A MASSIVE MOLECULAR GAS RESERVOIR IN THE z = 2.221 TYPE-2 QUASAR HOST GALAXY SMM J0939+8315 LENSED BY THE RADIO GALAXY 3C220.3

Synchrotron continuum emission from extended components of a radio galaxy decreases with increasing radio frequencies and the spectrum is commonly characterized by a power-law distribution S ∝ ν^−α, where the spectral index α is ≳ 0.5. While the contribution from extended components decreases, studies using samples of radio galaxies have suggested that the flat/inverted spectrum of the compact radio core component rises and dominates the flux density at higher frequencies (Kellermann & Pauliny-Toth 1981; Begelman et al. 1984). This has been observed in a FR-II galaxy at similar redshift—3C220.1 at z = 0.610, where observations were carried out at the observed-frame frequency of ∼90 GHz (Hardcastle & Looney 2008).

Previously, an upper limit of <0.17 mJy at 4.6 GHz has been established by Mullin et al. (2006) on the core component of 3C220.3 and an unambiguous detection of 0.8 mJy at 9 GHz has been reported by H14, suggesting a substantially inverted spectrum of the core (Figure 4). Consequently, we may naively expect the integrated flux density in our continuum detection of S_{104 GHz} = 7.39 ± 1.42 mJy to be dominated by the unresolved core component of the foreground FR-II galaxy, which is at z = 0.685. However, the deconvolved spatial size of the source matching that in the resolved image (see Figure 1) is suggestive of a marginally resolved detection of the extended lobe components. This is plausible given that the orientation of the synthesized beam in our observations is in alignment with the axis along the lobes of the radio galaxy, as shown in Figure 1. We investigate this disparity by fitting models to existing SED measurements as listed in Table 2 and extrapolating the fit to estimate the flux density of the lobes at the frequency of our continuum measurement.

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Following Equation (1) in Cleary et al. (2007), the fit to the lobe emission can be expressed as a parabolic function:

$$\begin{eqnarray}&&\mathrm{log}{F}_{\nu }^{\mathrm{lobe}}{(\nu )\propto -\beta (\mathrm{log}\nu -\mathrm{log}{\nu }_{{\rm{t}}})}^{2}+\mathrm{log}\left(\mathrm{exp}\left(\displaystyle \frac{\nu }{{\nu }_{c}^{\mathrm{lobe}}}\right)\right)\end{eqnarray} \tag{ 1 }$$

where ${F}_{\nu }^{\mathrm{lobe}}$ is the flux density of the lobes, β is a parameter representing the bending of the parabola, ν_t is the frequency at which the optical depth of the synchrotron emitting plasma reaches unity, and ${\nu }_{c}^{{\rm{lobe}}}$ is the frequency corresponding to the cutoff energy of the lobe plasma energy distribution. The extrapolated flux density at 104 GHz is consistent with the peak flux density of our continuum measurement (Figure 4). The 9σ detection of the continuum thereby suggests a dominant contribution from the lobes and that the peak flux density is not dominated by emission toward the core. Moreover, the peak position of the 104 GHz continuum is centered toward the brighter northern lobe (Figure 1), which further supports our argument. Consequently, a conservative upper limit of S_ν < 4.93 mJy on the core emission can be established using the measured peak flux density. Yet by considering the difference between the integrated flux density from our measurement and the flux density from an extrapolation of the model (see Figure 4; S_{104 GHz,fit} = 5.10 mJy), we establish a more stringent constrain on this upper limit of S_ν < 2.29 mJy. We did not extrapolate the core measurements to the frequency of our continuum, as previous measurements of the core are taken across different epochs and the core may be time-variable.

Studies by Meisenheimer et al. (1989) and Hardcastle & Looney (2008) have suggested that spectra of hotspots are flat up to optical frequencies where some exhibit spectral steepening in cm and mm wavelengths (e.g.,  3C123). At the resolution of our observations it remains unclear whether the measured flux density is dominated by emission from the compact hotspots or that from the surrounding diffuse lobe components.

