Super-Eddington Accretion in the WISE-selected Extremely Luminous Infrared Galaxy W2246−0526

At z = 4.601, the Mg ii 2799 Å line of W2246−0526 falls at 1.567 μm in the H band. W2246−0526 was observed with the Keck I telescope on UT 2016 October 21 in the first half of the night using OSIRIS (Larkin et al. 2006) while the originally proposed instrument (MOSFIRE) was being repaired. The weather was clear and the seeing was ∼07 over the observation. The spectra were taken with the Hbb filter covering 1.473–1.803 μm at 0.5 nm channel⁻¹ resolution. With the 4 × 4 dithering used, the 16 × 64 field of view of the integrated field unit covered 20 × 109 with 01 pixel⁻¹ at a position angle of 337° centered on W2246−0526. The final spectral resolution of ∼2.5 spaxels yielded R = λ/Δλ ≲ 3400. Atmospheric wavefront errors were partially corrected with Laser Guild Star Adaptive Optics (LGS-AO) and an R = 18.3 tip-tilt star 268 to the southwest of W2246−0526. The integration time for each individual frame was 900 s, and a total of 4 hr (16 frames) of on-source data was collected.

The OSIRIS data were reduced with the OSIRIS data-reduction pipeline v4.0.0. A custom procedure was used to remove the sky emission using pixels near the science target and frames adjacent in time. About 6% of the data at wavelengths with substantial sky line residual present were clipped. The telluric correction was applied using both the G2V star HD 216516 and the A0V star HD 219833. The flux calibration was done using the G2V star. Including the uncertainties due to calibrator flux, aperture correction, and Strehl ratio, the overall uncertainty in the calibrated fluxes is estimated to be ∼20%. The wavelength was calibrated to values in vacuum. The final mosaic data cube was produced using the LGS offsets between frames. Using the 2MASS point source catalog (Skrutskie et al. 2006) and the WFC3 image in F160W (Díaz-Santos et al. 2016) from the Hubble Space Telescope (HST), we registered the final science data cube with the uncertainty in absolute astrometry estimated to be <01.

Due to the LGS-AO, the spatial resolution was sufficient to resolve the continuum profile of W2246−0526, with an estimated extent of 036 × 029 at PA = 155°, consistent with the HST observations (Díaz-Santos et al. 2016). The Mg ii emission line of W2246−0526 was extracted from the OSIRIS data cube using a 03 aperture. An aperture correction was applied to the flux scale of the Mg ii spectrum to match the photometry from the HST F160W image. The extracted and flux-corrected spectrum is shown in Figure 1.

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For comparison to the SMBH mass estimate from Mg ii, we analyze an optical spectrum of the C iv line. To calculate the Eddington ratio, we estimate the luminosity using the observed spectral energy distribution (SED) of W2246−0526 from optical to submillimeter wavelengths. The flux densities and the references are listed in Table 1. These observations are described below.

2.2.1. Keck LRIS Observation of the C iv Line

2.2.2. SCUBA2 450 $\mu m$ Observation

SCUBA2 observations with the James Clerk Maxwell telescope (JCMT), as reported by Jones et al. (2014), were obtained on UT 2012 May 23 and 26. During the 450 μm observations, the CSO 225 GHz sky opacity was τ₂₂₅ ∼ 0.05, and the corresponding optical depth at 450 μm was τ_450μm ∼ 1. However, the two sets of observations identify a point source with a consistent flux density (within 1σ), slightly offset to the southeast from the WISE infrared position of W2246−0526. The position offset (24 ± 22) is consistent with the pointing uncertainty during the observation. The total time per source was 120 minutes using the CV DAISY mode, providing deep coverage in the central 3' diameter region. The final map that combines both sets of observations is shown in the left panel of Figure 2.

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2.2.3. Herschel Observations

The SED of W2246−0526 is shown in Figure 3, based on the updated photometric data listed in Table 1. Unlike optical QSOs in which a large fraction of energy escapes at UV wavelengths, most of the energy from W2246−0526 is seen at rest-frame infrared wavelengths (>1 μm). The broad Mg ii and C iv emission lines observed in W2246−0526 provide direct evidence for the presence of an AGN, and the infrared emission most plausibly arises from hot dust obscuring the AGN. The rest-frame UV and optical continuum emission, which is assumed to be primarily from the host galaxy of the obscured AGN, contributes ≲1% of the total luminosity. Like other Hot DOGs, the infrared SED of W2246−0526 shows this plateau but, interestingly, also shows a dip with respect to other Hot DOGs at rest-frame ∼12.5 μm (70 μm in the observed frame). This prompts us to suggest that silicate absorption may be affecting the SED.

