ISM Properties of a Massive Dusty Star-forming Galaxy Discovered at z ∼ 7

The redshift search for SPT0311-58 was performed in ALMA band 3 by combining five tunings covering 84.2–114.9 GHz (project ID: 2015.1.00504.S; see Weiß et al. 2013; Strandet et al. 2016 for further details on the observing setup). The observations were carried out on 2015 December 28 and 2016 January 2 in the Cycle 3 compact array configuration. The number of antennas varied from 34 to 41, with baselines up to 300 m yielding a synthesized beam size of $2\buildrel{\prime\prime}\over{.} 2\mbox{--}3\buildrel{\prime\prime}\over{.} 0$. Typical system temperatures for the observations were ${T}_{\mathrm{sys}}=50\mbox{--}80\,{\rm{K}}$ (SSB). Flux calibration was done with Uranus, bandpass calibration with J0334−4008, and phase calibration with J0303−6211 and J0309−6058. The on-source time varied between 60 and 91 s per tuning, accounting for a total of 6 minutes and 10 s. The data were processed using the Common Astronomy Software Application package (McMullin et al. 2007).

We created a cleaned 3 mm continuum image combining all five tunings. This yields a high signal-to-noise ratio (S/N) detection of ∼35. We also generated a spectral cube using natural weighting with a channel width of 19.5 MHz (50–65 km s⁻¹ for the highest and lowest observing frequency, respectively), which gives a typical noise per channel of 0.9–1.7 mJy beam⁻¹.

The ALMA 3 mm spectrum of SPT0311−58 was extracted at the centroid of the 3 mm continuum emission (α: 03^h11^m33142 δ: −58°23'3337 (J2000)) and is shown in Figure 1. We detect emission in the CO J = 6–5 and 7–6 lines and the ${[{\rm{C}}{\rm{I}}]}^{3}{P}_{2}{-}^{3}{P}_{1}$ line (in the following 2–1) and their noise-weighted line frequencies yield a redshift of $z=6.900\pm 0.002$. We also see hints of H₂O(${2}_{11}$–${2}_{02}$) and CH⁺(1–0), but these are not formally detected in this short integration.

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The line and continuum properties are given in Table 1. For the fit to the CO(7–6) and $[{\rm{C}}\,{\rm{I}}]$(2–1) lines we fix the line width to the mean value derived from the unblended lines. Their uncertainties include the variations of the line intensities for a fit where the line width is a free parameter.

Table 1.  Observed Properties of SPT0311-58

Line Properties					Continuum Properties
Transition	$\int {SdV}$	dVa	$L^{\prime}$	$L$	Wavelength	${S}_{\nu }$
	(Jy km s−1)	(km s−1)	×1011 (K km s−1 pc−2)	×108 (L⊙)	(μm)	(mJy)
CO(3–2)	0.96 ± 0.15	790 ± 150	1.52 ± 0.24	2.01 ± 0.32	3000	1.30 ± 0.05
CO(6–5)	2.10 ± 0.33	720 ± 140	0.83 ± 0.13	8.8 ± 1.4	2000	7.5 ± 1.3
CO(7–6)	2.78 ± 0.80	750b	0.81 ± 0.11	13.6 ± 1.8	1400	19.0 ± 4.2
$[{\rm{C}}\,{\rm{I}}]$(2–1)	1.29 ± 0.80	750b	0.37 ± 0.10	6.4 ± 1.8	870	32.0 ± 5.0
$[{\rm{C}}\,{\rm{II}}]$APEX	22.1 ± 5.1	890 ± 260	1.16 ± 0.27	254 ± 59	500	52.0 ± 8.0
$[{\rm{C}}\,{\rm{II}}]$ALMA	25.88 ± 0.65		1.36 ± 0.03	298.1 ± 7.5	350	38.0 ± 6.0
					250	29.0 ± 8.0

Notes.

^aFWHM. ^bFixed from CO(3–2) and CO(6–5).

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We used the 7 mm receivers of the Australia Telescope Compact Array (ATCA) to observe the CO(3–2) line (project ID: CX352). Observations were carried out with the hybrid H214 array, which yields a beam size of 5''–6'' at the observing frequency of 43.77 GHz. The line is detected with an S/N of 5.0 at a frequency and line width consistent with the ALMA derived redshift and line profiles.

