toft et al. 2007; Franx et al. 2008) show the existence of relationships between size, stellar mass, and star formation activity at z ∼ 2–3 (though with significant scatter). Among our five disks, MD 41 and BX 389 with highest A_V values have the lowest axis ratios, which seems consistent with the trend of higher extinction in more edge-on star-forming disks observed locally (e.g., Maller et al. 2009; Yip et al. 2010). However, clearly, only the strongest correlations would be discerned with our very small sample.

4.2.1. Methodology

The models considered in the previous section are admittedly very simplistic. Simple one- or two-component axisymmetric models can reproduce reasonably well the overall surface brightness distribution of some of our sources but do poorly for others. Such a parametric approach appears to be satisfactory to estimate global parameters such as the effective radius and shape of the radial light profile. On the other hand, it obviously does not capture the prominent small-scale and irregular structure of clumpy disks and merging systems. The difficulty of describing star-forming galaxies at z ∼ 2–3 within the framework of a Hubble sequence of more regular spiral and elliptical morphological types has been highlighted previously by several authors (e.g., Lotz et al. 2006; Law et al. 2007b; Peter et al. 2007). Accordingly, we also followed a non-parametric approach to characterize in detail morphologies of our galaxies, measuring the Gini, M₂₀, and multiplicity coefficients, which have been introduced and applied by Abraham et al. (2003), Lotz et al. (2004, 2006), and Law et al. (2007b).

The Gini parameter, G, is a measure of the uniformity with which the flux of a galaxy is distributed among its constituent pixels. G = 0 corresponds to the case where the flux is distributed evenly among all pixels, while G = 1 indicates that a single pixel contains all of the flux. The Gini parameter is formally defined such that

$$\begin{equation} \mathit {G} = \frac{1}{\bar{f}N_{{\rm pix}} (N_{{\rm pix}} - 1)} \sum ^{N_{{\rm pix}}}_{i=1} (2i - N_{{\rm pix}} -1)f_i, \end{equation} \tag{ 3 }$$

where $\bar{f}$ is the mean sky-subtracted flux per pixel, f_i is the sky-subtracted flux in pixel i, and the pixels have been sorted in order of increasing flux.

The M₂₀ parameter represents the second-order moment of the brightest 20% of a galaxy's flux. The total second-order moment is defined such that

$$\begin{equation} M_{{\rm tot}} = \sum _{i}^{N_{{\rm pix}}} f_i [(x_i - x_c)^2 + (y_i - y_c)^2], \end{equation} \tag{ 4 }$$

where f_i is the flux in each pixel, x_i and y_i indicate the pixel location, and x_c and y_c indicate the centroid of the galaxy light distribution, as determined from its first-order moments. M₂₀ is then computed by sorting galaxy pixels by flux, and summing M_i until the pixel is reached at which 20% of the total galaxy flux is contained in pixels that have brighter or equal fluxes. That is

$$\begin{equation} M_{20} \equiv \log _{10} \left(\frac{\sum _{i} M_i}{M_{{\rm tot}}} \right) \mbox{, while } \sum _{i} f_i < 0.2 f_{{\rm tot}}. \end{equation} \tag{ 5 }$$

Lotz et al. (2004) introduced M₂₀ as an indicator sensitive to merger signatures such as multiple nuclei.

Finally, a third classification parameter, the multiplicity (Ψ), introduced by Law et al. (2007b), is somewhat analogous to the M₂₀ parameter, in that it is sensitive to the presence and distribution of multiple clumps of flux. Ψ is conceptually akin to the total gravitational potential energy of a massive body. The "potential energy" of the pixel flux distribution can be described as

$$\begin{equation} \psi _{{\rm tot}} = \sum ^{N_{{\rm pix}}}_{i = 1} \sum ^{N_{{\rm pix}}}_{j=1,j\ne i} \frac{f_i f_j}{r_{ij}}, \end{equation} \tag{ 6 }$$

where r_ij is the distance between the ith and jth pixels. The greatest "potential energy" for a given set of pixel fluxes is the most compact distribution, with the brightest pixels at the center, and flux decreasing outward. Such a configuration would be described by

$$\begin{equation} \psi _{{\rm compact}} = \sum ^{N_{{\rm pix}}}_{i = 1} \sum ^{N_{{\rm pix}}}_{j =1,j\ne i} \frac{f_i f_j}{r^{\prime }_{ij}}, \end{equation} \tag{ 7 }$$

where r'_ij is the distance between the ith and jth pixels in the maximally compact configuration. The multiplicity, Ψ, is then defined to be

$$\begin{eqnarray} &&\Psi = 100 \log _{10} \left[ \frac{\psi _{{\rm compact}}}{\psi _{{\rm tot}}} \right]. \end{eqnarray} \tag{ 8 }$$

Law et al. (2007b) argued that Ψ provides larger dynamic range than M₂₀. Illustrative examples of the relationship between multiplicity and overall appearance are provided by both Peter et al. (2007) and Law et al. (2007b).

Some care must be taken in assigning pixels to a galaxy light distribution, especially when considering galaxies over a range of redshifts, where the differential effects of cosmological surface brightness dimming must be taken into account. We search for pixels associated with a galaxy within a 15 radius of the galaxy centroid. Pixel selection is performed on a lightly smoothed version of the data, which has been convolved with a circularly symmetric Gaussian kernel with a 1 pixel standard deviation. We select pixels to be associated with the galaxy if the smoothed flux is more than $1.5(\frac{1+z_{{\rm high}}}{1+z})^3 \times \sigma$ above the sky, with σ calculated from the raw data, and where z_high is the highest redshift for the subset of galaxies under consideration. The redshift-dependent factor counteracts the effects of surface brightness dimming in a given passband. Once pixels are assigned to a galaxy light distribution, the raw, unsmoothed data are used for morphological analysis.

4.2.2. Results for the NIC2 Targets

Figure 7 shows the resulting Gini, M₂₀, and Ψ coefficients for the SINFONI sample. To control for surface brightness dimming effects, each galaxy was analyzed as if it would be observed at the maximum redshift in the sample, i.e., z = 2.43. The Gini values range from G = 0.25–0.36, with a median of G_med = 0.33. The Ψ values are in the range 2.8–9.8, with a median of Ψ_med = 5.4. Finally, the M₂₀ values range from −1.1 to −0.6 with a median of M_20,med = −0.7.

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In order to interpret these numbers, we compare the NIC2 morphologies for objects in our sample with those derived from much larger samples of rest-UV-selected galaxies at similar redshifts with morphologies from optical imaging with the HST ACS. The ACS F814W (i₈₁₄-band) rest-UV morphologies from Peter et al. (2007) provide one such comparison sample, spanning a comparable redshift range to that of the objects in our NIC2 sample. To make a controlled comparison, we restrict the analysis to the subset of objects in the Peter et al. sample with the same average pixel-based S/N.¹³ This subset of objects in the Peter et al. (2007) sample has an identical median G value to the objects in our sample, and median Ψ and M₂₀ values that are very similar (Ψ_med = 7.0 and M_20,med = −0.8). The data set used to analyze the ACS i₈₁₄-band morphologies of rest-UV-selected galaxies by Peter et al. (2007) has similar depth to the summed BViz images featured in Law et al. (2007b), where rest-UV-selected objects were also analyzed. Accordingly, these authors found roughly identical rest-UV morphological results. Overall, the rest-frame optical morphologies for the objects in our sample are similar to the typical rest-frame UV morphologies for z ∼ 2 star-forming galaxies.

One of the objects in our sample, MD 41, has existing deep ACS F814W imaging. In Figure 8, both ACS and NIC2 images are shown side by side at their respective original spatial resolution, along with an RGB color composite after PSF matching of the ACS map to the resolution of the NIC2 map (as described in Section 7.1). The average pixel S/N of MD 41 is very similar in the two images, making for a fair comparison of the wavelength-dependent morphology. Overall, the morphologies in the two bands are strikingly similar. The most notable difference consists of the two brightest clumps in the ACS map at the southwestern edge of MD 41, which have only faint counterparts in the NIC2 image and, accordingly, exhibit bluer colors than the rest of the galaxy. In addition, two compact (radius ∼02) sources offset by ∼1'' from the main body of the galaxy appear in the ACS image, alone, indicating significantly bluer colors than the main region of galaxy emission. We have not yet determined if these sources are associated with MD 41. In particular, a search of the SINFONI data cube does not reveal any emission line at these locations and within $\rm \pm 1000 \;km\;s^{-1}$ of the Hα line of MD 41, which could support a physical association.

