NO MORE ACTIVE GALACTIC NUCLEI IN CLUMPY DISKS THAN IN SMOOTH GALAXIES AT z ∼ 2 IN CANDELS/3D-HST^*

Our samples of clumpy, smooth, and intermediate galaxies come from the 4 epoch CANDELS GOODS-S visual classification catalog (Kartaltepe et al. 2014). Each galaxy has high-resolution HST imaging in the rest-frame UV from ACS F606W and F850LP and in the rest-frame optical from WFC3 F125W and F160W (Grogin et al. 2011; Koekemoer et al. 2011). Galaxies were classified on the clumpiness/patchiness grid shown in Figure 1. Here "clumpiness" is a measure of the number of compact knots, while "patchiness" refers to the more diffuse irregularities within galaxies.

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We use visual classification because automated selection of clumps and patchiness remains a difficult computational problem (e.g., Guo et al. 2012). Inspectors were instructed to focus on the bluest passband for clumpiness classification, as clumps are typically most evident in the rest-UV (Guo et al. 2012). All galaxies in our sample (from the 4-epoch catalog of Kartaltepe et al. 2014) were inspected by at least five classifiers, and we combine the different classifications into a single averaged result for each galaxy.

We use both clumpiness and patchiness as indicators of violent disk instabilities within a galaxy. This is motivated by the presence of both compact/round clumps and diffuse/elongated structures in simulations of z ∼ 2 galaxies undergoing violent disk instabilities (Ceverino et al. 2012; Mandelker et al. 2014). In addition, if star-forming clumps are enshrouded by dust, their emission would likely be reprocessed in a patchy morphology. Observations show that galaxies appearing clumpy in the UV are merely patchy morphologies in the near-infrared: adding dust to such a system would cause it to appear patchy in the UV rather than clumpy. We also note that Guo et al. (2014) find better agreement between automated clump-finding and visual classification when patchiness is included in the visual clumpiness. Therefore we combine both axes in Figure 1 for the identification of clumpy galaxies.

The classifications on each axis are summed to give each galaxy a clumpiness+patchiness value ranging from 0 to 4. Here 0 represents the top left (no clumpiness, no patchiness) and 4 represents the lower right (3+ clumps and maximally patchy). The individual classification results are averaged together to assign "total clumpiness" parameter C, which we use to define the galaxies most and least likely to be dominated by violent disk instabilities. We define C ⩾ 2 galaxies as "clumpy," C < 1 galaxies as "smooth," and 1 ⩽ C < 2 galaxies as "intermediate." These divisions are chosen such that each category has roughly the same number of galaxies, for ease of comparing AGN fractions across morphologies.

We compare the visual classification C with the automated number of clumps from Guo et al. (2014) in Figure 2. There is a loose correlation between the two methods: the visually-identified smooth galaxies tend to have the fewest automated number of clumps, while the visually clumpy galaxies typically have the most automated number of clumps. There is some scatter due to the imperfection of both methods. Guo et al. (2014) include a more detailed comparison of automated clump-finding with the same visual classifications used here, finding ∼75% agreement between the two methods (see their Appendix).

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Figure 3 shows HST iJH (rest UV-optical) color composite images for several representative clumpy, smooth, and intermediate galaxies in our sample. Images of all galaxies are additionally shown in the Appendix (Figures 15–17).

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The GOODS-S region of CANDELS has near-complete spectroscopic coverage in the near-IR from publicly available 2 orbit HST/WFC3 G141 grism observations taken by the 3D-HST survey (Brammer et al. 2012). For redshifts and line measurements of individual galaxies, the data were reduced using the aXe software (Kümmel et al. 2009, available at http://axe-info.stsci.edu) to produce 2D and 1D wavelength- and flux-calibrated spectra at 1.1 < λ < 1.7 μm. We used the specpro IDL software¹⁵ (Masters & Capak 2011) to visually inspect and determine cross-correlation redshifts for the samples of clumpy, smooth, and intermediate galaxies. Spectra with significant (>10%) contamination (from neighboring objects) in the Hβ+[O iii] region are rejected from each sample: this occurs for about ∼15% of galaxies.

