The Role of the Most Luminous Obscured AGNs in Galaxy Assembly at z ∼ 2

We submitted the 53 objects in the parent sample for a Cycle 19 HST Snapshot program (HST-GO-12585; PI: Petty), of which 12 were observed (Table 1). These 12 objects have spectroscopic redshifts in the range 1.8 < z < 2.7. Other than a slightly lower median redshift, these 12 objects are statistically indistinguishable from the parent sample. None of their spectra show evidence for foreground lenses.

The 12 objects were observed with the Wide Field Camera 3 (WFC3) in the F160W filter (hereafter H-band). To facilitate the SNAP observations, the total exposure time per object was 1500 s, selected because it allowed each object to be observed within 48 minutes, after accounting for guide star acquisition and instrument overheads. This exposure time reaches a surface brightness limit in H of 23.5 mag arcsec⁻². Each exposure was divided into four equal-length subexposures using a dither box pattern of four pointings with 06 spacing.

All of the sample was clearly detected by WFC3. The WFC3 data were reduced using a standard Multidrizzle process. We started with the persistence-corrected output files from the calwf3 pipeline, which performs standard tasks including bias and dark current subtraction, linearity correction, flat fielding, bad-pixel masking, and removal of cosmic rays. We then removed geometric distortion from each file and combined them into a single image for each object using the Autodrizzle task. To extract fluxes, we used SExtractor (Bertin & Arnouts 1996) in MAG_BEST mode, which first determines the most appropriate elliptical aperture to use and then measures the flux inside that aperture. Finally, we corrected the photometry for Galactic absorption and converted the fluxes into magnitudes using the zero points provided by the WFC3 team.

We obtained reduced Spitzer (Werner et al. 2004) images at 3.6 and 4.5 μm from the IRAC instrument (Fazio et al. 2004) for our sample. These observations are significantly deeper than the W1 and W2 observations. For photometry, we adopted the methods in Lacy et al. (2005). We required 2σ levels for the detect and analysis threshold parameters and checked each object map for false detections.

We obtained Herschel (Pilbratt et al. 2010) photometry for all of our sample from the Herschel Science Archive. The data were taken with the Photoconductor Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) at 70 and 160 μm and with the Spectral and Photometric Imaging REceiver instrument (SPIRE; Griffin et al. 2010) at 250, 350, and 500 μm. The level 1 data were processed to level 2 using the Herschel Interactive Processing Environment (HIPE) version 14.2.0. For PACS, aperture photometry was carried out using the scanmap_pointsources_PhotProject.py HIPE script. For SPIRE, photometry was carried out using the Sussextractor algorithm (Savage & Oliver 2007; Wang et al. 2014). The complete set of Herschel data for the hDOGs, including those without HST data, is presented in C-W Tsai et al. (2017, in preparation).

We use five parameters to quantify the morphologies of our sample: Gini (G), M₂₀, asymmetry (A), Sérsic index (n), and effective radius (r_e).

The Gini coefficient (Abraham et al. 2003) is a measure of how concentrated the light is in an image:

$$\begin{eqnarray}&&G=\displaystyle \frac{1}{| \bar{f}| N(N-1)}\displaystyle \sum _{i=1}^{N}(2i-N-1)| {f}_{i}| ,\end{eqnarray} \tag{ 1 }$$

where $| \bar{f}|$ and $| {f}_{i}|$ are the absolute average flux and ith pixel flux from N total pixels, respectively. Here G ranges from zero to unity, with low values for galaxies with even light distributions and high values for galaxies whose light is concentrated into a small number of bright nuclear pixels. The M₂₀ coefficient (Lotz et al. 2004) is the second-order moment of the brightest 20% of the light,

$$\begin{eqnarray}&&{M}_{20}={\mathrm{log}}_{10}\left(\displaystyle \frac{{\displaystyle \sum }_{i}{M}_{i}}{{M}_{\mathrm{tot}}}\right),\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray}&&{M}_{i}={f}_{i}[{({x}_{i}-{x}_{c})}^{2}+{({y}_{i}-{y}_{c})}^{2}],\end{eqnarray} \tag{ 3 }$$

with

$$\begin{eqnarray}&&\displaystyle \sum _{i}{f}_{i}\lt 0.2{f}_{\mathrm{tot}},\end{eqnarray} \tag{ 4 }$$