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At z = 4.601, the broad 9.7 μm silicate absorption feature overlaps with the 60–85 μm bandpass of the PACS 70 μm filter and can account for the dip in the SED if the strength of the absorption in W2246−0526 is comparable to that in the heavily enshrouded nucleus of NGC 4418 (Roche et al. 1986; Spoon et al. 2001), the ultraluminous infrared galaxy Arp 220 (Polletta et al. 2007), or the hyperluminous infrared galaxy IRAS 08572+3915 (Spoon et al. 2007; Vega et al. 2008; Efstathiou et al. 2014). In Figure 3, we plot a template of the silicate absorption in NGC 4418 scaled to match the observed 70 μm photometry (for clarity we omit showing the relatively weak 9.66 μm H₂ 0–0 S(3) emission line).

We find the bolometric luminosity of W2246−0526 is L_bol = 3.6 ± 0.3 × 10¹⁴ L_☉, using the observed flux density measurements listed in Table 1. This estimate follows the methodology of Tsai et al. (2015) by integrating a power law interpolated between photometric data. We assume that essentially all of this luminosity comes from a quasar shrouded within a dust cocoon.

Hot dust emission dominates the energy output, as indicated by the SED. Because of the high luminosity, the dust sublimation radius is ∼15 pc for W2246−0526 (Barvainis 1987; Tsai et al. 2015), substantially larger than the radius of the broad line region (∼1.3 pc, based on Bentz et al. 2009). Thus the thermal dust emission cannot vary dramatically within the light-crossing rest-frame timescale of ∼50 years, or ∼280 years in the observed frame. This timescale is even longer for the dust emission at the longer wavelengths of the SED plateau. Therefore we do not anticipate observable variability in the bolometric luminosity of W2246−0526.

The observed Mg ii 2799 Å emission line and the line model are shown in Figure 1, which covers the spectrum at rest-frame wavelengths between 2630 Å and 3220 Å. The signal-to-noise ratio of the continuum and the Mg ii line (within FWHM from the line center) are 1.4 and 7.7 per spectral element (0.82 Å, rest), respectively.

The Mg ii doublet line profile was fit after modeling the blended Fe ii line complex and a power-law continuum. The profile of the Fe ii complex used templates from Tsuzuki et al. (2006). Least-squares model fitting was done using the Levenberg–Marquardt algorithm as implemented in IDL MPFIT (Markwardt 2009). Excluding the Mg ii region, we stepped through a grid of Fe ii widths with FWHM = 0 to 18,000 km s⁻¹ and a 600 km s⁻¹ step size, finding the best-fit continuum (given in the Figure 1 caption) and Fe ii model strength. We then fit the residual with a single Gaussian model for the Mg ii line, iterating up to 20 times until the parameters stay unchanged to floating-point precision.

Although the signal-to-noise ratios are not high, they do not significantly affect the reliability for the line profile measurements, because of the broad line width. The best-fit model yields a Gaussian with an FWHM of 3300 ± 600 km s⁻¹ and a blueshifted velocity offset of Δv = 1600 ± 300 km s⁻¹ with respect to the [C ii] redshift (Díaz-Santos et al. 2016).

At z = 4.601, the C iv line shifts to ∼8674 Å. As noted in Díaz-Santos et al. (2018), the C iv line in W2246−0526 is highly asymmetric, broad, and significantly blueshifted relative to this ALMA-derived [C ii] redshift. Following an approach similar to that used by Shen et al. (2008, 2011) and Jun et al. (2017), we model the C iv line of W2246−0526 with two components, as shown in Figure 4. The signal-to-noise ratios of the continuum and the C iv line are 4.2 and 13.4 per spectral element (2.1 Å, rest), respectively.

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As we did for Mg ii, we first solved for a power-law continuum (given in the Figure 4 caption) and the Fe ii line complex (using the template from Vestergaard & Wilkes 2001), as well as the He ii–1640 Å line. The strength of the Fe ii complex was matched to that of the Fe ii around the Mg ii region using overlapping wavelengths in the templates, and the Fe ii line widths were set to be identical for the Mg ii and C iv regions.

