THE SINS/zC-SINF SURVEY OF z ∼ 2 GALAXY KINEMATICS: REST-FRAME MORPHOLOGY, STRUCTURE, AND COLORS FROM NEAR-INFRARED HUBBLE SPACE TELESCOPE IMAGING^*

A detailed discussion of the selection of the SINS/zC-SINF AO sample can be found in FS14. In short, the galaxies were drawn from the optical spectroscopic surveys of parent samples selected photometrically based on:

• 1.  
  sBzK or "BX/BM" photometric criteria from the spectroscopic zCOSMOS-DEEP survey collected with VIMOS at the VLT ("zC" objects, Lilly et al. 2007, 2009; 18 targets);
• 2.  
  ${{U}_{n}}GR$ optical colors ("BX" objects, Steidel et al. 2004; 8 targets);
• 3.  
  Spitzer/IRAC 4.5 μm fluxes (Galaxy Mass Assembly ultra-deep Spectroscopic Survey or "GMASS," Cimatti et al. 2008; Kurk et al. 2013; 3 targets);
• 4.  
  combination of K-band and BzK color criteria (survey by Kong et al. 2006 of the "Deep-3a" field; 3 targets); and
• 5.  
  K-band magnitudes ("K20" survey, e.g., Cimatti et al. 2002; Gemini Deep Deep Survey or "GDDS," Abraham et al. 2004; 3 targets).

The specific selection criteria for the SINFONI instrument were then the observability of the Hα emission line and a minimum expected Hα line flux (corresponding roughly to a minimum SFR of $\sim 10\;{{M}_{\odot }}$ yr⁻¹; Förster Schreiber et al. 2009; Mancini et al. 2011). We considered only sources with redshifted Hα line falling in either the SINFONI H or K band, within spectral regions of high atmospheric transmission, and at least $400\;{\rm km}{{{\rm s}}^{-1}}$ away from OH airglow lines. These criteria constrain the target redshifts either in the range $z\approx 1.3-1.7$ or $z\approx 2-2.5$, respectively.

Our SINS/zC-SINF AO sample consists of 35 galaxies. From these, 29 galaxies have HST J- and H-band imaging and therefore make up the sample analyzed here. The whole sample is summarized in Table 1, which lists the Hα redshift, K-band magnitude, and main stellar properties. All but one galaxy lies in the redshift range $z\approx 2-2.5$ (GK-2540 lies at ${{z}_{{\rm H}\alpha }}=1.6146$).

Table 1.  Sample Galaxies with Their K-band Magnitude, Hα Redshifts, and Main Stellar Properties

Source	R.A.	Decl.	KABa	zHα b, c	${{M}_{\star }}$	SFR	sSFR	Age	${{A}_{{\rm V}}}$	${{(U-V)}_{{\rm rest}}}^{{\rm c}}$
			(mag)		(1010 M $_{\odot }$)	(${{M}_{\odot }}\;{\rm y}{{{\rm r}}^{-}}1$)	(Gyr−1)	(Myr)	(mag)	(mag)
D3A-15504	11:24:15.6	−21:39:31.2	21.28	2.3826	15.0	150	1.0	454	1.0	0.71
D3A-6004	11:25:03.8	−21:45:32.8	20.96	2.3867	45.8	210	0.5	641	1.8	1.52
GK-2303	03:32:38.9	−27:43:21.5	22.78	2.4501	0.97	21	2.2	286	0.4	0.61
GK-2363	03:32:39.4	−27:42:35.7	22.67	2.4518	2.92	64	2.2	286	1.2	0.69
GK-2540	03:32:30.3	−27:42:40.5	21.80	1.6146	2.66	21	0.8	509	0.6	0.78
K20-ID6	03:32:29.1	−27:45:21.1	22.14	2.2345	3.68	45	1.2	404	1.0	0.72
K20-ID7	03:32:29.1	−27:46:28.5	21.47	2.2241	8.71	110	1.3	509	1.0	0.65
Q1623-BX502	16:25:54.4	+26:44:09.3	23.90	2.1556	0.30	14	4.7	227	0.4	0.14
Q1623-BX599	16:26:02.5	+26:45:31.9	21.79	2.3313	8.89	34	0.4	2750	0.4	0.93
Q2343-BX389	23:46:28.9	+12:47:33.6	22.04	2.1733	6.39	25	0.4	2750	1.0	1.29
Q2343-BX610	23:46:09.4	+12:49:19.2	21.07	2.2103	15.5	60	0.4	2750	0.8	0.93
Q2346-BX482	23:48:13.0	+00:25:46.3	22.34d	2.2571	2.50	80	3.2	321	0.8	0.77
ZC400528	09:59:47.6	+01:44:19.1	21.08	2.3876	16.0	148	0.9	1140	0.9	0.84
ZC400569	10:01:08.7	+01:44:28.3	20.69	2.2405	23.3	241	1.0	1010	1.4	1.29
ZC401925	10:01:01.7	+01:48:38.2	22.74	2.1411	0.73	47	6.4	160	0.7	0.4
ZC404221	10:01:41.3	+01:56:42.8	22.44	2.2201	2.12	61	2.8	360	0.7	0.4
ZC405226	10:02:19.5	+02:00:18.1	22.33	2.2872	1.13	117	10.3	100	1.0	0.56
ZC405501	09:59:53.7	+02:01:08.9	22.25	2.1543	1.04	85	8.2	130	0.9	0.33
ZC406690	09:58:59.1	+02:05:04.3	20.81	2.1949	5.30	200	3.8	290	0.7	0.56
ZC407302	09:59:55.9	+02:06:51.3	21.48	2.1814	2.98	340	11.4	100	1.3	0.5
ZC407376	10:00:45.1	+02:07:05.0	21.79	2.1733	3.42	89	2.6	400	1.2	0.8
ZC409985	09:59:14.2	+02:15:47.0	22.30	2.4577	2.19	51	2.3	450	0.6	0.64
ZC410041	10:00:44.3	+02:15:58.5	23.16	2.4539	0.57	47	8.2	130	0.6	0.36
ZC410123	10:02:06.5	+02:16:15.5	22.80	2.1987	0.51	59	11.6	100	0.8	0.31
ZC411737	10:00:32.4	+02:21:20.9	22.81	2.4443	0.41	48	11.7	100	0.6	0.53
ZC412369	10:01:46.9	+02:23:24.6	21.39	2.0283	2.86	94	3.3	320	1.0	0.88
ZC413507	10:00:24.2	+02:27:41.3	22.52	2.4794	1.07	111	10.3	100	1.1	0.57
ZC413597	09:59:36.4	+02:27:59.1	22.58	2.4498	0.92	84	9.1	110	1.0	0.51
ZC415876	10:00:09.4	+02:36:58.4	22.38	2.4362	1.15	94	8.2	100	1.0	0.68

Notes. The stellar population properties are taken from Mancini et al. (2011) and Förster Schreiber et al. (2011a). We use the results computed for the Bruzual & Charlot (2003) model and constant star formation from Mancini et al. (2011), assuming a Chabrier (2003) IMF, solar metallicity, the Calzetti et al. (2000) reddening law, and either constant or exponentially declining SFRs. The uncertainties on the stellar properties are dominated by systematics from the model assumption and are up to a factor of ∼2–3 for ${{M}_{\star }}$ and at least ∼3 for SFRs.

^aTypical uncertainties on the K-band magnitudes range from $\approx 0.05$ for the brightest sources up to $\approx 0.15$ for the faintest. ^bSpectroscopic redshifts are based on the source-integrated Hα emission from the AO SINFONI data. Taken from FS15. ^cRest-frame $U-V$ colors have uncertainties of order 0.1 mag. Taken from FS14. ^dFor Q2346-BX482, no K-band magnitude is available, and listed here is the H-band magnitude measured from HST/NICMOS imaging with the NIC2 camera.

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The stellar mass ${{M}_{\star }}$,¹⁰ age, visual extinction (A_V), and absolute and specific SFR (sSFR) are obtained from stellar population synthesis modeling of the optical to NIR broadband spectral energy distributions (SEDs) supplemented with mid-IR 3–8 μm photometry when available. All details of the SED modeling are presented in Förster Schreiber et al. (2009, 2011a, 2011b) and Mancini et al. (2011). Briefly, we adopt the best-fit results obtained with the Bruzual & Charlot (2003) code, a Chabrier (2003) initial mass function (IMF), solar metallicity, the Calzetti et al. (2000) reddening law, and either constant or exponentially declining SFRs. The uncertainties on the derived quantities are dominated by model assumptions: the uncertainty on the stellar mass is a factor of $\sim 2-3$, on the SFRs and stellar ages even larger. Changing the star formation histories shifts the stellar mass less than the SFR, but both systematically (see Figures 2 and 3 of Mancini et al. 2011). For observed SEDs coverage from optical out to at least NIR wavelengths, the adoption of similar evolutionary tracks, and similar star formation histories return a robust relative ranking of galaxies in these properties.

