%0 Journal Article %T Molecular gas in the Herschel-selected strongly lensed submillimeter galaxies at zˋ~ˋ2每4 as probed by multi-J CO lines %A A. Beelen %A A. Cooray %A A. J. Baker %A A. Omont %A C. Yang %A D. Liu %A D. Riechers %A E. Gonz芍lez-Alfonso %A H. Dannerbauer %A I. Oteo %A I. Smail %A M. J. Michaˋowski %A M. Krips %A M. Lehnert %A P. Cox %A P. van der Werf %A R. Gavazzi %A R. Ivison %A R. Neri %A Y. Gao %A Z.-Y. Zhang %J - %D 2017 %R 10.1051/0004-6361/201731391 %X We present the IRAM-30ˋm observations of multiple-J CO (Jup mostly from 3 up to 8) and [CˋI](3P2ˋ↙ˋ3P1) ([CˋI](2每1) hereafter) line emission in a sample of redshift ~2每4 submillimeter galaxies (SMGs). These SMGs are selected among the brightest-lensed galaxies discovered in the Herschel-Astrophysical Terahertz Large Area Survey (H-ATLAS). Forty-seven CO lines and 7 [CˋI](2每1) lines have been detected in 15 lensed SMGs. A non-negligible effect of differential lensing is found for the CO emission lines, which could have caused significant underestimations of the linewidths, and hence of the dynamical masses. The CO spectral line energy distributions (SLEDs), peaking around Jup ~ˋ5每7, are found to be similar to those of the local starburst-dominated ultra-luminous infrared galaxies and of the previously studied SMGs. After correcting for lensing amplification, we derived the global properties of the bulk of molecular gas in the SMGs using non-LTE radiative transfer modelling, such as the molecular gas density nH2ˋ~ˋ102.5每104.1ˋcm-3 and the kinetic temperature Tk ˋ~ˋ20每750ˋK. The gas thermal pressure Pth ranging from~105ˋKˋcm-3 to 106ˋKˋcm-3 is found to be correlated with star formation efficiency. Further decomposing the CO SLEDs into two excitation components, we find a low-excitation component with nH2ˋ~ˋ102.8每104.6ˋcm-3 and Tk ˋ~ˋ20每30ˋK, which is less correlated with star formation, and a high-excitation one (nH2ˋ~ˋ102.7每104.2ˋcm-3, Tk ˋ~ˋ60每400ˋK) which is tightly related to the on-going star-forming activity. Additionally, tight linear correlations between the far-infrared and CO line luminosities have been confirmed for the Jup ≡ 5 CO lines of these SMGs, implying that these CO lines are good tracers of star formation. The [CˋI](2每1) lines follow the tight linear correlation between the luminosities of the [CˋI](2每1) and the CO(1每0) line found in local starbursts, indicating that [CˋI] lines could serve as good total molecular gas mass tracers for high-redshift SMGs as well. The total mass of the molecular gas reservoir, (1每30) ℅ 1010M×, derived based on the CO(3每2) fluxes and CO(1每0) = %U https://www.aanda.org/articles/aa/full_html/2017/12/aa31391-17/aa31391-17.html