MODERATE-LUMINOSITY GROWING BLACK HOLES FROM 1.25 < z < 2.7: VARIED ACCRETION IN DISK-DOMINATED HOSTS

The Chandra Deep Field-South is one of the best-observed parts of the sky, with deep multi-wavelength coverage from both ground- and space-based observatories. In particular, the 4 Ms of combined X-ray observations within the field (Xue et al. 2011) allow for selection of AGNs at z ∼ 2 that is relatively unbiased with respect to obscuration. Examination of those AGNs and their hosts at rest-frame optical wavelengths is possible with the multi-epoch deep observations of the GOODS-South field (chosen to coincide with the CDF-S; see Giavalisco et al. 2004) within the CANDELS survey (Grogin et al. 2011). We match the X-ray sources to WFC3 sources using a maximum-likelihood method (Cappelluti et al. 2009; Cardamone et al. 2010) that considers both positional overlap and uncertainties as well as multi-wavelength source fluxes to determine the most probable optical match to each X-ray source.

We select AGNs within the Chandra–GOODS-S–CANDELS field according to the following criteria:

• 1.  
  Redshifts (compiled by Xue et al. 2011) within the range 1.25 < z < 2.67, so that the observed wavelength ranges spanned by the F125W and F160W WFC3 HST filters are in the rest-frame B band.
• 2.  
  Source-type identification as AGNs within the Xue et al. (2011) 4 Ms X-ray catalog. Briefly, AGNs are identified via X-ray luminosity, photon index, X-ray-to-optical flux ratio, X-ray excess over measured star formation, and/or optical spectroscopic features. The criteria are described further in Xue et al.
• 3.  
  Extended source detection within the WFC3 image with a signal-to-noise ratio of at least 5 per pixel to ensure robustness of morphological fitting.
• 4.  
  Extended source detections in at least five optical and infrared bands (including WFC3 JH from CANDELS as well as ACS BVIz and ground-based Ks from GOODS; details of GOODS observations are given in Tables 1 and 2 in Giavalisco et al. 2004), to facilitate accurate determination of stellar masses and rest-frame colors.

Of the 57 X-ray-selected AGNs in the sample using the above criteria, 26 of the redshifts are spectroscopic (Szokoly et al. 2004; Zheng et al. 2004; Mignoli et al. 2005; Vanzella et al. 2008; Popesso et al. 2009; Silverman et al. 2010) and 31 are photometric (Luo et al. 2010; Cardamone et al. 2010; Rafferty et al. 2011). Forty-one are considered luminous AGNs by Xue et al. owing to their having absorption-corrected, rest-frame 0.5–8 keV luminosities L_X ⩾ 3 × 10⁴² erg s⁻¹. An additional 14 sources have 10⁴² ⩽ L_X < 3 × 10⁴² erg s⁻¹, and the remaining two have luminosities of 9.1 and 9.5 × 10⁴¹ erg s⁻¹. The median and mean X-ray luminosities of the sample are 4.4 and 7.3 × 10⁴² erg s⁻¹, respectively, and the most luminous X-ray AGN in the sample has L_X = 2.6 × 10⁴⁴ erg s⁻¹, consistent with expected detections within the volume of GOODS-S based on the AGN luminosity function (Croom et al. 2004).

The CANDELS survey (Grogin et al. 2011) includes several deep and wide fields on the sky with both the WFC3 and ACS cameras on HST. We perform morphological fits on the publicly available co-added six-epoch images in both the F125W and F160W bands, which were drizzled to a resolution of 006 per pixel. For details of the image processing, see Koekemoer et al. (2011).

Morphological decomposition of two-dimensional AGN+host galaxy images requires accurate determination of the point-spread function (PSF). We determine the PSF of the F125W and F160W CANDELS images using the PSF-modeling routines in the IRAF package daophot. This method balances the noise-free attributes of a simulated PSF model with the detailed particulars of the actual PSF of multi-drizzled, multi-epoch data. We verified that the WFC3 PSF is very stable across the deep mosaic in the GOODS-S field, so we determine a single PSF for each band and use it in the morphological analysis of each of the sources.