As mentioned before, our galaxies were selected based on a combination of criteria: first, the required optical redshift means in practice an optical magnitude cutoff (to ensure sufficient signal-to-noise ratio [S/N]; in the case of zCOSMOS: $B\lt 25$); second, the requirement of minimum Hα flux (or SFR) likely emphasizes younger, less obscured, and more actively star-forming systems (Förster Schreiber et al. 2009; Mancini et al. 2011). Our sample is therefore neither a mass nor sSFR complete sample. One expects our galaxies to lie above the main sequence and toward bluer colors than the bulk of the z ∼ 2 population.

However, our galaxies follow the trend of the main sequence well, as visible in the ${{M}_{\star }}$-SFR plane in Figure 1. The red points show the 35 SINS/zC-SINF AO galaxies, a subsample of the 110 galaxies of the SINS/zC-SINF Hα sample (shown with white points). Our AO sample represents well the underlying larger parent non-AO sample. The red stars mark the 29 galaxies that are in our sample on which we will focus in this paper. The SFRs are taken from the SED fits described above. Our targets probe two orders of magnitude in stellar mass ($\approx 3\times {{10}^{9}}-4\times {{10}^{11}}\;{{M}_{}}$), SFR ($\approx 10-300\;{{M}_{}}\;{\rm y}{{{\rm r}}^{-1}}$), and sSFR ($\approx 0.4-11.7\;{\rm Gy}{{{\rm r}}^{-1}}$) and cover the kinematic diversity of massive z ∼ 2 SFGs. Figure 1 compares our targets with a sample of ~6000 galaxies of the COSMOS sample ($2.0\lt z\lt 2.5$ SFGs with ${{K}_{s,{\rm AB}}}\lt 23.0$ mag and with sSFR $\gt \;t_{H}^{-1}(z)$ at the respective redshift of each object; SFR from UV+IR estimates). Our targets probe the main sequence of SFGs at z ∼ 2 (Daddi et al. 2007; Rodighiero et al. 2011; Whitaker et al. 2012), preferentially lying only slightly at higher sSFRs (on average 0.13 dex above the main sequence, which itself has a scatter of $\sim 0.4$ dex) and bluer rest-frame optical ${{(U-V)}_{{\rm rest}}}$ colors (on average 0.1 AB mag) compared to the underlying population of massive SFGs, which have a scatter of ${{(U-V)}_{{\rm rest}}}\approx 0.3$ AB mag (see FS14 for a more extended discussion). This validates that our galaxies are a representative sample of $\gtrsim {{10}^{10}}\;{{M}_{\odot }}$ main-sequence galaxies at z ∼ 2.

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As part of no. GO12578, we carried out WFC3/IR observations between 2012 March and 2012 November with the WFC3/IR camera on board HST and using the F160W (H) and F110W (J) filters. The targets for this program were the 17 (21) for which HST H-band (J-band) imaging was not available from other HST imaging campaigns. The H band, centered at 1536.9 nm (width = 268.3 nm), 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 NIR observations. The J band is centered at 1153.4 nm and has a width of 443.0 nm. Simulations based on population synthesis models indicate that the adjacent nonoverlapping J and H filter pair is best in terms of combined speed (integration time) and accuracy of ${{M}_{\star }}/L$ estimates for the typical brightnesses and redshift range ($2.0\lt z\lt 2.5$) of our targets. The H-band filter samples approximately the Sloan Digital Sky Survey (SDSS) g band in the rest frame at the median z = 2.2 of our targets, and the J−H color minimizes extinction effects, brackets optimally the age-sensitive Balmer/4000 Å-break, and the wide bandpasses maximize flux sensitivity.

Each target was observed for two orbits in H and one orbit in J, 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., cosmic rays, satellite trails). The individual exposure time was 653 s, giving a total on-source integration of 5224 s for the H band and 2612 s for the J band. We used a square four-point dither pattern with a dither box size that is driven by the two constraints of dithering over the science target while simultaneously ensuring that nearby bright objects (most notably the bright AO stars) do not overlap with any of the target location on the detector.

For the other 8 (12) galaxies with missing H-band (J-band) imaging, we used publicly available data. Eight galaxies lie in CANDELS fields (Grogin et al. 2011; Koekemoer et al. 2011) and therefore have public available imaging data in the following bands: ACS/WFC F606W (V), ACS/WFC F814W (I), WFC3/IR F105W (Y), WFC3/IR F125W (J), and WFC3/IR F160W (H). These data are treated in the same way as our newly obtained imaging data and resampled to a pixel scale of $0\buildrel{\prime\prime}\over{.} 05$, the same pixel scale as the rest of our imaging data. The differences between the two filter bands J (F110W) and J (F125W) are very minor, and the Balmer/4000 Å-break is equally well traced with both filters. Furthermore, six targets have already deep HST H data: three galaxies have four-orbit integration from our NIC2 Pilot program (PI Shapley; Förster Schreiber et al. 2011a), and one has three-orbit WFC3/IR H data from Cycle 17 program no. GO11694 (PI Law), which we reduced in the same way as our new data. In addition, 18 galaxies lie in the zCOSMOS field and therefore have HST/ACS F814W (I) imaging.

3.3.1. WFC3/IR Detector Calibration

3.3.2. Relative Astrometry and Distortion Corrections

3.3.3. Combining the Individual Images with MultiDrizzle

3.3.4. Residual Background Subtraction

We measure the PSF in each band from six well-exposed and nonsaturated stars. We align all stars with the IRAF task IMALIGN and normalize them to have the same integrated brightness. We then combine them with the IRAF task IMCOMBINE, taking the median of all the stars. The PSFs for the J and H band are shown in Figure 2. We have constructed for each target galaxy its own PSF, since each exposure was taken at different times and with different telescope orientations. The variation from PSF to PSF for the different targets is $\lesssim 1\%$ in the central parts, while in the outskirts it is $\sim 5\%$. The FWHM is $0\buildrel{\prime\prime}\over{.} 16$, $0\buildrel{\prime\prime}\over{.} 17$, and $0\buildrel{\prime\prime}\over{.} 10$ for J, H, and I band, respectively.

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With the PSF for each band in hand, we use the package IRAF PSFMATCH to calculate a smoothing kernel to convolve all images to the resolution of the H-band image, since the H-band PSF is the largest one. We test the effectiveness of PSF matching by comparing the fractional encircled energy of each PSF before and after the procedure, shown in Figure 3. The PSFs in all bands have identical profiles, especially within the central region, where the gradient is steepest.

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The background noise properties of the raw data are well described by the rms of the signal measured in each pixel, since both the Poisson and readout noise should be uncorrelated. For such uncorrelated Gaussian noise, the effective background rms for an aperture of area A is simply the pixel-to-pixel rms $\bar{\sigma }$ scaled by the linear size $N={{A}^{1/2}}$ of the aperture, $\sigma (N)=N\bar{\sigma }$. Instrumental features, the data reduction, and PSF matching have added significant systematics and correlated noise in our final data. Therefore, the simple linear scaling of the background rms $\sigma (N)$ would lead to underestimated flux uncertainties. To investigate the noise properties and the limiting depths, we used aperture photometry on empty parts of the image to quantify the rms of background pixels within the considered aperture size (Labbé et al. 2003; Förster Schreiber et al. 2006a). We randomly placed ∼300 nonoverlapping apertures at a minimum distance of $\sim 5^{\prime\prime}$ from the nearest segmentation pixels in a SExtractor segmentation map. For a given aperture size, the distribution of empty aperture fluxes is well fitted by a Gaussian, as illustrated in Figure 4. We model the background rms as a function of aperture size with a polynomial of the form

$$\begin{eqnarray}&&\sigma (N)=\frac{N\bar{\sigma }(a+bN)}{\sqrt{w}}\end{eqnarray} \tag{ 1 }$$

where the 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 (it will be absorbed in the coefficients a and b). The coefficient b represents the correlated noise contribution that becomes increasingly important on larger scales.

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The noise behavior is qualitatively the same for all the targets and for all the filter bands. Figure 4 shows the result for one of our targets for the J, H, and I bands, with the background rms measurements for the various apertures and the best-fit polynomial models (Equation (1)) compared to the expected linear relationship for uncorrelated Gaussian noise. The values for J band are $a=0.09\pm 0.03$ and $b=1.4\pm 0.2$, for H band $a=0.07\pm 0.02$ and $b=1.7\pm 0.2$, and for I band $a=0.02\pm 0.01$ and $b=1.2\pm 0.1$.