In addition, we used the Atacama Pathfinder Experiment (APEX) to observe $[{\rm{C}}\,{\rm{II}}]$ at 240.57 GHz. The observations were carried out in 2016 April–May in good weather conditions with a precipitable water vapor content <1.5 mm (project IDs: E-296.A-5041B-2016 and M-097.F-0019-2016). The observations were performed and the data processed as described by Gullberg et al. (2015). The $[{\rm{C}}\,{\rm{II}}]$ line is detected with an S/N of 4.3. From ALMA high spatial resolution observations of the $[{\rm{C}}\,{\rm{II}}]$ line (D. P. Marrone et al. 2017, in preparation; project ID: 2016.1.01293.S), we extract a $[{\rm{C}}\,{\rm{II}}]$ spectrum and flux, which are in good agreement with the APEX data. We adopt the ALMA $[{\rm{C}}\,{\rm{II}}]$ flux hereafter.

The line parameters derived from Gaussian fits to the data are given for both transitions in Table 1; the spectra are shown in Figure 1.

Table 1 (right) summarizes the dust continuum observations of SPT0311−58. With seven broadband continuum detections between 3 mm to 250 μm, the far-infrared spectral energy distribution (SED) of SPT0311−58 is thoroughly covered.

The SPT 1.4 and 2.0 mm flux densities were extracted and deboosted as described by Mocanu et al. (2013). We obtained a 870 μm map with APEX/LABOCA (project ID: M-091.F-0031-2013). The data were obtained and reduced, and the flux was extracted following Greve et al. (2012). Using Herschel/SPIRE, we obtained maps at 250, 350, and 500 μm (project ID: DDT_mstrande_1). The data were obtained and reduced as described by Strandet et al. (2016).

From our photometry, we derive an apparent far-infrared (FIR) luminosity (integrated between 40 and 120 μm rest) of ${L}_{\mathrm{FIR}}=4.1\pm \,0.7\,\times \,{10}^{13}$ L_⊙ (see Figure 2).

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ALMA high spatial resolution imaging (angular resolution of 0.3 × 05) of the $[{\rm{C}}\,{\rm{II}}]$ line in SPT0311−58 shows that the system consists of two galaxies in close proximity (D. P. Marrone et al. 2017, in preparation). Only the western source is significantly gravitationally magnified, and this source dominates the apparent continuum luminosity ($\gt 90$% of the rest-frame 160 μm continuum flux density is emitted by the western source). In the following, we assume that the contribution from the eastern source is negligible and models the system as a single object, using the system magnification of $\mu =1.9$ (D. P. Marrone et al. 2017, in preparation).

We use the FIR photometry and the line luminosities from Table 1 to simultaneously model the dust continuum, CO spectral line energy distribution (SLED), and the $[{\rm{C}}\,{\rm{I}}]$(2–1) line following the radiative transfer calculation presented in Weiß et al. (2007). In this model, the background radiation field is set to the cosmic microwave background (CMB) for the dust and to the CMB plus the dust radiation field for the lines. The line and dust continuum emission are further linked via the gas column density in each component that introduces the turbulence line width as a free parameter in the calculation (see Equation (7) in Weiß et al. 2007). The gas column density calculated from the line emission together with the gas-to-dust-mass ratio (GDMR) then determines the optical depth of the dust.

The calculations treat the dust and the kinetic temperature as independent parameters, but with the prior that the kinetic gas temperature has to be equal to or higher than the dust temperature. Physically, this allows for additional sources of mechanical energy (e.g., shocks) in the ISM in addition to photo-electric heating.

The chemical parameters in our model are the CO and $[{\rm{C}}\,{\rm{I}}]$ abundances relative to H₂ and the GDMR. We use a fixed CO abundance of $8\times {10}^{-5}$ relative to H₂ (Frerking et al. 1982), but keep the $[{\rm{C}}\,{\rm{I}}]$ abundance and the GDMR as free parameters. For the frequency dependence of the dust absorption coefficient we adopt ${\kappa }_{{\rm{d}}}{(\nu )=0.04(\nu /250\mathrm{GHz})}^{\beta }$ [m² kg⁻¹] (Krügel & Siebenmorgen 1994), which is in good agreement with ${\kappa }_{870\mu {\rm{m}}}=0.077$ m² kg⁻¹ used in other work (see Spilker et al. 2015 and references therein), for our best-fitting β.