in which f_i is the flux at (x_i, y_i), and (x_c, y_c) is the galaxy centroid. Here M₂₀ is a measure of the variance of the brightest 20% of the light and is anticorrelated with concentration; a single-nucleus system will have a more negative M₂₀ value than a double-nucleus system, for example. The asymmetry, A, is a measure of the mirror, or central rotational, symmetry of all of the light from a galaxy (Abraham et al. 1994; Conselice et al. 2000). It is determined by subtracting from the original image I₀ a 180° rotated image I_ϕ:

$$\begin{eqnarray}&&A=\displaystyle \frac{{\rm{\Sigma }}| {I}_{0}-{I}_{\phi }| }{2{\rm{\Sigma }}| {I}_{0}| }.\end{eqnarray} \tag{ 5 }$$

The Sérsic index (Sérsic 1963) is defined in the radial light intensity profile,

$$\begin{eqnarray}&&I(r)\propto {e}^{-\kappa {\left(\tfrac{r}{{r}_{e}}\right)}^{1/n}},\end{eqnarray} \tag{ 6 }$$

and is also called the concentration, or curvature, index. Finally, the effective radius, r_e, is the radius that encloses half of the total light emitted by the object.

We adopt the G, M₂₀, and A statistics because they have been used in many previous studies and their values have been compared against results from numerical simulations to calibrate morphological classifications (Lotz et al. 2008b). We include the Sérsic index and effective radius because they contain information complementary to the Gini coefficient. Both n and G are measures of central concentration, but n also depends on profile shape, in that increasing n gives a brighter center and a shallower falloff at large radii. Effective radius gives an estimate of the absolute size of an object. We use a Sérsic profile to fit our sample rather than, e.g., a Nuker profile (Hernquist 1990; Lauer et al. 1995), since each object covers a small number of pixels; fitting a geometric mean is thus more meaningful than considering minor and major axes separately.

To perform the G, M₂₀, and A measurements, we followed the approaches taken in Lotz et al. (2004) and Petty et al. (2009). We first subtracted an average sky flux from each frame, computed using the IRAF task imexamine. We then calculated the total flux within 1.5 times the Petrosian radius (r_p). Photometric uncertainties were estimated by changing the H-band center by up to 5'' in random directions about the best-fit galaxy centroid, measuring G, M₂₀, and A using the same radius, and calculating the standard error from 1000 iterations of this step. To estimate Sérsic indices and effective radii, we used GALFIT (Peng et al. 2002) to fit two-dimensional profiles of the form in Equation (6), following the approaches of previous authors (Ravindranath et al. 2006; Petty et al. 2009).

The light profiles of two objects—W0514 and W2337—suggested that point spread function (PSF) subtraction might unveil more details of the host galaxy, but our attempts to do so were unsuccessful. When we included a PSF, generated using the Tiny Tim tool, as an additional component within GALFIT when fitting these two objects, we could not extract stable host galaxy parameters, and the fit quality did not improve. We therefore conclude that an emerging AGN in the optical is unlikely in any part of our sample, but we cannot exclude that AGN light affects the central few pixels.

To quantify the origin—AGN activity or star formation—of the infrared emission, we fit radiative transfer models to the WISE, PACS, and, where available, submillimeter and millimeter-wave photometry. We do not fit to data at observed-frame 4.5 μm and shorter wavelengths due to the possibility of host galaxy contamination, but we do include these data as limits.

We assume that the infrared emission arises from a single episode of AGN activity and/or star formation. We then fit the infrared data simultaneously with two grids of precomputed radiative transfer models: one for AGNs (Efstathiou & Rowan-Robinson 1995; Efstathiou et al. 2013) and one for starbursts (Efstathiou et al. 2000). A model set for old stellar populations is not included, since it is likely that the infrared emission redward of 4.5 μm comes predominantly from obscured luminous activity, with a negligible contribution from unobscured older stars. These models have been used previously in Verma et al. (2002), Farrah et al. (2002, 2003, 2012), and Efstathiou et al. (2013). The AGN models assume that the dust geometry is a smooth tapered disk whose height, h, increases linearly with distance, r, from the AGN until it reaches a constant value. The dust distribution includes multiple species of varying sizes and assumes that the density distribution scales as r⁻¹. The starburst models combine the population synthesis code of Bruzual & Charlot (2003) with a prescription for radiative transfer through dust that includes the effects of small dust grains and polycyclic aromatic hydrocarbons (PAHs; Efstathiou & Siebenmorgen 2009). In total, there are 1680 starburst models and 4212 AGN models.