From the background rms, we can directly determine the limiting depths (sensitivity) for our images. The total limiting AB magnitudes ($5\sigma$) for point sources are 27.3 ± 0.5, 26.6 ± 0.4, and 26.4 ± 0.1 for J, H, and I, respectively. For a larger source of $1\;{\rm arcse}{{{\rm c}}^{2}}$, the $3\sigma$ limiting AB magnitudes are 25.9 ± 0.5, 25.2 ± 0.4, and 24.9 ± 0.1 for J, H, and I, respectively.

The choice of the center is fundamentally important for modeling the light and mass distribution of a galaxy. It sets the foundation for the physical interpretation. We focus our analysis on the following three definitions of centers: kinematic center (based on the velocity and dispersion maps), light-weighted center (we refer to the H-band weighted center as the general light-weighted center since the H band and the J band have a very similar light distribution), and stellar-mass-weighted center (based on the mass maps that are derived from the M/L based on the observed J−H colors, as presented in Tacchella et al. 2015). These different centers all have their advantages and disadvantages. For example, the light-weighted center can be affected by dust and/or spatial age (and hence M/L) variations, whereas the stellar-mass-weighted center is determined on mass maps, which depends on the alignment of the images.

For each galaxy, the three centers are determined and compared, shown in Figure 5 with different colors and symbols. The center of light, stellar mass, and dynamical center are plotted with a cross in blue, green, and orange, respectively. In $\gt 60\%$ cases the three centers agree very well ($\lt 1$ kpc difference), and it is straightforward to determine the fiducial center (indicated by the largest red plus sign). For the other $\lt 40\%$ cases where the centers disagree more, the kinematic center is usually separated by $\gtrsim 1$ pixel ($\gtrsim 0.4$ kpc) from the center of light and mass. This can partially be explained by the higher uncertainty in the alignment of the SINFONI data with respect to the HST imaging (∼1 pixel) than between the individual J- and H-band images ($\lt 0.2$ pixel). This higher uncertainty in the alignment of the SINFONI data is due to the small SINFONI FOV, which does not cover stars or other compact sources that could be used for more accurate cross-registration. This means that, naturally, the offsets between dynamical center and light-/mass-weighted centers are potentially larger and more uncertain.

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Since we are primarily interested in modeling the light distribution, we choose the light-weighted center as the fiducial center in most cases. Exceptions are Q2343-BX389, Q2346-BX482, and ZC406690, where we use the dynamical center, and K20-ID7, where we use the center of stellar mass. See Appendix A for a detailed description.

We let the center be fixed during the fitting process. In the fiducial fit, we fix the center to our fiducial center. However, to estimate the uncertainty coming from the choice of the center, we also run fits in which we fix the center to another center that is chosen from a box that scales with the spread of the different centers. With this procedure we are able to estimate how different choices of centers propagate in the measured and modeled quantities.

We use the program GALFIT (Peng et al. 2010) to fit the two-dimensional surface brightness distribution with a Sérsic (1968) profile:

$$\begin{eqnarray}&&I(r)={{I}_{0}}{\rm exp} \left[ -{{b}_{n}}{{\left( \frac{r}{{{r}_{e}}} \right)}^{(1/n)}} \right],\end{eqnarray} \tag{ 2 }$$

where I(r) is the intensity as a function of radius r and r_e is the effective radius enclosing half of the total light of the model. The constant b_n is defined in terms of Sérsic index n, which describes the shape of the profile. Ellipticals with de Vaucouleurs profiles have a Sérsic index n = 4, exponential disks have n = 1, and Gaussians have n = 0.5. In the case of single-component fits, we use one single Sérsic profile with all fitting parameters left free (Sérsic index n, the effective radius r_e, the axis ratio b/a, the position angle P.A. of the major axis, and the total magnitude). In the case of bulge-to-disk decompositions, we assume two Sérsic models, one for the bulge and one for the disk. All but one parameter is free: the Sérsic index n_d of the disk is fixed to 1. In the next two sections we explain the fitting procedure of the single- and double-component fits in more detail.

In the single- and double-component fits, GALFIT convolves the model with the effective resolution of the data (PSF) and finds the best-fit parameters with a ${{\chi }^{2}}$-minimization. As GALFIT input, we give our empirically determined PSF (Section 3.4), as well as the noise images (sigma image). The noise image is obtained by adding to the weight image¹³ the Poisson noise from the astronomical sources in the image. To reduce the impact of large-scale residuals from the flat fielding and background subtraction (Section 3.3), we perform the fits within a region of $10^{\prime\prime} \times 10^{\prime\prime}$ centered on the sources. We remove neighboring galaxies using an object mask. In the case of very close galaxies with overlapping isophotes (ZC400569, ZC404221, ZC405501, ZC407376, ZC412369, K20-ID6, and K20-ID7), objects are fitted simultaneously.

The H band is the reddest filter available for the galaxies in our sample, i.e., it traces the light of the older stellar populations the best and is the least affected by dust. We therefore use the H band as the reference/fiducial filter and start by fitting the light distribution in the H band first, allowing all parameters but the center to vary freely. We fix the centers to the fiducial centers defined in the previous section. For the J-band fits, we fixed the axis ratio b/a and position angle P.A. to the values of the H band to ensure that we fit the same spatial parts.

We fitted each galaxy ∼100 times, varying the input guess n between 1 and 4, r_e ± 25% of the half-light radius obtained by SExtractor, b/a ± 0.1 of the axis ratio obtained by SExtractor, and P.A. between $0{}^\circ$ and $90{}^\circ$. The Sérsic index n is limited to the interval $[0.1,8.0]$ during the fitting. All nonphysical solutions (i.e., ${{r}_{e}}\gt 20\;{\rm kpc}$ and $b/a\lt 0.1$) have been excluded, and also all residuals have been inspected. GALFIT converges in $\gtrsim 90\%$ of the cases to the same solution, which indicates that changing the input guesses has only a minor influence on the final fitted parameters.

The best-fit parameters are then taken as the ${{\chi }^{2}}$-weighted median of the results. For estimating the uncertainty of the best-fit parameters, we combine the errors from the choice of a specific center and a specific set of initial guesses ("fitting error") and from the reliability of the fitting procedure with GALFIT ("observational error"). For the fitting error, we have carried out a second set of runs where we varied the input guesses and the centers. The centers are shifted within a box of a size given by the distance between the different kind of centers (center of stellar mass, center of light, and kinematic center). The box size for each galaxy is indicated in Figure 5, first column in the upper right corners. For most galaxies ($\sim 75\%$), the box size is 4 × 4 pixels or smaller. For galaxies Q2346-BX482, ZC405226, and ZC406690, a substantially larger box (10 × 10 pixels) is chosen. We vary the centers in the mentioned box, letting them remain fixed during the fitting process. This run consists of ∼1000 GALFIT realizations. The errors from the fitting are then the 68% confidence intervals about the median of this run.

To quantify the observational error (such as sky background, noise, and PSF), we follow the approach described in Carollo et al. (2013a) and Cibinel et al. (2013b): we created ~100,000 mock galaxies, convolved them with the PSF, and added noise (see also Appendix B). Then, all the model galaxies are analyzed with GALFIT in the same way as described above. By comparing input and output, we obtained a correction matrix, so that for each galaxy with a given magnitude, size, Sérsic index, and axis ratio (ellipticity), we can determine its "true" unbiased values. In addition to this bias correction, we also obtain the scatter around the median of this correction vector. Since most of our galaxies are bright and also substantially larger than the PSF size, the observational bias vector is small and of the order 10%, i.e., smaller than the scatter. We therefore do not correct for the observation bias and only add the scatter to the uncertainty.