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The Gini values measured in the ACS and NIC2 images of MD 41 are both G ∼ 0.3, while the multiplicity is slightly lower for the rest-frame optical image (6.3) than the rest-frame UV image (9.7 with the two offset objects included and 8.1 without). The M₂₀ values are comparable as well, with −0.7 in the rest-frame optical and −0.9 in the rest-frame UV. While the parameters and appearance in each band are not identical, we stress that the differences are not significant. MD 41 does not display a strong morphological "k-correction," according to which the rest-frame UV and optical morphologies would trace light from very different stellar populations. Similar comparative studies of the rest-UV and optical morphologies of samples of z ∼ 1.5–4 galaxies based on ACS optical and recent WFC3 H₁₆₀-band imaging are presented by Overzier et al. (2010) and Cameron et al. (2010).

For another object in the sample, BX 482, the SINFONI Hα map obtained with LGS-AO and 017 PSF FWHM (Genzel et al. 2008; Förster Schreiber et al. 2009) is of sufficient resolution and S/N to measure the detailed morphological parameters using the same methodology and compare with the NIC2 H₁₆₀-band properties. We plot the morphological parameters derived from the Hα map of BX 482 in Figure 7, along with the NIC2-based parameters. The Hα line and H₁₆₀-band morphologies are quite similar in terms of G, Ψ, and M₂₀, with the prominent high surface brightness clump appearing in both SINFONI and NIC2 images.

We searched for correlations between the morphological (G, Ψ, and M₂₀) and stellar population parameters (M_⋆, age, A_V, absolute and specific SFR). The most significant (3σ) trend is found between stellar mass and G, such that more massive galaxies are characterized by higher G values. Correlations between G and other gauges of galaxy evolutionary state such as age and specific SFR are not readily apparent within our sample. However, our sample of six objects is obviously too small for discerning all but the strongest trends. Furthermore, with only actively star-forming galaxies in our sample, we do not probe the full dynamic range of z ∼ 2 star-forming histories. In Section 6, we return to the connection between morphology and other galaxy properties, considering our SINS sample alongside z ∼ 2 galaxies selected using very different criteria (van Dokkum et al. 2008; Dasyra et al. 2008; Kriek et al. 2009).

For proper comparison of the H₁₆₀ band and Hα maps, we first convolved the NIC2 images to the spatial resolution of the SINFONI data. The SINFONI FOV is too small to include neighboring stars observed simultaneously with the galaxies, and the PSFs are based on the average of broadband images synthesized from the SINFONI data cubes of stars observed immediately before or after the target. These non-simultaneous PSF calibrations are however estimated to provide good representations of the PSF of the targets' data, to ≈20% in terms of the FWHM (Förster Schreiber et al. 2009). We computed the smoothing kernels with a Lucy–Richardson deconvolution algorithm. Curve-of-growth analysis of the convolved NIC2 and original SINFONI PSFs indicates that the fraction of enclosed flux agrees to better than 5% in circular apertures with diameters in the range 015–15 in all cases.

After convolution, we resampled the NIC2 images to the pixel scale of the SINFONI data where appropriate ($\rm 0\farcs 125 \;pixel^{-1}$ for all sets but the AO $\rm 0\farcs 05 \;pixel^{-1}$ data of BX 482) and aligned them with the emission line maps relying primarily on the outer isophotes. The detailed emission line and broadband morphologies can plausibly differ for any galaxy. However, for our sources, and especially at a seeing-limited resolution of ≈05, the overall light distribution turns out to be very similar. We verified the registration with line-free continuum maps extracted from the SINFONI data cubes for the brighter sources. In contrast to the line maps, the continuum maps have lower S/N so that mostly only the central brighter regions or the continuum peak are reliable. The alignment based on line and continuum in those cases agrees well within 1–2 SINFONI pixels.

Figures 9 and 10 show, for each target, the original H₁₆₀-band image along with the Hα line map and velocity field with contours of the convolved H₁₆₀-band image overplotted. The most detailed comparison is possible for BX 482 with AO-assisted SINFONI data. Both the lower surface brightness component and the brighter substructure are comparable between the H₁₆₀ band and Hα emission. This similarity is reflected in the nearly equal values of Gini, multiplicity, and M₂₀ coefficients from the analysis in Section 4.2 (see Figure 7). In the details, there are however some noticeable differences. In particular, a few of the brighter peaks, or clumps, visible in the NIC2 or in the Hα image have no obvious counterparts in the other map. The properties of the clumps identified in these two images are studied in Paper II. The central regions of BX 482 also appear to be slightly brighter in H₁₆₀-band emission than in Hα emission.

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For the other galaxies with lower resolution SINFONI data, the small-scale substructure is smeared out but the overall H₁₆₀ band and Hα distributions at 04–06 resolution are very similar. For BX 389, the southern companion that is clearly separated from the main galaxy in the original NIC2 image is still apparent at lower resolution as an extension in the outer isophotes. The well-resolved SE and NW merger components of BX 528, and the bridge of emission connecting them, blend together and the PSF-matched NIC2 image strikingly resembles the fairly regular and centrally concentrated Hα line map. While in most cases, the general large-scale features of the morphologies are recognizable at ≈05 resolution, BX 528 offers an example where the nature of the system can only be reliably assessed with the additional information from either the kinematics or higher spatial resolution data.

We performed two-dimensional Sérsic model fits on both the Hα maps and the PSF-matched NIC2 images using GALFIT, following the procedure described in Section 4.1.1. For BX 482, we ran fits on the AO-assisted as well as the seeing-limited Hα data. For BX 528 and BX 389, we considered only single component fits since, at the ≈05 resolution of the SINFONI data, the merger components are unresolved in the former case, and the southern companion is blended with the primary galaxy in the latter. For consistency, fits on the convolved NIC2 images were restricted to a smaller region corresponding to the deepest area with effective ≈38 × 38 FOV of the SINFONI data at the $\rm 0\farcs 125 \;pixel^{-1}$ scale, and ≈23 × 23 FOV of the AO data at $\rm 0\farcs 05 \;pixel^{-1}$ for BX 482. This reduced area potentially affects the sky background estimates, degenerate with the profile shape and half-light radius. The smaller FOV as well as the broader PSF both contribute to the significantly larger uncertainties for the fits performed on the lower resolution maps compared to those using the maps at the original NIC2 resolution. Table 5 reports the best-fit structural parameters and Figure 11 compares the results from Hα with those from the PSF-matched NIC2 data.

