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tokens: the molecular gas mass determined by Riechers ( 2013 ), and can be a result of the different resolution of the observations. Regardless of this difference, it is clear that the companion has a massive gas reservoir. The quasar was not detected by Sharon et al. ( 2016 ) but a 3σ upper limit is obtained, yielding a CO(1–0) line luminosity upper limit of , which converts to a molecular gas mass of . We also calculated the molecular gas mass from the CO(5–4) emission of the quasar, as this is the lowest J detection available for this source. We assume that the CO(5–4) transition is thermally excited, based on CO(4–3) observations of high- z type I QSOs, which found a unity ratio (e.g. Riechers et al. 2006 ; Weiß et al. 2007 ). With this assumption the molecular gas mass of the quasar is . These results suggest that there is a significant amount of warm gas in the quasar and it cannot be considered gas-poor. 3.5 <monospace>RADEX</monospace> modelling of the CO spectra To put constraints on the excitation properties of SMM J04135+10277, we modelled the SLED of both sources using our ALMA detections combined with CO(1–0) and CO(3–2) line observations from the literature (Riechers 2013 ; Sharon et al. 2016 ). We used the non-LTE molecular radiative transfer code radex (van der Tak et al. 2007 ) to calculate the line intensities of CO from transitions J up = 1 to J up = 8, within a wide range of physical parameters: kinetic temperature ( T kin ), number density of molecular hydrogen (), and column density of CO ( N CO ). During each run we set the background radiation temperature to the value of the cosmic microwave background at z = 2.84, adopted spherical geometry and assumed that the only collisional partner of CO is molecular hydrogen. As the linewidths of the low- and high- J CO lines are different, we use an average value during the radex modelling. The radex code only considers photodissociation regions and does not include mechanical and X-ray heating. We compared our observations with the models using χ 2 -analysis. In the first run we varied all three physical parameters in case of each source but as most of the models converged to the same CO column density, we fixed N CO and continued with fitting only T kin and . During the radex modelling of the quasar we set the line width of , fixed N CO to and run radex on a grid of and . It is important to note, that as we only have two detections for the quasar and two upper limits, we do not expect to arrive to a straightforward conclusion about the excitation properties of this source. However, by using the available data we can narrow down the possible temperature and density ranges. Fig. 6 shows how the χ 2 value of the models vary as a function of temperature and density. The upper J transitions of the quasar can be fitted by models with a continuous range of kinetic temperatures of and molecular hydrogen density between . Models with the lowest χ 2 values are outside of the typical temperature