Traditionally, the bulge-disk decomposition is performed on the light distribution (e.g., Baggett et al. 1998; Lackner & Gunn 2012; Bruce et al. 2014). The "bulge" component is defined as the light excess above an exponential disk profile. The modeling is generally performed with two components: an n = 1 Sérsic profile plus an additional (free n, n = 2, or n = 4) Sérsic profile. Fitting directly on the light distribution has the advantage that it is robust and the errors are well known and describable. On the other hand, an actively star-forming thick disk can outshine the bulge component (Carollo et al. 2015), leading to an underestimation of the B/T. Furthermore, dust could play a role (e.g., higher extinction toward the center), i.e., hiding possible bulge components present. To circumvent these problems, we can do the analysis directly on the mass distribution. We will present in Tacchella et al. (2015) how to convert the J- and H-band light to the mass distribution by using the observed J−H color ($\propto {{(u-g)}_{{\rm rest}}}$) as a mass-to-light indicator. Briefly, we use the fact that observed colors and mass-to-light ratios of stellar populations are correlated (see, e.g., Rudnick et al. 2006; Zibetti et al. 2009; Förster Schreiber et al. 2011a): The different stellar population model curves occupy a well-defined locus in the observed J−H color versus mass-to-light ratio parameter space, reflecting the strong degeneracy between stellar age, extinction, and SFH in these properties. This degeneracy can be used to derive the mean mass-to-light ratio for a given observed color that, multiplied by the luminosity, yields a stellar mass estimate. There are then two ways to do a bulge-disk decomposition: the first one is to fit 2D mass maps (obtained from the 2D color maps); the second one is to use the fits to the individual bands. We prefer the latter approach since we find it to be more stable and robust, but both approaches converge within the errors to the same results, as we show in Tacchella et al. (2015).

An important assumption is that we let the Sérsic index of the bulge remain free within the range $[1.0,8.0]$ during the fitting procedure. The physical motivation comes from the fact that in the local universe, we can see two kinds of bulges: "classical" and "pseudo-"bulges (Kormendy & Kennicutt 2004). Traditionally, two different processes have been considered for the formation of galactic bulges: one is through merging, and the other is secular instability of the stellar disk. The merging channel is most likely to produce a bulge with a Sérsic index of ${{n}_{b}}\sim 4$; the secular evolution channel may favor ${{n}_{b}}\sim 1-3$, although even steeper slopes can also be obtained depending on the precise internal mechanisms. Since we do not know what kind of bulge our galaxies have, we let the Sérsic index remain free during fitting. In Appendix B we show with extensive simulation tests that if a structure in the sky has a low bulge Sérsic index, imposing an n = 4 fit leads to much larger errors on the B/T than when fitting it with a free n. This is somewhat obvious even without simulations, but the latter demonstrate it clearly. We show that, on average, the n_b–free fits have a 2.4 times smaller relative error on B/T than the n_b = 4 fixed fits.

We conduct the bulge-to-disk decomposition in both J and H bands. Excluded from this analysis are the following five objects: Q2346-BX482, K20-ID7, ZC406690 (all not centrally peaked, i.e., no apparent bulge present), Q1623-BX502, and ZC404221 (both barely resolved). Therefore, our initial sample for the bulge-disk decomposition consists of 24 galaxies. As mentioned above, we assume two Sérsic models, one for the bulge and one for the disk (n_d = 1 fixed). For all the fits, we use additional constraints for the following parameters of the bulge: axis ratio ${{(b/a)}_{b}}\in [0.6,1.0]$, Sérsic index ${{n}_{b}}\in [1.0,8.0]$, and ${{r}_{e,b}}\in [0.04,4.2]\;{\rm kpc}$. As an initial guess we set n_b = 4.0, ${{r}_{e,b}}=1\;{\rm kpc}$, ${{(b/a)}_{b}}=1.0$, and ${\rm P}.{\rm A}{{.}_{b}}=0{}^\circ$. The centers are again fixed to the fiducial centers.

As in the single-component fits, we use the H band as the reference/fiducial filter and fit it first. There are clear advantages and disadvantages in performing either independent or constrained fits to the two bands. By fixing the J-band structural parameters to the H band, one ensures that bulge and disk colors are measured consistently over the same regions: this, however, prevents the detection of structural differences and color gradients of the individual bulge and disk components. Here we follow a mixed approach, similar to Cibinel et al. (2013b). For the J-band fits, we apply three different runs, progressively increasing the number of constraints:

• 1.  
  R1: same assumptions as for the H band, i.e., centers fixed and n_d = 1;
• 2.  
  R2: in addition to the assumptions in R1, setting the axis ratio and the position angle of the bulge and disk of the J band to the ones of the H band (i.e., ${{(b/a)}_{J}}={{(b/a)}_{H}}$ and ${\rm P}.{\rm A}{{.}_{J}}={\rm P}.{\rm A}{{.}_{H}}$ of disk and bulge);
• 3.  
  R3: in addition to the assumptions in R1 and R2, assuming that the Sérsic index and the effective radius of the bulge are the same in both bands (i.e., ${{n}_{b,J}}={{n}_{b,H}}$, and ${{r}_{e,b,J}}={{r}_{e,b,H}}$).

We flag all unphysical models (i.e., where bulge is larger in size than the disk: ${{r}_{e,b}}\gt {{r}_{e,d}}$; in total 5 objects), and all residual images are visually inspected to look for possible failure of the fitting algorithm. In general, the reliable fits of R1, R2, and R3 give all similar B/T (variations less than 10% between R1, R2, and R3), i.e., the B/T is a robust quantity.

We use a quantitative procedure to select among the three different runs (R1, R2, and R3). We require that all J-band disk and bulge fits always have bulge and disk position angles and axis ratios within a sensible range from those of the H band. The allowed range of variation for J and H bulge disk position angles and axis ratios is ${\Delta P}.{\rm A}.\leqslant 15{}^\circ$ and ${\Delta }(b/a)\leqslant 0.15$ (Cibinel et al. 2013b). In addition, the fit has to reliable. When this is achieved with unconstrained fits (R1) for the J-band images, these unconstrained fits are retained as a fair description of the J-band bulge-disk decomposition. This choice maximizes the detection of possible wavelength-dependent structural difference and color gradients. For galaxies in which such a consistency requirement is not achieved with the unconstrained J fits, we adopt those that satisfy such a requirement with a minimum number of parameters tied to the H-band fit parameters (i.e., first R2 and then R3 fits). After identifying the best run, we have added a central point source to the model to test for possible AGN contribution. The model fits do not improve for any of our galaxies by including an additional point source, nor did the final result change substantially (i.e., the results stayed within the errors for all fitted parameters). We therefore conclude that possible AGN activity does not influence the conclusions of this work.

We combine again two different sources of uncertainties to estimate the error on the B/T. First, for the fitting error, we have applied a variation of the fixed center in a box (same procedure as described in Section 6.3) to account for possible uncertainties in the choice of different centers. On average over all galaxies, this gives an absolute error on the B/T of 0.09 for the H band and 0.11 for the J band.

The second, observational error contribution (accounting for the general fitting procedure) was estimated from the reliability of the GALFIT bulge-disk decomposition. See Appendix B for details. Briefly, we have simulated galaxies and decomposed bulge and disk with the same method as described above. We found that the B/T can be recovered very well, i.e., there is no systematic bias. On the other hand, other parameters of the bulge such as Sérsic index n_bulge and size ${{r}_{e,{\rm bulge}}}$ are very degenerate and cannot be reliably estimated. The main reason for this is that the bulges' sizes are at or below the resolution limit.

Although galaxies have multiple components, it is nevertheless informative to treat galaxies as single entities when looking at the global parameters that describe the light distribution. The columns for "Single Component" in Tables 3 and 4 show the best-fit parameters for the J and H bands. Figure 5 show in the first column the H-band image, with a red ellipse that represents the best-fit parameters r_e, b/a, and P.A.. The third column in the figures shows the J- and H-band surface brightness profiles.