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Table 5. Best-fit Structural Parameters from the SINFONI Hα Maps and PSF-matched NIC2 H₁₆₀-band Images

Object	Map	FWHM Resolutiona	Reb	nb	b/ab	P.A.b
			(kpc)			(deg)
Q1623-BX528	Hα	063	5.06+0.68−1.56	0.29+0.69−0.19	0.53+0.26−0.10	−42.1+30.4−6.5
	H160	063	4.91+1.64−1.73	0.25+0.66−0.23	0.44+0.32−0.15	−31.3+14.7−9.0
Q1623-BX663	Hα	039	3.97+1.15−0.99	0.68+0.73−0.41	0.72+0.17−0.12	4.9+24.3−27.4
	H160	039	3.37+0.58−0.68	0.36+0.32−0.16	0.82+0.14−0.16	−9.3+46.6−34.0
SSA22a-MD41	Hα	044	5.30+0.99−1.02	0.28+0.60−0.19	0.50+0.33−0.09	33.2+9.3−17.6
	H160	044	5.64+0.85−1.54	0.35+0.55−0.24	0.40+0.41−0.11	36.7+9.0−8.3
Q2343-BX389	Hα	054	6.10+1.62−1.19	0.31+0.86−0.23	0.48+0.35−0.11	−50.9+14.8−10.7
	H160	054	5.99+0.49−0.90	0.25+0.61−0.13	0.47+0.33−0.09	−44.6+10.7−5.8
Q2343-BX610	Hα	039	5.12+2.01−1.13	0.56+0.71−0.35	0.75+0.17−0.10	11.9+20.1−14.9
	H160	039	4.37+0.62−0.49	0.45+0.26−0.20	0.66+0.22−0.09	10.1+12.5−23.0
Q2346-BX482	Hα	017	6.07+7.09−1.46	0.35+3.47−0.28	0.59+0.21−0.12	−50.2+32.4−6.7
	H160	015	6.22+0.13−0.12	0.14 ± 0.01	0.48 ± 0.01	−60.9+1.9−1.5
	Hα	050	6.01+2.74−1.46	0.27+0.70−0.19	0.64+0.20−0.11	−58.0+23.4−10.2
	H160	050	6.22+2.11−0.91	0.15+0.50−0.11	0.50+0.17−0.06	−55.4+13.7−8.0

Notes. Structural parameters derived from single-component Sérsic profile fits to the two-dimensional Hα maps from SINFONI and to the H₁₆₀-band images from NIC2 convolved to the effective spatial resolution and resampled to the pixel scale of the SINFONI data. The results are obtained from a series of 500 GALFIT runs as described in Section 4.1, and the best-fit value and uncertainties correspond to the median and 68% confidence intervals of the distribution of results in each parameter. ^aPSF FWHM of the SINFONI Hα maps, and of the convolved NIC2 H₁₆₀-band images. ^bMain structural parameters derived from the GALFIT fits: the effective radius radius R_e, the Sérsic index n, the ratio of minor to major axis b/a, and the position angle P.A. (in degrees east of north).

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Overall, there is good agreement between the measurements based on the different data sets, with differences almost always within the (larger) 1σ uncertainties of the results obtained from the lower resolution maps. BX 663 is the most deviant source, with largest offsets in Sérsic index (smaller by $\rm 1.3\hbox{--}1.6$), half-light radius (smaller by factors of 1.14–1.35), and P.A. (differences by ≈15°–25°) between the lower resolution Hα and PSF-matched H₁₆₀-band maps and the original resolution H₁₆₀-band image. On the other hand, the parameters derived from the Hα and PSF-matched H₁₆₀ maps are in closer agreement, with R_e and n for Hα higher by 18% and 0.3, respectively, and b/a lower by 13%, all within the 1σ uncertainties. To investigate the cause of the differences in parameters obtained from the original H₁₆₀-band image of this galaxy and from the smoothed and resampled version, we created a pure n = 2 Sérsic model with total magnitude, R_e, b/a, and P.A. equal to the values of the best fit to the original NIC2 map of BX 663. The mock galaxy was pasted into an empty area of the full NIC2 map, which was then convolved to the SINFONI PSF, and finally resampled to $\rm 0\farcs 125\;pixel^{-1}$. The input parameters are recovered within <1σ by the fitting procedure in the $\rm 0\farcs 05\;pixel^{-1}$ data, both at the original NIC2 and the lower SINFONI resolution (with differences of ⩽4% in R_e and <0.2 in n). Significantly lower R_e and n index are derived after resampling to the larger pixel scale with, however, the best-fit parameters for the mock galaxy in excellent agreement with those of the real PSF-matched and resampled H₁₆₀-band image of BX 663 (within <1σ, with 4% difference in R_e and 0.12 in n). These tests indicate that the information on the steep inner profile of BX 663 leading to n = 2 is lost with the coarser $\rm 0\farcs 125\;pixel^{-1}$ sampling despite the good ≈04 resolution of its SINFONI data.

For the other five sources, a comparison of the fits to the smoothed and original H₁₆₀ maps indicates that the half-light radii, Sérsic indices, and P.A.s agree on average to <1%, 0.1, and $\rm 4^{\circ }$, respectively, with differences among individual galaxies of at most 2%, 0.2, and 7°. The axis ratios are higher by ≈30% on average (in the range 5%–55%) for the fits to the smoothed NIC2 data. Among these five sources, the differences between fits to the ≈05 resolution Hα and PSF-matched H₁₆₀ maps are on average 3% for R_e, 0.08 for n, and 5° for P.A. (at most 17%, 0.12, and 11°). The axis ratios from the Hα maps are higher than those from the smoothed H₁₆₀ data by 20% on average (in the range 3%–30%). For BX 482, the differences between the parameters obtained based on the seeing-limited and AO Hα maps are in the same ranges as for the smoothed versus unsmoothed H₁₆₀-band maps for the other sources (excluding BX 663). The close agreement between the parameters derived from the Hα and H₁₆₀-band emission for BX 482, either at ≈015 or ≈05 resolution, is unsurprising in view of their similar morphologies in the high-resolution SINFONI and NIC2 data (Figures 7 and 10).

One important implication of the Sérsic model fits is that the global Hα and rest-frame $\rm {\approx} 5000$ Å light distributions do not differ significantly from each other. This result is further supported by the comparison of the radial light profiles extracted along ellipses with center, axis ratio, and P.A. from the best-fit model to the H₁₆₀-band maps in Figure 12. In this Figure, the lower resolution Hα and PSF-matched H₁₆₀ maps are used for all sources, except for BX 482 where the profiles are extracted from the AO-assisted Hα data and original H₁₆₀-band image. At ≈05 resolution, the Hα and H₁₆₀-band profiles follow closely each other, with differences becoming important only beyond ≈1.5–2 R_e or typically $\rm 8\hbox{--}10 \;kpc$. For the low flux levels reached at these large radii, systematic residuals in background subtraction and flat fielding potentially affect the profiles in a substantial way. At radii ≲1.5–2 R_e, some of the (small) discrepancies may reflect differences in the detailed morphologies as well as uncertainties in the exact SINFONI PSF and thus the convolution kernel applied to smooth the NIC2 data. For the higher resolution profiles of BX 482, the ring-like feature that is dominated by the very bright clump on the southeast side of the galaxy is prominent in both Hα and rest-frame $\rm {\approx} 5000$ Å; as seen also from Figure 10, the regions in the vicinity of the galaxy center are comparatively fainter in Hα than in H₁₆₀-band light.

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The comparisons above do not indicate significant beam-smearing effects between angular resolution of $\rm FWHM \approx 0\farcs 15$ and ≈05 for the objects in our NIC2 sample. The galaxies are sufficiently large that their overall radial light distributions remain well resolved at ≈05 resolution. The most noticeable difference is the systematic shift to higher axis ratios for all sources. The coarser $\rm 0\farcs 125\;pixel^{-1}$ sampling leads to a significant decrease in the Sérsic index for BX 663, the object with steepest inner light profile (n = 2) at $\rm 0\farcs 05\;pixel^{-1}$. The parametric fits do not reveal any major difference between Hα and broadband rest-frame ≈5000 Å emission in terms of R_e, n, and P.A. for the five sources with n < 1.

In view of the similarity between the H₁₆₀ band and Hα maps for our targets, it is important to assess the contribution of emission lines to the broadband emission. At the redshift of our targets, the NIC2 F160W bandpass includes the [O iii] λλ 4959, 5007 doublet and Hβ. For all sources except BX 528, SINFONI seeing-limited observations of these lines with the H-band grating were taken as part of the SINS survey (Förster Schreiber et al. 2009). These data are analyzed and discussed by P. Buschkamp et al. (2011, in preparation), to which we refer for details. The [O iii] lines are detected in all galaxies but BX 663, while Hβ is detected in MD 41 and BX 610. Some of the non-detections can be attributed to the galaxies' lines being redshifted to the wavelength of bright telluric lines (in particular Hβ for BX 663 and BX 482). For all non-detections, we derived upper limits on the fluxes.