Model solutions are calculated employing a Monte Carlo Bees (Pham & Castellani 2009) algorithm that randomly samples the parameter space and gives finer sampling for good solutions (as evaluated from a ${\chi }^{2}$ analysis for each model). In total, we sample $\sim {10}^{7}$ models. Parameter values and uncertainties were calculated using the probability-weighted mean of all solutions and the standard deviations.

Figure 2 shows the CO-SLED, the continuum SED, and $[{\rm{C}}\,{\rm{I}}]$ flux density. From the figure, it is apparent that the dust continuum SED cannot be modeled with a single-temperature modified blackbody, so we instead fit two components. Since we have no information on the high-J CO transition, we use the shape of the CO-SLED of Arp220 (Rosenberg et al. 2015) and HFLS3 (Riechers et al. 2013) as priors. With this choice, we compare the moderately excited CO-SLED of Arp220 (see Rosenberg et al. (2015) for a comparison of Arp220 to other local ULIRGs) to the more extreme case of HFLS3 where the CO-SLED stays high up to the ${J}_{\mathrm{up}}=9$ level (see Figure 2). The use of the priors mainly affects the parameters of the warm gas and therefore only has a small effect on our derived gas mass (see below). Table 2 lists the parameters obtained from the radiative transfer calculations for the Arp220 prior, not corrected for magnification.

Table 2.  ISM Parameters of SPT0311-58 from the Radiative Transfer Calculation

Parameter	Unit	Overall	Cold Component	Warm Component
Equivalent radiusa	pc	(4000 ± 1700)${\mu }^{-1/2}$	(3700 ± 1300)${\mu }^{-1/2}$	(1500 ± 1200)${\mu }^{-1/2}$
${T}_{\mathrm{dust}}$	K		36 ± 7	115 ± 54
${T}_{\mathrm{kin}}$	K		58 ± 23	180 ± 51
log(n(H2))	cm−3		3.7 ± 0.4	5.1 ± 1.9
${{dv}}_{\mathrm{turb}}$	km s−1		130 ± 17	100 ± 4
${\kappa }_{\mathrm{vir}}$ b			1.9 ± 1.9	3.1 ± 2.5
GDMR			110 ± 15d
β			1.91 ± 0.05d
$[{\rm{C}}\,{\rm{I}}]$/[H2]			(6.0 ± 1.4) $\times \,{10}^{-5}$	(1.7 ± 2.3) $\times \,{10}^{-5}$
${M}_{\mathrm{dust}}$	M⊙	(5.7 ± 0.8) $\times \,{10}^{9}$ ${\mu }^{-1}$	(5.2 ± 0.7) $\times \,{10}^{9}$ ${\mu }^{-1}$	(4.8 ± 0.7) $\times \,{10}^{8}$ ${\mu }^{-1}$
${M}_{\mathrm{gas}}$	M⊙	(6.3 ± 3.7) $\times \,{10}^{11}$ ${\mu }^{-1}$	(5.7 ± 3.8) $\times \,{10}^{11}$ ${\mu }^{-1}$	(5.3 ± 3.8) $\times \,{10}^{10}$ ${\mu }^{-1}$
${\alpha }_{\mathrm{CO}}$	M⊙/K km s−1 pc2	4.8 ± 2.9	5.5 ± 4.0	3.1 ± 2.5
${L}_{\mathrm{FIR}}$	L⊙	(4.1 ± 0.7) $\times \,{10}^{13}$ ${\mu }^{-1}$	$(1.2\pm 1.1)\times {10}^{13}$ ${\mu }^{-1}$	$(2.9\pm 0.7)\times {10}^{13}$ ${\mu }^{-1}$
SFRc	${M}_{\odot }\,$ yr−1	$(4100\pm 700$)${\mu }^{-1}$
${t}_{\mathrm{dep}}$	Myr	150 ± 90

Notes. The values here are apparent values. Intrinsic values can be calculated using $\mu =1.9$.