Table 4.  Overview measurements done on the J-band images

		GALFIT: Single Component					GALFIT: Double Component (Disk+Bulge)
Source		${{r}_{e}}$ (kpc)	$n$	$b/a$	P.A. (deg)		${{r}_{e,disk}}$ (kpc)	${{(b/a)}_{disk}}$	P.A.$_{{\rm disk}}$ (deg)	${{r}_{e,bulge}}$ (kpc)	${{n}_{bulge}}$	$B/T$
D3A15504		5.0 ± 0.8	0.9 ± 0.4	0.68 ± 0.13	−28 ± 2		4.9 ± 0.7	0.73 ± 0.14	−24 ± 2	0.5 ± 0.1	8.0 ± 3.4	$0.00_{-0.00}^{+0.07}$
D3A6004		6.8 ± 2.9	2.9 ± 0.8	0.81 ± 0.13	55 ± 10		4.7 ± 2.1	0.84 ± 0.14	55 ± 10	0.6 ± 0.3	1.0 ± 0.3	$0.03_{-0.03}^{+0.09}$
GK2303		1.3 ± 0.4	1.0 ± 0.4	0.64 ± 0.16	19 ± 17		1.3 ± 0.4	0.64 ± 0.16	17 ± 15	0.9 ± 0.3	1.0 ± 0.4	$0.03_{-0.03}^{+0.1}$
GK2363		1.7 ± 0.4	1.0 ± 0.3	0.52 ± 0.14	61 ± 2		1.8 ± 0.4	0.52 ± 0.14	60 ± 2	0.1 ± 0.1	5.3 ± 1.7	$0.02_{-0.02}^{+0.06}$
GK2540		8.8 ± 1.4	1.3 ± 0.4	0.86 ± 0.17	86 ± 10		7.5 ± 1.2	0.89 ± 0.18	88 ± 11	0.3 ± 0.1	2.4 ± 0.6	$0.03_{-0.03}^{+0.04}$
K20ID6		3.7 ± 0.4	0.5 ± 0.2	0.86 ± 0.13	37 ± 5		3.8 ± 0.4	0.85 ± 0.13	40 ± 5	3.8 ± 0.4	1.0 ± 0.5	$0.30_{-0.21}^{+0.20}$
K20ID7a		5.9 ± 1.4	0.1 ± 0.1	0.46 ± 0.15	18 ± 1		...	...	...	...	...	...
Q1623-BX502		1.0 ± 0.4	0.5 ± 0.5	0.66 ± 0.18	1 ± 4		...	...	...	...	...	...
Q1623-BX599		2.8 ± 0.6	2.6 ± 0.7	0.69 ± 0.14	−57 ± 23		4.9 ± 1.1	0.68 ± 0.14	−3 ± 1	1.3 ± 0.3	1.0 ± 0.3	$0.43_{-0.11}^{+0.11}$
Q2343-BX389a		3.1 ± 0.4	0.2 ± 0.2	0.28 ± 0.14	−48 ± 3		3.8 ± 0.6	0.32 ± 0.16	−45 ± 3	3.3 ± 0.5	1.0 ± 2.5	$0.20_{-0.10}^{+0.15}$
Q2343-BX610a		3.5 ± 0.5	0.1 ± 0.1	0.54 ± 0.14	17 ± 1		3.3 ± 0.5	0.56 ± 0.15	−15 ± 0	0.5 ± 0.1	8.0 ± 16.0	$0.15_{-0.12}^{+0.15}$
Q2346-BX482a		4.3 ± 0.6	0.1 ± 0.1	0.50 ± 0.20	−62 ± 10		...	...	...	...	...	...
ZC400528		3.0 ± 1.2	6.1 ± 1.6	0.78 ± 0.12	−65 ± 9		3.0 ± 1.2	0.88 ± 0.13	−85 ± 12	1.7 ± 0.7	1.0 ± 0.3	$0.35_{-0.09}^{+0.11}$
ZC400569		8.1 ± 2.0	3.6 ± 0.6	0.89 ± 0.17	38 ± 5		5.6 ± 1.4	0.8 ± 0.15	22 ± 3	0.9 ± 0.2	1.0 ± 0.2	$0.13_{-0.05}^{+0.05}$
ZC401925		1.7 ± 0.6	1.6 ± 0.6	0.38 ± 0.12	−60 ± 6		1.8 ± 0.6	0.36 ± 0.12	−58 ± 5	0.5 ± 0.2	8.0 ± 3.1	$0.11_{-0.09}^{+0.11}$
ZC404221		0.4 ± 0.2	7.2 ± 1.5	0.45 ± 0.15	−13 ± 3		...	...	...	...	...	...
ZC405226		4.1 ± 0.8	0.5 ± 0.3	0.60 ± 0.16	−66 ± 18		4.6 ± 0.8	0.59 ± 0.16	−67 ± 18	2.6 ± 0.5	8.0 ± 4.1	$0.04_{-0.04}^{+0.12}$
ZC405501a		3.3 ± 0.5	0.1 ± 0.1	0.31 ± 0.13	11 ± 1		3.4 ± 0.5	0.43 ± 0.18	15 ± 1	1.9 ± 0.3	1.0 ± 4.0	$0.33_{-0.13}^{+0.16}$
ZC406690a		5.4 ± 1.0	0.1 ± 0.1	0.62 ± 0.18	−77 ± 5		...	...	...	...	...	...
ZC407302b		2.3 ± 0.4	1.2 ± 0.3	0.45 ± 0.15	47 ± 3		2.0 ± 0.3	0.37 ± 0.12	52 ± 3	3.5 ± 0.6	1.0 ± 0.3	$0.24_{-0.12}^{+0.13}$
ZC407376		1.8 ± 1.0	5.0 ± 1.8	0.81 ± 0.16	−68 ± 39		2.6 ± 1.4	0.7 ± 0.13	−66 ± 38	0.5 ± 0.3	1.0 ± 0.4	$0.49_{-0.14}^{+0.13}$
ZC409985		1.6 ± 0.2	2.2 ± 0.5	0.67 ± 0.15	−14 ± 4		1.6 ± 0.3	0.67 ± 0.15	−22 ± 6	0.2 ± 0.1	4.3 ± 1.0	$0.14_{-0.07}^{+0.06}$
ZC410041b		2.2 ± 0.5	0.2 ± 0.2	0.22 ± 0.10	−64 ± 1		1.8 ± 0.4	0.18 ± 0.08	−69 ± 1	3.2 ± 0.8	1.0 ± 1.9	$0.11_{-0.07}^{+0.16}$
ZC410123		2.2 ± 0.8	1.8 ± 0.5	0.38 ± 0.12	16 ± 5		2.3 ± 0.8	0.36 ± 0.12	19 ± 6	0.9 ± 0.3	5.1 ± 1.6	$0.22_{-0.12}^{+0.13}$
ZC411737		1.7 ± 0.2	0.8 ± 0.2	0.83 ± 0.13	−19 ± 17		1.8 ± 0.2	0.75 ± 0.11	−5 ± 4	1.4 ± 0.2	1.0 ± 0.3	$0.23_{-0.12}^{+0.16}$
ZC412369		2.7 ± 1.7	5.2 ± 2.3	0.47 ± 0.13	−54 ± 7		3.1 ± 2.1	0.4 ± 0.11	−58 ± 8	0.2 ± 0.1	8.0 ± 3.5	$0.39_{-0.22}^{+0.21}$
ZC413507b		1.9 ± 0.5	0.6 ± 0.5	0.66 ± 0.19	−22 ± 10		2.0 ± 0.5	0.62 ± 0.18	−19 ± 9	2.9 ± 0.8	1.0 ± 0.8	$0.04_{-0.04}^{+0.05}$
ZC413597b		1.1 ± 0.4	2.2 ± 1.0	0.46 ± 0.14	15 ± 10		0.5 ± 0.2	0.22 ± 0.07	8 ± 5	2.2 ± 0.8	1.0 ± 0.5	$0.45_{-0.12}^{+0.12}$
ZC415876b		1.7 ± 0.7	1.4 ± 0.6	0.78 ± 0.15	−80 ± 42		1.7 ± 0.7	0.65 ± 0.13	87 ± 46	3.2 ± 1.3	1.3 ± 0.5	0.23$_{-0.09}^{+0.10}$

^aSingle-component fits are less reliable because light distribution is not centrally concentrated (assumed models do not represent the galaxy well). ^bDouble-component fits give nonphysical solutions, i.e., bulge component is larger than disk component.

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About two-thirds of the galaxies in our sample are well fitted by a single Sérsic, i.e., $1\lesssim \chi _{{\rm red}}^{2}\lesssim 2$, and our PSF-convolved model agrees well with the data. Galaxies Q2343-BX389, Q2343-BX610, Q2346-BX482, ZC405501, and ZC406690 all have bright clumps $\sim 4-5$ kpc away from their centers, making the flux distributions asymmetric and not centrally peaked. This drives the Sérsic n toward the lower limit of 0.1. Therefore, the fits to these galaxies have large residuals, basically because Sérsic profiles are not a good representation of the data, and the fits have to be treated with caution. Also, galaxy K20-ID7 belongs to this category with a very bright clump in its outskirts. However, in this case the clump is so bright that the center gets severely affected, and we had to model it in addition with a separate Sérsic profile. These six galaxies are marked in the following plots with a circle and cross, in contrast to the reliably fitted galaxies, which are shown with a gray filled circle. In addition, galaxies Q1623-BX502 and ZC404221 are very compact and small, i.e., are just at our resolution limit. The fits to these galaxies therefore have to be taken with care (sizes have large relative uncertainties).