Table 6 reports the fractional emission line contribution based on the integrated H₁₆₀-band flux density and line fluxes (or 3σ upper limits). In all five sources with SINFONI H-band data, Hβ is the weakest line. The largest line contribution is inferred for BX 389, where the [O iii] lines make up 24% of the total H₁₆₀-band flux density and, with the 3σ upper limit on Hβ, the total line contribution is estimated at <29%. BX 610 has the smallest contributions, amounting to ≈6% for all three lines combined. The broadband H₁₆₀ emission of our NIC2 targets is thus clearly dominated by the continuum, with only a modest to very small fraction from the [O iii] and Hβ lines.

Table 6. Emission Line Contributions to the H₁₆₀-band Flux Densities

Object	$f_{\rm BB}({\rm [O\,\mathsc{iii}]\,\lambda \,5007})$	$f_{\rm BB}({\rm [O\,\mathsc{iii}]\,\lambda \,4959})$	fBB(Hβ)	fBB(tot)
Q1623-BX528	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
Q1623-BX663	<0.05	<0.02	<0.12	<0.20
SSA22a-MD41	0.11 ± 0.01	0.043 ± 0.005	0.023 ± 0.004	0.17 ± 0.01
Q2343-BX389	0.19 ± 0.02	0.050 ± 0.008	<0.054	<0.29
Q2343-BX610	0.034 ± 0.004	0.013 ± 0.002	0.018 ± 0.002	0.064 ± 0.005
Q2346-BX482	0.062 ± 0.006	0.019 ± 0.003	<0.037	<0.12

Notes. Individual and total fractional contributions of the [O iii] λλ 4959, 5007 and Hβ emission lines to the integrated broadband flux density measured from the NIC2 H₁₆₀-band data. The uncertainties correspond to 1σ uncertainties from the line fluxes and broadband magnitudes. For undetected lines, the 3σ upper limit on the line flux has been used.

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While the general appearance of the targets in [O iii] emission, and in Hβ where detected, resembles that in Hα, there are in some cases measurable differences. These gradients in line ratios reflect spatial variations in line excitation or gas-phase oxygen abundance, and in dust extinction across the targets (Genzel et al. 2008; P. Buschkamp et al. 2011, in preparation). To assess possible spatial variations in the emission line contributions, we also examined the galaxies on a pixel by pixel basis after convolving the NIC2 maps to the PSFs of the SINFONI H-band data, resampling them to $\rm 0\farcs 125 \;pixel^{-1}$, and aligning them following the same procedure as for Hα. We considered only pixels with $\rm S/N \ge 3$ in both H₁₆₀ flux density and line flux (the summed fluxes over these pixels represent typically >75% of the integrated measurements of the galaxies in 3''diameter apertures). The mean and median of the [O iii] λ 5007 contributions for the four sources where the line is detected are within ≈7% of the estimates from the integrated fluxes. The top (75%) quartile of the pixel line contributions range from 7% (BX 610) to 16% (BX 389). For Hβ, detected in MD 41 and BX 610, the mean and median contributions in individual pixels are within ⩽5% of those determined from the total fluxes, with top quartiles of 7% for MD 41 and 2% for BX 610. We conclude that spatial variations in line emission are not likely to affect significantly the observed H₁₆₀-band morphologies.

As a first step in our comparison, we considered the global structural parameters and, more specifically, the effective radius R_e and Sérsic index n. While each of the SINS targets was observed for four orbits, 17 of the 19 K-selected targets were observed for three orbits and the two brightest objects for two orbits. In the 24 μm selected sample, five objects were observed for two orbits, and six for only one orbit. Moreover, the published images from van Dokkum et al. (2008) and Kriek et al. (2009) were drizzled to 0038 pixels, while those of Dasyra et al. (2008) to 0076 pixels. To match both the imaging depth and sampling of the two comparison samples, we created 1-, 2-, and 3-orbit subsets of the NIC2 data of our SINS targets, and also drizzled them to 0038 and $\rm 0\farcs 076 \;pixel^{-1}$. We repeated our single-component Sérsic model fitting as described in Section 4.1.1 for each combination of exposure time and pixel sampling. Because of the differences in depth and pixel sampling of the van Dokkum et al. (2008) and Kriek et al. (2009) NIC2 data with respect to those of Dasyra et al. (2008), we compare our SINS targets separately with the K-selected and 24 μm selected samples.

For the K-selected galaxies, van Dokkum et al. (2008) and Kriek et al. (2009) derived the structural parameters using the same code as we employed (GALFIT) and a conceptually analogous approach was followed in treating the sky background. We thus adopted the best-fit R_e and n parameters as published by these authors, converting the circularized effective radii to standard effective radii. None of our conclusions is affected if we convert our radii to circularized radii instead. For the SINS galaxies, the difference in structural parameters between the 3- and 4-orbit subsets is negligible. The pixel scale has fairly little impact on the derived parameters of extended, well-resolved sources but more so for compact ones. Accordingly, for all but one of our SINS targets, the resulting best-fit R_e and n obtained from the 0038 and $\rm 0\farcs 05 \;pixel^{-1}$ images are nearly identical and within the (small) 1σ–2σ uncertainties, depending on the source and parameter. For BX 663, the AGN host with a compact central peak, the changes are significantly larger than for the other five SINS sources although they are formally within 1.5σ of the best-fit values for each pixel scale.¹⁵

For the 24 μm selected dusty IR-luminous sample, Dasyra et al. (2008) did not perform single-component Sérsic profile fitting for their analysis. We thus applied our fitting procedure using their images to obtain the R_e and n for comparison with our sample. The resulting effective radii agree on average within 20%, or <1σ based on our fitting uncertainties, with those estimated using the SExtractor software by Dasyra et al. The most important difference (by 30%, or 3σ) occurs for the largest, most diffuse and asymmetric source (MIPS 8242). For our SINS targets, and compared to the nominal fits for the 4-orbit $\rm 0\farcs 05 \;pixel^{-1}$ data, the differences resulting from the shallower subsets and larger $\rm 0\farcs 076 \;pixel^{-1}$ sampling are typically ≲3σ. Again, BX 663 shows the largest changes with R_e smaller by $\rm {\approx} 0.6\hbox{--}1.2 \;kpc$ and n lower by ≈0.7–1, depending on the subset.

Figure 13 plots the best-fit n index versus R_e of our SINS sample along with those of the K-selected and 24 μm selected comparison samples. In terms of size and Sérsic index, the quiescent sample of van Dokkum et al. (2008) is clearly distinct from our SINS galaxies, with overall significantly smaller R_e and typically higher n values. The Kriek et al. (2009) objects are intermediate between the passive objects of van Dokkum et al. and our actively star-forming SINS sources with, as already discussed by Kriek et al., a clear separation between the AGN sources that have sizes and n indices in a narrow range and fully overlapping with the passive objects whereas the purely star-forming sources span wider ranges shifted toward larger sizes and lower n values.

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Quantitatively, our SINS objects lie at the large size − low n end with sample median R_e,med = 5.1 kpc and n_med = 0.35 (or 5.7 kpc and 0.33, respectively, when excluding the AGN source BX 663). In the K-selected comparison sample, the six star-forming sources have median values of R_e,med = 4.3 kpc and n_med = 0.95, the four AGN sources have R_e,med = 1.4 kpc and n_med = 2.46, and the nine passive objects have R_e,med = 1.5 kpc and n_med = 2.30. Our AGN source BX 663 is not as compact as the Kriek et al. AGNs but, among our SINS sample, it reflects the trend toward lower R_e and higher n of AGN relative to star-forming galaxies seen in the K-selected sample. One source (HDFS1-1849) from van Dokkum et al. appears to be an "outlier" with respect to the other eight passive K-selected objects: its R_e = 4.4 kpc and n = 0.5 is clearly more characteristic of the SINS and Kriek et al. (2009) star-forming galaxies. As we will see below, it is also more similar to the star-forming sources in terms of the non-parametric Gini, Ψ, and M₂₀ coefficients. This object is anomalous within the sample of quiescent galaxies insofar as its broadband SED fit indicates in fact active star formation. The lack of emission lines that formed the basis of the "quiescent" classification may only be due to this object's dusty, edge-on nature (Kriek et al. 2009). Excluding this object, the median values for the eight remaining passive K-selected sources are R_e,med = 1.4 kpc and n = 2.55.

