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tokens: the power-law slope α , the dust temperature , and the spectral slope of the dust emissivity as fitting parameters, using the observed-frame 500 μ m flux density as a normalization factor. We also fit “general” models that allow for wavelength-dependent changes in optical depth, adding the wavelength , where the optical depth reaches unity as an additional fitting parameter. The optically thin fitting procedure yields statistical mean values of K, , and . 19 19 α is only poorly constrained by the data. The general fit yields mean values of μ m, K, , and . The fit also implies rest-frame infrared (8–1000 μ m) and FIR (42.5–122.5 μ m) luminosities of L ⊙ and L ⊙ , respectively. 20 20 The measured agrees to within ∼2% with independent estimates based on integrating a normalized MAGPHYS-based SED template based on the z = 6.34 starburst HFLS3 (Cooray et al. 2014 ), showing that the adopted power-law approximation of the short wavelength emission has a minor impact on the measured quantities. Assuming a dust absorption coefficient of m 2 kg −1 at 125 μ m (e.g., Dunne et al. 2003 ), we also find a dust mass of M ⊙ . 21 21 Given the limited photometry, the uncertainties may be somewhat underestimated. Assuming a Chabrier ( 2003 ) stellar initial mass function, these parameters suggest a total SFR of ∼2400 M ⊙ yr −1 . Given the limited SED constraints in the rest-frame optical, we obtain an estimate for the stellar mass M ⋆ of ADFS-27 by normalizing the MAGPHYS-based SED template of HFLS3 in Figure 4 to the observed-frame 4.5 μ m limit. This yields M ⋆ 1.2 × 10 11 M ⊙ . 4.2. Molecular Gas Mass, Gas-to-dust Ratio, and Gas Depletion Time The value of ADFS-27 (based on the adopted r 51 = 0.39) implies a total molecular gas mass of M ⊙ . 22 22 We here adopt a conversion factor of M ⊙ (K km s −1 pc 2 ) −1 for nearby ultra-luminous infrared galaxies and SMGs (e.g., Downes Solomon 1998 ; Tacconi et al. 2008 ). Taken at face value, this yields a gas-to-dust ratio of /, which is comparable to that in the z = 6.34 starburst HFLS3 and within the range of values found for nearby infrared-luminous galaxies (Wilson et al. 2008 ; Riechers et al. 2013 ), but ∼4× lower than that for the z = 5.30 starburst AzTEC-3 (Riechers et al. 2014 ). At its current SFR, this implies a gas depletion time of /SFR ≃ 100 Myr, consistent with the general SMG population (e.g., Carilli Walter 2013 ). 4.3. SFR and Gas Surface Densities, Gas Dynamics, and Conversion Factor The apparent 870 μ m continuum sizes of ADFS-27N (mal) and ADFS-27S (yong) imply physical sizes of (1.83 ± 0.18) × (1.28 ± 0.16) and (2.05 ± 0.18) × (0.87 ± 0.15) kpc 2 at z = 5.655, which are comparable to the ∼2.5 kpc diameters found for other z > 4 dusty starbursts like AzTEC-3, HFLS3, and SGP-38326 at similar wavelengths (Riechers et al. 2013 , 2014 ; Oteo et al. 2016 ). Assuming that their flux ratios at 870 μ m are representative at the peak of the SED, this implies surface densities of and 7.5 × 10 12 L ⊙ kpc −2