Both model sets have several free parameters (e.g., inner half-opening angle for the AGNs, age and initial optical depths of the molecular clouds for the starbursts), which we lack the data to constrain. Instead, we use the full model sets to obtain a realistic estimate of the uncertainties on the luminosities by using all possible combinations of SED fits for each object to construct a weighted probability distribution for the total, AGN, and starburst luminosities. The only constraint we impose is on the AGN model set: that the viewing angle is greater than the torus half-opening angle, as measured from pole-on, so that the broad-line region is not visible in direct light. This reduces the number of AGN models to 2064. This approach assumes that all models exist in the high-redshift population and are comparably likely. This assumption lacks strong supporting evidence, but the model sets do span the properties found in lower-redshift populations. Moreover, our approach is superior to simply normalizing a single template or fitting a small number of templates, as such an approach is effectively a small set of δ functions in the same parameter space.

In the following, we make comparisons to five samples from the literature. First are the "bump" DOGs (bDOGs) and "power-law" DOGs (pDOGs; Bussmann et al. 2009, 2011; Melbourne et al. 2012). The bDOGs have mid-infrared continua showing an opacity minimum arising from H⁻ in stellar atmospheres, while the pDOGs have mid-infrared continua showing an AGN power law. The bDOGs have fainter 22 μm flux densities and less extreme R − [22] colors than the pDOGs. Second are two samples of SMGs, one from Bussmann et al. (2011) and one from Aguirre et al. (2013). The SMGs from Bussmann et al. (2011) are the 25 SMGs with redshifts in the range 0.7 < z < 3.4, originally presented in Swinbank et al. (2010) and selected from the spectroscopic catalog of Chapman et al. (2005). The parent sample is the radio-identified subset of sources detected at 850 μm in surveys with the Sub-millimeter Common User Bolometer Array (SCUBA). The SMGs from Aguirre et al. (2013) lie in approximately the same redshift range as our sample and include both unlensed and lensed sources and sources selected at both 850 μm and 1.2 mm. While their selection is heterogeneous compared to that of Bussmann et al. (2011), they publish asymmetries, so we include them for comparison. The final comparison sample is the sample of M_* > 10¹¹ M_⊙ galaxies at 1.7 < z < 3.0 from the GOODS NICMOS Survey (GNS; Buitrago et al. 2008; Conselice et al. 2011). This sample comprises massive galaxies with infrared luminosities much lower than any of the other comparison samples and is not subdivided into quiescent and star-forming subsamples.

Each comparison sample includes only a subset of the morphological parameters we consider. In summary, the samples used for morphological comparisons are:

• 1.  
  hDOGs (#1, our sample): G, M₂₀, A, r_e, and n
• 2.  
  bDOGs (#2, Bussmann et al. 2011): G, M₂₀, r_e, and n
• 3.  
  pDOGs (#3, Bussmann et al. 2009): G, M₂₀, r_e, and n
• 4.  
  B12 SMGs (#4, Bussmann et al. 2011): G, M₂₀, r_e, and n
• 5.  
  A13 SMGs (#5, Aguirre et al. 2013): G, M₂₀, and A
• 6.  
  GNS galaxies (#6, Buitrago et al. 2008): G, M₂₀, A, r_e, and n

All of the comparison samples were observed by HST at rest-frame wavelengths closely matched to our sample (we do not consider the minor difference in resolution between NICMOS-NIC2 and redrizzled WFC3). In all cases, we include only those objects within approximately the same redshift range as our sample. At z = 2, the spatial scale is 8.37 kpc arcsec⁻¹. For these reasons, we do not include comparisons to objects within the COSMOS field observed with the Advanced Camera for Surveys (ACS) or to low-redshift ULIRGs and Hubble sequence galaxies (Lotz et al. 2004), as the finer spatial resolution and different rest-frame wavelengths could lead to invalid comparisons.