With the Dasyra et al. (2008) sample, we can explore variations in different regimes of bolometric luminosity. While the four SINS objects with Spitzer/MIPS data are among the most luminous of the rest-UV-selected high z population, their observed 24 μm fluxes and total IR luminosities are still on average almost an order of magnitude lower than those of the 24 μm selected sources of Dasyra et al. (2008). Overall, the 24 μm selected dusty IR-luminous sample is distinct from our SINS objects, and appears to be intermediate between the rest-UV SINS and K-selected star-forming galaxies and the K-selected passive and AGN objects. The 24 μm selected sources have a median size and Sérsic index of R_e,med = 2.6 kpc and n_med = 1.45. These values are comparable to the median rest-frame optical structural parameters derived from NIC2 imaging for a sample of high-z submillimeter-selected galaxies by Swinbank et al. (2010), which overlap in bolometric luminosity with the Dasyra et al. objects. Sampled at the same $\rm 0\farcs 076 \;pixel^{-1}$ scale, and 1- and 2-orbit integration times, the SINS sample has about twice larger R_e,med = 5.4 kpc and significantly lower n_med = 0.37. The trend for the 24 μm selected sources to lie toward smaller radii and steeper inner profiles with respect to the SINS galaxies may reflect the prevalence of AGN activity among the Dasyra et al. sample (10 out of 11 objects).

Clearly, the various samples probe different regimes in structural parameters, and this appears to be related to both the level of star formation and AGN activity. To further quantify the differences between our SINS galaxies and the comparison samples, we analyzed the images through the non-parametric approach described in Section 4.2.1, using the relevant data sets for the SINS targets matching the depth and pixel sampling of the K- and 24 μm selected samples. In addition, to take into account the redshift range of our targets and remove the effects of surface brightness dimming, particularly important in this approach, we selected pixels for our analysis as if all objects were observed at the maximum redshift among the three samples, i.e., z = 2.6.

We estimated Gini, Ψ, and M₂₀ for galaxies in the three samples, and the results are shown in Figure 14. All panels contain our SINS galaxies, and the top two panels show G versus Ψ and G versus M₂₀, using the K-selected sample for comparison. The bottom two panels show the same parameters, but feature the 24 μm selected sample for comparison. For the top two panels, the SINS targets have been reanalyzed using 3- and 2- orbit subsets of the data at $\rm 0\farcs 038 \;pixel^{-1}$, in order to match the depth and sampling of the van Dokkum et al. (2008) and Kriek et al. (2009) images. Given the compact and axisymmetric nature of the quiescent K-selected subsample featured in van Dokkum et al., we applied the same non-parametric analysis to our empirical PSF, constructed from multiple stars as described in Section 2.5 but from our 0038 pixel set of images. This analysis indicates that while the quiescent, K-selected objects are extremely compact, the majority of them can be distinguished from unresolved point sources, with significantly lower Gini values. For the bottom two panels, our SINS targets have been reanalyzed using 2- and 1-orbit subsets of the data at $\rm 0\farcs 076 \;pixel^{-1}$, in order to match the depth and sampling of the Dasyra et al. (2008) images. The non-parametric statistics were calculated as well for the empirical PSF sampled with this pixel scale. In all panels, the shallower 3-, 2-, and 1-orbit SINS data subsets result in lower Gini coefficient for a given object, while higher values are obtained for Ψ and M₂₀.

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The non-parametric morphological analysis reinforces the qualitative visual impression from the images and the results from the Sérsic profile fitting of the different samples of galaxies. The K-selected passive and AGN sources occupy a disjoint region of G − Ψ − M₂₀ morphological parameter space from that of the SINS targets. They are virtually all offset toward higher Gini, and both lower Ψ and M₂₀ values, with sample median values of G_med = 0.54, Ψ_med = 0.8, and M_20,med = −1.8 for the passive galaxies and essentially identical G_med = 0.53, Ψ_med = 0.8, and M_20,med = −1.8 for the AGN sources. As was the case for the structural parameters, only a single galaxy from the K-selected passive sample (HDFS1-1849) even approaches the lower Gini (median of 0.28), and higher Ψ (median of 7.8) and M₂₀ (median of −0.5) values of our SINS sample.¹⁶ In contrast to the passive and AGN objects, the six K-selected star-forming objects show considerably more overlap with the SINS sample. The median values for the K-selected star-forming sources are G_med = 0.34, Ψ_med = 3.6, and M_20,med = −1.4, which are intermediate between the parameters describing the SINS sample and the K-selected passive and AGN objects.

One slight caveat to these results is the difference in typical S/N among the samples, with the K-selected quiescent and AGN objects ∼2–3 times higher in average surface brightness than the SINS targets, and the K-selected star-forming sources ∼1.5 times brighter. As discussed by Peter et al. (2007) and Abraham et al. (2007), using a fixed surface brightness threshold (effectively what we have done) will lead to a "truncation bias" in the Gini coefficients estimated for fainter systems, in that their pixel flux distribution functions will be sampled over a smaller dynamic range than those of more luminous objects. To test for the significance of this effect, we applied a higher surface brightness threshold to the K-selected samples, such that the resulting pixel flux distribution functions span the same dynamic range as those of our SINS targets. We find G_med = 0.45 for the truncated pixel flux distribution functions for K-selected passive and AGN sources, still significantly higher than the median of the SINS sample, and still with no overlap in morphological parameter space. Applying the same type of truncation to the K-selected star-forming galaxies, we find very little effect on the sample median properties, with G_med = 0.33.

Turning to the properties as a function of bolometric luminosity, in the G − Ψ − M₂₀ parameter space, the 24 μm selected dusty IR-luminous sample separates on average from the SINS sample in the same sense as the K-selected sample, if not as significantly as the passive and AGN objects. The median parameter values for the 24 μm selected dusty IR-luminous sources are G_med = 0.44, Ψ_med = 2.1, and M_20,med = −1.2. Sampled at the same pixel scale and exposure time, the SINS targets have lower Gini (median of 0.30), and higher Ψ (median of 6.4) and M₂₀ (median of −0.6). The typical S/N of objects in the two samples is very similar, so no issue of truncation bias applies in this comparison. These quantitative morphological results confirm again the qualitative visual impression that our SINS targets have systematically more irregular, extended, and clumpy morphologies than those of the 24 μm selected dusty IR-luminous sample of Dasyra et al. (2008).

Luminous dusty systems with L_IR > 10¹² L_☉ are commonly associated with major mergers in the local universe (e.g., Genzel et al. 2001). The 24 μm selected sample of Dasyra et al. (2008) falls well above this luminosity threshold, yet the processes giving rise to extreme bolometric luminosities at high redshift may be more diverse, based on theoretical grounds (e.g., Davé et al. 2010), and supported by observational evidence (e.g., Dasyra et al. 2008; Swinbank et al. 2010). Dasyra et al. find roughly 50% of their full NIC2 sample to appear morphologically "quiescent." Furthermore, consistent with the results of Kriek et al. (2009), these authors show that objects in their sample with mid-IR AGN signatures also tend to have more compact rest-frame optical morphologies than those with starburst-dominated spectra. Given that all but one object in the Dasyra et al. z = 2.0–2.5 subsample show evidence of AGN activity, the 24 μm selected dusty IR-luminous galaxies included in Figure 14 are among the more compact objects in the full Dasyra et al. sample. Dasyra et al. hypothesize that 24 μm selected IR-luminous objects, with warmer mid-IR/far-IR colors than the submillimeter-selected IR-luminous high z population (Chapman et al. 2003), may represent the merged, dynamically relaxed counterparts of the (major-) merging submillimeter galaxies. On the other hand, the rest-frame optical structural parameters and sizes of submillimeter galaxies as presented by Swinbank et al. (2010) are very similar to those of the 24 μm selected IR-luminous objects. A more careful morphological comparison of the two bolometrically luminous samples is clearly required to construct an evolutionary sequence.

