INTERFEROMETRIC FOLLOW-UP OF WISE HYPER-LUMINOUS HOT, DUST-OBSCURED GALAXIES

Table 1 lists the three Hot DOGs reported in this paper. They are among the first Hot DOGs identified by our program, which now includes over 100 spectroscopically confirmed sources (P. R. M. Eisenhardt et al., in preparation). Basic observing information is presented in Table 2.

We observed W2238+2653 in ∼1.2 mm continuum on UT 2011 October 6, 13 and UT 2011 November 2, with the average opacities at 230 GHz of 0.32, 0.47 and 0.07, respectively. The receivers were tuned at a local oscillator frequency of 248 GHz, and the continuum was observed using contiguous ∼500 MHz bands (with ∼5 MHz channels) on the upper and lower correlator sidebands of all 15 antennas, for a total coverage of ∼3 GHz with our setting. We reduced CARMA continuum data for W2238+2653 with the software package Multichannel Image Reconstruction Image Analysis and Display (MIRIAD; Sault et al. 1995). We flagged and calibrated the visibility data using standard calibration procedures with MIRIAD. For each band we flagged the first two and last two frequency channels due to poor sensitivity at the bandpass edges. For data taken on UT 2011 October 6 and 13, we used MWC 349 as the flux calibrator, 3C84 as the passband calibrator, and 2203+317 as the gain calibrator. For data taken on UT 2011 November 2, we used Uranus as the flux calibrator and 3C454.3 as the gain calibrator. The calibrated visibilities from the data sets were then combined. The imaging and deconvolution were done using MIRIAD tasks invert and mossdi. We used natural weighting to maximize the sensitivity to broad, faint structures. The mossdi deconvolution task uses a Steer CLEAN algorithm (Steer et al. 1984).

The CARMA CO line data for W1814+3412 were taken on UT 2011 April 13, May 25 and June 1, with the average opacities at 230 GHz of 0.11–0.13. Only 7 antennas were used on April 13, while all 15 antennas were used on May 25 and June 1. We used Uranus as the flux calibrator, 3C454.3 as the passband calibrator, and 1801+440 as the gain calibrator for W1814+3412 observations. The CO data for W0149+2350 were taken on UT 2011 June 21–23, with the average opacities at 230 GHz of 0.15–0.25, and 15 antennas were used. We used Uranus as the flux calibrator, 3C454.3 as the passband calibrator, and 0152+221 as the gain calibrator for W0149+2352 observations. All these CO observations used contiguous ∼500 MHz bands with ∼5 MHz channels. Individual source was phase, amplitude and passband calibrated using the standard routines in MIRIAD for each track. The files were then combined and the UV data were Fourier transformed and cleaned using the tasks invert and mossdi in MIRIAD. This produced a data cube with a resolution of 100 km s⁻¹.

SMA imaging of W0149+2350 was obtained as part of program 2010A-S052 (PI: R. S. Bussmann). Observations were conducted in the compact array configuration (maximum baseline length of ∼76 m) on UT 2010 November 5 (t_int = 7.6 hr on-source integration time, τ_225 GHz ≈ 0.08). Extended array observations (maximum baseline length of 226 m) were obtained on UT 2010 September 19 (t_int = 4.0 hr on-source integration time, τ_225 GHz ≈ 0.09) and on UT 2010 September 20 (t_int = 4.5 hr on-source integration time, τ_225 GHz ≈ 0.10). The phase stability was good for all observing nights (phase errors between 10°and 30°rms).

We used the SMA single-polarization 230 GHz receivers, tuned such that the CO (J = 8–7) line was covered at the center of the lower sideband. For W0149+2350 (z = 3.228), we set the center frequency at 218.519 GHz for all observations. The SMA receivers provide an intermediate frequency coverage of 4–8 GHz, totaling 8 GHz bandwidth considering both sidebands.

Calibration of the uv visibilities was performed using the Interactive Data Language (IDL) MIR package. The blazar 3C84 was used as the primary bandpass calibrator and Callisto was used for absolute flux calibration. The nearby quasar 0237+288 (F_10 μm = 1.0Jy, 11° from target) was used for the phase gain calibration.

