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We present ALMA 2-mm continuum and CO (2-1) spectral line imaging of thegravitationally lensed z=0.654 star-forming/quasar composite RX J1131-1231 at240-400 mas angular resolution. The continuum emission is found to be compactand coincident with the optical emission, whereas the molecular gas forms acomplete Einstein ring, which shows strong differential magnification. Thede-lensed source structure is determined on 400-pc resolution using avisibility-fitting lens modelling technique. The reconstructed molecular gasvelocity-field is consistent with a rotating disk with a maximum rotationalvelocity of 280 km/s. From dynamical model fitting we find an enclosed massM(r<5 kpc)=(1.46+/-0.31)*10^11 M_sol. The molecular gas distribution is highlystructured, with clumps that are co-incident with higher gas velocitydispersion regions 40-50 km/s and with the intensity peaks in the opticalemission, which are associated with sites of on-going turbulent star-formation.The peak in the CO (2-1) distribution is not co-incident with the AGN, wherethere is a paucity of molecular gas emission, possibly due to radiativefeedback from the central engine. The intrinsic molecular gas luminosity isL'_CO=(1.2+/-0.3)*10^10 K km/s pc^2 and the inferred gas mass isM(H2)=(8.3+/-3.0)*10^10 M_sol, which given its dynamical mass is consistentwith a CO-H2 conversion factor of alpha = 5.5+/-2.0 M_solar(K km/s pc^2)^-1.This suggests that the star-formation efficiency is dependent on the hostgalaxy morphology as opposed to the nature of the AGN. The far-infraredcontinuum spectral energy distribution shows evidence for heated dust,equivalent to an obscured star-formation rate ofSFR=69^(+41)_(-25)*(7.3/u_IR)M_sol/yr, which demonstrates the compositestar-forming/AGN nature of this system.  RX J1131-1231

ALMA view of RX J1131-1231: Sub-kpc CO (2-1) mapping of a molecular disk in a lensed star-forming quasar host galaxy