Figure 6 compares the best-fit results for n and r_e for the J- and H-band filters. The error bars are obtained from varying the centers, changing the initial guess for the fitting parameters, and simulations of the observational biases (Section 6.3). Varying the center dominates the error ($\sim 70\%$). For nearly all galaxies, there is only a minor difference between the two bands. The exceptions are D3A-6004, GK-2520, and ZC400569 (all have a larger r_e in J than in H). The average normalized difference in size $({{r}_{e,H}}-{{r}_{e,J}})/{{r}_{e,H}}={\Delta }{{r}_{e}}/{{r}_{e,H}}=-0.07$, i.e., the J-band sizes are 7% larger on average (left panels of Figure 6). Comparing the Sérsic index n of the H and J bands shows that toward small n, the H band predicts a larger n than the J band. On the other hand, toward larger values of n, the J band has larger values. Overall, the average normalized difference is ${\Delta }n/{{n}_{H}}=0.04$, i.e., the H band is slightly more concentrated, and therefore the average galaxy has blue outskirts and a red center. Even though r_e and n are comparable in both bands, the small differences seen in some galaxies are enough to introduce a color gradient (see Section 8.3).

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Table 3 presents the results for the bulge-disk decompositions on the H band, which we have fitted first. We find bulges of all sizes ${{r}_{e,b}}$ ($0.2-4.2$ kpc) and Sérsic indices n_b ($1.0-8.0$). We find that the majority of galaxies are fitted the best with an ${{n}_{b}}\sim 1$ (16 galaxies), while five and three galaxies are fitted well by n_b = 8 and ${{n}_{b}}\sim 4$, respectively. As discussed in Section 6.4 and Appendix B, the bulge is of the size of the PSF and therefore only barely resolved in most cases, making the degeneracy between ${{r}_{e,b}}$ and n_b strong. We therefore cannot make any strong statements about the shape of the bulges in our sample.

We can now go one step further and look at the J-band bulge-disk decomposition. After applying the selection described in Section 6.4, we end up with a total of 24 galaxies with a bulge-disk decomposition in J and H (16 galaxies with R1, 7 with R2, and 1 with R3), out of which 5 galaxies are flagged owing to ${{r}_{b}}\gt {{r}_{d}}$. All results are listed in the columns for "Double Component" in Tables 3 and 4. In Figure 7 we compare the B/T for the two filter bands. There is a good agreement between the J- and H-band B/T values. This is not surprising since the galaxies have very similar morphologies in the two bands. We find substantial bulge components in about half of our sample: 40% of the galaxies have a $B/T\approx 20-60\%$, and about 15% of galaxies show well-developed bulge components with $B/T\gt 0.3$. About two to three galaxies of our sample (i.e., 7%–10%) are bulge dominated with $B/T\gtrsim 0.5$, which is consistent with investigations of much larger samples: Bruce et al. (2014) presented H-band bulge-disk decompositions of ∼400 galaxies with $\gt {{10}^{11}}\;{{M}_{\odot }}$ at $1\lt z\lt 3$ and found that 11% ± 3% of the massive SFGs are bulge dominated.

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As discussed in the next section, the high SFR in the outskirts of our galaxies is causing the disk to outshine the inner bulge components. Therefore, the quoted numbers above are lower limits, i.e., the typical B/T in stellar mass will be higher than what we measure in light.

The J−H color profiles are based on the difference of the individual surface brightness profiles I(r) of the J and H bands. We use the single-component Sérsic models, which are described in Section 6.3. The advantage of this approach is the substantial removal of the observational biases, including PSF smearing. The PSF-convolved color profiles are shown in Figure 5, including their uncertainties, which are substantial at large radii.

In a large fraction of galaxies (19 out of 29), the color profiles show no significant color variation from the centers to their outskirts ($\lesssim 0.3$ mag). For 10 galaxies ($\sim 1/3$ of the sample) we find negative color gradients such that their cores are redder. These color gradients can be explained by radial variation in dust content, age of the stellar populations, or a combination of both. To be able to disentangle the contribution from dust and age to the reddening of the stellar population, we would need additional passbands in the blue spectral range.¹⁴ In addition, there are six galaxies (GK-2303, ZC404221, ZC407302, ZC409985, ZC413597, and ZC415876) that show a peculiar color distribution: the color profile is slightly increasing out to $\sim {{r}_{e}}$ and then declining. Such trends indicate the presence of red clumps in the outskirts, as seen in some color maps that we present next.

First, the J−H color maps are obtained by taking the difference between the J- and H-band image (in magnitudes). A good alignment of the two images is crucial, as offsets down to a fraction of a pixel can generate a fake color gradient. As mentioned in Section 3.3.2, we pay careful attention to the alignment of the images in the data reduction: we find a mean offset below 0.20 pixels, with an rms below 0.10. If we use a Sérsic profile and take the worst-case scenario, i.e., a 0.30 pixel offset with ${{r}_{e}}=0\buildrel{\prime\prime}\over{.} 5$ (10 pixels), we get a maximum color offset below 0.07 AB mag. Hence, we can safely discard misalignments as a possible source of systematic uncertainty in the color gradients.

Another key step for obtaining the color map image of an extended source is to quantitatively select the pixels in the color map with reliable color determination. For this, we compute the S/N of the color map image pixel by pixel. Adopting the approximation that the Poisson noise distribution function in an HST image is close to a lognormal law, one can obtain that for two images with signals ${{\mu }_{{{F}_{J}}}}$, ${{\mu }_{{{F}_{H}}}}$ and noises $\sigma _{{{F}_{J}}}^{2}$, $\sigma _{{{F}_{H}}}^{2}$, the noise of the J−H color image satisfies (see Zheng et al. 2004 for details)

$$\begin{eqnarray}&&{{\sigma }^{2}}={{{\rm log} }_{10}}\left( \frac{\sigma _{{{F}_{J}}}^{2}}{\mu _{{{F}_{J}}}^{2}}+1 \right)+{{{\rm log} }_{10}}\left( \frac{\sigma _{{{F}_{H}}}^{2}}{\mu _{{{F}_{H}}}^{2}}+1 \right).\end{eqnarray} \tag{ 3 }$$

To increase the S/N of the color maps in the outer regions of a galaxy, where the flux from the sky background is dominant, we perform an adaptive local binning of pixels using a Voronoi tessellation (VT) approach. The main idea behind the method is to group adjacent pixels into bigger units that have a minimum scatter around a desired S/N. We perform the VT on the J−H color maps by using the publicly available IDL code of Cappellari & Copin (2003) and adopting the generalization (weighted VT) proposed by Diehl & Statler (2006) (see also Cibinel et al. 2013b).

Pixels with very low S/N, which would affect the robustness of the algorithm, are excluded from the binning by imposing a minimum threshold of S/N = 1.0. A target S/N of 5–10 was chosen to construct the binned color maps, depending on the average S/N of the input color map. The final color maps are obtained by extrapolating the nontessellated pixels from their neighbors, as well as at very large distance from the center, by extrapolating toward the median of the tessellated color maps. The effect of the VT is shown in Figure 8, where we show the S/N as a function of radius before and after VT. The VT clearly enables a more robust measurement of the color distribution of galaxies at large radii and removes the high-frequency fluctuation associated with the noise in the original color maps, while retaining substantial information on lower-frequency, physical color variation within galaxies.

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An overview of the J−H color maps is given in Figure 9. A large fraction of galaxies (e.g., D3A-15504, D3A-6004, Q2343-BX389, ZC405501) show a red center. Several galaxies also show blue and red substructures in the outskirts that are $\lesssim 0.3$ mag bluer and redder, respectively. In Förster Schreiber et al. (2011b) we found that—consistently with our findings in Figure 9—clumps identified at different wavelengths do not fully overlap: NIR-identified clumps tend to be redder/older than I-band or Hα identified clumps without rest-frame optical counterparts. We further discuss this clumpy structure in the J−H color maps in Section 8.3 (and Figure 10).

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Since we are interested in comparing our z ∼ 2 galaxies with local $z\sim 0$ galaxies, we convert the observed J−H color to the rest-frame $u-g$ color (SDSS filter bands), using the best-fit SED of each galaxy individually. The color conversion amounts, on average, to $+0.14$ mag. From the azimuthally averaged $u-g$ color profile, we determine the color gradient, ${\Delta }{{(u-g)}_{{\rm rest}}}/{\Delta }({{{\rm log} }_{10}}r)$, i.e., change in color per decade in radius. Logarithmic color gradients are calculated by fitting the linear relation ${{(u-g)}_{{\rm rest}}}={{(u-g)}_{{\rm rest},{{r}_{e}}}}+\alpha \cdot {{{\rm log} }_{10}}(r/{{r}_{e}})$ to the color radial profiles. The slope $\alpha ={\Delta }{{(u-g)}_{{\rm rest}}}/{\Delta }({{{\rm log} }_{10}}r)$ defines what we will refer to as the "radial color gradient"; ${{(u-g)}_{{\rm rest},{{r}_{e}}}}$ defines the color at the galaxy's effective radius r_e. Fits are performed within the radial range $0.5{{r}_{e}}-1.5{{r}_{e}}$. The error bars of the color gradients are estimated by varying the fitting range: the upper limit of the fitting range is varied from $0.7{{r}_{e}}$ to $3.0{{r}_{e}}$ while letting the lower limit remain constant.