Line fluxes and ratios of Hβ and [O iii]λ5007 Å were also measured from the aXe-reduced 3D-HST spectra. The low resolution of the WFC3 slitless grism (R ≃ 130 and 46.5 Å pixel⁻¹, worse for extended sources) means that the Hβ and [O iii]λ4959,5007 Å lines are somewhat blended. We simultaneously fit all three lines with Gaussians, constraining each line to be fit within (rest frame) 50 Å (∼2–3 pixels) of the line center. We do not constrain the width of each line because the spatial broadening of the slitless grism frequently causes unusual profiles which can differ for each line. The Hβ line flux is measured directly from the Gaussian fit, while the [O iii]λ5007 flux is measured as 3/4 of the total flux from both blended [O iii] Gaussians (Storey & Zeippen 2000). If we instead fix the two ${[{\rm O}\,{\scriptsize {\rm III}}]}$ Gaussians to have total fluxes with a 1:3 ratio, the measured line fluxes do not significantly change. Examples of the line fits are shown in Figure 4.

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Uncertainties in the line ratios are computed by re-fitting continua and Gaussians on 10000 realizations of the resampled data. Our sample includes only galaxies with [O iii]λ5007 Å fluxes measured at the 3σ level. We do not set any requirement on the  Hβ line flux measurements, and  Hβ line fluxes less than the 1σ error are treated as upper limits (using the 1σ error as the limit). In general, the unique asymmetric shape of the blended ${[{\rm O}\,{\scriptsize {\rm III}}]}$ lines enables secure redshifts even when  Hβ is poorly detected.

To study spatially resolved line ratios, we used separate reductions of the WFC3 G141 data from the 3D-HST pipeline, as described in Brammer et al. (2012, 2013). The 3D-HST reduction method produces superior spatially resolved spectra because it interlaces rather than drizzles: this mitigates the correlated noise associated with drizzling in the final high-resolution (006 pixel⁻¹) combined 2D spectra.

We calculate stellar masses and SFRs for the clumpy, smooth, and intermediate galaxies using the extensive UV/optical/IR photometry in GOODS-S, with 18 bands including 8 with high-resolution HST imaging (Guo et al. 2013). First, the spectroscopic redshift from the HST/WFC3 grism is used to shift the observed photometry to the rest frame. We then fit the rest-frame spectral energy distribution (SED) with Bruzual & Charlot (2003) models that include a Chabrier (2003) initial mass function, exponentially declining star-formation histories, and a Calzetti (2001) extinction law. Stellar mass is given by the best-fit model. Example SED fits (for the same galaxies shown in Figure 4 are shown in Figure 5.

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There is some evidence that z ∼ 2 galaxies are more likely to have constant star-formation histories rather than the exponentially declining models used here. In practice, our best-fit SEDs generally have τ values which are very long (parameterizing the star formation history as SFR ∼ e^−t/τ). We also tested the effects of forcing a constant star formation history, and found the masses to change by only ≲0.1 dex in all cases.

Meanwhile SFRs are calculated following the method of Wuyts et al. (2011) when mid- and far-IR data are available, and SED-fitting following the method of Barro et al. (2013) otherwise. IR emission from an intrinsically luminous AGN might contaminate the IR with a hot dust bump (effectively observed as red IRAC colors, e.g., Donley et al. 2012), influencing both the stellar mass and SFR estimates. This occurs for one of our objects: the clumpy galaxy and X-ray AGN 16985, shown in Figure 5. The remainder of the sample have well-fit galaxy SEDs without evidence for significant AGN contribution. This is unsurprising, as only intrinsically luminous (log (L_X) ≳ 44) AGNs tend to have hot dust IR emission which dominates over the galaxy emission (Trump et al. 2011a; Donley et al. 2012).

Figure 6 (top panel) shows the mass distributions for each of the clumpy, smooth, and intermediate galaxy samples. The three samples are selected to be matched in stellar mass: starting with the clumpy galaxy sample, we constructed the smooth and intermediate galaxy samples to have a similar mass distribution. All three samples have median and mean M_* = 10^9.8 M_☉.