We perform two-dimensional parametric morphological fitting on the F125W and F160W images for the 57 sources using GALFIT (Peng et al. 2002), which is very reliable for recovering both normal galaxy morphologies and AGN-host decomposition (see Häussler et al. 2007; Simmons & Urry 2008; Pierce et al. 2010a, for relevant simulations).

Our detailed fitting procedure is similar to that performed in previous simulations and studies of AGN host morphologies (Simmons & Urry 2008; Simmons et al. 2011). We determine initial guesses for fit parameters such as total source magnitude, half-light radius, axis ratio, position angle and centroid position using SExtractor (Bertin & Arnouts 1996). The value of the sky background varies slightly across the CANDELS mosaic, so we fix the SExtractor-determined value for each source and each iteration of the morphological fitting in order to avoid the confusion of sky background and extended source light that can ensue when the sky background is allowed to vary along with the other fit components.

We fit each galaxy with two models in each band: (1) a host galaxy modeled by a Sérsic profile (Sérsic 1968), and (2) a host galaxy with a central point source. We determine the final fit parameters via an iterative process that initially fits only the central portion of the AGN+host, to find the best-fit centroid positions of each fit component. Those positions are then held fixed in successive iterations, which zoom outward to eventually encompass a large enough image region such that the extended portions of the central source are well sampled. Where necessary, we fit nearby, bright, and/or extended companions in order to simultaneously model their extended light distributions. Companion fitting (and masking of fainter, more compact companions further from the central source) ensures a more realistic fit to the central source. The first three fits to each source are performed with the use of a customized adaptive batch-fitting code. Each source is then followed up individually to ensure the true minimum reduced χ²_ν value within the parameter space is achieved.

For each source and each fit (Sérsic only and Sérsic+Point Source), we perform one final iteration where every parameter (with the exception of the sky background) is allowed to vary. This final iteration ensures that GALFIT has found the true best fit and also allows for an estimate of the computational uncertainties for each parameter, including the centroid positions of each component. For all sources, the differences between the final fit parameters and those of the penultimate iteration are well within the reported parameter uncertainties; thus, we are confident that we have found the true best-fit parameters for each source and fit type. Typically, an AGN+host galaxy in the sample requires six to eight total iterations for a Sérsic+PSF fit, with one to four fitted companions. Some of the sources require additional iterations, usually due to the presence of multiple (occasionally more than four) bright, nearby companions.

The final step in the determination of AGN+host morphologies involves comparing the Sérsic-only and the Sérsic+Point Source fits for each of the 57 sources in order to determine whether we significantly detect a central point source. Detailed simulations of the recovery of central point sources within ACS data (Simmons & Urry 2008) suggest that failed detections of intrinsically detectable point sources (i.e., false negatives) are rare, but spurious point-source detection (i.e., false positive) rates are strongly dependent on host morphology, ranging from ∼1% in a sample of pure disk galaxies to ∼25% for a sample of pure bulges. When GALFIT does not detect a central point source, therefore, this is most likely a robust indicator that any light from a central AGN is below the detection threshold of the image. Detection of a central point source in a Sérsic+Point Source fit, on the other hand, is not a guarantee of its authenticity.

We therefore assess the robustness of each point-source detection based on a number of criteria. First, if an F-test indicates that the addition of a point source significantly improves the χ²_ν goodness-of-fit parameter, we consider the point source genuine. Alternatively, we consider a point source genuine if the Sérsic-only fit converges to an unrealistically high value for the Sérsic index n (generally galaxies have n ≲ 10; e.g., Caon et al. 1993). Last, we examine the central portion of the fit residuals. We consider a point source genuine if the residual of the Sérsic-only fit shows obvious signs of additional light from an unresolved source (however, in practice at least one of the other two criteria also apply if this last criterion is true).