The MIRIAD software package was used to invert the uv visibilities and clean the dirty map. Natural weighting provided maximum sensitivity and resulted in an elliptical Gaussian beam with an FWHM of 224 × 208 at a position angle of 80°east of north for the combined compact and extended array image.

W2238+2653 was observed with NIRC2 behind the Keck II laser guide star adaptive optics (AO) system (Wizinowich et al. 2006; Van Dam et al. 2006) on the night of UT 2011 August 16. We used the R = 14.2 USNO-B star 1168-0602706 (Monet et al. 2003) located 50'' from the target for the tip–tilt reference star. Images were obtained with the Kp filter, which is shifted to shorter wavelengths than the K or Kshort filters and has a slightly wider bandpass (Wainscot & Cowie 1992); we used this filter because it is more sensitive due to lower thermal background. We used the wide camera setting (nominal pixel scale = 00397 pixel⁻¹) which provided a single-frame field of view of 40''× 40''. Nine Kp-band images (120 s per image) were obtained using a three-position dither pattern that avoided the noisy, lower-left quadrant.

The images were reduced using a custom set of IDL scripts. The raw images were first dark-subtracted and then sky-subtracted using a sky frame created from the median average of all frames whose frame-level median value was less than a factor of 1.2 from that of the image being reduced. Finally, a dome flat was used to correct for pixel-to-pixel sensitivity variations. The reduced images were superposed on a larger array and shifted such that a star in common on all images was aligned to the same pixel location. The aligned images were median averaged to form the final mosaic.

W0149+2350 was imaged for 2600 s in the F160W filter with WFC3 on HST as part of program 12481 (PI: C. Bridge) on UT 2011 November 7. The images were obtained at four dithered positions with the "WFC3-IR-DITHER-BOX-MIN" pattern, using the MULTIACCUM mode with 14 samples 50 s apart at each position. The standard CALNICA and CALNICB pipeline from the Space Telescope Science Institute was used for image reduction.

To constrain the cold dust temperatures of Hot DOGs detected in our CARMA and SMA observations, we used CSO 450 μm and Herschel 500 μm continuum measurements. The 450 μm continuum data for W0149+2350 were taken using SHARC2 at the CSO, with details reported in Wu et al. (2012). The 500 μm continuum was observed by SPIRE on Herschel (PI: P. Eisenhardt, Proposal ID: OT1_peisenha_1) on UT 2011 January 3 and UT 2012 January 27 for W2238+2653 and W0149+2350, respectively. The SPIRE maps were made using small jiggle map mode, with a 487 s integration time per source. The data were processed and analyzed with HIPE v11.1.0. The complete Herschel observations for these and other Hot DOGs, with a more detailed analysis of the warm dust components, will be presented in C.-W. Tsai et al. (in preparation).

In Table 3, we present the continuum measurements obtained from the CARMA and SMA continuum images for two Hot DOGs. W0149+2350 was well detected at 1.37 mm in both the compact and extended configuration of the SMA, with a flux density of 1.8 ± 0.2 mJy in the combined image (Figure 1(a)). The source is unresolved in both the combined image and in the extended configuration image, with the highest resolution from the extended configuration of 10. The flux densities derived from the compact and extended configurations are consistent within the calibration uncertainty, which is about 20% for our SMA observations in addition to the uncertainties quoted in Table 3. This implies that the cold dust extends over less than 10, or 7.6 kpc at z = 3.228. The HST WFC3 image (F160W, effective wavelength 1.537 μm) of W0149+2350 is presented in Figures 1(b) and (c). At the redshift of the source, F160W corresponds to rest-frame 3600 Å, tracing the young stellar light of the host galaxy. The resolution of the HST WFC3 image is 013, and the source is well resolved with an effective radius (Re, the radius within which half the light is enclosed) of 034 (2.6 kpc).