In analogy with trends seen in the local universe (Kauffmann et al. 2003; Shen et al. 2003), the structural properties of z ∼ 2 galaxies appear to be correlated with their stellar populations. Based on imaging with both NICMOS/NIC3 from space (Zirm et al. 2007; Toft et al. 2007), and with VLT/ISAAC (Franx et al. 2008; Toft et al. 2009) and UKIRT/WFCAM (Williams et al. 2010) from the ground, it has been shown that quiescent, high-redshift galaxies have systematically smaller sizes and higher stellar mass surface densities than actively star-forming systems. Based on the sample of 19 K-selected galaxies discussed in the previous subsections, Kriek et al. (2009) used their higher resolution NICMOS/NIC2 imaging to demonstrate that specific SFR and rest-frame U − B color are strongly correlated with galaxy structural parameters. We here examine the structural properties in connection with the stellar populations for our SINS sample, complemented with the van Dokkum et al. (2008) and Kriek et al. (2009) K-selected samples for which stellar properties from SED modeling are available.

As proxies for galaxy stellar populations, we consider the stellar mass and specific SFR. Within our SINS NIC2 sample, the absence of correlation between morphology and stellar population properties includes parameters derived from Sérsic models (R_e and n) as well as the non-parametric morphological coefficients (G, Ψ, and M₂₀). This result echoes previous ones from Law et al. (2007b) and Peter et al. (2007) demonstrating a lack of correlation between stellar populations and rest-UV morphologies for UV-selected galaxies at z ∼ 2. However, as described by Peter et al. (2007) the UV-selected galaxies do not span the full range of stellar population properties that exist at z ∼ 2 (see also, e.g., van Dokkum et al. 2006; M. Damen et al. 2011, in preparation). The K-selected sample with NIC2 imaging from van Dokkum et al. (2008) and Kriek et al. (2009) ideally augments our SINS NIC2 sample in this respect, considerably extending the range probed in specific SFR by over two orders of magnitude, in the same redshift range and at comparable stellar masses as our SINS targets.

Figures 15 and 16 combine the morphological properties of our SINS and K-selected samples, now plotted as a function of the stellar mass and specific SFR derived from SED modeling. The SINS and K-selected samples overlap in stellar mass over the range from ≈3 × 10¹⁰ to ≈10¹¹ M_☉. Over this range, there is significant diversity in structural parameters, with the SINS targets exhibiting the largest R_e, smallest n, largest Ψ and M₂₀, and smallest G values. At the other extreme, we find the AGN and quiescent K-selected galaxies, with the star-forming K-selected galaxies showing intermediate properties. More specifically, over this interval in stellar mass, the galaxies cover a wide range in R_e, consistent with the spread of about an order of magnitude in rest-frame optical sizes for z ∼ 2 galaxies of similar masses found in previous studies (e.g., Trujillo et al. 2006; Zirm et al. 2007; Toft et al. 2007, 2009; Franx et al. 2008).

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On the other hand, the K-selected and SINS samples separate more cleanly in specific SFR. A clear sequence of increasing specific SFR is represented, respectively, by the quiescent and AGN K-selected galaxies, the star-forming K-selected galaxies, and the SINS sample. In turn, significant connections with specific SFR are found for every morphological coefficient considered here, with systematically higher R_e, Ψ, and M₂₀, and systematically lower n and G, as the specific SFR increases. These strong trends with star formation activity are consistent with the previous work from Toft et al. (2007, 2009), Zirm et al. (2007), and Franx et al. (2008), but are based on higher resolution NIC2 imaging. Furthermore, they extend the NIC2-based correlations between morphology and stellar populations from van Dokkum et al. (2008) and Kriek et al. (2009) toward higher specific SFR values. The results presented here reinforce the conclusion by Franx et al. (2008) that galaxy structural parameters are better correlated with specific SFR and color than with stellar mass. These results highlight the fact that stellar mass alone is not a good predictor of structural parameters, nor of detailed morphologies as we find from our non-parametric morphological analysis.

In that respect, it is also interesting to consider morphologies as a function of the stellar mass surface density of the galaxies. Indeed, in the local universe, the specific SFR (as well as rest-frame optical colors) is observed to be much more closely related to stellar mass surface density than to stellar mass (e.g., Kauffmann et al. 2003, 2006, for the Sloan Digital Sky Survey (SDSS) sample), and these relationships are found to persist out to at least z ∼ 2 (Franx et al. 2008; Maier et al. 2009). This trend is again reflected among the SINS and K-selected samples discussed here. Figure 17 plots the specific SFR as a function of the projected stellar mass surface density Σ(M_⋆) of the objects. We calculated the surface density assuming that the observed 1.6 μm light (rest-frame ≈5000 Å) from the NIC2 images traces well the stellar mass (as we will demonstrate for one of our SINS targets in Section 7.1), and thus that half of the total stellar mass is enclosed at r < R_e. We find a clear trend of decreasing specific SFR with increasing mass surface density, which is fully consistent with the median relationship at z ∼ 2 derived by Franx et al. (2008). Our six actively star-forming SINS targets lie at the lower end of projected mass surface density with median of $\log (\Sigma (M_{\star })\,[{M_{\odot }\;\rm kpc^{-2}}]) = 9.0$ (or 8.8 when excluding the AGN source BX 663) and the nine quiescent galaxies of van Dokkum et al. (2008) lie at the higher end with median of $\log (\Sigma (M_{\star })\,[{M_{\odot }\;\rm kpc^{-2}}]) = 10.5$ (or 10.6 when omitting the anomalous HDFS1-1849). The ten emission line galaxies of Kriek et al. (2009) span the intermediate range, with sample median of $\log (\Sigma (M_{\star })\,[{M_{\odot }\;\rm kpc^{-2}}]) = 9.5$. Among these objects, the subsamples of six star-forming and four AGN sources have, respectively, lower and higher mass surface densities (median values of $\log (\Sigma (M_{\star })\,[{M_{\odot }\;\rm kpc^{-2}}]) = 9.2$ and 10.3). Since the structural and morphological properties of the SINS and K-selected samples considered here are strongly connected with the specific SFR, it follows from the specific SFR versus Σ(M_⋆) trend that they are also closely related to the stellar mass surface density. We note here that the high-z submillimeter-selected galaxies of Swinbank et al. (2010) have properties implying on average both higher specific SFR and Σ(M_⋆) than the SINS galaxies, and do not follow the median relationship of Franx et al. (2008), pointing toward differences in their assembly histories.

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In this section, we focus on MD 41, the target among our NIC2 sample with additional high-resolution optical imaging with HST/ACS. We first combine the ACS and NIC2 images to compare the structural parameters derived from the rest-frame UV and optical surface brightness distributions. We then use the observed optical-to-near-IR color map to construct the spatially resolved stellar mass map of the galaxy.

7.1.1. Rest-frame UV Structural Parameters

7.1.2. Rest-frame Colors, Mass-to-light Ratio, and Mass Distribution

We can further exploit the ACS and NIC2 images to investigate spatial variations in observed colors and mass-to-light ratio, and derive the stellar mass distribution within MD 41. In Figure 18, the left panel shows the observed i₈₁₄ − H₁₆₀ color map, over the region for which the pixel flux densities have $\rm S/N > 3$ in each of the ACS and NIC2 map. The observed colors are fairly uniform across most of the disk of MD 41, with mean and median of (i₈₁₄ − H₁₆₀)_AB = 0.8 and 0.9 mag, respectively, and standard deviation of 0.37 mag. This compares reasonably well with the integrated color of 0.63 measured in a circular aperture of 3'' diameter.¹⁷ Only two small regions exhibit significantly different colors: the southwestern edge of MD 41 at the location of the two brightest clumps in i₈₁₄ emission with bluer colors ((i₈₁₄ − H₁₆₀)_AB ≈ 0.2 on average), and an area around the center of the galaxy characterized by redder colors ((i₈₁₄ − H₁₆₀)_AB ≈ 1.2 mag on average).

