THE MOST LUMINOUS GALAXIES DISCOVERED BY WISE

The mid-IR photometry of the WISE ELIRGs is listed in Table 2. WISE photometry is from the AllWISE Data Release (Cutri et al. 2013), which contains enhanced data products relative to the WISE All-Sky Source Catalog (Cutri et al. 2012) from improved data processing pipelines on the full seven months of cryogenic data at 12 and 22 μm, and 12 months of both cryogenic and post-cryogenic data at 3.4 and 4.6 μm. By selection, the Hot DOGs are not well detected at WISE 3.4 and 4.6 μm in the seven-month WISE All-Sky Source Catalog. However, more than half of them are detected at ≳5σ using the deeper 3.4 and 4.6 μm data in the AllWISE Source Catalog. The [3.6] and [4.5] photometry for the W1W2-non-detected sources are from Spitzer IRAC obtained during the Spitzer warm mission phase, as reported by Griffith et al. (2012). For sources with AllWISE [3.4] and [4.6] detections, we convert the data to IRAC [3.6] and [4.5] using the color correction [3.6] = W1 − 0.29 × (W1 − W2).¹⁷ The anticipated color difference in between IRAC [4.5] and WISE [4.6] is less than 0.1 magnitude, or about 10% in flux density, thus no color correction has been applied for that band.

The far-IR and submillimeter photometry of the WISE selected ELIRGs, listed in Table 2, was acquired with Herschel. The Herschel data (PI: P. Eisenhardt, Proposal ID: OT1_peisenha_1 and OT2_peisenha_2) include both PACS (Poglitsch et al. 2010) and SPIRE (Griffin et al. 2010) observations. The SPIRE maps were made using small jiggle map mode, with a total 487 s integration time per source. The PACS images were obtained with two concatenated mini-scans for a total of 679 s on each source. The data were processed and analyzed with hipe v11.1.0. For W0831+0140, which was not included in the Herschel program but was covered by the Herschel ATLAS survey (Eales et al. 2010), the far-IR photometry was taken from the public Herschel archive.

As a comparison sample, we identified known quasars with L_bol > 10¹⁴ L_☉ from the following large-scale quasar catalogs: (i) the 13th edition of the Catalogue of Quasars and Active Nuclei (Véron-Cetty & Véron 2010), (ii) the 2dF QSO Redshift Survey (Croom et al. 2004), (iii) the 2dF-SDSS LRG and QSO Survey (Croom et al. 2009), (iv) the SDSS Quasar Catalog V from the 7th SDSS data release (Schneider et al. 2010), and (v) the Sloan Digital Sky Survey (SDSS) Quasar Catalog from SDSS 9th data release (Pâris et al. 2012). In addition, we considered objects with the spectroscopic class of "QSO" in the SDSS 10th Data Release (DR10; Ahn et al. 2013). For the luminous SDSS DR10 quasar sample, we visually checked for mis-identified spectral features or artifacts. We also included 46 objects that are listed as "HyLIRGs" in the NASA/IPAC Extragalactic Database (2013 August 27th version). We utilized the redshift information of quasars reported in these catalogs, and estimated their bolometric luminosities using photometric data from GALEX GR7 (Martin et al. 2005), SuperCosmos (Hambly et al. 2001), SDSS DR10 (Ahn et al. 2013), 2MASS (Skrutskie et al. 2006), UKIDSS DR9 (Lawrence et al. 2007), the AllWISE Data Release (Cutri et al. 2013), IRAS (Neugebauer et al. 1984), and Akari (Murakami et al. 2007).

We then visually inspected the SEDs and images of ∼1300 sources with estimated L_bol > 5 × 10¹³ L_☉ in the optical, near-IR, and mid-IR to identify possible cases where the photometry used for the luminosity calculation was confused by nearby objects. Some sources from the low spectral resolution surveys (e.g., Iovino et al. 1996) showed WISE colors close to zero, much bluer than typical for quasars (Stern et al. 2012; Assef et al. 2013), and their SEDs resemble the thermal emission of stellar objects. Furthermore, the objects clustered at z = 1.97–2. 20, triggering suspicions that their redshifts might be incorrect. Other quasars with unusual blue mid-IR colors such as J071046.20+473211.0 and J072810.14+393027.7 were removed due to known photometric contamination from nearby stars (Meisenheimer & Roeser 1983; Vigotti et al. 1997). Some of the sources have proper motions detected between the 2MASS and WISE observations, and their SEDs suggest they are likely late-type dwarf stars (e.g., J003332.60–392245.0, an M-type dwarf star; Plavchan et al. 2008) or known brown dwarfs (e.g., J144825.70+103158.0, an L3.5 brown dwarf; Wilson et al. 2003). After this culling from visual inspection, a total of 140 optically selected quasars reach the luminosity cut of 10¹⁴ L_☉, assuming their emission is isotropic.

To ensure that the intrinsic luminosities of the optically selected quasars are greater than the 10¹⁴ L_☉ threshold, we removed known gravitationally lensed systems and blazars. We invoked the catalog of strong gravitational lensing systems from "the Master Lens Database"¹⁸ (L. A. Moustakas et al. 2015, in preparation), and the list of blazars from "the Roma-BZCAT Multi-frequency Catalogue of Blazars" (Massaro et al. 2009) version 4.1.1—2012 August). Of the 140 luminous quasars, 9 are in known strong gravitational lensing systems, and 15 are known blazars. This leaves a total of 116 hyperluminous quasars with L_bol > 10¹⁴ L_☉, including 68 quasars from the SDSS DR7 quasar search (Schneider et al. 2010). These quasars are listed in Table 3.