The narrower Gaussian component has an FWHM = 1600 ± 140 km s⁻¹, blueshifted by 3000 ± 80 km s⁻¹ with respect to the system redshift, while the broader component has FWHM = 9000 ± 140 km s⁻¹ and is blueshifted by 3420 ± 70 km s⁻¹. The composite double-Gaussian profile has FWHM = 5900 ± 100 km s⁻¹ and a blueshift of 3300 ± 70 km s⁻¹. This blueshift of the C iv line profile in W2246−0526 is significantly higher than the median blueshift observed in SDSS QSOs (median of 890 km s⁻¹ for 492 quasars at 4.5 < z < 4.7; Shen et al. 2011) and is more comparable to the median blueshift of 2520 km s⁻¹ for nine quasars at z ≳ 6.4 that have C iv emission line measurements (Mazzucchelli et al. 2017).

Masses of the SMBH in AGNs are usually determined from the measurements of broad emission lines, assuming virialized gas motion. This approach was established via variability monitoring (reverberation mapping; see, e.g., Peterson 1993) and subsequently calibrated to single-epoch measurements of the Hβ line width and 5100 Å continuum (e.g., Wandel et al. 1999; Kaspi et al. 2000; Vestergaard 2002) and extended to other line widths. For objects at z > 1, the Hβ line is redshifted into the infrared, stimulating the use of the broad Mg ii line from optical spectroscopy for SMBH mass determination (McLure & Jarvis 2002; Onken & Kollmeier 2008; Trakhtenbrot & Netzer 2012; Marziani et al. 2013). Advances in near-IR instrumentation have made near-IR spectroscopy of distant objects feasible, enabling the Balmer lines to be used for SMBH measurement to z ∼ 2.5–3.5 (e.g., Wu et al. 2018). At z > 3.5, the Mg ii line is also observed at >1 μm, and Mg ii is usually used for black hole mass (M_BH) measurements of objects at the highest redshifts (Wu et al. 2015; Bañados et al. 2018). The calibration of Mg ii-determined SMBH masses with respect to those from Hβ has been established (McLure & Dunlop 2004; Wang et al. 2009; Shen et al. 2011; Jun et al. 2015; Suh et al. 2015). In this paper, we adopt the Mg ii-based SMBH mass formulation from Equation (10) of Wang et al. (2009):

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right) & = & (7.13\pm 0.27)+0.5\,\mathrm{log}\left(\displaystyle \frac{{L}_{3000}}{{10}^{44}\,\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)\\ & & +\,(1.51\pm 0.49)\mathrm{log}\left(\displaystyle \frac{{\mathrm{FWHM}}_{\mathrm{Mg}\mathrm{II}}}{1000\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right),\end{array}\end{eqnarray} \tag{ 1 }$$

where L₃₀₀₀ is the monochromatic luminosity at rest-frame 3000 Å, and FWHM_{Mg II} is the FWHM of the Mg ii line profile (given in Section 3.2).

Because of the high extinction in W2246−0526, estimates of L₃₀₀₀ from the rest-UV continuum are uncertain. Instead, we use L₃₀₀₀ ∼ 0.19 × L_bol based on the empirical unobscured AGN SED model of Richards et al. (2006). For L_bol = 3.6 × 10¹⁴ L_☉, L₃₀₀₀ = 2.6 × 10⁴⁷ erg s⁻¹. The observed rest-frame 3000 Å continuum flux in W2246−0526 is only about 0.02 of the anticipated value from this template. With the Mg ii FWHM of 3300 ± 600 km s⁻¹, this yields log(M_BH/M_☉) = 9.6 ± 0.4. The error range includes the 1σ systematic uncertainties from Equation (1) and from the Mg ii profile fitting. The statistical uncertainty of M_BH due to the Mg ii line width uncertainty is 0.05 dex.

The Richards et al. (2006) SED model assumes the emission from a quasar is isotropic. However, the unobscured quasars used to construct the SED presumably have a surrounding dusty torus with a low inclination and a covering factor that intercepts and reprocesses some of the quasar emission so that it appears again in the IR. Thus the L_bol from the SED model would be overestimated by (1 + CF_u), where CF_u is the covering factor for the unobscured quasars used in Richards et al. (2006), and L₃₀₀₀ would represent a larger portion of the true L_bol. For W2246−0526, which has a well-determined L_bol, this suggests using a ratio of L₃₀₀₀/L_bol, which is (1 + CF_u) larger. The covering factor cannot be higher than 1 (especially for an unobscured quasar sample), so using Equation (1), this correction would increase log(M_BH/M_☉) by <0.15. Both of these terms are smaller than other estimates of the overall systematic uncertainty, which are up to 0.3 dex (Denney et al. 2009; Wang et al. 2009; Jun et al. 2015).