The color maps contain, of course, more information than 1D profiles and gradients; in particular, they enable us to study also the color rms dispersion (scatter) around the smooth average color profiles within galaxies. This is defined and computed as $\sigma (J-H)=\sqrt{{{\sum }_{i}}\xi _{i}^{2}/N}$, with ξ being the residuals with respect to the azimuthally smoothed radial color profile (Cibinel et al. 2013a). The observed internal color structure and dispersion in galaxies at high redshift were considered previously. For example, Papovich et al. (2003, 2005) investigated this issue in a quantitative fashion by using a dedicated statistical tool.

The results of the color gradients and dispersions as a function of stellar mass are shown in Figure 10. The white crossed points indicate again the objects with less reliable fits. We measure a mean color gradient of ${\Delta }{{(u-g)}_{{\rm rest}}}/{\Delta }({{{\rm log} }_{10}}r)=-0.17$ mag per dex with a wide range of $[-0.61,0.21]$. In our sample, there is a weak trend that for more massive systems the color gradient is steeper and more negative, i.e., they have redder centers and bluer outskirts. A simple linear regression (mass in log) gives a marginally negative slope of −0.16 ± 0.06. To check whether the low-mass (${{M}_{\star }}\lt 2\cdot {{10}^{10}}{{M}_{\odot }}$) and high-mass (${{M}_{\star }}\gt 7\cdot {{10}^{10}}\;{{M}_{\odot }}$) galaxies are drawn from the same distribution, we apply the Anderson & Darling (1952) test to falsify the null hypothesis that the high- and low-mass samples are drawn from the same population. We find a p-value of 0.02, i.e., we can reject at about 2.3σ confidence level the null hypothesis.

Simultaneously, these massive galaxies have also a higher color dispersion, i.e., these galaxies have more variation in their color maps, showing that these galaxies have substructure in the color distribution. The mean color dispersion amounts to 0.12 mag with a range of $[0.05,0.19]$. We find a positive slope of 0.03 ± 0.01. Using again Anderson & Darling (1952), we find a p-value of 0.02, i.e., we can reject at about 2.3σ confidence level the null hypothesis that low- and high-mass galaxies at z ∼ 2 are drawn from the same population. Clearly, these results presented here have to be verified on larger and more homogeneously selected samples in the future. A comparison with the underlying $z\sim 0$ sample is done in Section 9.3.

In Figure 11 we show the best-fit Sérsic index n of the single component fits (left panel) and B/T (right panel) of the light distribution in H band, as a function of stellar mass ${{M}_{\star }}$. The color-coded points show the local $z\approx 0$ galaxies from the ZENS (Carollo et al. 2013b; Cibinel et al. 2013a, 2013b). The color-coding of the ZENS sample is based on the galaxies' morphological classification: ellipticals, S0, bulge-dominated spirals, intermediate disks, and late-type disks.

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At the lower masses, z ∼ 2 galaxies have Sérsic indices $n\approx 0.5-2.0$, i.e., typical of z = 0 late-type disks; the galaxies with $n\gtrsim 3$, i.e., with structural properties that are similar to those of local early-type galaxies, are all more massive than $\gt {{10}^{10}}\;{{M}_{\odot }}$. Overall, the z ∼ 2 galaxies cover the same $n-{{M}_{\star }}$ space as the local $z\sim 0$ galaxies. When we analyze, however, the B/T distribution of the z ∼ 2 galaxies (right panel of Figure 11), we find several galaxies with high ${{M}_{\star }}$ but only small $B/T\lt 0.10$, which are very rare at $z\sim 0$. A first reason for this, as mentioned in Section 7.2, is that these massive galaxies at z ∼ 2 are still heavily star-forming in comparison with their local counterparts. Since most of the star formation takes place in the outskirts (see the next section), the outer parts are substantially brighter than the central component, leading to outshining of the central bulge and an underestimation of B/T for the most massive galaxies (Carollo et al. 2013a, 2015). The difference between the z ∼ 2 and $z\sim 0$ population can also be explained by our selection of only SFGs: adding passive or nearly passive galaxies to our z ∼ 2 sample will add several galaxies in the high-${{M}_{\star }}$ and high-B/T regime (e.g., Bruce et al. 2014). For our intermediate-mass galaxies—${{M}_{\star }}\sim {{10}^{10}}\;{{M}_{\odot }}$—the central regions are still star-forming and therefore very bright. This explains why the bulge-to-disk decomposition performed on the light distributions converges to relatively high B/T values of $\sim 0.3-0.6$.

The rest-frame optical sizes r_e obtained by fitting with GALFIT the HST H-band images are shown as a function of stellar mass in Figure 12. Specifically, the ${{M}_{\star }}-{{r}_{e}}$ relation for our galaxies is compared with the z ∼ 2 estimates of Franx et al. (2008) and van der Wel et al. (2014) and also with the z = 0 relations for early- and late-type galaxies of Shen et al. (2003) and Cibinel et al. (2013b). When appropriate, results have been put on a common ground by converting all values to a Chabrier IMF and to circularized effective half-light radii; stellar masses defined as "actual" masses (excluding mass returned to the ISM) have been shifted upward by 0.14 dex (for SFGs; e.g., Bruzual & Charlot 2003), so as to be comparable with our masses (which are defined as the integral of the SFR). The Franx et al. (2008) sample is a K_s-selected sample with photometric redshifts. The sizes have been determined in the band redward of the redshifted 4000 Å-break and closest to the rest-frame g band. The van der Wel et al. (2014) sample is extracted from the HST CANDELS survey; these authors used a similar approach to size measurements to the one used in this work; therefore, their sizes should be directly comparable with ours. We limit the comparison to their SFGs (based on UVJ selection) in the redshift bin $2.0\lt z\lt 2.5$. The error bars indicate the 16%–84% range and show a large spread in the measured sizes for a given stellar mass.

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A fit to our data in Figure 12 gives ${{r}_{e}}\propto {{M}^{0.3\pm 0.1}}$ (including only the reliable fits), which is close to the size–mass relation of van der Wel et al. (2014). At any given stellar mass, there is a large dispersion of measured sizes: the most massive galaxies in our sample have sizes similar to local $z\sim 0$ early-type galaxies of the same mass, while others lie clearly below the local relation. It is well known that there is evolution with cosmic time of the median size–mass relation for both star-forming and quenched galaxies, although high-z galaxies as large as correspondingly massive z = 0 counterparts have also been identified (e.g., Onodera et al. 2010; Mancini et al. 2010). The origin of this evolution is debated (e.g., Daddi et al. 2005; Trujillo et al. 2007; McGrath et al. 2008; van Dokkum et al. 2008; Szomoru et al. 2011; Newman et al. 2012a; Barro et al. 2013; Dullo & Graham 2013; Poggianti et al. 2013; Shankar et al. 2013; Carollo et al. 2013b; Cassata et al. 2013; van der Wel et al. 2014). As argued by, e.g., Carollo et al. (2013b), Cassata et al. (2013), and Poggianti et al. (2013), understanding the causes of this evolution requires taking into account the evolution of the number densities of galaxies of a given size at each epoch, which is beyond the scope of this paper. Here we simply highlight two important points related to our sample: (1) our galaxies are ∼0.13 dex above, but still within the scatter of, the size–mass relation of other z ∼ 2 samples (our galaxies are, on average, 1.3 times larger at a given mass); and (2) at the same time, the small shifts between the different samples highlight the impact of difference in the measurement definitions of sizes, star formation flag (e.g., based on Hα flux in our study and on a color selection criterion in van der Wel et al.), and masses (e.g., through different galaxy template libraries). The small offset toward larger size comes from selecting SINFONI-AO targets with slightly larger sizes so as to be able to resolve the dynamics better.

In Figure 10 we compare the ${{(u-g)}_{{\rm rest}}}$ color gradients and color scatter measurements for our sample with the corresponding measurements for the $z\sim 0$ of the ZENS sample split into different morphological types.