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Table 3. 1.3 mm Continuum Measurements for Hot DOGs

Source	Telescope/Config	Wavelength	Beam Size	P.A.	Flux Densitya	Peak Position
		(mm)		(deg)	(mJy)	(J2000.0)
W0149+2350	SMA/Compact	1.37	34 × 30	80	1.8 ± 0.2	01:49:46.18 +23:50:14.8
W0149+2350	SMA/Extended	1.37	13 × 10	80	2.3 ± 0.4	01:49:46.19 +23:50:14.7
W0149+2350	SMA/Combine	1.37	22 × 21	80	1.8 ± 0.2	01:49:46.19 +23:50:14.7
W2338+2653	CARMA/D	1.21	18 × 17	140	4.5 ± 0.8	22:38:10.20 +26:53:20.1

Note. ^aThe quoted uncertainties do not include in uncertainty in the calibration, which is about 20% for SMA observations, and 15% for CARMA observations.

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W2238+2653 was detected by CARMA at 1.21 mm with a flux density of 4.5 ± 0.8 mJy (Figure 1(d)), with an additional 15% uncertainty from calibration. The beam size of the image is 18 × 17 while the source size is 29(± 03) × 26(± 03). Although it seems that the source size is about 50% bigger than the beam and it is promising that the source is resolved, given the low signal-to-noise ratio (S/N; ∼5), we cannot be very certain about its extent based on the CARMA data alone. W2238+2653 was also detected by Bolocam at CSO at 1.1 mm with a flux density of 6.0 ± 2.2 mJy (Wu et al. 2012). Assuming β = 1.5 and T_d = 35 K (see Section 4.2 for why these parameters were chosen), this corresponds to a flux density of 4.6 ± 1.7 mJy at 1.21 mm within the 42'' Bolocam beam, essentially identical to the 4.5 ± 0.8 mJy CARMA value shown in Table 3. The consistency between the CARMA and Bolocam flux densities (within their uncertainties) suggests that not much emission comes from the region outside the ∼2'' CARMA beam. Figures 1(e) and (f) present the NIRC2 image of W2238+2653 in the Kp band, centered at 2.124 μm. This wavelength corresponds to rest frame 6230 Å, tracing old stellar light from the host galaxy. The NIRC2 image resolution is 016, and the effective radius of the source is 042 (3.4 kpc).

Our CO observations of W0149+2350 and W1814+3412 with CARMA also obtained continuum at ∼3 mm. However, since the flux density of these Hot DOGs drops dramatically from 1 mm to 3 mm, and the CO observations were designed to optimize line detection and thus have limited bandwidth, the noise obtained from these 3 mm continuum observations is much higher than predicted flux density. As expected, neither source was detected in the 3 mm continuum, with 2σ upper limits of 2.2 mJy and 1.2 mJy for W0149+2350 and W1814+3412, respectively. The predicted 3 mm continuum flux densities (assuming β = 1.5 and T_d = 35 K, see Section 4.2) based on the 1.3 mm SMA detection for W0149+2350 and the Bolocam 1.1 mm upper limits for W1814+3412 (Wu et al. 2012) are 0.11 mJy and less than 0.07 mJy for W0149+2350 and W1814+3412, respectively, which are an order of magnitude lower than the observed limits.

For both W2238+2653 and W0149+2350, the peak position in the SMA and CARMA images agrees well with the WISE position (see Figures 1(c) and (f), differences are less than 04) where the redshift is measured, confirming that the high luminosity source coincides with the WISE-selected target. From the HST and Keck AO images and the submillimeter interferometric maps, there is no clear morphological evidence for strong gravitational lensing, in which case the source would likely have a multiple, offset, or arc-like distortion set of light peaks, rather than the simple centrally concentrated and roughly axisymmetric features we see at all wavelengths (Figure 1). These are in marked contrast with known and confirmed strongly lensed star-forming galaxies. Examples include candidates selected from Sloan Digital Sky Survey data and confirmed by HST observations (e.g., Bolton et al. 2008), and candidates selected by South Pole Telescope observations and confirmed by ALMA (Hezaveh et al. 2013). At the sensitivity of the data we report on here, a configuration suggestive of strong lensing behavior would have been evident.