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Our galaxies are plotted in SFR–M_* space in Figure 6 (bottom panel). For comparison we also show the SFR and M_* of the larger population of GOODS-S galaxies with photometric redshifts calculated by Dahlen et al. (2013) in the same 1.3 < z < 2.4 redshift range. Our z ∼ 1.85 galaxies are limited to M_* ≳ 10⁹ M_☉ by the H < 24 selection criterion. The requirement for [O iii] detection at the 3σ level imposes a flux limit of $f({[{\rm O}\,{\scriptsize {\rm III}}]}) \gtrsim 5 \times 10^{-17}$ erg s⁻¹ cm⁻² in the 2 orbit WFC3 grism data. Although we estimate SFR from the SED (following Wuyts et al. 2011) rather than from emission lines, this ${[{\rm O}\,{\scriptsize {\rm III}}]}$ line flux translates roughly to the observed SFR limit of SFR ≳ 10 M_☉ yr⁻¹ (assuming $f({{\rm H}\alpha }) \sim f({[{\rm O}\,{\scriptsize {\rm III}}]})$ and using the Kennicutt 1998 relation). For the lower-mass half of the sample (M_* < 10^9.8 M_☉), this SFR limit restricts the galaxies to be starbursting and above the star-forming "main sequence" (see also Noeske et al. 2007; Daddi et al. 2007). On the other hand, the higher-mass half of the sample (M_* > 10^9.8 M_☉) generally lies on the main sequence for star-forming galaxies at 1.3 < z < 2.4. The only notable exception is a few high-mass smooth galaxies below the main sequence which might be quenching.

The CANDELS GOODS-S field also contains 4 Ms of Chandra X-ray data (Xue et al. 2011). The 4 Ms depth corresponds to an on-axis flux limit of 3.2 × 10⁻¹⁷ erg s⁻¹ cm⁻², which corresponds to a luminosity limit of L_X > 10^41.9 erg s⁻¹ at our sample's median redshift of z = 1.85. We use the classifications of Xue et al. (2011) to separate X-ray galaxies (with X-ray detections consistent with the L_X–SFR relation, Lehmer et al. 2010; Mineo et al. 2014) from the more luminous and hard-spectrum AGNs. The X-ray data for undetected sources in each morphology category are also stacked, as discussed in Section 3.3.

It has long been known that the high-ionization emission of AGNs results in a different emission line signature than observed in typical H ii regions associated with star formation (SF): in particular, AGN narrow line regions tend to exhibit higher ratios of collisionally excited "forbidden" lines to hydrogen recombination lines (Seyfert 1943; Osterbrock & Parker 1965). The classic Baldwin et al. (1981, BPT) and Veilleux & Osterbrock (1987; VO87) AGN/SF diagnostics use the ratios of $f({[{\rm O}\,{\scriptsize {\rm III}}]}\lambda 5007)/f({{\rm H}\beta})$ versus $f([{\rm N}\,{\scriptsize II}]\lambda 6584)/f({{\rm H}\alpha })$ or $f([{\rm S}\,{\scriptsize II}]\lambda 6718+6731)/f({{\rm H}\alpha })$: the small wavelength separation of each line pair means that these ratios are effectively insensitive to reddening.

The low resolution of the WFC3 grism means that the [N ii] and Hα lines are not resolved from one another, and so the standard BPT or VO87 diagnostics cannot be used on our data. Instead we use the "mass-excitation" (MEx) method (Juneau et al. 2011), which uses the ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratio with the stellar mass M_* to separate AGNs and SF galaxies. Functionally, the MEx method uses the correlation between mass and metallicity (e.g., Tremonti et al. 2004) to separate low-metallicity galaxies from AGNs, both of which exhibit similarly high ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratios. Compared to X-ray or infrared surveys, line ratio selection is often more sensitive to obscured and moderately accreting AGNs, but it also less reliable (e.g., Juneau et al. 2014). There is also some debate whether line ratio diagnostics remain applicable in z > 1 galaxies at all, since higher redshift galaxies may have different gas properties (Liu et al. 2008; Brinchmann et al. 2008; Kewley et al. 2013), changing their line ratios in the absence of AGNs (but for counterarguments, see Wright et al. 2010; Trump et al. 2011b, 2013b). Juneau et al. (2014) also demonstrate that the different selection effects in high- and low-redshift samples have important effects on their observed MEx distributions. For this reason we avoid comparing the z ∼ 1.5 galaxy samples with local objects. Instead, we simply compare clumpy, smooth, and intermediate galaxies all within the same redshift range.