To make quantitative comparisons between populations, we employ two-sample Bayesian hypothesis testing using a nonparametric Polya tree prior (Holmes et al. 2015). This approach is superior to the traditional Kolmogorov–Smirnov test (or other frequentist approaches), as it gives the probability for the null hypothesis that the two populations are identical, rather than the probability of obtaining the same or a more extreme result assuming that the two populations are identical. The probabilities are given in Table 3.

In the WISE images, our sample is consistent with point sources at 12 and 22 μm. The PACS and SPIRE images are also consistent with point sources. In all cases, the WISE and (where detected) Herschel sources are centered closely on the primary HST source. This, combined with the absence of foreground objects in the spectra and the hDOG selection that biases against bright foreground objects, means that significant gravitational-lensing amplification of our sample is unlikely.

The fitted total rest-frame infrared luminosities of our sample span 1.8 × 10¹³ to 1.4 × 10¹⁴ L_⊙, making them among the most luminous objects in the universe (see also Bridge et al. 2013; Tsai et al. 2015). They are much more infrared-luminous than z < 0.2 ULIRGs (e.g., Farrah et al. 2003) and have comparable luminosities to hyperluminous infrared galaxies (HyLIRGS) found at other redshifts that were selected at observed-frame wavelengths of less than 100 μm (Rowan-Robinson 2000). They match or exceed the luminosities found for the most luminous SMGs (Chapman et al. 2005). Four members of our sample (W0542, W1316, W1830, and W1835) have infrared luminosities in Fan et al. (2016); in three cases, our luminosities are consistent with theirs, while for the fourth (W1835), our luminosity is a factor of 2 higher. This difference likely arises from our more comprehensive infrared data and the different approaches to modeling the AGN and starburst emission. W1835 also has a published infrared luminosity in two previous papers; our luminosity is 60% higher than that derived by Wu et al. (2012) but consistent with the (template) luminosity of Jones et al.(2014).

The combination of WISE, PACS, SPIRE, and (in some cases) ground-based submillimeter and millimeter-wave photometry means we can constrain the fraction of the total infrared luminosity that arises from AGNs (f_AGN). In all cases, the infrared SED fits mark our sample as consisting of luminous, obscured, AGN-dominated systems. In some cases, it is possible to explain all of the infrared emission as arising from AGN activity, though the best-fit solution usually includes some star formation, with star formation rates of up to a few hundred M_⊙ yr^–1. The AGN fractions of our sample are consistently higher than those in the bDOGs and higher or comparable to those in the pDOGs (Pope et al. 2008; Assef et al. 2015).

We note three caveats to the results from the infrared SEDs. First, since the AGN models are axisymmetric, the total infrared luminosity cannot be precisely inferred simply by integrating the line-of-sight infrared luminosity over 4π sr. However, in all cases, the anisotropy correction to the AGN luminosity is a factor of 2 or less, and, in most cases, the 1σ uncertainties on the anisotropy correction encompass unity, so we do not apply them here. Second, there is a possibility that the bias toward hotter dust in our sample compared to other classes of DOGs is consistent with younger starbursts, rather than a particular AGN phase. This possibility arises because younger starbursts have a more intense interstellar radiation field and therefore have elevated dust temperatures compared to older starbursts (Efstathiou & Siebenmorgen 2009). We cannot, however, explore this possibility, since the lack of rest-frame mid-infrared spectra means that the constraints on the starburst ages from the model fits are weak—the 90% confidence intervals on the starburst ages are 10–60 Myr or wider in all cases. Tighter constraints than this would require higher-quality infrared data (Farrah et al. 2016). Third, we cannot exclude the possibility of a contribution to the total infrared luminosity from "cirrus" dust heated by quiescent starlight.

Since the uncertainties on the fractional AGN luminosities are significant, we define two classes of AGN fractions for subsequent analysis. These classes are f_AGN < 0.95 and f_AGN > 0.95. The choice of boundary is to some extent arbitrary and is intended to help frame the discussion; we do not adopt it out of any physical motivation. We define the classes such that one is an "AGN composite" class and the other is a "pure AGN" (or close to) class.