We attempted to detect CO 3–2 for W1814+3412, and CO 4–3 for W0149+2350 at 3 mm using CARMA in the D configuration. Both targets were undetected, with the implied 1σ CO (4–3) limits of 0.85 Jy km s⁻¹ for W0149+2350 and CO (3–2) limits of 0.46 Jy km s⁻¹ for W1814+3412. The CO (8–7) transition was also covered by the 1 mm continuum observation of W0149+2350 using the SMA. No detection was obtained on this high-J transition, with a 1σ CO (8–7) limit of 0.45 Jy km s⁻¹. Although two J ladder transitions (CO 4–3 and CO 8–7) were observed for W0149+2350, its CO excitation cannot be further constrained since both lines were undetected. In order to estimate the molecular gas traced by the CO (1–0) luminosity, we used empirical conversion factors from Carilli & Walter (2013). These are 0.97 for CO (3–2) to CO (1–0), and 0.87 for CO (4–3) to CO (1–0). These luminosity ratios are for quasar-like targets, which we adopted since Hot DOGs are dominated by strong AGNs. The conversion factors are lower for SMGs: 0.66 for CO (3–2) to CO (1–0), and 0.46 for CO (4–3) to CO (1–0), leading to up to a factor of two lower CO luminosity and gas mass estimate, and can be considered a lower limit. Higher J CO transitions like CO (8–7) generally do not contribute significantly to the total CO luminosity for high-z quasars and SMGs (e.g., Weiß et al. 2007b), except in unusual cases like APM J08279+5255 (e.g., Weiß et al. 2007a), where the CO ladder SED peaks at J = 10. Although we know little about the excitation for these Hot DOGs, the non-detection of W0149+2350 in CO (8–7) at a lower limit than the non-detection in CO (4–3) suggests it is unlikely to be a very high excitation AGN like APM J08279+5255. Therefore, in this paper we only use the CO (4–3) limit to estimate the gas mass limit for W0149+2350.

To calculate the upper limit of molecular gas mass from the CO measurement, we assumed an FWHM line width of 400 km s⁻¹, the median value for detected CO lines in z > 1 quasars (e.g., Carilli & Walter 2013). Taking the approach used in Solomon et al. (1997), the line luminosity of CO is given by

$$\begin{equation} L^{\prime }_{\rm CO}=3.25\times 10^{7}\times I_{\rm CO} \nu _{\rm obs}^{-2} D_{L}^{2} (1+z)^{-3}, \end{equation} \tag{ 1 }$$

where $L^{\prime }_{\rm CO}$ is in units of K  kms⁻¹pc⁻², I_CO is the integrated intensity of the CO line in Jy km s⁻¹, ν_obs is the observing frequency in GHz, and D_L is the luminosity distance in Mpc. To convert CO (1–0) luminosity to total molecular gas mass $M_{{\rm H}_{2}}$, an empirical relation is taken: $M_{{\rm H}_{2}}=\alpha L^{\prime }_{\rm CO}$, where $M_{{\rm H}_{2}}$ is in units of M_☉ and $L^{\prime }_{\rm CO}$ is in units of K km s⁻¹ pc⁻². The converting factor α has a typical value of 0.8 for bursting galaxies, and a much higher value (∼4) for main sequence galaxies (e.g., Bolatto et al. 2013; Carilli & Walter 2013). We use α = 0.8 for Hot DOGs in this paper. The derived parameters are listed in Table 4. Another attempt to measure CO and resolved continuum emission at observed frame 1 mm for W1814+3412 was conducted using the IRAM telescope, which is reported in A. Blain et al. (in preparation).

Table 4. CO Measurements for Hot DOGs

Source	Line	1σ rms	rms Bin	ICO Limit (1σ)	$L^{\prime }_{\rm CO}$ Limit (2σ)	$M_{\rm H_{2}}$ Limit (2σ)
		(mJy beam−1 km s−1)	(km s−1)	(Jy km s−1)	(1010 K km s−1 pc−2)	(1010 M☉)
W0149+2350	CO 4–3	4.3	100	0.85	<4.8	<3.3
W1814+3412	CO 3–2	2.3	100	0.46	<3.0	<2.3