To compare the far-IR SEDs of hyperluminous quasars and Hot DOGs, we have gathered the available Herschel photometry for our quasar sample. Herschel SPIRE data are available for 15 quasars, and 2 of them also have PACS measurements. This photometry is listed in Table 4.

The WISE mid-IR color–color diagram at [3.4], [4.6], and [12] is shown in Figure 2. The WISE-selected ELIRG Hot DOGs occupy a wider range of [3.4]–[4.6] color than do the hyperluminous quasars, and the Hot DOGs are ∼2–3 mag redder in [4.6]–[12] color. The Hot DOG redshifts span 2.8 < z < 4.6, which is narrower than the quasar redshifts range of 0.9 < z < 4.9. This is likely due, in part, to a selection effect which biases the Hot DOG selection to z ≳ 1.5 (Assef et al. 2015). The large gap between 4 < [4.6]–[12] < 5 is a result of the W1W2-dropout selection criteria. Some hyperluminous objects have been discovered in this color region based on different mid-IR color selection criteria accompanied by criteria at other wavelengths (e.g., Bridge et al. 2013; Lonsdale et al. 2015; D. Stern et al. 2015, in preparation).

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The SEDs of the WISE-selected ELIRGs are shown in Figure 3, normalized by the integrated luminosity over the plotted SEDs. The SEDs of the L_bol ≥ 10¹⁴ L_☉ Hot DOGs are similar to those of their less luminous siblings, which are outlined by the shaded region. The steep rise from rest frame 1–4 μm reflects the selection criteria. These SEDs do not match empirical starburst or dusty AGN templates, although they are close to the torus model of Polletta et al. (2006). However, they are steeper than the torus model at λ < 4 μm and drop faster toward the far-IR at λ > 60 μm. The rest-frame flux density peak is at shorter wavelengths than the peak of the dusty starburst system Arp 220, which is at about 60 μm. This indicates emission from hotter dust in these WISE-selected hyperluminous galaxies. The emission excess around rest frame 6 μm can be explained by dust emission T_d ∼ 450 K, as shown in the upper panel of Figure 3. This suggested temperature does not imply a single-temperature dust system, but is rather a characteristic temperature for the hot dust emission component. Further discussion of the SEDs and implied dust temperatures is included in Section 4.3.

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The bolometric luminosity L_bol is calculated very conservatively by integrating over the photometric data, only considering >3σ detections, with a power law interpolated between observed flux density measurements, and extrapolated to 20% beyond the shortest and longest wavelength bands by assuming no luminosity beyond these wavelengths. We do not incorporate any extinction correction or SED model in our luminosity estimate. The resulting luminosity values from this approach can be considered as conservative lower limits. If the best-fit SED templates or spline-smoothed SEDs are considered, the luminosity values typically increase by a factor of 2.

The SEDs of the quasars do not extend to rest frame wavelengths >8 μm due to a lack of comprehensive far-IR data. The contribution to the bolometric luminosity at longer wavelengths is expected to be <35% of the L_bol based on quasar SED templates (Polletta et al. 2006; Assef et al. 2010). Using available Herschel archival data, we estimate the contribution to L_bol by far-IR emission is <20% for the optically selected quasars in this paper.

To estimate the luminosity contributed by different components to the SED, we separate the SED into three parts: rest-frame blue emission (∼1000 Å) to 1 μm, emission from 1 to 20 μm, and emission from 20 μm and beyond. The corresponding luminosities from these wavelength ranges are referred to as L_{0.1–1 μm}, L_1–20, and L_{>20 μm}, respectively. For simplicity, we refer to L_{1–20 μm} as L_MIR hereafter. The L_{>20 μm} should be distinguished from infrared luminosity, L_IR, which is defined as the accumulated luminosity between 8–1000 μm, and from the traditional far-infrared luminosity, L_FIR, which covers emission from 40 to 500 μm. The results are listed in Table 5.

The luminosities reported in this paper are calculated based on the assumption of isotropic emission in the observed wavebands. If the escaped energy is beamed, the intrinsic luminosity could be significantly overestimated. However, beaming, which is observed in blazars, is associated with variable light curves. In addition, Hot DOGs are only weakly detected or undetected in shallow (1 mJy), wide-area radio surveys (C.-W. Tsai et al. 2015, in preparation), unlike beamed objects which are typically radio bright (Urry & Padovani 1995).

Beaming implies small physical scales, hence the potential for rapid variability. We do not see significant variation in the WISE data. None of the Hot DOGs varies in W3 and W4 to a limit of 30% over 6 months, and none are flagged as significantly varying in the AllWISE catalog. Finally, many Hot DOGs have emission-line spectra (Wu et al. 2012; P. R. M. Eisenhardt et al. 2015, in preparation), unlike the featureless spectral characteristic of BL Lac objects. These properties distinguish Hot DOGs from known beamed populations.

Another possible explanation for the high luminosity of Hot DOGs is gravitational lensing by massive foreground systems. The most luminous known quasars, J0831+5245 and ${\rm J}1424+2256$ with apparent L_bol ≳ 10¹⁵ L_☉, are both gravitationally lensed (Lawrence et al. 1992; Patnaik et al. 1992; Irwin et al. 1998). For the WISE ELIRGs, while we cannot completely rule out the lensing hypothesis for these hyperluminous Hot DOGs, we consider the likelihood of strong lensing to be small based on the following arguments.

First, we consider what may be inferred from the WISE imaging data, estimating upper bounds on the possible magnification. Significant lensing requires the magnified source to be close to the effective Einstein radius (θ_E) of the lens. In general, θ_E is governed by the redshifts of background target and foreground lens, as well as the mass of the lens. In Case 1, θ_E is larger than the angular resolution of W1 (6''). In Case 2, θ_E is smaller than 6'' and the lensed images and foreground lens could be blended.