Figure 7 shows the MEx diagram for the clumpy, smooth, and intermediate galaxies. The solid line in each panel shows the empirical line from Juneau et al. (2014) dividing AGN and SF galaxies, adjusted for the redshift (z ∼ 1.85) and line flux limit ($f({[{\rm O}\,{\scriptsize {\rm III}}]}) \gtrsim 5 \times 10^{-17}$ erg s⁻¹ cm⁻²):

$$\begin{equation} y = 0.375/(m-10.4)+1.14\ {\rm if}\ m \le 9.88 \end{equation} \tag{ 1 }$$

$$\begin{equation} y = 290.2 - 76.34m + 6.69m^2 - 0.1955m^3\ {\rm otherwise.} \end{equation} \tag{ 2 }$$

Here $y=\log ({[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta})$ and m = log (M_*/M_☉) − 0.51. Assuming that all galaxies above this line are AGNs, clumpy galaxies seem to have the highest AGN fraction (12/44, 27%), followed by smooth galaxies (11/41, 27%) and intermediate galaxies (7/35, 20%).

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However, the simple binary classification of counting objects above and below the AGN/SF line is not entirely appropriate, given that most galaxies have emission lines with composite contribution from both SMBH accretion and H ii regions. The MEx diagram is much more suited to a probabilistic classification approach, as introduced by Juneau et al. (2011). The MEx probabilities, updated for use at z > 1 by Juneau et al. (2014) and assuming an error of 0.2 dex in M_*, indicate that $39_{-6}^{+8}\%$ of clumpy, $36_{-6}^{+8}\%$ of smooth, and $35_{-7}^{+9}\%$ of intermediate galaxies are AGN-dominated. Given the uncertainty of the MEx diagram at z > 1 (e.g., Kewley et al. 2013; Newman et al. 2014; Juneau et al. 2014), these probabilities do not necessarily represent absolute AGN fractions, but they remain useful for comparing relative AGN fractions among the three morphology classes. The three AGN fractions are all consistent with one another, and the clumpy galaxies have only marginally (<1σ) more AGNs than smoother galaxies. In the next two subsections, we show that the higher line ratios in clumpy galaxies are likely an effect of high ionization in extended regions (due to shocks or dense star-forming clumps) rather than nuclear AGNs.

The traditional BPT and MEx methods use line ratios integrated over the entire galaxy, and thus may be diluted by star formation and/or affected by non-nuclear ionization that has nothing to do with AGN activity. In particular, the violent disk instabilities of clumpy galaxies may lead to high-velocity shocks or dense ${\rm H}\,{\scriptsize II}$ regions which can mimic AGN-like line ratios (e.g., Rich et al. 2011; Newman et al. 2014). For this reason, we use the spatial resolution of the WFC3 grism spectroscopy to go beyond integrated line ratios and investigate line ratio gradients, following Wright et al. (2010); Trump et al. (2011b). Spatially resolved line ratios can reveal if AGNs selected by integrated line ratios are the product of nuclear AGNs or extended phenomena (like shocks or high-ionization star formation).

The two-dimensional (2D) spectra of individual sources generally lack the signal to noise for well-measured spatially resolved line ratios, so we stack spectra of galaxies in each of the clumpy, smooth, and intermediate galaxy samples. Two stacks are constructed for each morphology class: one with all galaxies, and another using only galaxies classified as AGNs on the MEx diagram in Section 3.1. Centers of galaxies are defined by the SExtractor (Bertin & Arnouts 1996) coordinates in the F160W detection image, translated to a spectral trace in the dispersed G141 2D spectrum using well-calibrated polynomials from aXe which are typically accurate to ≲0.2 pixels. The image centroid and resultant spectral trace may not coincide with the brightest (continuum or emission line) flux of a galaxy, particularly for clumpy galaxies: we investigate centering on the brightest flux rather than image centroids in Section 4.1. Each galaxy spectrum is also normalized by its total ${[{\rm O}\,{\scriptsize {\rm III}}]}$ flux so that the stack is equal-weighted and not dominated by the most ${[{\rm O}\,{\scriptsize {\rm III}}]}$-luminous AGNs. (This normalization means that the stacked line ratios are slightly lower than the mean of the individual ratios.) The stacked 2D spectra of all galaxies in each morphology class are shown in Figure 8. It is immediately evident that the clumpy galaxies are typically larger than the intermediate or smooth galaxies: for a galaxy to be classified as clumpy, it must be large enough for the clumps to be resolved in the HST data. Still, the smooth and intermediate galaxies are not so small as to be unresolved, and they have enough signal beyond the central three pixels to have well-measured extended (non-nuclear) spectra. We return to a discussion of the different sizes of the clumpy and smooth galaxies in Section 4.2.