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For both W2238+2653 and W0149+2350 only a single, centrally condensed source is seen in the near-IR and millimeter images, with no obvious signatures of merging such as multiple cores, tails or arms. The consistent flux densities from both the compact and extended configurations for W0149+2350, and from the CARMA and CSO observations for W2238+2653, suggest neither a halo of faint emission, nor do fainter compact sources seem to be contributing substantially. This argues that these two sources are single and compact. (Here we refer sources as compact when their angular size is less than 2''.) If these Hot DOGs do have a merging origin, and if the theory of galaxy evolution through merging (e.g., Hopkins et al. 2008) and a galaxy evolutionary sequence of SMGs–DOGs–Hot DOGs–quasars suggested in Wu et al. (2012) is true, then the morphology of these two Hot DOGs support the scenario that the merging event was not in the recent past (i.e., ∼80 Myr; Mihos & Hernquist 1996), and the Hot DOGs are likely closer to the quasar phase. We use the Sérsic (1968) index to explore if the sources have a disk-type or bulge-type light profile (e.g., Simmons & Urry 2008). Using GALFIT (Peng 2002), we obtained Sérsic indices n from the NIRC2 image and HST images. The Sérsic index is 1.4 for W2238+2653, and 1.6 for W0149+2350, indicating a disk-type morphology. These values are similar to the typical n < 2 found for DOGs (Bussmann et al. 2009a, 2011).

About one-third of optically selected quasars have submillimeter/millimeter continuum detections at mJy levels out to high redshift (Priddey et al. 2003; Beelen et al. 2006; Wang et al. 2008a, 2008b), and most of the submillimeter-detected quasars yield CO detections. The size of their CO reservoirs are typically compact, less than a few kiloparsecs (e.g., Walter et al. 2004; Riechers et al. 2011). These gas-rich quasars are thought to correspond to an earlier phase of activity than submillimeter-faint quasars. SMG galaxies, however, have been found to have larger cold gas reservoirs, typically larger than ∼10 kpc (e.g., Ivison et al. 2010; Carilli et al. 2011; Hodge et al. 2012). Based on our 1.3 mm images, the cold dust size is <8 kpc in diameter for W0149+2350, consistent with the size of the stellar emission in near-IR image. The cold dust may be more extended for W2238+2653, but the size of dust emission is quite uncertain due to the low S/N CARMA detection, and the agreement between the 2'' CARMA flux density and that from the 42'' CSO Bolocam data argues against significant emission beyond a 16 kpc diameter. The half-light radius in the near-IR image of W2238+2653 is 3.4 kpc. (Without a much higher S/N submillimeter interferometric observation, we cannot meaningfully compare the cold dust extent to the stellar extent.) These two cases suggest the size of Hot DOGs is compact compared to SMGs and likely similar to gas-rich quasars.

The most striking characteristic feature of Hot DOGs is that their SEDs have unusually strong mid-IR emission compared to their submillimeter emission, implying hot dust dominates the energy output of these objects. Wu et al. (2012) found that despite the much stronger mid-IR luminosity (presumably due to AGN heating) for Hot DOGs than for SMGs and standard DOGs, the cold dust emission traced by 350 μm is actually not very different for these populations. If we simplistically assume that there are two major dust components in these galaxies—an AGN-heated hot dust component and a starburst-heated colder dust component—then the similar submillimeter emission levels of Hot DOGs, SMGs and DOGs suggest that these populations share a similar level of star formation activity.

In reality, these systems are likely more complicated than this simple two-temperature dust component model, but our longest wavelength data tend to trace the coldest major dust component, which is less likely to be heated by an AGN, and more likely to be heated by star formation. Wu et al. (2012) used data at 350 μm and 1.1 mm to constrain the cold dust properties of Hot DOGs, finding that they are not very different from local starburst galaxies like Arp220 (a local analog to SMGs) and the AGN/starburst composite system Mrk231 (a good SED template for standard power-law DOGs; e.g., Bussmann et al. 2009b; Melbourne et al. 2012). In addition to the hotter component, with dust temperatures ranging up to several hundred K, Hot DOGs likely also have a starburst-related cold dust component with a temperature between 30 and 50 K, as suggested by their 350 μm to 1.1 mm ratios (Wu et al. 2012). The real typical temperature could be closer to 30 K than 50 K considering that 350 μm data could be affected more by the AGN heating than the 1.1 mm data, and such a temperature is similar to cold dust temperatures found in SMGs and DOGs (e.g., Magnelli et al. 2012a; Melbourne et al. 2012). The presence of a millimeter-wave continuum limit allows the possible combinations of temperature and mass in such a cold dust component to be constrained.