Case 1 is addressed by Figure 5, which shows the W1 photometry versus separation for objects in the 20 ELIRG fields. We use a SWIRE elliptical galaxy SED template and assume a total mass-to-light ratio of M/L_B ∼ 5 in solar units (e.g., Faber & Gallagher 1979; Napolitano et al. 2005) to show the relationship between θ_E, W1 photometry, and the mass of the lens. The maximum θ_E occurs near a lens redshift ∼2.5, for a source at z = 3.2 (the median ELIRG redshift), and the value of θ_E versus W1 for a lens at this redshift is shown by the solid blue line. Neighboring objects must be above this line to produce high magnification of the Hot DOG. No source falls above the line, and only one comes close. At the observed separations of W1 objects in the ELIRG fields, such objects would need masses well above 10¹⁴ M_☉.

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Galaxies with masses >10¹³ M_☉ exist, such as ESO 146-5 ($M\;\sim$ 10¹³ M_☉; Carrasco et al. 2010), which dominates the Abell 3827 cluster of galaxies, but massive galaxy clusters are not in evidence near the ELIRGs (Griffith et al. 2012; Assef et al. 2015). We conclude that the resolved individual WISE sources that we detect are not likely to be able to cause strong magnification of the ELIRGs.

There is the additional possibility that a much larger scale galaxy cluster potential could magnify ELIRGs near a correspondingly larger scale critical curve, which would not necessarily show extreme distortions or local multiple-images, particularly if the sources are quite compact intrinsically. However, the gravitational lensing magnification under this condition is usually small. Although the current optical and near-IR imaging data are not sufficient to fully explore that possibility, the Spitzer data do not show the aggregation of objects within 1' as expected for a massive foreground lensing cluster of galaxies (Assef et al. 2015).

Case 2 is addressed in Figure 6, which shows the lens mass versus redshift for a source at z = 3.2, the median redshift of the ELIRGs. In this case the lens would need to have W1 > 16.8 (or <58 μJy) to be consistent with the observed ELIRG data (see Table 2). As shown by the blue curve, this excludes 10¹² M_☉ lenses up to z = 1.5, assuming M/L_B ∼ 5. Lower mass lenses are possible, of course, but they must reach the critical mass surface density for gravitational lensing (see e.g., Subramanian & Cowling 1986). The remaining parameter space is highlighted as the gray shaded region in Figure 6. This parameter space can be investigated where we have high-resolution near-IR imaging.

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We have obtained high angular resolution (PSF FWHM ≲015) near-IR imaging of over 30 Hot DOGs, including 5 ELIRGs reported in this paper, with the NIRC2 camera on Keck-II with adaptive optics, and with HST. These images do not show lensing features such as multiple images or arcs (Wu et al. 2014; S. Petty et al. 2015, in preparation; C. R. Bridge et al. 2015, in preparation). For the six ELIRGs in our sample with high-resolution near-IR imaging data, it is not uncommon to see other objects a few arcseconds from the ELIRGs in the images from HST or Keck with adaptive optics. However, these objects' morphologies are typical of recent or ongoing mergers, rather than characteristic lensing geometries, based on our experience with strong lensing work (Eisenhardt et al. 1996; Moustakas et al. 2007). There are sources which fall in the gray shaded area in Figure 6, but in no case is the θ_E corresponding to the inferred mass as large as their separation from the ELIRG. Thus, unless the lensing galaxies are anomalously faint or highly obscured, the high luminosity of Hot DOGs seems to be intrinsic rather than due to gravitational lensing.

We have also examined all of our 2D spectra. We have closely examined the four cases (W1248–2154, W2042–3245, W2246–0526, and W2246–7143) where nearby objects appear in the data (P. R. M. Eisenhardt et al. 2015, in preparation). Other than W1248–2154, discussed below, we have not identified any cases of two different redshifts superimposed that might be indicative of strong lensing (e.g., SLACS survey sample; Bolton et al. 2004, 2006). As discussed in detail below, we conclude that gravitational lensing is not causing the high luminosity of W1248–2154.

4.2.1. W1248–2154

Among the optical spectra of all 20 ELIRGs, only W1248–2154 suggests lensing. The spectrum of W1248–2154 shows two sources at z = 0.339 and z = 3.326 separated by 13 (P. R. M. Eisenhardt et al. 2015, in preparation). To explore the lensing hypothesis, we obtained K-band images of W1248–2154 using the NIRC2 camera with the Laser Guide Star Adaptive Optics (LGS-AO) system on the Keck II Telescope (van Dam et al. 2006; Wizinowich et al. 2006). WISE J1248–2154 was observed on the night of 2014 May 18 (UT) under good weather conditions. USNO-B star 0681-0325487 (Monet et al. 2003) with R = 16.9 located 49'' from the target was used for the tip-tilt reference. Images were obtained with the MKO K filter with field of view of 40'' × 40'' per frame and pixel scale of 00397/pixel. Thirty K-band images (120 sec per image) were obtained using a three-position dither pattern that avoided the noisy, lower-left quadrant. The total effective exposure time was 60 minutes.

The raw images were dark-subtracted and then sky-subtracted using a sky frame based on the median average of all frames, and a dome flat¹⁹ was used to correct for pixel-to-pixel sensitivity variations. The co-added image (Figure 7) is the median average of aligned single frame images based on the pixel location of a star in the field. The FWHM of point-like sources in the field is ∼014. The final NIRC2 image was registered to the seeing-limited J-band image from Assef et al. (2015), which has its WCS matched to the AllWISE WCS using W1 sources in the field of view.