In Figure 3, we plot the luminosities of our sample against both redshift and AGN fractional luminosity. There is, perhaps, a trend with redshift, with the more luminous objects lying at higher redshifts, though this could be a selection effect. There is also a hint of a trend with AGN fraction, with 5/6 objects with the lowest infrared luminosities having the highest AGN fractional luminosities. Compared to samples from the literature, our sample is more luminous than either the bDOGs or pDOGs by factors of approximately 3 and 10, respectively. This is consistent with the idea that the hDOG selection preferentially finds obscured, extremely infrared-luminous AGNs. Our sample is also more luminous than any of the SMGs in the same redshift range. Finally, we compare to the HyLIRG sample of Tsai et al. (2015; hereafter TS15). The TS15 sample was selected in the same way as ours but comprises the most luminous 20 objects in the parent spectroscopic catalog of hDOGs. Compared to the TS15 sample, our sample is at lower redshifts than the TS15 sample and slightly lower, on average, infrared luminosities, though at z ≳ 2.2 their luminosities are comparable.

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Turning to the infrared colors, in Figure 4, we consider two color–color plots: f₂₂/f₁₂−f₁₂/f_1.6 and f₂₂/f_4.5−f_4.5/f_1.6 (the TS15 HyLIRG sample is not plotted, because 1.6 μmphotometry is not available for this sample). Starting with the f₂₂/f₁₂−f₁₂/f_1.6 plot, our sample has f₁₂/f_1.6 colors similar to those of the pDOGs, consistent with both populations having similar AGN–to–host galaxy luminosity ratios, at least at 12 μm. However, our sample has significantly redder f₂₂/f₁₂ colors than the pDOGs or bDOGs. This is consistent with the AGNs in the hDOGs being more obscured than in other classes of DOG. In the f₂₂/f_4.5−f_4.5/f_1.6 plot, we see a clear separation; the hDOGs have higher f₂₂/f_4.5 ratios than the pDOGs, which are themselves higher than the bDOGs, consistent with a rising contribution from an obscured AGN for the same host galaxy mass. However, the hDOGs have lower f_4.5/f_1.6 ratios than either the pDOGs or bDOGs, which are similar to each other. This is consistent with a host galaxy that is younger, less massive, and/or less obscured, and/or that there is some contribution to the optical light from the central AGN.

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The WFC3 images show a range of morphologies. One object, W0542, has a symmetric light profile, appears undisturbed, and has no close companions. Three objects (W1206, W1316, and W1835) show evidence for a disturbed, irregular light profile but do not clearly have close companions. The remaining eight objects all show disturbed profiles with what appears to be one or more close companions. In all cases, the spatial extents of the sources lie approximately in the range 10–25 kpc. No object shows evidence for significant gravitational lensing (see also Wu et al. 2014).

For an initial morphological classification, we use boundaries in the G−M₂₀−A plane. In the G−M₂₀ plane, we use the boundaries determined by Lotz et al. (2008a) for mergers,

$$\begin{eqnarray}&&G\gt -0.14{M}_{20}+0.33\end{eqnarray} \tag{ 7 }$$

early-type systems,

$$\begin{eqnarray}&&G\leqslant -0.14{M}_{20}+0.33;\,\mathrm{and}\,G\gt 0.14{M}_{20}+0.80\end{eqnarray} \tag{ 8 }$$

and late-type systems,

$$\begin{eqnarray}&&G\leqslant -0.14{M}_{20}+0.33;\,\mathrm{and}\,G\leqslant 0.14{M}_{20}+0.80,\end{eqnarray} \tag{ 9 }$$

as determined from comparisons to galaxies at z ∼ 0.3 observed in the rest-frame B-band at an effective resolution of 0.62 kpc (see also Lotz et al. 2004, 2008b). To classify mergers versus nonmergers in the G−A plane, Conselice et al. (2003) and Lotz et al. (2004) proposed a boundary of

$$\begin{eqnarray}&&G\gt -0.4A+0.68;\,\mathrm{or}\,A\geqslant 0.35.\end{eqnarray} \tag{ 10 }$$

Our sample and these boundaries are shown in Figure 5.