The C iv line profiles of AGNs often show an enhanced blue wing, significantly different from their Hβ line profiles. This highlights the issue of the virial assumption for C iv and results in a large and biased offset when comparing C iv-based M_BH estimates to those based on Hβ and Mg ii (Netzer et al. 2007; Shen et al. 2011). In addition, the broad C iv 1549 Å feature is often substantially blueshifted with respect to the system rest frame (e.g., Richards et al. 2002), especially for high-luminosity objects (Baskin & Laor 2005). The blueshift is usually attributed to the wind component of the broad line region, or outflow (Gaskell 1982; Murray & Chiang 1997; Leighly 2004). Nevertheless, because of the accessibility of the C iv line from the ground for the quasars over a large range of redshift (1.3 ≲ z ≲ 5), efforts have been made to calibrate C iv-based M_BH estimates to Hβ-based values in Type 1 AGNs (Vestergaard & Peterson 2006; Assef et al. 2011; Shen et al. 2011; Denney 2012; Denney et al. 2013; Runnoe et al. 2013; Park et al. 2017), although C iv is not considered as reliable as Mg ii (Fine et al. 2010; Jun et al. 2015; Mejía-Restrepo et al. 2016). Motivated by the significance of the C iv asymmetry in a principal component analysis of AGNs (Sulentic et al. 2007), a simple correction to the C iv-based M_BH estimate has recently been suggested (Brotherton et al. 2015; Coatman et al. 2016, 2017; Jun et al. 2017). This correction calibrates the FWHM of the C iv line to the expected virial C iv FWHM from the Balmer line widths using the C iv blueshift.

As noted in Section 3.3, the C iv line in W2246−0526 is highly asymmetric, broad, and significantly blueshifted relative to the [C ii] redshift. Using the composite Gaussian model and adopting the correction of Coatman et al. (2017),

$$\begin{eqnarray}&&\begin{array}{l}{\mathrm{FWHM}}_{{\rm{C}}\,\mathrm{IV}}^{\mathrm{Corr}.}\\ \quad =\,\displaystyle \frac{{\mathrm{FWHM}}_{\ {\rm{C}}\,\mathrm{IV}}^{\mathrm{Measured}}}{\left(0.36,\pm ,0.03,),\left(\tfrac{{\rm{C}}\,{\mathrm{IV}}_{\mathrm{blueshift}}}{{10}^{3}\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right),+,(,0.61,\pm ,0.04\right)},\end{array}\end{eqnarray} \tag{ 2 }$$

we obtain a corrected FWHM for the broad C iv component of FWHM_{C IV}^Corr. = 3300 ± 400 km s⁻¹, which is a factor of 1.8 smaller than the FWHM derived from our two-component analysis.

To estimate the black hole mass, we adopt the methodology of Coatman et al. (2017):

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right) & = & 6.71+2\,\mathrm{log}\left(\displaystyle \frac{{\mathrm{FWHM}}_{{\rm{C}}\,\mathrm{IV}}^{\mathrm{Corr}.}}{{10}^{3}\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)\\ & & +\,0.53\,\mathrm{log}\left(\displaystyle \frac{{L}_{1350}}{{10}^{44}\,\mathrm{erg}\,{{\rm{s}}}^{-1}}\right).\end{array}\end{eqnarray} \tag{ 3 }$$

Here, L₁₃₅₀ is the monochromatic luminosity at 1350 Å and is estimated to be L₁₃₅₀ ∼ 0.26 × L_bol = 3.6 × 10⁴⁷ erg s⁻¹ using the AGN template of Richards et al. (2006).

Using the corrected value for the broad C iv component, this yields log(M_BH/M_☉) = 9.6 ± 0.4 including systematic uncertainty, which is nearly identical to the M_BH estimated using the Mg ii line. The agreement of the M_BH estimate using the C iv line profile with that from the Mg ii line measurement may be coincidental. It has been argued that a large component of the broad C iv emission line is observed to not reverberate for nearby AGNs, based on reverberation mapping studies (e.g., Denney 2012).