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The red cross in Figure 7 shows the AllWISE position of W1248–2154, which has an uncertainty of 025. The 02 extent of the cross indicates the astrometric uncertainty of the K-band image with respect to the AllWISE coordinate system. We do not find any significant gravitational lensing signatures in this image. We identify the brighter K-band source on the right of the cross as W1248–2154 at z = 3.326. The object to the left of the r = 1'' dashed circle is at z = 0.339. The source on the left just within the dashed circle is blended with the z = 0.339 object, and does not show noticeable spectroscopic features in our spectrum. The z = 0.339 object's K-band magnitude of ∼22.4 mag corresponds to a lensing mass of 2 × 10⁹ M_☉, and an Einstein radius of <012, significantly smaller than the separation between the companion and the ELIRG. So this foreground source is not producing strong lensing of the W1248–2154 Hot DOG. Thus we conclude that W1248–2154 is not a lensed system.

We also considered whether source confusion in the AllWISE mid-IR photometry might cause the luminosity for W1248–2154 to be overestimated. Like other Hot DOGs, the SED for W1248–2154 is dominated by the AllWISE photometry at 12 and 22 μm. The z = 0.34 galaxy and z = 3.3 Hot DOG are blended in the AllWISE Atlas images. However, the separation is significantly larger than the 025 positional uncertainty of W1248–2154 in the AllWISE catalog. W1248–2154 does not have noticeable blending in the AllWISE catalog, suggesting that the foreground galaxy is not detected in the W1 and W2 bands. While we do not have 3 and 4 μm images with resolution better than the AllWISE W1 images, the z = 0.34 source is significantly bluer than the z = 3.3 source between the J- and K-bands. Thus we believe that the foreground galaxy does not contribute significantly to the W3 and W4 photometry or the L_bol estimate for W1248–2154.

The Hot DOG SEDs generally peak between rest-frame 4 and 10 μm (see Figure 3), suggesting that the emitting dust can have temperatures up to T_d ∼ 450 K. The SED becomes Rayleigh–Jeans around 40–60 μm, corresponding to T_d ∼ 60 K (Wu et al. 2012; Bridge et al. 2013). Ground-based sub-millimeter follow-up observations of Hot DOGs indicate the rest-frame far-IR luminosity of Hot DOGs is about an order of magnitude lower than the rest-frame mid-IR luminosity (Wu et al. 2012; Jones et al. 2014). Considering the three SED components introduced in Section 3.3, the blue component (0.1–1 μm) represents direct emission from the host galaxy, as well as direct or scattered emission from the AGN and its accretion disk; the mid-IR component (1–20 μm) represents emission from the AGN dust torus, or dust emission from the cocoon of highly obscured AGNs; and the >20 μm component represents far-IR emission from dust at the outskirts of the AGN, or starburst-powered dust emission from the host galaxy.

L_{1−20 μm}, or L_MIR as shown in Figure 8, is a better indicator of the hot dust-dominated luminosity of these hyperluminous systems, in contrast to the traditional infrared luminosity L_IR value which is more sensitive to diffuse dust emission powered by a starburst. As shown in Table 5, L_MIR > L_{>20 μm} for every ELIRG. The bolometric contribution of emission blueward of 1 μm is negligible for the Hot DOGs and is likely redistributed by dust to rest-frame mid-IR wavelengths, resulting in the high L_MIR/L_bol ∼ 65% (median value). In optically selected populations, especially the high luminosity quasars, L_MIR contributes only ∼30% (median value) of L_bol.

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Figure 9 shows ν L_ν at 5.8 μm (L_{5.8 μm}) and 7.8 μm (L_{7.8 μm}), which have often been used to characterize AGN luminosities in the literature (e.g., Weedman et al. 2012). Common practice is to interpolate the SED to obtain these numbers, or to estimate them from an SED model. These numbers are convenient for statistical analyses such as deriving the quasar luminosity function. However, these monochromatic luminosities do not capture the variation in dust temperature distribution in different AGNs, which could be dramatic in obscured systems such as Hot DOGs. The ratios of L_{5.8 μm}/L_bol and L_{7.8 μm}/L_bol are substantially offset between ELIRG quasars and ELIRG Hot DOGs, and the scatter is large for both populations, particularly for quasars. The conversion from these monochromatic values to total L_bol can vary by a factor of ∼3 (Figure 9). Hence we suggest that ν L_ν at 5.8 or 7.8 μm as an estimate of total bolometric AGN luminosity should be used with caution.

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The extremely red SEDs of Hot DOGs suggests the extinction toward their central AGNs is very high, reaching A_V ≳ 30 mag (Eisenhardt et al. 2012; Assef et al. 2015; Stern et al. 2014). The absorbed energy is released at mid-IR wavelengths via thermal dust emission. As discussed in the previous two sections, the reprocessed energy (L_MIR) output in hyperluminous Hot DOGs dominates the total luminosity, and matches the luminosity emitted directly from the accretion disk (L_{0.1–1 μm}) in optically selected hyperluminous quasars. This enormous thermal dust luminosity suggests a dust covering fraction close to unity, rather than an edge-on dusty torus.