To constrain the dust and gas properties in the ISM of SMM J0939, we perform SED fitting to the photometric data obtained with Herschel/PACS and SPIRE at wavelengths between observed-frame 70–500 μm, and the interferometric data obtained with the SMA at 1 mm (H14). We use the publicly available software mbb_emcee ¹ to perform the SED fitting; the code uses an affine-invariant Markov chain Monte Carlo (MCMC) approach and further details of the code are given by Riechers et al. (2013) and Dowell et al. (2014).

The functional form of the fit comprises a single-temperature modified blackbody function joined to a ${B}_{\lambda }\propto {\lambda }^{\alpha }$ power law on the blue side of the SED. We fit both optically thick and optically thin models. In the optically thick case, the wavelength λ₀ = c/ν₀ is an additional parameter representing the rest-frame wavelength at which the optical depth τ_ν = (ν/ν₀)^β reaches unity. Thus, the functional form of the modified blackbody in the optically thick regime is as follows.

$$\begin{eqnarray}&&{B}_{\lambda }\propto \displaystyle \frac{\left(1-{\mathrm{exp}}^{-{(\frac{{\lambda }_{0}(1+z)}{\lambda })}^{\beta }}\right){\left(\displaystyle \frac{c}{\lambda }\right)}^{3}}{{\mathrm{exp}}^{\frac{{hc}}{\lambda {\rm{kT/(1+z)}}}}-1}.\end{eqnarray} \tag{ 2 }$$

In the optically thin regime, the functional form reduces to

$$\begin{eqnarray}&&{{\rm{B}}}_{\lambda }\propto \displaystyle \frac{{\left(\displaystyle \frac{c}{\lambda }\right)}^{\beta +3}}{{\mathrm{exp}}^{\frac{{hc}}{\lambda {\rm{kT/(1+z)}}}}-1}\end{eqnarray} \tag{ 3 }$$

where T is the rest-frame cold dust temperature, β is the dust emissivity index, and α is the mid-infrared power-law spectral index. The overall fit is normalized using the observed-frame 500 μm flux density, hence this becomes an additional parameter (f_{norm,500 μm}) in the fit. For both models we impose an upper limit of 60 K on the observed-frame dust temperature (T/(1 + z)), and an upper limit of 2.2 on β. For the optically thick model we impose an additional upper limit of 3000 μm on λ₀ (1 + z).

The best-fit values in both regimes are listed in Table 3 and the correlation plots are available in the Appendix. The best-fit solution of optically thin models corresponds to χ² = 5.31 with three degrees of freedom whereas that of optically thick models corresponds to χ² = 2.25 with two degrees of freedom, suggesting a better fit than in the optically thin case. In the subsequent analysis we employ the inferred values from the optically thick model. The best-fit solution yields a far-infrared luminosity (rest-frame 42.5−122.5 μm) of L_FIR = ${53.3}_{-1.1}^{+1.1}$ × 10¹² L_⊙ and a total infrared (IR; rest-frame 8−1000 μm) luminosity of L_IR = ${88.5}_{-2.6}^{+2.6}$ × 10¹² L_⊙.² Assuming a dust absorption coefficient of κ_ν = 2.64 m² kg⁻¹ at 125.0 μm(Dunne et al. 2003), we find a dust mass of M_dust = ${50.5}_{-20.2}^{20.4}\times$10⁸ M_⊙; the uncertainties do not include those in the dust absorption coefficient (κ_ν). These properties are derived based on the SED fitting to the photometric data, i.e., prior to lensing correction. We note that the dust mass is weakly constrained owing to the dearth of data in the rest-frame FIR waveband. As such, we investigate how the dust mass would be affected by fitting additional optically thick models with an upper limit of β adjusted from 2.2 to 3.0. While the difference in each best-fit parameter between this scenario and the previous models (with an upper limit of β = 2.2) is within 3%, we find that the dust mass inferred from this best-fit SED model is boosted by a factor of ∼2.