Figure 1 shows a selection of fitted AGN+hosts; we present the full catalog of best-fit morphological parameters for each source in Table 1. The uncertainties reported in Table 1 are determined by combining in quadrature the reported computational uncertainties from GALFIT and the uncertainties in morphological parameter recovery determined from the simulation of over 50,000 AGN host galaxies by Simmons & Urry (2008). The latter typically dominate the overall uncertainty in a morphological fit.

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Just under half (25) of the host galaxies in this sample are best described as single-component galaxies with smooth residuals after subtracting a single-component host fit. Fourteen have clumpy morphologies, with multiple offset components either embedded in a larger component or very closely separated. Eighteen host galaxies (≈32%) show signs of asymmetric features or tidal tails in the images and/or fit residuals; 8 of these appear to be involved in major mergers, consistent with an independent assessment of an overlapping sample using visual morphologies (Kocevski et al. 2012).

Using the F-test to assess the significance of improvements to the fit with the addition of a central point source, we find that 90% of AGN+hosts have point source detections with at least 3σ significance. The majority are at least 5σ point-source detections. We quote point-source-subtracted host morphologies for the 51 sources that have a point source at a minimum significance level of 3σ; for the remaining six sources we quote the morphology from the Sérsic-only fit. As expected, for those sources where the addition of a point source was not significant, the host morphology does not significantly change between the Sérsic only and the Sérsic + point source fit.

We show the fitted Sérsic indices for the AGN host galaxies in Figure 2. Morphologies of the hosts, or (for the clumpy hosts) of the component within the host associated with the nuclear source, are typically disky. Just over half the sample have n < 1.5 (29 of 57 hosts), an unambiguously disk-dominated morphology. An additional 15 have 1.5 ⩽ n < 3, which is consistent with intermediate morphologies (bulge-to-total ratios between 20% and 65%). Indeed, Simmons & Urry (2008) have shown that even galaxies fit with n = 4 can have a significant disk component (up to 45%). Five sources have 3 < n < 4, and eight have n > 4. The overall sample can therefore be characterized as having a mix of morphological types, but disks are present in roughly three-quarters of the sample, and ∼50% of hosts are consistent with having a bulge fraction of less than 20%. (In fact, 21 of the 29 disk-dominated sources have n ⩽ 1, consistent with a bulge-to-total ratio of ⩽10%.)

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The redshift range over which the F125W and F160W WFC3 filters sample the rest-frame B band spans approximately 2.6 Gyr of cosmic time. Splitting the sample into two sub-samples of Δt ≈ 1.3 Gyr each reveals no difference in the distribution of morphologies between the two bins, according to a Kolmogorov–Smirnov (K-S) test.

We determine stellar masses of the host galaxies using the multi-wavelength GOODS+CANDELS BVIzJHKs spectral energy distributions (SEDs). We minimize the effect of the AGN on the host-galaxy SED fitting by first subtracting the point-source contribution to the flux in each HST band before fitting the SEDs with the stellar population synthesis templates of Maraston (2005) using FAST (Kriek et al. 2009).

Subtracting the point sources in the BVIzJH bands generally has only a small effect on the recovered galaxy masses and colors due to the fact that the host galaxies dominate the observed SEDs: the median L_host = 10 × L_AGN in JH. However, the effect is systematic: because using removing the AGN flux lowers the source flux used to calculate mass, the recovered stellar mass is lower than it would be were the presence of the AGN not accounted for. Additionally, for a sample such as this, where there is little bias against obscured AGNs due to hard X-ray selection, but unobscured AGNs are selected against by the requirement that the host galaxy morphology be recoverable, most nuclear point sources are reddened. Removing the AGN flux from the SED therefore tends to recover a slightly bluer color than would be calculated if the effect of the AGN were neglected. This is likewise a small but systematic effect.