We estimate a dust sublimation radius (Barvainis 1987) of ∼8 pc for the ≥10¹⁴ L_☉ Hot DOGs if they are heavily obscured by graphite-silicate mixed dust grains with a sublimation temperature of ∼1500 K. Here we assume that the bolometric luminosity is equal to the dust absorbed UV luminosity in these highly obscured systems. Unlike optically selected quasars, in which the variation timescale of optical emission is much shorter because the optical light comes directly from smaller physical scales (Schmidt 1963), the fluctuations of luminosity over time in Hot DOGs will be smoothed out by radiation reprocessing by the dust. The 16 pc diameter of the sublimation region sets the shortest variation timescale to be ∼50 yr in the rest frame. However, the timescale for luminosity changes is more likely to be related to the scale of the dust that produces the peak emission in the SED. In Section 3.2, we show that the highest temperature dust and therefore smallest scale that contributes substantially to the SED is at a temperature of T_d ∼ 450 K. If we assume the emitting dust is approximately in thermal equilibrium, the characteristic radius at that temperature is ∼40 pc. Therefore we do not expect large luminosity variations over a rest-frame timescale less than ∼200 yr, or many centuries in the observed frame. As noted in Section 4.1, the flux variation at 12 and 22 μm is less than 30% over a six-month period based on WISE observations.

In 200 years at 10¹⁴ L_☉, the total energy output is ≳2.5 × 10⁵⁷ erg, or six orders of magnitude higher than the total energy output of a long gamma-ray burst (GRB, E_total ∼ 10⁵¹ erg). Rowan-Robinson (2000) argues that a starburst component is necessary for explaining the far-IR and submillimeter (λ ≥ 50 μm) SEDs of HyLIRGs. Could an extreme starburst provide this much energy for ELIRGs?

Without obvious starburst examples in the ELIRG luminosity range, we consider He 2–10, a local dwarf galaxy and a highly obscured starburst system, as an analogy to evaluate the possibility that the high luminosity is supported by star formation. In He 2–10, compact starburst regions are highly obscured and show mid-IR emission from hot dust (Beck et al. 2001). Beck et al. (2001) estimate an infrared luminosity L_IR ∼ 2 × 10⁵ L_☉ for the Lyman continuum photon rate N_Lyc = 10⁴⁹ s⁻¹ derived from radio measurements. If the obscured starburst case applies to the hyperluminous Hot DOGs, 10¹⁴ L_☉ would correspond to N_Lyc ∼ 5 × 10⁵⁷ s⁻¹.

We use the STARBURST99 simulation (Leitherer et al. 2010) with instantaneous starburst models to estimate the star formation needed to produce such a Lyman continuum photon rate. For a flat IMF (observed in compact starbursts in extreme environments such as young and massive clusters near the Galactic center—Figer et al. 1999, 2002), a total star formation of ∼2 × 10¹⁰ M_☉ is needed, with higher masses for a Salpeter (1955) IMF. These must be formed within a few Myr—the lifetime of massive stars which produce most of the Lyman continuum photons. The implied star formation rate is SFR > 5 × 10³ M_☉ yr⁻¹, at least an order of magnitude higher than known extreme starburst systems such as sub-millimeter galaxies (Michałowski et al. 2010; Swinbank et al. 2014) or Lyman break galaxies (Shapley et al. 2005) at high redshift. Large masses of molecular gas and cold dust should accompany this level of star formation, but we observe neither substantial CO emission from these systems (A. Blain et al. 2015, in preparation) nor abundant cold dust (Wu et al. 2012; Jones et al. 2014). Thus we conclude, as did Eisenhardt et al. (2012), that a starburst is unlikely to be the dominant mechanism driving the high luminosity in Hot DOGs.

Like quasars, Hot DOGs are likely powered by efficiently accreting SMBHs, albeit with extremely high obscurations. Here we consider the constraints on the mass and growth history of the SMBHs in the extremely luminous Hot DOGs and quasars based on their luminosities and redshifts. Below we show that the existence of ELIRGs at z > 3 implies SMBHs in ELIRGs have (1) a seed mass ≫10³ M_☉; (2) a sustained super-Eddington accretion phase; or (3) a sustained radiation efficiency of <15%, producing less radiation feedback to limit accretion.

4.6.1. Current Eddington Ratio

The Eddington luminosity corresponds to the total emission from an isotropic accreting AGN when its radiation pressure is balanced by the gravitation of the SMBH. If we assume a hydrogen-dominated plasma, the SMBH mass at observed redshift z is thus

$$\begin{eqnarray}&&{{M}_{{\rm Eddington}}}=M(z)\sim \frac{3\times {{10}^{9}}\;{{M}_{}}}{\epsilon (z)}\frac{{{L}_{{\rm bol}}}}{{{10}^{14}}\;{{L}_{}}},\end{eqnarray} \tag{ 1 }$$

where (z) is the Eddington ratio.

If Hot DOGs are accreting below the Eddington limit the SMBH masses for ELIRGs are >3 × 10⁹ M_☉. This implies stellar masses ∼10¹² M_☉ if the host galaxies follow the M–σ correlation, comparable to local giant elliptical galaxies in clusters. If (z) < 0.1 for ELIRGs, the implied SMBH mass would be M_BH ≥ 3 × 10¹⁰ M_☉, larger than the most massive SMBHs known in the local universe (McConnell et al. 2011). The lack of such massive black holes at the present epoch is not easy to explain when the abundance of Hot DOGs matches that of powerful quasars (Assef et al. 2015), whose abundance is in turn consistent with the distribution of large elliptical galaxies today. Furthermore, if M_BH > 10¹⁰ M_☉ for Hot DOGs, we would expect more massive host galaxies than observed unless Hot DOGs deviate substantially from the empirical M–σ relation (Assef et al. 2015). While the extremely massive black holes and galaxy hosts expected for ELIRGs with low Eddington ratios are not found, there is some evidence that Hot DOGs are in rich environments. Follow-up observations using the SCUBA-II camera on JCMT show enhanced numbers of 850 μm continuum sources within 15 of Hot DOGs (Jones et al. 2014), and Spitzer IRAC images also show enhanced densities of sources with red IRAC colors ([3.6] − [4.5] > 0.37), indicative of galaxies at z ≳ 1 (Assef et al. 2015).