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We separately extract nuclear and extended one-dimensional (1D) spectra from the stacked data, shown in Figure 9. Here "nuclear" is defined as the central 3 pixels, corresponding to 018 across and a ∼1 kpc radius at 1.3 < z < 2.4. The "extended" spectra are extracted from pixels 3–6 on either side of the trace, translating to an annulus extending radially from ∼2–4 kpc. It is possible that some emission from the AGN narrow line region extends into the extended aperture (Hainline et al. 2013; van der Laan et al. 2013), and the ∼1 kpc nuclear region is also likely to include some galaxy starlight. Although our regions will not perfectly disentangle AGN and galaxy light, the nuclear region preferentially includes AGN light and the extended region includes more galaxy starlight. Thus the spatially resolved line ratios are likely to be significantly more sensitive than the integrated line ratios.

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The [O iii] and Hβ emission lines are measured from each nuclear and extended spectrum following the same method as in Section 2.2: three Gaussians were simultaneously fit to the continuum-subtracted spectra, with the [O iii]λ5007 flux given as 3/4 of the total [O iii]λ4959+5007 emission. Figure 10 shows the nuclear and extended ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratios for the stacks of all clumpy, smooth, and intermediate galaxies in the MEx diagram (using the median stellar mass of each sample with small offsets between the points). Figure 11 shows the nuclear and extended line ratios using the stacked spectra of MEx AGNs only. The nuclear and extended line ratio measurements for each stack are also presented in Table 2.

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In the stacks of all galaxies in Figure 10, the nuclear and extended spectra are nearly indistinguishable. This indicates that there is not a dominant AGN population in any of the morphology classes. Nuclear AGNs begin to marginally emerge in Figure 11 in the stacked spectra of MEx AGNs among smooth galaxies. This implies that AGN classification using the updated Juneau et al. (2014) MEx method is effective for smooth galaxies at z ∼ 2, with their stacked spectra indicating nuclear AGNs. The clumpy galaxies classified as MEx AGNs, however, have essentially no difference in nuclear and extended ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratios. The high ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratios observed in the integrated spectra of clumpy galaxies are probably caused by extended phenomena like shocks or high-ionization star formation, both of which are likely in dense star forming clumps (Kewley et al. 2013; Newman et al. 2014; Rich et al. 2014). Spatial line ratios indicate that clumpy galaxies may actually be less likely to host nuclear AGNs than smooth or intermediate galaxies. We further investigate the possibility of off-nuclear AGNs in Section 4.1.

X-rays tend to be the most efficient and least contaminated indicator of AGN activity, and so we also use the X-ray data to quantify the AGN fraction among clumpy, smooth, and intermediate morphology galaxies. All galaxies are matched to the Xue et al. (2011) 4 Ms Chandra catalog. In total, 5/44 clumpy, 4/41 smooth, and 2/35 intermediate galaxies have X-ray counterparts. X-ray detection is not sufficient for AGN classification, however, as luminous starburst (SFR ∼ 300 M_☉ yr⁻¹) galaxies can have enough X-ray binaries to exceed an integrated luminosity of L_X ∼ 10⁴² (Lehmer et al. 2010; Mineo et al. 2014). Xue et al. (2011) classify the GOODS-S X-ray sources into galaxies consistent with pure star formation or systems likely to be AGNs on the basis of their spectral shape, X-ray to optical flux ratio, and X-ray luminosity. These classifications reveal that 2/48 clumpy, 3/41 smooth, and 2/35 intermediate galaxies are likely to be X-ray AGNs. The detection fractions and full-band luminosities of the X-ray AGNs are broadly consistent across the morphology categories, ranging from 10⁴²–10⁴⁴ erg s⁻¹. X-ray data for the detected galaxies, as well as for the stacked non-detections (discussed below), are presented in Table 3.

Figure 12 presents the L_X–SFR relationship for X-ray detected sources, for both hard-band (2–8 keV) and soft-band (0.5–2 keV) luminosities. Also shown is the L_X–SFR relation for star-forming galaxies without AGNs, log (L_X) = [39.6 ± 0.4] + log (SFR) (Mineo et al. 2014), with L_X the full-band luminosity in erg s⁻¹ and SFR in M_☉ yr⁻¹. This relation is translated to the soft and hard bands by assuming a spectral index of Γ = 1.8: the resultant relation is consistent with the hard-band L_X–SFR/M_* relation of Lehmer et al. (2010). A few X-ray sources that are undetected in the hard band lie near the soft-band L_X–SFR relation and might not host AGNs, but most have sufficient X-ray luminosities to be robustly considered as having X-ray emission powered by an AGN.