Table 3.  SED Fitting Results

Parameters	Optically Thick	Optically Thin
χ2	2.25	5.31
DOF	2	3
T (K)	${63.1}_{-1.3}^{+1.1}$	${52.0}_{-1.2}^{+1.3}$
β	${1.9}_{-0.5}^{+0.6}$	${0.7}_{-0.3}^{+0.2}$
α	${2.9}_{-0.4}^{+0.3}$	${2.8}_{-0.2}^{+0.2}$
λ0a (μm)	${248.7}_{-123.8}^{+86.0}$	⋯
λpeakb (μm)	${254.7}_{-6.1}^{+6.2}$	${301.4}_{-30.1}^{+29.0}$
fnorm, 500μmc (mJy)	${267.4}_{-16.3}^{+16.7}$	${244.3}_{-15.3}^{+15.3}$
LIRd(1012L⊙)	${88.5}_{-2.6}^{+2.6}$	${89.2}_{2.5}^{+2.5}$
Mduste(108M⊙)	${50.5}_{-20.2}^{+20.4}$	${25.7}_{-5.5}^{+3.9}$

Notes. Errors reported here are ±1σ. L_IR and M_d are reported prior to lensing correction.

^aRest-frame wavelength where τ_ν = 1. ^bObserved-frame wavelength of the SED peak. ^cObserved-frame flux density at 500 μm. ^dRest-frame 8–1000 μm luminosity. ^eDerived assuming a standard absorption mass coefficient κ = 2.64 m² kg⁻¹ at λ = 125.0 μm (Dunne et al. 2003).

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While the ground state CO transition line traces the cold molecular gas in the ISM (e.g., Wilson et al. 1970; Downes & Solomon 1998), transition lines of higher rotational states (J > 1) are frequently observed in high-redshift sources as the ground state transition line is redshifted to lower frequencies that can only be observed with traditional radio telescopes (Carilli & Walter 2013). Consequently, assumptions on the CO excitation conditions are required to derive the molecular gas mass using the M (H₂)-to-${L}_{{\rm{CO}}}^{\prime }$ conversion factor (α_CO) when extrapolating from higher-J CO lines.

Recent observations in high-redshift quasar hosts suggest that the ratio is R₃₁ ∼ 1 (Riechers et al. 2006, 2011c). In the case of high-redshift type-2 quasars Riechers et al. (2011c) report a brightness temperature ratio of R₃₁ = 1.00 ± 0.10 for IRAS F10214+4724 (hereafter F10214), which is currently the only known type-2 quasar with both CO(J = 3 $\to$ 2) and CO(J = 1 $\to$ 0) line measurements. Here we derive the molecular gas mass assuming thermalized excitation of CO, as SMM J0939 is postulated to be hosting a type-2 quasar (H14).

We calculate the CO(J = 1 $\to$ 0) line luminosity using a standard relation (e.g., Solomon & Vanden Bout 2005) and assuming a conversion factor of α_CO = 0.8 M_⊙ (K km s⁻¹ pc²)⁻¹ based on empirical relations from local ULIRGs, which is typically adopted for SMGs (e.g., Tacconi et al. 2006, 2008; Bothwell et al. 2013). This corresponds to ${L}_{{\rm{CO(1-0)}}}^{\prime }$ = (3.42 ± 0.71) × 10¹⁰ (10.1/μ_L) K km s⁻¹ pc², hence the inferred total molecular gas mass is M_gas = (2.74 ± 0.57) × 10¹⁰ M_⊙ after correcting for lensing magnification. This results in a gas-to-dust ratio of f_gas-dust = M_gas/M_dust = 55 ± 24. This is in good agreement with the values found for other SMGs (Coppin et al. 2008; Michałowski et al. 2010; Riechers et al. 2011a).