Although super-Eddington accretion (i.e., (z) > 1) is considered to be an unstable phase, it has been suggested to be common at z > 1.7 (Steinhardt & Elvis 2010). It is possible that Hot DOGs are in a transitional super-Eddington phase which produces their extraordinary luminosity. Indeed, super-Eddington accretion is commonly invoked to explain the non-nuclear "ultraluminous X-ray" source populations seen in local galaxies (e.g., Bachetti et al. 2014). However, super-Eddington accretion requires a special configuration for the accretion disk, and the timescales for super Eddington accretion in AGNs are not thoroughly investigated and understood. Begelman (2002) suggests that the Eddington limit can be exceeded by 10–100 times via small scale inhomogeneities in the thin disk accretion. Ohsuga & Mineshige (2007) suggest accreting material through the photon trapping regions around the accreting black hole can help the system stably bypass the radiation feedback. Statistical study of SDSS quasars suggests the maximum Eddington ratio for Type 1 quasars is ∼ 3 (Kelly & Shen 2013), though Hot DOGs could be in a different accretion phase from Type 1 quasars.

At high Eddington rates, the black hole mass in ELIRGs can grow by an order of magnitude over 10⁷ yr, much faster than the growth of stellar bulges. The relatively tight M–σ relation seen in the local universe suggests that high Eddington rate phases do not account for a significant fraction of cosmic SMBH mass growth.

4.6.2. Time-averaged Eddington Ratios and Radiation Efficiency

The ELIRG Hot DOG systems are at z > 2.5, leaving the SMBHs in them <3 Gyr to grow to the mass at which we observe them. Based on the arguments of Shapiro (2005), we can estimate the time-averaged Eddington ratio in these systems. In the following discussion, we do not consider BH mass growth via BH mergers, although these may play a role at high redshift when the BH density is relatively high. However, the merging timescale, driven by the coalescence timescale of stellar relaxation of host galaxies, is much longer than the Salpeter timescale for BH mass growth by accretion. Thus, compared to mass accretion, mass increase by mergers plays a relatively minor role in BH mass growth history.

For a black hole with mass M_BH(z) at redshift z, accretion rate ${{\dot{M}}_{{\rm acc}}},$ black hole mass growth rate ${{\dot{M}}_{{\rm BH}}},$ and radiative efficiency η(z), the observed luminosity at redshift z is

$$\begin{eqnarray}&&L(z)=\eta {{\dot{M}}_{{\rm acc}}}{{c}^{2}}=\frac{\eta {{{\dot{M}}}_{{\rm BH}}}}{(1-\eta )}{{c}^{2}}.\end{eqnarray} \tag{ 2 }$$

We can also relate the observed luminosity to the Eddington luminosity,

$$\begin{eqnarray}&&L(z)=\epsilon (z){{L}_{{\rm Edd}}}=\epsilon (z)a{{M}_{{\rm BH}}}(z)\end{eqnarray} \tag{ 3 }$$

where _z is the Eddington ratio, and a is a constant associated with the opacity of accreting materials. By combining Equations (2) and (3) with cosmic time t(z), one can derive

$$\begin{eqnarray}&&\frac{d{{M}_{{\rm BH}}}}{dt}=\epsilon (t)(1-\eta )\frac{a}{\eta {{c}^{2}}}{{M}_{{\rm BH}}}=\frac{\epsilon (t){{M}_{{\rm BH}}}}{{{\tau }_{{\rm Salpeter}}}}.\end{eqnarray} \tag{ 4 }$$

The factor τ_Salpeter ≡ $\frac{\eta {{c}^{2}}}{(1-\eta )a}$ is the Salpeter (1964) timescale, which describes the time span for an e-fold mass increase of a black hole accreting at its Eddington limit. For a hydrogen-dominated plasma, a ≃ 3.3 × 10⁴ L_☉/M_☉, and with η = 0.057 for a Schwarzschild black hole (Bardeen et al. 1973) rather than the more commonly adopted empirical value of 0.1 (Yu & Tremaine 2002), τ_Salpeter is ∼50 Myr. For a Kerr black hole where η = 0.3 (Thorne 1974), τ_Salpeter ∼ 192 Myr. In other words, a non-spinning black hole experiences less radiation feedback to accreting material due to its lower radiation efficiency, thus its mass doubling time could be ≳3 times shorter than a fast spinning black hole.

Assuming black holes of seed mass M_seed appear at z ∼ 20 (Couchman & Rees 1986; Bromm et al. 2009), the age of the black holes since their appearance is ${{T}_{{\rm age}}}(z)\equiv \int _{z}^{z\sim 20}dt$, and the time-averaged Eddington ratio $\bar{\epsilon }(z)$ is

$$\begin{eqnarray}&&\bar{\epsilon }(z)\equiv \frac{\int _{z}^{z\sim 20}\epsilon (t)dt}{\int _{z}^{z\sim 20}dt}=\frac{\int _{z}^{z\sim 20}\epsilon (t)dt}{{{T}_{{\rm age}}}}\end{eqnarray} \tag{ 5 }$$

between z ∼ 20 and redshift z. Thus, from Equation (4), we derive that the evolution of black hole mass M_BH can be written as