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To interpret the color map of MD 41, we turn to synthetic colors and M/L ratios calculated for the z = 2.2 of MD 41 from Bruzual & Charlot (2003) models for a range of ages, extinction, SFHs, and two stellar metallicities (solar and 1/5 solar). The details are given in the Appendix. Stellar age, extinction, and SFH are highly degenerate in observed i₈₁₄ − H₁₆₀ colors (or rest-frame 2600–5000 Å colors at the redshift of MD 41). However, there is a fairly well defined relationship between the stellar mass to rest-frame optical light ratio (with luminosity uncorrected for extinction) and the observed colors, with very little dependence on our choice of metallicity. For our purposes, we used model predictions through the SDSS g-band filter, a good approximation to the rest-frame ≈5000 Å luminosity probed by the NIC2 F160W filter (see the Appendix).

We thus derived a mean relationship between the observed (uncorrected for extinction) M_⋆/L^rest_g ratio and observer's frame i₈₁₄ − H₁₆₀ colors for z = 2.2. We used this relationship to compute the M_⋆/L^rest_g ratio map of MD 41, shown in the middle panel of Figure 18. Unsurprisingly, the M_⋆/L^rest_g ratio map looks similar to the i₈₁₄ − H₁₆₀ map, given the roughly linear relation (in logarithmic units for the M/L). The mean and median values of individual pixels are log(M_⋆/L^rest_g[M_☉ L⁻¹_g,☉]) ≈ −0.9, with standard deviation of $\rm {\approx} 0.2 \,dex$. The observed integrated color gives nearly the same value, −0.83, while the model with best-fit parameters from the optical/near-IR SED modeling for MD 41 (Table 3) has a somewhat lower value of −1.08. An average value of ≈−1.3 is measured in the regions of bluest colors at the southwestern edge of MD 41, and of ≈−0.7 in the redder regions around the center. The fairly small scatter among individual pixels implies roughly constant observed M_⋆/L^rest_g ratio across most of the galaxy.

Multiplying the observed M_⋆/L^rest_g map by the H₁₆₀-band image as a proxy for the extrinsic rest-frame g-band luminosity then leads to the spatial distribution of stellar mass across MD 41. The map of projected stellar mass surface density Σ(M_⋆) is shown in the right panel of Figure 18. It is remarkably similar to the H₁₆₀-band image itself, indicating that the observed 1.6 μm emission does trace closely the stellar mass distribution in MD 41. The typical (mean, median) values of individual pixels is $\log (\Sigma (M_{\star }\,[{M_{\odot }\;\rm kpc^{-2}}])) \approx 8.0$, with standard deviation of 0.3 dex. At the largest radii probed, and especially on the southwestern edge, the surface density drops to log(Σ(M_⋆)) ≈ 7.5, and it increases toward the center by about an order of magnitude to log(Σ(M_⋆)) ≈ 8.4. The deprojected surface density from the total stellar mass of MD 41, assuming half of it is enclosed within a radius of R_e, is log(Σ(M_⋆, r < R_e)) = 7.6; for this fairly inclined system, this increases significantly when considering the projected surface density to log(Σ(M_⋆, r < R_e)) = 8.1, virtually the same as inferred on average at individual locations across the galaxy. Compared to the properties derived for massive 1.5 < z < 2.5 galaxies by Franx et al. (2008; see also Figure 17), MD 41 lies at the low surface mass density end, consistent with its high specific SFR of $\rm 24 \;Gyr^{-1}$ and blue estimated integrated rest-frame (U − B)_AB ≈ 0.5 color.

The total stellar mass obtained by summing up the inferred stellar mass of individual pixels with $\rm S/N > 3$ in the i₈₁₄- and H₁₆₀-band images is 7.3 × 10⁹ M_☉, or 95% of the value derived from the modeling of the integrated optical/near-IR SED (Section 3.3). The sum of the H₁₆₀-band flux densities over the same pixels corresponds to 65% of the total as measured in a 3''diameter aperture (Section 3.2). Multiplying the $\rm S/N > 3$ pixels' luminosity densities by the M_⋆/L^rest_g from the best-fit SED model of MD41 results in a stellar mass of only 5.0 × 10⁹ M_☉. This difference with respect to the spatially resolved estimate reflects the difference between the pixel-averaged M_⋆/L^rest_g and that from the integrated SED noted above. It suggests the total SED-derived stellar mass may be underestimated by ≈30% because dustier and/or more evolved, redder stellar populations are under-represented in the effectively luminosity-weighted integrated rest-UV and optical photometry of MD 41. A similar effect between stellar masses computed by integrating spatially resolved mass maps and by modeling unresolved photometry was found for nearby galaxies (Zibetti et al. 2009). This effect may be more important for MD 41 (possibly also for BX 482) because the SED fits rely more heavily on the rest-UV photometry than for the other galaxies with better rest-optical coverage (three near-IR bands compared to two for MD 41 and one for BX 482).

Our analysis of ACS i₈₁₄ and NIC2 H₁₆₀-band imaging of MD 41 shows modest variations in the M_⋆/L^rest_g ratio, within a factor of ∼1.5 over most of the galaxy and on spatially resolved scales as small as $\rm {\approx} 1.2 \;kpc$. In addition, the results indicate that the 1.6 μm (rest-frame ≈5000 Å) is a fairly good tracer of the stellar mass distribution of MD 41. The spatially resolved color-based mass map suggests nevertheless that luminosity-weighting biases may have led to a ≈30% underestimate of the total stellar mass based on modeling of the integrated SED of MD 41. It will undoubtedly be interesting to investigate this effect more systematically with larger high z galaxy samples from combined high-resolution optical and near-IR imaging in future studies.

Size is a fundamental property of galaxies. The redshift evolution of disk sizes and scaling relations involving size (e.g., size–velocity, size–mass) set sensitive constraints on the coupling between the baryonic and dark matter, on the mechanisms through which disks acquire their angular momentum, and on the physical processes that drive galaxy growth (e.g., White & Rees 1978; Fall & Efstathiou 1980; Blumenthal et al. 1984; Dalcanton et al. 1997; Mo et al. 1998; Navarro & Steinmetz 2000). Size determinations, however, can be affected by various factors, and reconciling observed sizes with theoretical predictions remains a challenge (e.g., Dutton et al. 2007; Dutton & van den Bosch 2009; Dutton et al. 2011; Somerville et al. 2008; Sales et al. 2009; Burkert et al. 2010). In the following, we consider whether the sizes derived for our NIC2 sample are affected by their particular morphologies and interpret them in the broader context of the size distribution of the general z ∼ 2 galaxy population. Our sample has high-quality data that allow, for the first time, a reliable and consistent comparison of rest-frame optical continuum and Hα sizes, and we discuss implications for disk formation at high redshift.

7.2.1. Rest-frame Optical Continuum and Hα Sizes

7.2.2. Possible Caveats

Arguably, one of the key aspects in the study of high-redshift galaxies is a characterization of the mass assembly process, and, in particular, pinpointing evidence for the occurrence of major mergers and interactions or, in their absence, for the establishment of disk-like systems, which are a prediction of models of galaxy formation. There are several inherent difficulties in studies based on morphologies, including bandshifting, intrinsically complex structure, and uncertainties in the timescales over which key merger signatures are observable (e.g., Toft et al. 2007; Elmegreen et al. 2007, 2009; Lotz et al. 2008, 2010a, 2010b). Therefore, kinematics appear to be a prerequisite for a robust distinction although there are possible complications as well (for instance, particular merger configurations mimicking disk-like kinematics; e.g., Law et al. 2006; Shapiro et al. 2008; Robertson & Bullock 2008; Förster Schreiber et al. 2009; Épinat et al. 2010). Morphologies and kinematics together make for a powerful combination, mitigating the respective potential limitations as well as providing a more complete picture of individual galaxies (see also Neichel et al. 2008).