Our z ∼ 2 sample spans a similar broad range of color gradients as the z = 0 late-type disk galaxies. The galaxies with the highest masses (${{M}_{\star }}\gt 7\cdot {{10}^{10}}\;{{M}_{\odot }}$) in our sample show slightly steeper color gradients than correspondingly massive galaxies at z = 0: the median color gradient of our z ∼ 2 galaxies is −0.34 ± 0.10, while the one of $z\sim 0$ galaxies is −0.16 ± 0.01. For the massive galaxies (${{M}_{\star }}\gt 7\cdot {{10}^{10}}\;{{M}_{\odot }}$), the Anderson & Darling (1952) test indicates that the null hypothesis that the high- and low-z samples belong to the same parent population concerning their color gradient can be rejected with a low confidence level ($\sim 2.1\sigma$). At such high masses, the local counterparts are, however, in contrast with our z ∼ 2 systems, quenched galaxies with an early-type morphology.

The central ${{(u-g)}_{{\rm rest}}}$ colors within 1 kpc of our massive z ∼ 2 galaxies are ∼0.47 mag bluer on average than those of the z = 0 massive early-type galaxies (median values of 1.22 ± 0.16 and 1.69 ± 0.14 at z ∼ 2 and z = 0, respectively, with the error quantifying the scatter). This color difference is most likely a combination of active star formation and younger stellar ages in our z ∼ 2 galaxies. The negative color gradients at z = 2 (steeper than for equivalent massive $z\sim 0$ galaxies) suggest, however, that star formation at these early epochs is sustained in the galaxy outskirts. This is also indicated by Genzel et al. (2014) and discussed in detail in Tacchella et al. (2015). In terms of different stellar age, we estimate the ${{(u-g)}_{{\rm rest}}}$ color to redden owing to aging from z ∼ 2 to $z\sim 0$ by about 0.5 ± 0.1 mag.

At lower masses, the color dispersion from the color maps of our z ∼ 2 galaxies is similar to what is measured at $z\sim 0$. In contrast, our massive z ∼ 2 galaxies have a higher color dispersion (median value of 0.15 ± 0.01) than the correspondingly massive galaxies at $z\sim 0$ (0.056 ± 0.002). Using again the Anderson & Darling (1952) test, we find that the null hypothesis that the high- and low-z samples belong to the same parent population concerning their color dispersion can be rejected at the $4.2\sigma$ level. The higher color dispersion in higher-z galaxies is not unexpected, given that the massive z ∼ 2 galaxies in our sample are star-forming and show clumpy substructure, while the z = 0 massive counterparts are quenched early-type galaxies. The comparison is nevertheless interesting, since it highlights that quenching of star formation in the massive z ∼ 2 main-sequence population should leave behind similarly massive quenched remnants with patchy, inhomogeneous stellar populations in their outer regions. In addition, when restricting the local sample to SFGs, the color dispersion of high-z systems, particularly at the massive end, still lies among the high color dispersion tail of nearby SFGs. This implies that the star formation distribution in z ∼ 2 galaxies has more substructure and is not as uniformly distributed as at $z\sim 0$. As mentioned previously, the presented trends have to be confirmed on larger and more homogeneously selected samples.

The resolution of the HST/WFC3 data for the J and H bands is 1–2 kpc. This implies that bulge components are barely resolved. To test whether it is feasible to do a bulge-disk decomposition (double-component fit) or not, we run simulations. In summary, we are able to recover the bulge-to-total ratio B/T very well without any bias. However, we are not able to estimate the size and/or Sérsic index of the bulge, i.e., we are not able to derive any corrections for accounting for any biases.

In the simulations, we create ~100,000 mock galaxies with GALFIT; each galaxy consists of two Sérsic components (bulge and disk). We vary the B/T (between 0 and 0.9), sizes (${{r}_{e,d}}\in [2.0,4.8]\;{\rm kpc}$ and ${{r}_{e,b}}\in [0.4,2.4]\;{\rm kpc}$), axis ratios ($b/a\in [0.6,1.0]$), and position angles (${\rm P}.{\rm A}.\in [-90{}^\circ ,90{}^\circ ]$) of the disk and bulge. In addition, we vary the Sérsic of the bulge n_b between 1 and 6 and the integrated magnitude of the disk between 21.5 and 24.5. These simulated galaxies are convolved with the PSF and added on real background images. Then all the model galaxies are processed in exactly the same way as the real galaxies.

The result of the simulations, i.e., the comparison of the measured to the intrinsic quantities, is shown in Figure A1. We find that we are able to recover the bulge-to-total (B/T) values well, i.e., B/T—the quantity we are interested in—is very robustly determined with our fitting procedure. The top left panel of Figure A1 shows in red and green the points for which ${{(B/T)}_{{\rm input}}}$ and $(B/T){{)}_{{\rm output}}}$ differ more than 0.3 and between 0.15 and 0.3, respectively. We see that only in 2%–3% of all the runs is ${\Delta }(B/T)$ larger than 0.3. In 90% of the cases, we are able to recover ${{(B/T)}_{{\rm input}}}$ better than 0.15. As one sees in the bottom right panel of Figure A1, the cases where we fail to recover B/T are the ones with a disk-like bulge ($n\approx 1-2$, i.e., pseudo-bulge).

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However, the bulge properties are subject to relatively large uncertainties, especially ${{r}_{e,b}}$ and n_b (see Figure A1, bottom panels). The scatter is much larger, and there is not a clear trend. This is also due to the well-known degeneracy between size and Sérsic index. Therefore, we are not able to make any conclusive statements about these two quantities of the bulge.

For estimating the error on the B/T itself, we use for a given magnitude of the bulge, bulge Sérsic index, and the ratio of the size of the disk to the bulge (${{r}_{e,b}}/{{r}_{e,d}}$) the dispersion in B/T values, as shown in Figure A2. We get larger errors for fainter and more disk-like bulges.

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After the analysis of the error of the B/T, we would like to shed more light on the modeling assumptions. Specifically, we investigate how the relative error in the B/T changes when fixing the Sérsic index of the bulge to 4, n_b = 4, in comparison with letting n_b remain free during the fitting process. As described in Section 7.2, the main physical motivation for these two modeling approaches is directly linked to the two different processes for the formation of galactic bulges: from merging one expects ${{n}_{b}}\sim 4$ ("classical" bulge), while from secular instability of the stellar disk ${{n}_{b}}\sim 1-3$ ("pseudo-"bulge). At z ∼ 2, we do not know whether the galaxies have a classical or pseudo-bulge. Hence, we simulate galaxies with a variety of physically sensible bulge Sérsic indices (${{n}_{b}}\in [0.0,4.5]$), recovering each galaxy with the two different fitting methods.

In the spirit of the section before, we simulate ~25,000 mock galaxies, recovering each galaxy with the n_b = 4 fixed and n_b free (initial value is set to n_b = 4) methods. As before, for the mock galaxies, we vary the sizes and brightnesses of the bulge and disk. The Sérsic index of the bulge is also varied (${{n}_{b}}\in [0.0,4.5]$), while the Sérsic index of the disk is fixed to 1. Furthermore, in contrast to the simulations above, we fix the axis ratio to 1.0 and the position angle to $0{}^\circ$ to minimize the parameter space. We therefore expect—for both fitting methods—smaller relative errors than from the analysis above.

The results of the simulations for n_b = 4 fixed and n_b free methods are shown in Figures A3 and A4, respectively. The galaxies get fainter (total magnitude H_tot) and smaller (half-light radius r_e of the total light profile, i.e., bulge and disk) in panels toward the right and bottom. Each panel displays the relative error in B/T as a function of the Sérsic index n_b of the simulated galaxy. The three different colored lines show galaxies with different size ratios of the bulge to the disk ${{r}_{b}}/{{r}_{d}}$: red, blue, and green indicate the intervals $[0.6,1.0]$, $[0.3,0.6]$, and $[0.0,0.3]$, respectively. The dashed lines show the bins with $\lt 20$ galaxies, while the bins indicated by the solid lines have $\gt 20$ galaxies (on average 140 galaxies). The shaded areas show the $1\sigma$ scatter.

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We find smaller relative errors in B/T with the n_b free method than with the n_b = 4 fixed method, for all Sérsic indices n_b, brightnesses H_tot, sizes r_e, and size ratios ${{r}_{b}}/{{r}_{d}}$. On average, the relative error in B/T for the n_b free method is ∼0.08, in contrast to the n_b = 4 fixed method, which gives ∼0.19. For both methods, the relative errors vary only a little for different size ratios. As expected, the relative errors increase toward fainter and smaller galaxies. In summary, we have shown that the n_b free method is able to recover the B/T of galaxies with a variety of bulge Sérsic indices much more reliable than the n_b = 4 fixed method.