^a ${r}_{0}={D}_{{\rm{A}}}\,\sqrt{{{\rm{\Omega }}}_{s}/\pi }$. ^bdv/dr = ${\kappa }_{\mathrm{vir}}\times 3.1\sqrt{n({{\rm{H}}}_{2})/1e4};$ we calculate the velocity gradient for virialized clouds (${\kappa }_{\mathrm{vir}}=1$; Goldsmith 2001) but also consider nonvirial, unbound motions (${\kappa }_{\mathrm{vir}}\gt 1$; Greve et al. 2009). ^cUsing SFR = ${10}^{-10}\times {L}_{\mathrm{FIR}}$ based on a Chabrier initial mass function (Kennicutt 1998; Chabrier 2003). ^dFitted in the radiative transfer calculation but set to be the same for both components.

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For both priors, the warm dust component dominates the peak of the CO-SLED and the short-wavelength part of the dust spectrum and therefore the FIR luminosity. Its size is small compared to the cold gas with an area ratio of ∼6 (${r}_{0}=1.7\pm 1.4\,\mathrm{kpc}$ where r₀ is the equivalent radius defined as ${r}_{0}={D}_{{\rm{A}}}\,\sqrt{{{\rm{\Omega }}}_{s}/\pi }$; Weiß et al. 2007; for HFLS3 and slightly smaller for Arp220), which implies that the region of intense FIR continuum emission is significantly smaller than the overall gas distribution. Due to a lack of observations of CO transitions beyond (7–6), its properties are mainly driven by the assumed shape of the CO-SLED for the high-J transitions. However, the models for both priors indicated consistently that the warm gas has a substantial density (of the order of 10⁵ cm⁻³), a dust temperature of ∼100 K, and a kinetic temperature in excess (but consistent within the errors) of the dust temperature (T_kin = 180 ± 50 K when using Arp220 priors).

The cold dust component is required to fit the CO(3–2) and $[{\rm{C}}\,{\rm{I}}]$ line emission and the long-wavelength part of the dust SED. Due to its large extent and relatively high density (r₀ = 3.7 ± 1.3 kpc, log(n(H₂) = 3.7 ± 0.4)), it carries ≈90% of the gas mass. The abundance of neutral carbon in this gas phase is $[{\rm{C}}\,{\rm{I}}]/[{{\rm{H}}}_{2}]=6.0\pm 1.4\times {10}^{-5}$, in agreement with other estimates at high redshift and in nearby galaxies (e.g., Weiß et al. 2005 and references therein). For both priors, the cold gas dominates the CO(1–0) line luminosity. As for the warm gas, we find that the kinetic temperature is above the dust temperature (T_dust = 36 ± 7 K, T_kin = 58 ± 23 K), which may suggest that the ISM in SPT0311-58 experiences additional mechanical energy input, e.g., via feedback from stellar winds or AGN driven outflows. This is also supported by the large turbulent line width of order 100 km s⁻¹ and super-virial velocity gradients (${\kappa }_{\mathrm{vir}}\gt 1$; see footnote b in Table 2) that we find for both components and priors.

We use the kinematic parameters (dv_turb and ${\kappa }_{\mathrm{vir}}$) together with the source size and the H₂ density for each component (see Equation (8) in Weiß et al. 2007) to derive a total apparent gas mass of ${M}_{\mathrm{gas}}$ = (6.3 ± 3.7)× 10¹¹ M_⊙ (including a 36% correction to account for the cosmic He abundance). For the HFLS3 prior, the gas mass is ∼30% higher.

With the independent gas mass estimate from the radiative transfer models in hand we can also derive the GDMR and the CO-to-H₂ conversion factor (${\alpha }_{\mathrm{CO}}$) for SPT0311−58. Since the CO(1–0) transition has not been observed, we use the flux density from the radiative transfer model that predicts ${I}_{\mathrm{CO}(1-0)}$ = 0.10 ± 0.03 Jy km s⁻¹. In our models, we assume that each gas component has the same GDMR, and we find GDMR = 110 ± 15. Due to the different physical conditions in each gas component, there is a specific ${\alpha }_{\mathrm{CO}}$ value for each component. For the cold dust component, we find ${\alpha }_{\mathrm{CO}}=5.5\pm 4.0$ M_⊙(K km s⁻¹ pc²)⁻¹, and for the warm dust component, ${\alpha }_{\mathrm{CO}}=3.1\pm 2.5$ M_⊙(K km s⁻¹ pc²)⁻¹. Combining both gas components we find for SPT0311−58 ${\alpha }_{\mathrm{CO}}\,=4.8\pm 2.9$ M_⊙(K km s⁻¹ pc²)⁻¹.