The kinematic classification of our six SINS targets, all disks except BX 528, was first based on SINFONI data sets taken with the $\rm 0\farcs 125 \;pixel^{-1}$ scale, at ≈05 or $\rm {\approx} 4.1 \;kpc$ resolution (039 and 3.2 kpc for the NGS-AO data of BX 663). Initially based on qualitative assessment of both the Hα velocity field and velocity dispersion map (Förster Schreiber et al. 2006b), the classification into disk- and merger-like systems was quantitatively confirmed through the application of kinemetry (Shapiro et al. 2008), with the exception of BX 663 due to S/N limitations outside of the inner regions. To date, BX 482 is the only target among our NIC2 sample followed-up with AO and the $\rm 0\farcs 05 \;pixel^{-1}$ scale, with effective resolution of 017. Its kinematic classification as a disk is further confirmed with the higher resolution data, although more detail in the Hα emission and kinematic maps is resolved. Fourteen other galaxies from the full SINS survey were classified by kinemetry, of which four have follow-up AO observations at ∼015–020 resolution (Shapiro et al. 2008; Genzel et al. 2008; Förster Schreiber et al. 2009; Genzel et al. 2011; P. Buschkamp et al. 2011, in preparation). In all cases, as for BX 482, the kinematic classification is the same whether it is based on the seeing-limited or the AO data sets.

At first glance, the NIC2 H₁₆₀ images of our six targets at 0145 resolution ($\rm {\approx} 1.2 \;kpc$) reveal rich substructure at all surface brightness levels. Qualitatively, multiple bright compact components can be interpreted as distinct interacting/merging units, asymmetries in the more diffuse emission or distorted isophotes on large scales can be attributed to tidal features (e.g., Lotz et al. 2004; Conselice et al. 2005). On the other hand, these characteristics may also result from internal dynamical processes within gas-rich disks, such as bar- and spiral-like features from non-axisymmetric perturbations or luminous kpc-sized clumps resulting from disk instabilities and tidal-like features induced by the mutual interactions between massive clumps (e.g., Bournaud et al. 2007, 2008). It may therefore not be immediately obvious whether a system is a disk or a merger from simple visual inspection. Quantitatively, as found in Section 4.1.2, all the kinematically classified disks among our NIC2 sample have Sérsic indices n ⩽ 2 (and even <1 when excluding the AGN source BX 663), consistent with structurally late-type, disky systems.

Among our NIC2 sample, BX 610 appears to be a particularly striking example where the rest-frame optical morphology reflects tell-tale signatures of internal dynamical processes. Indeed, its appearance, as outlined in Section 3.1, exhibits evidence for a bar and features reminiscent of spiral arms, and there is no evidence for any nearby companion in our NIC2 and SINFONI data, nor of recent merging. This galaxy is one of the most robust examples of rotating disk kinematics among the SINS survey (Förster Schreiber et al. 2006b; Genzel et al. 2008; Shapiro et al. 2008; Cresci et al. 2009), with the Hα velocity field exhibiting the classical "spider diagram" of isovelocity contours, a nearly axisymmetric and centrally peaked velocity dispersion map, and a close correspondence of the kinematic center and major axis with the geometrical center and morphological major axis (from both the rest-frame optical and Hα emission). BX 610 shows several prominent clumps and direct observations of CO molecular gas indicate a very high gas to baryonic mass fraction of ∼55% (Tacconi et al. 2010). All these properties suggest that BX 610 may be one such apparently isolated galaxy where clumps formed from fragmentation in a Toomre-unstable gas-rich disk and where efficient secular processes drive its early dynamical evolution (Genzel et al. 2008, see also Carollo et al. 2007; Bournaud et al. 2007; Dekel et al. 2009; Agertz et al. 2009; Ceverino et al. 2010). While BX 610 is a particularly remarkable case, the other disks among our NIC2 targets as well as other high z samples studied at high resolution (e.g., Bournaud et al. 2008; Elmegreen & Elmegreen 2005; Elmegreen et al. 2009; Genzel et al. 2011; and Paper II) show prominent clumps and properties consistent with the above theoretical scenario.

While the majority of objects in our SINS NIC2 sample are classified as disks, it is noteworthy to highlight examples of how the unique combination of Hα kinematics and rest-frame optical morphologies sheds light on galaxy interactions. For BX 528, the Hα kinematics clearly indicate its merger nature even at the ≈06 seeing-limited resolution of the SINFONI data (Förster Schreiber et al. 2006b; Shapiro et al. 2008). The reversal in velocity gradient across the system could be produced by a counterrotating binary merger. In the NIC2 image, the system is resolved into two main "SE" and "NW" components separated by about 1'' (8 kpc) in projection, and connected by a fainter "bridge" of emission. Single-component Sérsic model fits to the H₁₆₀ map, either at the original NIC2 resolution or convolved to the lower resolution of the SINFONI observations, imply a shallow inner light profile with n ∼ 0.2, evidently caused by the lower surface brightness between the SE and NW components. As seen in Section 3.1, at 06 resolution, both the Hα and smoothed H₁₆₀-band morphologies appear rather regular and the SE and NW components are not discerned, making it impossible to distinguish from disk-like systems. Moreover, BX 528 does not stand out compared to the disks in our sample in the G − Ψ − M₂₀ parameter space based on the high-resolution NIC2 image (Figure 7). Thus, for BX 528, both the Hα kinematics and the high-resolution rest-frame optical imaging are necessary to fully characterize the nature of this system.

Even if not as significantly as BX 528, BX 389 also presents evidence for galaxy interaction (Figure 10). The Hα kinematics at 05 resolution show fairly regular motions consistent with rotation in a highly inclined disk. The various line maps from the K- and H-band seeing-limited SINFONI data all exhibit an extension to the south of the center, and the rest-frame optical line ratios ([N ii]/Hα, [O iii]/Hβ) are consistent with either a low-metallicity companion or shock excitation in a starburst-driven galactic outflow (Lehnert et al. 2009; P. Buschkamp et al. 2011, in preparation). This extension does not appear kinematically distinct from the main part of the source, with line-of-sight velocities similar to those along the major axis of the main body of the galaxy, on the same side and at the same projected radii. The NIC2 H₁₆₀-band imaging reveals that this is a separate component, at a projected distance of 5 kpc below the galactic plane of BX 389, supporting the nearby satellite interpretation. For BX 389, therefore, the high-resolution near-IR imaging resolves the companion from the main part of the source and the kinematics confirm the physical association between the two components.

Assuming that the observed 1.6 μm light traces closely the stellar mass in our NIC2 targets (see Section 7.1.2), we can set constraints on the mass ratios of the different components in BX 528 and BX 389. Various estimates based on the two-component Sérsic model fits (Section 4.1), on simple aperture photometry, and on the fractional light contributions of the associated "clumps" (presented in Paper II) imply a mass ratio in the range 1.2:1 to 1.9:1 for BX528−SE relative to BX528−NW, and 6:1 to 20:1 for the main part of BX 389 relative to the southern companion. From the stellar mass ratio, BX 528 is a nearly equal-mass major merger, in agreement with the signatures and classification from the Hα kinematics. In contrast, the southern companion of BX 389 represents a minor merger, unlikely to have strong impact on the large-scale kinematics of the primary component and consistent with the lack of substantial disturbances in the kinematics expected for major mergers.

We conclude from the above that the Hα kinematics and rest-frame optical continuum morphologies of our NIC2 sample draw a consistent picture for the nature of each target and are very complementary. The kinematics, even at $\rm {\sim} 3\hbox{--}5 \;kpc$ resolution, are sufficient (and in some cases necessary, as for BX 528) to reliably distinguish between disks and major mergers. We caution that there will be specific cases where a system's configuration will lead to ambiguous or erroneous classification, also depending on the data quality (Shapiro et al. 2008; Law et al. 2009), but this does not appear to be the case for the objects studied in this paper. Morphologies (as well as kinematics) at higher $\rm {\sim} 1 \;kpc$ resolution then reveal further details and are important to identify minor mergers, and more subtle or smaller scale signatures of internal dynamical processes (e.g., Bournaud et al. 2008; Genzel et al. 2008, 2011).