Morpho-kinematics of the molecular gas in a quasar host galaxy at redshift $z$=0.654

We present a new study of archival ALMA observations of the CO(2-1) line emission of the host galaxy of quasar RX J1131 at redshift $z$=0.654, lensed by a foreground galaxy. A simple lens model is shown to well reproduce the optical images obtained by the Hubble Space Telescope. Clear evidence for rotation of the gas contained in the galaxy is obtained and a simple rotating disc model is shown to give an excellent overall description of the morpho-kinematics of the source. The possible presence of a companion galaxy suggested by some previous authors is not confirmed. Detailed comparison between model and observations gives evidence for a more complex dynamics than implied by the model. Doppler velocity dispersion within the beam size in the image plane is found to account for the observed line width.