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} {\rm ln} \left( \frac{{{M}_{{\rm BH}}}(z)}{{{M}_{{\rm seed}}}} \right) & = & (1-\eta )\frac{a}{\eta {{c}^{2}}}\int _{z}^{z\sim 20}\epsilon (t)dt \\ {} & = & \bar{\epsilon }(z)\frac{{{T}_{{\rm age}}}(z)}{{{\tau }_{{\rm Salpeter}}}}, \\ \end{array}\end{eqnarray} \tag{ 6 }$$

and

$$\begin{eqnarray}&&\bar{\epsilon }(z)={\rm ln} \left( \frac{L(z)}{\epsilon (z){{L}_{{\rm Edd}}}({{M}_{{\rm seed}}})} \right){{\left( \frac{{{T}_{{\rm age}}}(z)}{{{\tau }_{{\rm Salpeter}}}} \right)}^{-1}}.\end{eqnarray} \tag{ 7 }$$

For the ELIRG Hot DOGs at 2.8 ≲ z ≲ 4.6, we assume the current value (z) ∼ 1 (see discussion of Section 4.6.1). The age of the universe at that redshift is ∼1.4–2.4 Gyr. If M_seed of the SMBHs in these systems is of order 10–100 M_☉ as suggested by simulations of SMBH seeds from population III stars (Zhang et al. 2008; also see review by Volonteri 2010), the derived time-averaged Eddington ratios of our systems are $\bar{\epsilon }\sim 0.71$ (z = 4.6) or ∼0.46 (z = 2.8). We note that the uncertainties in assumptions on (z), M_seed, and L(z) do not affect the $\bar{\epsilon }$ estimate significantly due to the logarithmic scaling (Equation (7)). An order of magnitude uncertainty in these parameters will change the estimate of $\bar{\epsilon }$ by 0.1 at the most. T_age depends on the when SMBH seeds appear (z ∼ 20), so the maximum possible T_age would decrease $\bar{\epsilon }$ by less than 0.15. Differences in τ_Salpeter will affect $\bar{\epsilon }$. The higher η of rapidly spinning black hole results in even higher value of $\bar{\epsilon }$. The same arguments apply to the ELIRG quasars in the same redshift range. Thus, the time-averaged Eddington ratios $\bar{\epsilon }$ of the ELIRG systems we discuss here are securely larger than 25%. In comparison, the most massive black hole known so far with ∼2 × 10¹⁰ M_☉ (McConnell et al. 2011) would have $\bar{\epsilon }\sim 0.07$ over the Hubble time.

4.6.3. Seed Black Hole Mass and Black Hole Spin

The previous section discusses a simple model of M_BH growth history (Equation (6)) in which the variables are the seed black hole mass M_seed, the radiative efficiency η, and the Eddington ratio (z). Current models suggest seed black hole masses ranging from ∼10 M_☉ from simulations of the end products of population III stars (e.g., Zhang et al. 2008) to ∼100 M_☉ from run away collisions between stars in dense clusters (e.g., Begelman & Rees 1978) to as much as 10⁶ M_☉ for supermassive stars that quickly accumulate ambient material and collapse into black holes (Wise et al. 2008; Regan & Haehnelt 2009).

Figure 10 shows L_bol versus z for hyperluminous Hot DOGs and quasars, and for quasars at z > 6. The curves in the Figure show the luminosity versus redshift tracks followed by black holes as they grow for various choices of M_seed and η. Although in reality the Eddington ratio is likely to vary, the overall averaged Eddington ratio $\bar{\epsilon }$ should be lower than unity. With the assumption of ∼ 1 constantly, we consider cases with η ∼ 0.1, a commonly adopted value for a slowly spinning or non-spinning black hole, η ∼ 0.2 for an intermediate spinning black hole, and η ∼ 0.3 for a rapidly spinning black hole. The radiative efficiency is a factor of 3 higher for a Kerr black hole because the material can still radiate gravitational energy to the last stable circular orbit, which is three times smaller compared to a non-spinning Schwarzschild black hole or a slowly spinning black hole (Thorne 1974). The curves on Figure 10 represent the theoretical limits of black hole mass growth, and the objects toward the upper right of the curves can not be produced with the given initial seed mass and radiative efficiency unless the SMBH is in a super-Eddington state for a significant period of its history.

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If η ∼ 0.2–0.3 is adopted, the higher radiative efficiency means that the SMBH accumulates less mass to produce the same luminosity. Assuming black hole merging is not important, black holes with η = 0.3 cannot produce the observed ELIRGs and z > 6 quasars unless their seed mass M_seed ≫ 10⁴ M_☉ or/and they have been accreting at super-Eddington rates since their formation in the early universe. For the most luminous Hot DOGs and quasars, the required seed mass is M_seed > 10⁷ M_☉, higher than the most massive seed masses predicted by current models (Begelman et al. 2008; Agarwal et al. 2012; Hosokawa et al. 2013). On the other hand, for η = 0.1 (dotted lines in Figure 10), relatively modest seed black holes can grow to Hot DOGs if they are accreting at (z) > 0.4. If the seed mass exceeds 10⁴ M_☉, even accretion rates < 0.1 can appropriately create hyperluminous quasars at z > 6 and ELIRGs at z < 5.