Once the point-source SED is subtracted from the HST bands, extrapolating it to remove an estimated contribution to the Ks-band flux makes no difference within the uncertainties. We therefore subtract the nuclear point-source contribution to the SED in the HST bands where we have enough angular resolution to confidently separate AGN from host galaxy, and refrain from unnecessary extrapolation of the SED to the ground-based Ks band.

To test the dependence of recovered stellar masses on the choice of template, we compared stellar masses calculated using the templates of Bruzual & Charlot (2003) to the masses calculated from Maraston (2005) templates; we found that the recovered stellar mass is not strongly dependent on the choice of template set. The distribution of derived masses is shown in Figure 3. The minimum and maximum masses of the sample are 2 × 10⁸ and 6 × 10¹¹ M_☉, respectively; the average and median masses are 1.7 × 10¹⁰ and 2.3 × 10¹⁰ M_☉, respectively. 70% of the sample have M_* > 10¹⁰ M_☉, which is expected since AGNs are typically found in massive hosts (Cardamone et al. 2010); this probably reflects a selection effect missing slow-growing black holes in low-mass galaxies rather than an intrinsic distribution (Aird et al. 2012). The average uncertainty in the mass is 0.8 dex.

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We visually inspected each of the best-fit templates from FAST and verified the goodness-of-fit. We use the best-fit templates to determine the rest-frame (U − V) colors of each host galaxy, following Brammer et al. (2009) in assuming a Calzetti et al. (2000) dust law to correct for dust, such that (U − V)_corr = (U − V) − ΔA_V, where ΔA_V = 0.47A_V. We show the color–mass diagrams for the AGN host sample in Figure 4, compared to inactive galaxies with the same redshifts (from the NEWFIRM medium-band survey; Whitaker et al. 2011). We separate the sample into two redshift bins divided at z = 1.76, so that each bin represents a time interval of Δt ≈ 1.3 Gyr.

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A K-S test indicates no significant difference between the stellar mass distributions of the AGN hosts in the two redshift bins. The uncorrected U − V colors between the bins are inconsistent with being drawn from the same parent sample at the 97% level, but the significance is reduced to 75% (∼1σ) once the dust correction is applied: correcting for dust shifts more galaxies into the blue cloud in the lower redshift bin than in the higher. A detailed comparison of the colors of morphological sub-samples in different redshift bins is highly uncertain due to small numbers in each sub-sample. However, we observe intrinsically red disk-dominated hosts in each bin (at 85% confidence given the uncertainties), as well as blue strong-bulge hosts (99% confidence).

Note that, although the stellar mass determination is unaffected (within the uncertainties) by the choice of model templates, the value of the dust correction A_V can vary significantly depending on the choice of template. We include differences in each source's dust-correction between the Bruzual & Charlot (2003) and Maraston (2005) templates in the uncertainties shown in Figure 4, noting that the choice of template does not change the overall result.

Black hole mass, one of the fundamental properties of an AGN, can be measured directly only for very nearby sources. If a black hole is unobscured, measurements of broad spectral lines from the region near the black hole allow for calculations of central masses via the virial method. However, this is not generally possible for more obscured sources like those that dominate the present sample: only one AGN in this sample has a measurable broad line (see below), so this method is not feasible for the entire sample. Instead, we use well-characterized relations between host galaxy properties and black hole masses, which allow estimates of black hole masses out to high redshift as long as evolutionary corrections are considered.