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The use of these boundaries for our sample comes with four caveats. First, the spatial resolution at which the boundaries were determined, ∼0.6 kpc, is finer than the 1.26 kpc resolution of WFC3/IR at z = 2. The general effect of this is to lower the G and elevate the M₂₀ values. We do not believe that this difference in resolution will impact our results, since Lotz et al. (2008a) used these boundaries up to z = 1.2 with little change in their effectiveness, and the change in spatial resolution from z = 1.2 to 2 is insignificant. Second, the boundaries were determined at a rest-frame central wavelength of ∼400 nm, compared to the ∼530 nm of our sample. The effect of this difference is that our images may be smoother, as they are less affected by extinction and do not sample any emission below the Balmer break. Quantifying the effect of this difference is beyond the scope of this paper, so we simply note it as a caveat. Third, we are assuming that the observed-frame 1.6 μm light traces stellar mass, rather than line-emitting gas, in most pixels. Based on previous observations, this seems likely (e.g., Förster Schreiber et al. 2011), but we cannot exclude the possibility of significant [O iii] 5007 Å contamination. Fourth, the selection of objects with spectroscopic redshifts may predispose the sample to having more centrally concentrated rest-frame ultraviolet emission (Section 2).

Compared to the GNS sample, our sample has markedly different G values; we find that ${P}_{1,6}^{G}=0.12 \%$, with the hDOGs having values higher by ΔG ∼ 0.17, on average, indicative of more centrally concentrated light distributions. The M₂₀ values of our sample are also different from those of the GNS sample; we find that ${P}_{1,6}^{{M}_{20}}=2.2 \%$, with the values lower in our sample by ΔM₂₀ ∼ 0.35, indicating that the brightest 20% of light in our sample shows less variance and is more concentrated into a small number of nuclei. Conversely, the asymmetries of the hDOGs are similar to those of the GNS sample, with ${P}_{1,6}^{A}=99.5 \%$.

Other studies similar to the GNS exist; while these studies do not tabulate their data, we can still make comparisons. Compared to the M_* ≳ 10¹⁰ M_⊙ systems at z ≲ 2 in Lee et al. (2013), our sample has comparable G but slightly more negative M₂₀ values than their quiescent samples but higher G and more negative M₂₀ values than their star-forming samples. Compared to the M_* ≳ 10¹¹ M_⊙ systems at z ∼ 2 selected via extremely red  "IRAC-selected Extremely Red Objects" (IERO) colors ([z₈₅₀] − [3.6] > 3.25 and [3.6] < 21.5; Wang et al. 2012), our sample has comparable G and slightly more negative M₂₀ values than their quiescent sample but higher G and substantially more negative M₂₀ values than their star-forming sample.

Comparisons to the pDOGs and bDOGs can only be made in the first panel of Figure 5, as these two samples do not have asymmetry measures. Both the pDOGs and the bDOGs separate from the hDOGs in the G−M₂₀ plane, with lower G values and less negative M₂₀ values, though the pDOGs are closer to our sample in M₂₀ than the bDOGs. We find, for the comparison with the bDOGs, ${P}_{1,2}^{G}=0.56 \%$ and ${P}_{1,2}^{M20}=0.23 \%$, while for the pDOGs we find ${P}_{1,3}^{G}=0.07 \%$ and ${P}_{1,3}^{M20}=9.7 \%$. Overall, the hDOGs have more concentrated and less asymmetric inner light distributions than do either other class of DOG.

Finally, we compare our sample to the two SMG samples. The distribution of the A13 SMGs is wider than that of our sample in all three panels of Figure 5; our sample lies only within part of the SMG distribution, corresponding to lower-than-average asymmetries. Conversely, the G and M₂₀ values for the two samples are (marginally) comparable. We find ${P}_{1,5}^{G}=66.4 \%$, ${P}_{1,5}^{{M}_{20}}=54.9 \%$, and ${P}_{1,5}^{A}=35.1 \%$. We see no dependence on AGN fraction for members of our sample in terms of their positions within the A13 SMG distribution. Conversely, the B12 SMGs are offset from our sample and lie close to the other two DOG samples. We find ${P}_{1,4}^{G}=1.1 \%$ and ${P}_{1,4}^{{M}_{20}}=2.4 \%$. Both SMG samples also avoid the bulk of the GNS sample in all three panels.

We next examine the relations between morphological parameters and redshift (Figure 6). No trends are apparent in any parameter.¹⁴ There are also no clear trends with AGN fraction. Finally, there are no clear trends among any of the comparison populations. This is consistent with the h/b/pDOG and SMG selections isolating brief phases in luminous galaxy evolution and with the physical processes that these selections signpost not changing substantially over 1.8 < z < 2.7.

