We present an analysis of CO spectroscopy and infrared-to-millimetre dust photometry of 11 exceptionally bright far-infrared (FIR) and sub-mm sources discovered through a combination of the Planck all-sky survey and follow-up Herschel-SPIRE imaging -"Planck's Dusty Gravitationally Enhanced subMillimetre Sources". Each source has a secure spectroscopic redshift z = 2.2-3.6 from multiple lines obtained through a blind redshift search with EMIR at the IRAM 30-m telescope. Interferometry was obtained at IRAM and the SMA, and along with optical/near-infrared imaging obtained at the CFHT and the VLT reveal morphologies consistent with strongly gravitationally lensed sources, including several giant arcs. Additional photometry was obtained with JCMT/SCUBA-2 and IRAM/GISMO at 850 µm and 2 mm, respectively. The SEDs of our sources peak near either the 350 µm or 500 µm bands of SPIRE with peak flux densities between 0.35 and 1.14 Jy. All objects are extremely bright isolated point sources in the 18 beam of SPIRE at 250 µm, with apparent FIR luminosities of up to 3 × 10 14 L (not correcting for the lensing effect). Their morphologies, sizes, CO line widths, CO luminosities, dust temperatures, and FIR luminosities provide additional empirical evidence that these are amongst the brightest strongly gravitationally lensed high-redshift galaxies on the sub-mm sky. Our programme extends the successful wide-area searches for strongly gravitationally lensed high-redshift galaxies (carried out with the South Pole Telescope and Herschel) towards even brighter sources, which are so rare that their systematic identification requires a genuine all-sky survey like Planck. Six sources are above the 600 mJy 90% completeness limit of the Planck catalogue of compact sources (PCCS) at 545 and 857 GHz, which implies that these must literally be amongst the brightest high-redshift FIR and sub-mm sources on the extragalactic sky. We discuss their dust masses and temperatures, and use additional WISE 22-µm photometry and template fitting to rule out a significant contribution of AGN heating to the total infrared luminosity. Six sources are detected in FIRST at 1.4 GHz, and the others have sensitive upper limits. Four have flux densities brighter than expected from the local FIR-radio correlation, but in the range previously found for high-z sub-mm galaxies, one has a deficit of FIR emission, and 6 are consistent with the local correlation, although this includes 3 galaxies with upper limits. We attribute this to the turbulent interstellar medium of these galaxies, rather than the presence of radio AGN. The global dust-to-gas ratios and star-formation efficiencies of our sources are predominantly in the range expected from massive, metal-rich, intense, high-redshift starbursts. An extensive multi-wavelength follow-up programme is being carried out to further characterize these sources and the intense star formation within them.Key words. galaxies: high-redshift -galaxies: star formation -galaxies: starburst -submillimeter: galaxies -gravi...

We present an extensive CO emission-line survey of the Planck’s dusty Gravitationally Enhanced subMillimetre Sources, a small set of 11 strongly lensed dusty star-forming galaxies at z = 2–4 discovered with Planck and Herschel satellites, using EMIR on the IRAM 30-m telescope. We detected a total of 45 CO rotational lines from Jup = 3 to Jup = 11, and up to eight transitions per source, allowing a detailed analysis of the gas excitation and interstellar medium conditions within these extremely bright (μLFIR = 0.5 − 3.0 × 1014L⊙), vigorous starbursts. The peak of the CO spectral-line energy distributions (SLEDs) fall between Jup = 4 and Jup = 7 for nine out of 11 sources, in the same range as other lensed and unlensed submillimeter galaxies (SMGs) and the inner regions of local starbursts. We applied radiative transfer models using the large velocity gradient approach to infer the spatially-averaged molecular gas densities, nH2 ≃ 102.6 − 104.1 cm−3, and kinetic temperatures, Tk ≃ 30–1000 K. In five sources, we find evidence of two distinct gas phases with different properties and model their CO SLED with two excitation components. The warm (70–320 K) and dense gas reservoirs in these galaxies are highly excited, while the cooler (15–60 K) and more extended low-excitation components cover a range of gas densities. In two sources, the latter is associated with diffuse Milky Way-like gas phases of density nH2 ≃ 102.4 − 102.8 cm−3, which provides evidence that a significant fraction of the total gas masses of dusty starburst galaxies can be embedded in cool, low-density reservoirs. The delensed masses of the warm star-forming molecular gas range from 0.6to12 × 1010 M⊙. Finally, we show that the CO line luminosity ratios are consistent with those predicted by models of photon-dominated regions (PDRs) and disfavor scenarios of gas clouds irradiated by intense X-ray fields from active galactic nuclei. By combining CO, [C I] and [C II] line diagnostics, we obtain average PDR gas densities significantly higher than in normal star-forming galaxies at low-redshift, as well as far-ultraviolet radiation fields 102–104 times more intense than in the Milky Way. These spatially-averaged conditions are consistent with those in high-redshift SMGs and in a range of low-redshift environments, from the central regions of ultra-luminous infrared galaxies and bluer starbursts to Galactic giant molecular clouds.