Locally, black hole mass correlates with the velocity dispersion (e.g., Ferrarese & Merritt 2000; Gebhardt et al. 2000), mass (e.g., Magorrian et al. 1998; Häring & Rix 2004) and optical luminosity (e.g., Marconi & Hunt 2003; Ferrarese & Ford 2005; Graham 2007) of the stellar bulge. These relations may evolve as a result of multiple effects (Treu et al. 2004; Borys et al. 2005; Woo et al. 2005, 2008; Peng et al. 2006; Alexander et al. 2008; Jahnke et al. 2009; Decarli et al. 2010; Merloni et al. 2010; Bluck et al. 2011). It appears that bulge stellar populations are younger at earlier times, and it also appears that bulge growth may trail behind black hole growth at early times. However, the evolutionary corrections are highly uncertain. Recent work (Cisternas et al. 2011; Merloni et al. 2010) suggests that the relationship between the central black hole mass and the total stellar mass of the host galaxy does not evolve to z ∼ 2. Other groups find that the relation evolves by a factor of ∼2–4 to z ∼ 2 (Trakhtenbrot & Netzer 2010; Bennert et al. 2011b), but the highest-redshift measurement to date of a single black hole with spatially resolved spectroscopy (Inskip et al. 2011) is consistent with the local black hole–galaxy relation.

There are therefore many sources of uncertainty in the estimation of z ∼ 2 black hole masses using galaxy–black hole correlations. In order to accurately characterize the uncertainties of our estimated black hole masses, we calculate black hole masses from host galaxy stellar masses via Monte Carlo simulations that account for the uncertainties in each quantity involved in the calculation—stellar mass, redshift, and a possible evolutionary correction of up to a factor of three—as well as the scatter in the black hole mass-host stellar mass correlation of Häring & Rix (2004). We simulate 10⁵ observations via Gaussian-random sampling within the uncertainties for each source and report the median black hole masses and 1σ widths of the distributions of each source as our uncertainties.

Table 1 gives the black hole mass estimates for each of our sources. We find that the black hole masses span a large range, from 2⁺¹⁹_{− 1.5} × 10⁵ M_☉ to 2⁺²¹_{− 1.8} × 10⁹ M_☉, with median and mean masses of 4 × 10⁷ M_☉ and 3 × 10⁷ M_☉, respectively. Typical uncertainties are −0.7 and +1.0 dex, with asymmetries in the uncertainties primarily due to uncertainties in the host stellar masses, which are also calculated by Monte Carlo methods (Kriek et al. 2009). As a sanity check, we determined the black hole mass of X577 using the FWHM of the Mg ii broad line and the continuum luminosity at 3000 Å (McLure & Dunlop 2004). The latter is uncertain in the spectrum (Szokoly et al. 2004), but the calculated mass of 1.0^+0.8_{− 0.3} × 10⁸ M_☉ is fully consistent with that determined using the Monte Carlo method described above.

In addition to black hole masses, bolometric (total) luminosities are useful quantities because they allow for an estimate of the mass accretion rate onto the black hole (modulo the radiative efficiency). Simmons et al. (2011) have shown that the model-dependent bolometric corrections to the hard X-ray luminosity of Treister et al. (2009) are in very good agreement with bolometric luminosities recovered for obscured AGNs by leveraging the observed point-source luminosities to extract the SEDs from the far-infrared to X-ray of each AGN. We therefore use the absorption-corrected X-ray luminosity of each source, along with the bolometric corrections of Treister et al. (2009), to estimate the bolometric luminosities of each source. Given the X-ray luminosities in the sample, the bolometric correction ranges from 25 to 76.

With estimates of both bolometric luminosity and black hole mass, we explore the growth rates of the black holes in the sample in Figure 5. The growth rates of moderate-luminosity AGNs at z ∼ 2 span several orders of magnitude, from super-Eddington accretion to 10⁻³ L_Edd, with average and median L/L_Edd values of 0.06 and 0.05, respectively. One-quarter of the sample (19 of 57 AGNs) have L/L_Edd < 0.01; 21 AGNs have 0.01 ⩽ L/L_Edd ⩽ 0.1. The sample cannot therefore be characterized by a single growth rate/Eddington ratio, but at least half of the sample are growing at less than 10% of the Eddington (maximum) rate (96% confidence level).

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