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Next, we search for trends of morphological parameters with infrared luminosity (Figure 7). No trends are evident in any parameter. We also see no trends in any of the comparison populations. There is, perhaps, a trend between L_IR and G if our sample and the pDOGs are considered together, but the trend is not strong. Finally, we see no trends of morphological parameters with AGN fractional luminosity, except, perhaps, with asymmetry, where all the objects with f_AGN > 0.95 have A < 0.35. As with the lack of trends with redshift, this is consistent with the DOG and SMG selections isolating brief phases in the duty cycle of active galaxies and/or that infrared luminosity trends do not trace galaxy assembly processes.

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Most of our sample has Sérsic indices close to unity. Two objects have n ∼ 2, and one has n < 0.5. This is at the lower end of the range of Sérsics of all galaxies, consistent with them being disk or merger systems. They are not ellipticals or systems with de Vaucoleurs profiles. Smaller, lower-luminosity ellipticals can have n < 4, with values as low as unity (Caon et al. 1993), but our sample members are unlikely to be small ellipticals with low Sérsic indices, given that their effective radii are all >1.15 kpc. One classification scheme that uses the Sérsic index is that of Ravindranath et al. (2006), who proposed that mergers have $\langle n\rangle \lt 0.8$, exponential profile systems have $0.8\lt \langle n\rangle \lt 2.5$, and bulge systems have $\langle n\rangle \gt 2.5$. According to this scheme, three of our objects are mergers, while the rest are disklike.

Figure 8 compares the G, M₂₀, A, and r_e measurements for our sample to their Sérsic indices. We see no trends, except that the two objects with n ≃ 2 have the most negative M₂₀ and lowest asymmetries, consistent with these two objects being the most dynamically relaxed of the sample. We also see no trends in Sérsic index with AGN fraction. Compared to the other samples, ours has Sérsic indices that are somewhat dissimilar to those of the two DOG samples (${P}_{1,2}^{n}=35.4 \%$ and ${P}_{1,3}^{n}=18.7 \%$; see also Schawinski et al. 2012) but are similar to those of both the GNS sample (${P}_{1,6}^{n}=99.8 \%$) and the B12 SMGs (${P}_{1,4}^{n}=99.7 \%$). Compared to the Lee et al. (2013) sample, the hDOGs have Sérsic indices that are comparable to those of their star-forming M_* ≳ 10¹⁰ M_⊙ systems but lower by Δn ≃ 1 than those of their passive systems. The hDOG Sérsic indices are also comparable to those of "main-sequence" star-forming galaxies (with star formation rates in the range 20–350 M_⊙ yr⁻¹) at z ∼ 2 (the H-band single-component fits of Tacchella et al. 2015; see also Morishita et al. 2014). This similarity indirectly suggests that the star formation in hDOGs can be located at kpc-scale galactocentric distances.

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Using rest-frame optical spectroscopy, Wu et al. (2017) proposed that hDOGs have black hole masses of order 10⁹ M_⊙ and Eddington ratios close to unity. We compare these measurements to the black hole masses that are predicted for our sample based on locally observed relations between n and black hole mass. These relations arise because local samples are dynamically relaxed, with a stable bulge. This condition is not satisfied in our sample. Nevertheless, we explore its consequences. Applying the log-normal relation of Graham & Driver (2007) yields predicted black hole masses for our sample of order 10⁷ M_⊙, or two orders of magnitude below the measured average. This is consistent with the idea that the black holes assembled at least a few hundred Myr before the bulges in these systems.

We compare the effective radii of our sample to the G−M₂₀−A parameters in Figure 9. No trends are apparent. The effective radii of our sample are comparable in distribution to those of all four of the comparison populations (column 5 of Table 3). They are also comparable to those of other samples of massive, star-forming galaxies at similar redshifts (Morishita et al. 2014; Tacchella et al. 2015) and larger than those of the compact star-forming or quiescent systems at z ≲ 2 (Daddi et al. 2005; van Dokkum et al. 2008, 2010; Weinzirl et al. 2011). The effective radii of our sample are also similar to those of cluster galaxies at z = 1.62 but have lower Sérsic indices, on average (Papovich et al. 2012).

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