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We also performed X-ray stacking of the three samples in the full band, soft band (0.5–2 keV), and hard band using the 4 Ms CDF-S data (Xue et al. 2011). X-ray detected galaxies and galaxies near any detected X-ray source (within twice the soft-band 90% encircled-energy aperture radius of the X-ray source) were excluded from the stacking. The final clumpy, smooth, and intermediate samples used in the stacking contain 40, 38, and 33 galaxies, respectively. We adopted the same stacking procedure as described in Section 3.1 of Luo et al. (2011). Briefly, we extracted total (source plus background) counts for each galaxy within a 3'' diameter circular aperture centered on its optical position. The corresponding background counts within this aperture were determined with a Monte Carlo approach which randomly (avoiding known X-ray sources) places 1000 apertures within a 1' radius circle of the optical position to measure the mean background. The total counts (S) and background counts (B) for the stacked sample were derived by summing the counts for individual sources. The net source counts are then given by (S − B), and the signal-to-noise ratio (S/N) is calculated as $(S-B)/\sqrt{B}$. A stacked signal is considered undetected if it has a binomial no-source probability of P_b > 0.01 (equivalent to S/N ≲ 2.6σ): for these sources we derive 90% confidence upper limits using the Bayesian method of Kraft et al. (1991). Aperture corrections were applied when converting the source count rates to fluxes and luminosities.

The stacked luminosities are shown with the median SFR of each subset in Figure 12. The small number of objects in each morphology subset means that none are well-detected in the hard band, and only the clumpy and smooth stacks are detected in the soft band. Due to these poor hard-band detections, the hardness ratios are unconstrained in all three stacks. The stacked X-ray luminosities (and upper limits) for all three samples lie only marginally above the L_X–SFR line for SF galaxies, indicating a weak or sub-dominant AGN contribution in the X-ray undetected galaxies. This is consistent with the location of most galaxies in the star-forming region of the MEx diagram (Figure 7), and with the lack of nuclear AGNs in the resolved line ratios among all galaxies (Figure 10). We also stack the MEx AGNs in each morphology class, but the numbers of objects are too small to make any meaningful conclusions.

Clumpy, smooth, and intermediate galaxies all have similar detected X-ray AGN fractions (∼5%) and stacked X-ray luminosities for undetected sources (log (L_X) ∼ 41.4). In agreement with the spatially resolved line ratios, the X-ray data show essentially no differences for clumpy, smooth, and intermediate morphology galaxies at z ∼ 2.

In Section 3.2, we argued that the high ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratio in the extended regions of clumpy galaxies indicates shocks or high-ionization H ii regions rather than AGN activity (see also Rich et al. 2011; Newman et al. 2014; Rich et al. 2014). However, it is instead possible that some clumpy galaxies host off-nuclear AGNs (e.g., Schawinski et al. 2011; K. Schawinski et al. 2014, in preparation). We test for the presence of off-nuclear AGNs by creating a 2D stack of clumpy galaxies classified as MEx-AGNs, centering on the ${[{\rm O}\,{\scriptsize {\rm III}}]}$ emission lines rather than the continuum trace. The brightest knot of ${[{\rm O}\,{\scriptsize {\rm III}}]}$ emission would be most likely to correspond to any off-nuclear AGNs.¹⁶ The "nuclear" region of the ${[{\rm O}\,{\scriptsize {\rm III}}]}$-centered stack corresponds to the brightest ${[{\rm O}\,{\scriptsize {\rm III}}]}$ knots rather than the galaxy center, and should therefore be where off-nuclear AGNs are most likely to reside.

Figure 13 compares the nuclear and extended ${[{\rm O}\,{\scriptsize {\rm III}}]}/{{\rm H}\beta}$ ratios for the continuum-centered stack with the ${[{\rm O}\,{\scriptsize {\rm III}}]}$-centered stack of clumpy galaxies. The right panel suggests that the brightest ${[{\rm O}\,{\scriptsize {\rm III}}]}$ knots are somewhat less likely to host AGNs than the galaxy centers. The lack of widespread off-nuclear AGNs is also supported by the X-ray data, which indicate that clumpy galaxies do not host a greater number of X-ray AGNs (whether nuclear or off-nuclear) than smoother mass-matched galaxies. We conclude that there is unlikely to be a large population of off-nuclear AGNs in clumpy galaxies misclassified by the spatially resolved line ratio method.