Under the conservative assumption of constant accretion at the Eddington limit since z = 20, the existence of hyperluminous Hot DOGs and quasars at z > 3.5 implies a constraint on the upper limit to the radiative efficiency for given seed black hole mass values. In Figure 11, we show the upper limits of radiative efficiency in the cases of M_seed = 10³ M_☉ and M_seed = 10⁶ M_☉. The first case represents the upper bound on the predicted black hole seed mass from the first stars (Hirano et al. 2014 and references therein). The 10⁶ M_☉ case is upper bound of the seed mass from direct collapse of pristine gas clouds (Agarwal et al. 2012), or from rapid mass accretion onto primordial massive stars (Hosokawa et al. 2013). The hyperluminous Hot DOGs and quasars at z > 3.5 place similar constraints on black hole radiative efficiency η as z > 6 quasars. If the black hole seeds have masses of ∼10³ M_☉, we expect that SMBHs have radiative efficiency on average lower than 15% to form the ELIRGs and hyperluminous quasars at z > 4. If a higher seed mass is adopted, the upper limits of η are still <25%, which corresponds to the radiative efficiency of a mildly rotating black hole. This suggests that the SMBHs in these most luminous systems are either (1) born with high mass (as discussed by Johnson et al. 2013, for quasars at z > 7), (2) experience substantial super-Eddington accretion episodes in their growth history (Kelly & Shen 2013), or (3) have sustained lower radiation feedback to accretion due to lower radiation efficiency for slowly spinning black holes. In the latter case, some mechanism, such as accretion with randomized directions (King & Pringle 2006; King et al. 2008; Fanidakis et al. 2012), has to interrupt the increase of black hole spin by angular momentum transported from a regulated accretion disk, otherwise a black hole can be spun up close to the theoretical limit over a few Salpeter timescales.

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Analysis of the black hole mass function at z = 0 suggests that SMBHs spend ∼1% of their lifetime in a luminous, high accretion rate mode, and 99% in a dim, low accretion phase (Hopkins et al. 2006b). The high accretion phase dominates the BH mass growth. For ELIRGs, the accretion rate $\dot{M}$ required to radiate at the ELIRG luminosity level is $\dot{M}=L/(\eta {{c}^{2}})\sim (7/\eta )\;{{M}_{}}\;{\rm y}{{{\rm r}}^{-1}}$. For the typical η = 0.1 radiative efficiency of a slow-spinning black hole, $\dot{M}\sim 70\;{{M}_{}}\;{\rm y}{{{\rm r}}^{-1}}.$

The minimum lifetime of the high luminosity phase in hyperluminous Hot DOGs can be estimated by considering the depletion time of the observed dusty material. The peak of the ELIRG SEDs suggests that the luminosity is dominated by radiation from hot dust at T_d ∼ 450 K. At that temperature, the required dust mass to produce the observed L_MIR ∼ 8 × 10¹³ L_☉ is on the order of 2700 M_☉. This dust mass is just ∼40 times the mass annually accreted by the SMBH in Hot DOGs. This timescale is shorter than the light-crossing timescale of 200 yr discussed in Section 4.4.

On the other hand, Assef et al. (2015) have studied the luminosity functions of Hot DOGs and luminous quasars, finding they have comparable number density. This suggests similar lifetimes for both the obscured and the unobscured phases of hyperluminous black hole accretion. Using the life cycle of broad line quasars at z = 1 (Kelly et al. 2010) as an analog, this time scale is ∼100 Myr, likely to be the upper bound for Hot DOG phase. This timescale is a few times the Salpeter timescale. The accreted mass onto the SMBH exceeds 7 × 10⁹ M_☉.

Our systematic search for ELIRGs using the "W1W2-dropout" selection criteria has identified about 1000 candidates in the WISE database (Eisenhardt et al. 2012). Among the 150 of these candidates from which we have redshift information, a total of 20 ELIRGs at z > 2.5 have been discovered as reported in this paper, including the most luminous system, W2246–0526 at z = 4.593 with L_bol ∼ 3.5 × 10¹⁴ L_☉.

Are there other infrared objects, either starbursts or obscured AGNs, with similarly high luminosities? Recently, 1HERMES X24 J161506.65+543846.9 at z = 4.952 was discovered by Herschel HerMES survey (Casey et al. 2012a). Its L_IR is reported to be ∼1.2 × 10¹⁴ L_☉ based on an SED model with T_dust = 98 K. It is the brightest object in their sample, and tentatively classified as a starburst system based on its optical spectrum (Casey et al. 2012a). Our conservative estimate using WISE and Herschel photometry would imply its L_bol is ∼8 × 10¹³ L_☉, slightly shy of our L_bol threshold, but likely making it one of the most powerful starburst systems known. In addition to Herschel studies, a few systems discovered by WISE using different selection criteria have L_bol at the ∼10¹⁴ L_☉ level (Lonsdale et al. 2015; D. Stern et al. 2015, in preparation), but they all show obvious AGN features in their spectra or have radio emission.

The L_bol ∼ 10^14.5 L_☉ of W2246–0526 exceeds the most luminous quasars listed in Table 3 (see Figure 4). Could there be even more luminous Hot DOGs?

In Figure 10, a few quasars at z > 6 have implied black hole mass ≳10⁹ M_☉ at an age of <1.0 Gyr. If they accrete at the Eddington limit, they could potentially reach >10¹⁵ L_☉ by z ∼ 5. Thus far, we have not observed any system at that L_bol level. Such systems are expected to be rare: no more than a few over the whole sky based on the luminosity function of Hot DOGs and optical quasars. At z > 5, the hot dust emission peak at 6 μm will shift to ∼40 μm, well beyond the WISE 22 μm (W4) filter. To identify such sources would require deeper imaging at 30–70 μm from future missions such as SPICA, or submillimeter photometry at 200 μm—1 mm with ALMA or CCAT. As noted by Assef et al. (2015), such objects may also have been detected by WISE but failed to meet the W1W2-dropout selection, because they will be detectable by WISE at 3.4 and 4.6 μm. If we relax the W1 and W2 flux limits for Hot DOGs, many contaminants fall into the selection criteria, making it much more difficult to identify the ELIRG systems. It is also possible that AGNs at ∼10^14.5 L_☉ have reached a physical limit for BH accretion, or that the accreting material is depleted after z ∼ 5. If so, this might explain the upper luminosity bound at 10^14.5 L_☉ for hyperluminous Hot DOGs and quasars in Figure 10.