Cold dust mass is a key parameter for understanding galaxies, providing insight into gas and thus total baryonic mass via assumed conversions. The SEDs of Hot DOGs are flat (in units of νf_ν) from mid-IR to submillimeter wavelengths (Wu et al. 2012; Bridge et al. 2013; Jones et al. 2014; C.-W. Tsai et al., in preparation), implying the AGN-heated mid-IR component is of comparable strength to the starburst-related submillimeter component in terms of energy output. Since energy output goes as the fourth power of temperature at short wavelengths where the dust emission is optically thick, and which contributes significantly to the near- to mid-IR SED, the colder dust (T_d < 50 K) associated with star formation constitutes a significant fraction of the overall dust mass. We can roughly estimate the mass of the cold dust using the longest wavelength data and a single temperature blackbody model:

$$\begin{equation} M_d= \ \frac{D_{L}^{2}}{(1+z)} \cdot \frac{S(\nu _{\rm obs})}{ \kappa (\nu _{\rm rest})B(\nu _{\rm rest},T_d)}, \end{equation} \tag{ 2 }$$

where M_d is the dust mass, D_L is the luminosity distance, ν_rest is the rest frequency of the observed band (which are 925 GHz and 824 GHz for W0149+2350 and W2238+2653, respectively), B_ν is the Planck function, κ_ν = κ₀(ν/1 THz)^β is the dust mass absorption coefficient, and β is the emissivity index. In this paper, we adopt κ₀ = 2.0 m² kg⁻¹ (Draine 2003), and assume a dust temperature of 35 K (roughly the median dust temperature found in SMGs and DOGs; Magnelli et al. 2012a; Melbourne et al. 2012) and β = 1.5 (typical emissivity index assumptions for SMGs and DOGs).

Based on the ∼1.3 mm continuum measurements, we calculate cold dust masses of 2.0× 10⁸ M_☉ for W0149+2350 and 3.9 × 10⁸ M_☉ for W2238+2653. However, there are large uncertainties in these estimates. Besides the 10%–20% statistical flux density uncertainties, we also need to consider uncertainties in κ and T_d. Changing β from 1.5 to 2.0 only changes κ by less than 10%; however, κ₀ is uncertain to at least a factor of two (Dunne et al. 2003). Dust temperature uncertainties can bring in another a factor of two or more uncertainty, and likely dominate the overall uncertainty in dust mass estimates.

To constrain the cold dust temperature, we set upper limits on the cold dust component temperature (and lower limits on the cold dust mass) for W0149+2350 and W2238+2653, by using the longest wavelength (500 μm) continuum data available from Herschel. W2238+2653 was detected at 500 μm by SPIRE on Herschel, with a flux density of 61.2 ± 6.0 mJy. While no Herschel detection was made of W0149+2350 (3σ upper limit of 57 mJy), we detected a flux density of 35 ± 9 mJy at 450 μm using SHARC2 at the CSO (Wu et al. 2012). Using the flux density ratios of the 450 μm or the 500 μm measurements to the ∼1.3 mm measurements, we estimate upper limits for the cold dust temperatures with a single-temperature blackbody model, adopting β = 1.5. The derived temperature limits are noticeably warmer: 55 K for W0149+2350, and 69 K for W2238+2653, corresponding to cold dust masses of 1.1 × 10⁸ M_☉ and 1.4 × 10⁸ M_☉ for W0149+2350 and W2238+2653, respectively.