From a sample of five Hot DOGs with M_BH measurements, Wu et al. (2018) found that the ratio of M_BH to the stellar mass in the spheroidal component of the host galaxy (M_BH–M_sph) in these systems is closer to the M_BH–M_sph relation seen in local active galaxies (Bennert et al. 2011) than are the ratios seen in z ∼ 1.3 quasars.

We estimate the bulge mass in W2246−0526 from K and 4.5 μm photometry using the synthesized elliptical galaxy SED template from the GRASIL code (Silva et al. 1998) to represent the spheroidal component, omitting the 3.6 μm data point, which may be significantly elevated by the Hα emission line (see Figure 3). In Figure 3, the brown solid line shows the SED of an elliptical galaxy at an age of 1.3 Gyr with M_sph = 1.1 × 10¹² M_☉. This can be considered as an upper limit of the bulge mass of W2246−0526. This value is similar to the log(M_sph/M_☉) = 11.9 value expected from the local M_BH–M_sph relation (Bennert et al. 2011):

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot }) & = & -3.34\pm 1.91\\ & & +(1.09\pm 0.18)\times \mathrm{log}({M}_{\mathrm{sph}}/{M}_{\odot }).\end{array}\end{eqnarray} \tag{ 4 }$$

This suggests that W2246−0526 has an M_BH–M_sph relation similar to that of the Hot DOGs shown in Figure 9 of Wu et al. (2018).

In Wu et al. (2018), we argue that Hot DOGs are on the high-luminosity tail for a given M_BH with respect to SDSS QSOs because they achieve the highest accretion rates, implying that they are accreting material at the highest rates possible. To illustrate this, in Figure 5, we plot Eddington ratio (λ_Edd ≡ L_AGN/L_Edd) versus M_BH. With log(M_BH/M_☉) = 9.6 ± 0.4 and log(L_bol/L_☉) = 14.6, the Eddington ratio of W2246−0526 is ${\lambda }_{\mathrm{Edd}}={2.8}_{-0.7}^{+0.9}$ (statistical uncertainty), the highest of all the Hot DOGs for which we have so far obtained M_BH measurements (Wu et al. 2018) and putting the SMBH of W2246−0526 well into the super-Eddington accretion region. The total uncertainty for the λ_Edd, as shown by the dotted error bars in Figure 5 for W2246−0526, is 0.4 dex, dominated by the systematic uncertainty of M_BH. This systematic uncertainty also applies to all objects at z > 4 in Figure 5.

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Eddington ratios this large may attain a saturation level suggested by theoretical models (Wang & Zhou 1999; Watarai et al. 2000; Mineshige et al. 2000). At high accretion rates, radiation pressure may dominate the accretion flow geometry, making the accretion disk "slim" (Abramowicz et al. 1988). In these models, the fast radial transportation of mass in the accretion flow geometry can trap most photons, preventing them from escaping, and carrying them inward to the SMBH. This photon-trapping accretion makes the radiation efficiency inversely proportional to the mass accretion rate. As a result, the luminosity of a super-Eddington accreting black hole may reach saturation at an apparent Eddington ratio of λ_Edd ∼ 2. The bolometric luminosity will increase much more slowly than the accretion rate, and the M_BH can increase much faster than the growth rate under the Eddington limit. In this scenario, the actual accretion rate of W2246−0526 may be higher than the observed λ_Edd suggests.

Although they have similarly high luminosities, as shown in Figure 5, the λ_Edd of W2246−0526 may have reached saturation while the QSO J0100+2802 has not. The difference in the λ_Edd of the sources is significant, considering only the statistical uncertainties from the measurements, but may not be when including systematic uncertainties in the M_BH estimate. We speculate that the difference between the sources, if real, is due to the much higher obscuration (and thus more material to accrete) in W2246−0526 or due to a different accreting geometry such as mass inflow from merging events. In this context, it is intriguing to note that recent ALMA observations of W2246−0526 of dust continuum emission at rest 212 μm reveal bridges of dusty, metal-enriched material connecting three companions to the central galaxy (Díaz-Santos et al. 2018), implying that a multiple merger is in progress. Díaz-Santos et al. (2018) estimate that accretion rates of as high as $\dot{M}\sim 900\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ onto the central core of W2246−0526 could be underway, sufficient to power the high luminosity of W2246−0526, which has a BH accretion rate of 24 M_☉ yr⁻¹ if a radiation efficiency of 0.1 is assumed.