When calculating gas masses for ULIRGs, a factor of ${\alpha }_{\mathrm{CO}}=0.8$ M_⊙(K km s⁻¹ pc²)⁻¹ is typically assumed (Downes & Solomon 1998), significantly below our estimate. The difference can easily be explained by the much higher densities we find in both components compared to the models from Downes & Solomon (1998), in which most of the CO(1–0) luminosity arises from a diffuse inter-cloud medium. Since the bulk of the gas mass of this source is in the dense component, it is vital to include the higher-J CO transitions in the calculation of ${\alpha }_{\mathrm{CO}}$.

A similar two-component analysis was done for the broad absorption line quasar APM08279+5255 at z = 3.9 (Weiß et al. 2007), where the dense component was found to dominate the CO(1–0) line by 70%. They find a high conversion factor of ${\alpha }_{\mathrm{CO}}\sim 6$ M_⊙(K km s⁻¹ pc²)⁻¹, similar to what we find in the dense gas component. A similar reasoning for higher CO conversion factors owing to the presence of dense gas was put forward by Papadopoulos et al. (2012) based on the CO-SLED in local (U)LIRGs.

From our $[{\rm{C}}\,{\rm{II}}]$ detection, we derive a ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{FIR}}$ ratio of (7.3 ± 0.1) $\times \,{10}^{-4}$. Figure 3 shows that this puts SPT0311−58 into the lower region of the ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{FIR}}$ ratio observed in a larger sample of SPT-DSFGs (Gullberg et al. 2015). Similarly, low ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{FIR}}$ ratios are found for the z = 6.3 star-forming galaxy HFLS3 (Riechers et al. 2013) and for the z = 7.1 QSO host galaxy J1120+0641 (Venemans et al. 2012).

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The ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{CO}(1\mbox{--}0)}$ ratio in SPT0311−58 is similar to what is observed in the SPT sample (4300 ± 1300 compared to 5200 ± 1800; Gullberg et al. 2015) and HFLS3 (∼3000; Riechers et al. 2013). This is consistent with the picture in which the $[{\rm{C}}\,{\rm{II}}]$ emission stems from the surface of dense clouds exposed to the strong UV field from the intense starburst in SPT0311−58 (Stacey et al. 2010; Gullberg et al. 2015; Spilker et al. 2016).

The larger $[{\rm{C}}\,{\rm{II}}]$ deficit together with the decreasing ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{CO}(1\mbox{--}0)}$ ratio of SPT0311−58 and other high-redshift sources compared to local galaxies may be understood as a consequence of an increasing gas surface density (Narayanan & Krumholz 2017): the higher molecular gas surface density pushes the ${{\rm{H}}}_{{\rm{I}}}$ + H₂ mass budget toward higher H₂ fractions. Since $[{\rm{C}}\,{\rm{II}}]$ mainly arises from the PDR zone associated with ${{\rm{H}}}_{{\rm{I}}}$ and the outer H₂ layer, this effect reduces the size of the $[{\rm{C}}\,{\rm{II}}]$ emitting region and therefore the $[{\rm{C}}\,{\rm{II}}]$ line intensity. At the same time, the ratio of ${L}_{[{\rm{C}}{\rm{II}}]}$/${L}_{\mathrm{CO}(1\mbox{--}0)}$ will decrease due to an increase in the fraction of carbon locked in CO compared to $[{\rm{C}}\,{\rm{II}}]$.

Both our radiative transfer model and fine structure line results indicate that SPT0311-58 resembles typical DSFGs, just at $z\sim 7$. This is also supported by its extreme SFR surface density of ${{\rm{\Sigma }}}_{\mathrm{SFR}}\sim 600$ ${M}_{\odot }$ yr⁻¹ kpc⁻² (derived using the size of the warm gas component that dominates the FIR luminosity), which approaches the modeled values for radiation pressure limited starbursts (10³ M_⊙ yr⁻¹kpc⁻²; Thompson et al. 2005) and is comparable to what is found in other starbursts like Arp220, HFLS3, and other SPT-DSFGs (Scoville 2003; Riechers et al. 2013; Spilker et al. 2016). Future observations of this source will explore its spatial structure, physical conditions, formation history, and chemical evolution in great detail as it is one of very few massive galaxies known at $z\sim 7$.