These temperatures derived by including both 450/500 μm and 1.3 mm data are higher than the representative temperatures of SMGs and DOGs. Since the mid-IR to submillimeter ratio is unusually high in these Hot DOGs, it is plausible that even continuum at 450–500 μm (rest-frame 100–150 μm) is significantly affected by the AGN contribution, and Herschel data does not trace the star-formation-related cold dust well as it does in typical SMGs. Checking continuum data for Hot DOGs in Wu et al. (2012) that have both 350 μm and 1.1 mm detections, we find a similar trend, that including both 350 μm and 1.1 mm measurements, the derived dust temperature are higher, and the derived cold dust masses are generally a factor of two smaller than those derived from 1.1 mm emission alone using the same single-temperature blackbody model. This implies a more significant contribution from AGN heating to the 350 μm emission than to the 1.1 mm continuum. For this reason, we consider the above cold dust mass estimates including the ∼450–500 μm data as a lower limit. To constrain the upper limit of the cold dust mass, we take a lower limit of the dust temperature as 20 K, which is about the average dust temperature of the Milky Way (Wright et al. 1991). Assuming β = 1.5, this corresponds to cold dust mass upper limits of 7.0 × 10⁸ M_☉ and 1.2 × 10⁹ M_☉ for W0149+2350 and W2238+2653, respectively. A more accurate way to estimate the star-formation related cold dust mass is to obtain multiple measurements at a range of wavelengths longer than 1 mm and fit the cold dust component. Alternatively, one can construct a complete mid-IR to millimeter SED and decompose the different dust components with different temperatures, separating contributions from the AGN and starburst, as a recent example shown in Drouart et al. (2014). This is beyond the scope of this paper, and could be subject to free–free contamination at very long wavelengths.

Although simplistic in nature, our approach to estimate cold dust masses based on the continuum measurement at ∼1 mm allows one to compare Hot DOGs with other z ∼ 2 bursting galaxy populations (SMGs, DOGs, quasars, RGs), as shown in Figure 2. Longer wavelength detections were reported in Wu et al. (2012) for six additional Hot DOGs at 1.1 mm and in Jones et al. (2014) for six Hot DOGs at 850 μm. We included longer wavelength detections for other bursting galaxy populations, mostly from Carilli & Walter (2013) and references therein. We use a consistent dust temperature T_d = 35 K and emissivity β = 1.5 for all calculations. Known lensed targets have been excluded from our sample.

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The cold dust masses of Hot DOGs are comparable to those in submillimeter-detected quasars and RGs, implying they are both massive populations. This may be a hint of a possible evolutionary connection between Hot DOGs and visible quasars: Hot DOGs may be the progenitors of very luminous quasars, but are still deeply embedded in a hot dust cocoon, which obscures the AGN at optical/near-IR wavelengths (Assef et al., 2014) and X-ray wavelengths (Stern et al. 2014). The SMGs in Figure 2 are about a factor of two less massive than quasars and Hot DOGs. However, considering the large uncertainty due to dust temperature, and that both quasars and Hot DOGs host powerful AGNs as an additional heating source, this difference in cold dust mass may not be significant. High-redshift main sequence galaxies are generally very faint at ∼1 mm (e.g., Magnelli et al. 2012b), implying that their derived cold dust masses are generally smaller, or their cold dust temperatures are lower than the bursting galaxies in Figure 2.

Molecular gas probed by CO is another important measurement of total mass for starburst galaxies. Although we did not obtain detections, we compare the 2σ upper limit on gas mass for the two Hot DOGs to detected molecular gas mass in other populations in Figure 3. The detected molecular gas mass of SMGs, DOGs, quasars, and RGs plotted in Figure 3 are collected from public references (see caption for references). Their gas masses are directly quoted as reported in the references, which were all converted from solid CO detections, with proper CO excitation models applied to convert to CO 1–0 luminosity, and adopted converting factor of 0.8 from CO luminosity to molecular gas mass. In Figure 3, the gas mass of SMGs and quasars are comparable, while starburst DOGs are slightly less massive. Our upper limits suggest that these two Hot DOGs might not be as gas-rich as the quasars in Figure 3. However, due to the limited number of Hot DOGs reported here and the shallowness of our CARMA data, we do not yet have strong constraints on the molecular gas content of Hot DOGs. Longer integrations and/or larger interferometer arrays (e.g., the ALMA) are needed to better constrain the CO gas mass of Hot DOGs.

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