We derive the SFR using the lensing-corrected far-infrared luminosity, assuming that the dominant heating source of cold dust is young massive stars and that a contribution from the dust-enshrouded AGN is negligible. This assumption stems from the results of recent studies using various approaches such as spectral decomposition techniques and correlations between far-infrared luminosity and other tracers of star formation. These results suggest that far-infrared emission dominantly originates from star formation in host galaxies, even in the most energetic QSOs (e.g., Netzer et al. 2007; Mullaney et al. 2011; Harrison et al. 2015). Using the Kennicutt (1998) relation and adopting a Chabrier (2003) stellar initial mass (IMF) function, we find a SFR_FIR = 526 ± 73 M_⊙ yr⁻¹. The starburst in SMM J0939 can be maintained at its current rate for a time that can be approximated by the gas depletion timescale, τ_depl = M_gas/SFR, which assumes no replenishment of gas and feedbacks. This corresponds to τ_depl = 52 ± 8 Myr, which is in good agreement with those found in other SMGs (e.g., Greve et al. 2005).

The SFR per unit mass of molecular gas is commonly taken as a measure of the star formation efficiency. We compute this ratio using the far-infrared and CO luminosities. The derived SFE is therefore independent of the magnification factor, the CO luminosity to gas mass conversion factor (α_CO), and the IMF. However, this assumes that differential lensing between the CO and far-infrared emission is negligible. The resulting ratio is SFE_FIR = 154 ± 25 L_⊙ (K km s⁻¹ pc²)⁻¹, which is comparable to those found in "typical" SMGs (Greve et al. 2005; Tacconi et al. 2006; Riechers et al. 2011a).

We compute the surface densities by dividing half the SFR and gas mass by the area subtended by the half-light radius (e.g., Genzel et al. 2010; Harrison et al. 2015), yielding Σ_SF = 106 M_⊙ yr⁻¹ kpc⁻² and Σ_gas = 5.48 × 10⁹ M_⊙ kpc⁻², respectively. These results are in good agreement with values typical for SMGs (Tacconi et al. 2006; Hodge et al. 2015). The inferred surface densities of SMM J0939 follow a universal Schmidt-Kennicutt relation between the SFR surface density and the molecular gas surface density: Σ_SF = 9.3(±2) × 10⁻⁵ (M_gas/2$\pi {R}_{{\rm{1/2}}}^{2}{)}^{1.71(\pm 0.05)}$, which was derived using a sample of local star-forming galaxies and high-redshift galaxies out to z ∼ 2.5, assuming a Chabrier IMF (Bouché et al. 2007).

Our lens model suggests a half-light radius of r_s ∼ 1 kpc for the dust-emitting region in SMM J0939. This is comparable to the half-light radii found in other SMGs with high-resolution imaging. Similar sizes have been reported by Bussmann et al. (2013) who find typical radii of 1.5 kpc for a sample of Herschel—selected lensed SMGs with S_{500 μm} > 100 mJy. Also, Simpson et al. (2015) report a radial extent of 1.2 kpc for a sample of unlensed SMGs with S_{850 μm} = 8−16 mJy.

We estimate the dynamical mass of SMM J0939 using our CO(J = 3 $\to$ 2) line measurement and assuming that the molecular gas is virialized. With this assumption, we use an isotropic virial estimator (e.g., Engel et al. 2010) with the FWHM of the CO(J = 3 $\to$ 2) line profile and the half-light radius from our lens model for R_eff, assuming that the dust emission traces the same emitting region as the CO. We find a dynamical mass of M_dyn = (7.84 ± 2.84) × 10¹⁰ M_⊙ and a gas-to-dynamical mass fraction of f_gas-to-dyn = 0.35 ± 0.14, which is consistent with those of other SMGs (Tacconi et al. 2006). We note that a derived dynamical mass based on this assumption is likely to be biased toward low values, as the CO-emitting region can be apparently more extended than the dust-emitting region due to the low dust optical depth at larger radii. This is supported by recent studies in which CO source sizes ranging from ∼4−20 kpc have been found, which are larger than typical dust continuum sizes (Tacconi et al. 2006; Ivison et al. 2011; Riechers et al. 2011a; Hodge et al. 2013, 2015).