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At first glance, our z ∼ 1.85 result is in apparent contrast to the preference for AGNs in clumpy galaxies at z ∼ 0.7 observed by Bournaud et al. (2012). Our clumpy galaxy sample has very similar images and morphologies to theirs, as seen in a comparison of Figure 3 with Figure 4 of Bournaud et al. (2012). Although we study a much larger sample (three times more clumpy galaxies), Bournaud et al. (2012) performed a comprehensive bootstrap analysis which indicates that sample size is very unlikely to lead to the difference. Our studies differ greatly, however, in the comparison samples of smooth galaxies.

Bournaud et al. (2012) required that both their clumpy and smooth galaxy samples be extended disks. Meanwhile, we impose no requirements on morphology beyond the clumpiness classification, and Figure 14 demonstrates that our z ∼ 2 clumpy and smooth galaxies are quite different in size and Sérsic (1968) index. These quantities were measured using GALFIT (Peng et al. 2010) and presented by van der Wel et al. (2012). Clumpy galaxies are much more likely to be extended disks, with a median semi-major axis of 046 and 41/44 galaxies having disk-dominated Sérsic indices (n < 2.5). The smooth galaxies are still mostly disk-dominated, as 30/41 have n < 2.5, but they are significantly smaller (with a median semi-major axis of 020) and have higher Sérsic indices.

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It is interesting that so few smooth extended disks are observed in CANDELS and 3D-HST. The data are sensitive to the z ∼ 2 star-forming main sequence at M_*/M_☉ > 10^9.8 (Figure 6), and so if smooth extended disks exist they must be low-mass and/or weakly star-forming. Kassin et al. (2012) and Elmegreen & Elmegreen (2014) argue that ordered disks are rare in z > 1 galaxies of any mass, suggesting that the lack of smooth extended disks at z ∼ 2 is a consequence of galaxy evolution rather than selection effects. Regardless, the lack of smooth extended disks at z ∼ 2 means we cannot perform the same comparison between clumpy and smooth extended disks as Bournaud et al. (2012) at z ∼ 0.7. Instead, we conclude that clumpy extended galaxies have the same AGN fraction as more compact and higher-Sersic smooth galaxies matched in stellar mass.

Our results demonstrate that clumpy galaxies at z ∼ 2 are no more likely to host AGNs than are smooth galaxies of the same stellar mass and similar SFR. What does this indicate about AGN fueling modes at z ∼ 2?

Dekel & Burkert (2014) argue that compact star-forming galaxies (also called blue nuggets) might actually be constructed by a history of violent disk instabilities. Our smooth galaxies, which tend to be more compact and bulgy than the clumpy extended disks, have sizes and Sersic indices consistent with this category (see also D. Ceverino et al. 2014, in preparation). The observed similarity in AGN fraction between z ∼ 2 clumpy and smooth galaxies would then indicate that nuclear inflow onto the AGN must persist until after the galaxy becomes stable and the star-forming clumps are no longer visible. In this scenario, the violent disk instabilities are responsible for building a gas reservoir in the galaxy's center. Since the actual nuclear inflow onto the AGN persists into the smooth compact galaxy phase, it must not depend on violent instabilities in the larger disk. So while the gas reservoir is deposited by violent disk instabilities, the AGN fueling within ∼1 kpc must instead be driven by secular processes.

On the other hand, the disk-dominated nature of the smooth galaxies might imply that they are unlikely to have experienced violent mixing in the past from extreme disk instabilities (or major mergers). It is also not clear that the smooth galaxies are older than the clumpy galaxies, given their similar position in the SFR–M* plane (excepting the most massive galaxies: see Figure 6). This might imply that even the large-scale fueling occurs via secular processes, perhaps due to stochastic turbulence from the high gas fractions which are common in z ∼ 2 galaxies (Tacconi et al. 2010). Indeed, Hopkins et al. (2014) predict that this turbulence-driven stochastic fueling is the dominant mode of SMBH growth for z ∼ 2 galaxies with M_BH < 10⁷ M_☉ (or M_* < 10¹⁰ M_☉): the same mass range occupied by much of our sample. Assuming that the smooth and clumpy morphologies in our sample trace different fueling modes, then our data best support the scenario of Bellovary et al. (2013), where AGN growth depends not on fueling mode, but on gas fraction.